title: Dysgeusia

text: Because medications have been linked to approximately 22% to 28% of all cases of dysgeusia, researching a treatment for this particular cause has been important. Xerostomia, or a decrease in saliva flow, can be a side effect of many drugs, which, in turn, can lead to the development of taste disturbances such as dysgeusia. Patients can lessen the effects of xerostomia with breath mints, sugarless gum, or lozenges, or physicians can increase saliva flow with artificial saliva or oral pilocarpine. Artificial saliva mimics the characteristics of natural saliva by lubricating and protecting the mouth but does not provide any digestive or enzymatic benefits. Pilocarpine is a cholinergic drug meaning it has the same effects as the neurotransmitter acetylcholine. Acetylcholine has the function of stimulating the salivary glands to actively produce saliva. The increase in saliva flow is effective in improving the movement of tastants to the taste buds.


title: Dysgeusia

text: Approximately one half of drug-related taste distortions are caused by a zinc deficiency. Many medications are known to chelate, or bind, zinc, preventing the element from functioning properly. Due to the causal relationship of insufficient zinc levels to taste disorders, research has been conducted to test the efficacy of zinc supplementation as a possible treatment for dysgeusia. In a randomized clinical trial, fifty patients with idiopathic dysgeusia were given either zinc or a lactose placebo. The patients prescribed the zinc reported experiencing improved taste function and less severe symptoms compared to the control group, suggesting that zinc may be a beneficial treatment. The efficacy of zinc, however, has been ambiguous in the past. In a second study, 94% of patients who were provided with zinc supplementation did not experience any improvement in their condition. This ambiguity is most likely due to small sample sizes and the wide range of causes of dysgeusia. A recommended daily oral dose of 25–100 mg, as zinc gluconate, appears to be an effective treatment for taste dysfunction provided that there are low levels of zinc in the blood serum. There is not a sufficient amount of evidence to determine whether or not zinc supplementation is able to treat dysgeusia when low zinc concentrations are not detected in the blood.


title: Dysgeusia

text: A Cochrane Review in 2017 assessed the effects of different interventions for the management of taste disturbances. There was very low-quality evidence to support the role of zinc supplementation in the improvement of taste acuity and taste discrimination in patients with zinc deficiency or idiopathic taste disorders. Further research is required to improve the quality of evidence for zinc supplementation as an effective intervention for the management of dysgeusia.


title: Dysgeusia

text: It has been reported that approximately 68% of cancer patients undergoing chemotherapy experience disturbances in sensory perception such as dysgeusia. In a pilot study involving twelve lung cancer patients, chemotherapy drugs were infused with zinc in order to test its potential as a treatment. The results indicated that, after two weeks, no taste disturbances were reported by the patients who received the zinc-supplemented treatment while most of the patients in the control group who did not receive the zinc reported taste alterations. A multi-institutional study involving a larger sample size of 169 patients, however, indicated that zinc-infused chemotherapy did not have an effect on the development of taste disorders in cancer patients. An excess amount of zinc in the body can have negative effects on the immune system, and physicians must use caution when administering zinc to immunocompromised cancer patients. Because taste disorders can have detrimental effects on a patient's quality of life, more research needs to be conducted concerning possible treatments such as zinc supplementation.


title: Dysgeusia

text: The effects of drug-related dysgeusia can often be reversed by stopping the patient's regimen of the taste altering medication. In one case, a forty-eight-year-old woman who had hypertension was being treated with valsartan. Due to this drug's inability to treat her condition, she began taking a regimen of eprosartan, an angiotensin II receptor antagonist. Within three weeks, she began experiencing a metallic taste and a burning sensation in her mouth that ceased when she stopped taking the medication. When she began taking eprosartan on a second occasion, her dysgeusia returned. In a second case, a fifty-nine-year-old man was prescribed amlodipine in order to treat his hypertension. After eight years of taking the drug, he developed a loss of taste sensation and numbness in his tongue. When he ran out of his medication, he decided not to obtain a refill and stopped taking amlodipine. Following this self-removal, he reported experiencing a return of his taste sensation. Once he refilled his prescription and began taking amlodipine a second time, his taste disturbance reoccurred. These two cases suggest that there is an association between these drugs and taste disorders. This link is supported by the "de-challenge" and "re-challenge" that took place in both instances. It appears that drug-induced dysgeusia can be alleviated by reducing the drug's dose or by substituting a second drug from the same class.


title: Dysgeusia

text: Alpha lipoic acid (ALA) is an antioxidant that is made naturally by human cells. It can also be administered in capsules or can be found in foods such as red meat, organ meats, and yeast. Like other antioxidants, it functions by ridding the body of harmful free radicals that can cause damage to tissues and organs. It has an important role in the Krebs cycle as a coenzyme leading to the production of antioxidants, intracellular glutathione, and nerve-growth factors. Animal research has also uncovered the ability of ALA to improve nerve conduction velocity. Because flavors are perceived by differences in electric potential through specific nerves innervating the tongue, idiopathic dysgeusia may be a form of a neuropathy. ALA has proven to be an effective treatment for burning mouth syndrome spurring studies in its potential to treat dysgeusia. In a study of forty-four patients diagnosed with the disorder, one half was treated with the drug for two months while the other half, the control group, was given a placebo for two months followed by a two-month treatment of ALA. The results reported show that 91% of the group initially treated with ALA reported an improvement in their condition compared to only 36% of the control group. After the control group was treated with ALA, 72% reported an improvement. This study suggests that ALA may be a potential treatment for patients and supports that full double blind randomized studies should be performed.


title: Dysgeusia

text: In addition to the aforementioned treatments, there are also many management approaches that can alleviate the symptoms of dysgeusia. These include using non-metallic silverware, avoiding metallic or bitter tasting foods, increasing the consumption of foods high in protein, flavoring foods with spices and seasonings, serving foods cold in order to reduce any unpleasant taste or odor, frequently brushing one's teeth and utilizing mouthwash, or using sialogogues such as chewing sugar-free gum or sour-tasting drops that stimulate the productivity of saliva. When taste is impeded, the food experience can be improved through means other than taste, such as texture, aroma, temperature, and color.


title: Dysgeusia

text: People with dysgeusia are also forced to manage the impact that the disorder has on their quality of life. An altered taste has effects on food choice and intake and can lead to weight loss, malnutrition, impaired immunity, and a decline in health. Patients diagnosed with dysgeusia must use caution when adding sugar and salt to food and must be sure not to overcompensate for their lack of taste with excess amounts. Since the elderly are often on multiple medications, they are at risk for taste disturbances increasing the chances of developing depression, loss of appetite, and extreme weight loss. This is cause for an evaluation and management of their dysgeusia. In patients undergoing chemotherapy, taste distortions can often be severe and make compliance with cancer treatment difficult. Other problems that may arise include anorexia and behavioral changes that can be misinterpreted as psychiatric delusions regarding food. Symptoms including paranoia, amnesia, cerebellar malfunction, and lethargy can also manifest when undergoing histidine treatment.


title: Dysgeusia

text: Every year, more than 200,000 individuals see their physicians concerning chemosensory problems, and many more taste disturbances are never reported. Due to the large number of persons affected by taste disorders, basic and clinical research are receiving support at different institutions and chemosensory research centers across the country. These taste and smell clinics are focusing their research on better understanding the mechanisms involved in gustatory function and taste disorders such as dysgeusia. For example, the National Institute on Deafness and Other Communication Disorders is looking into the mechanisms underlying the key receptors on taste cells and applying this knowledge to the future of medications and artificial food products. Meanwhile, the Taste and Smell Clinic at the University of Connecticut Health Center is integrating behavioral, neurophysiological, and genetic studies involving stimulus concentrations and intensities in order to better understand taste function.


title: Equipartition theorem

text: In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in translational motion of a molecule should equal that in rotational motion.


title: Equipartition theorem

text: The equipartition theorem makes quantitative predictions. Like the virial theorem, it gives the total average kinetic and potential energies for a system at a given temperature, from which the system's heat capacity can be computed. However, equipartition also gives the average values of individual components of the energy, such as the kinetic energy of a particular particle or the potential energy of a single spring. For example, it predicts that every atom in a monatomic ideal gas has an average kinetic energy of in thermal equilibrium, where is the Boltzmann constant and "T" is the (thermodynamic) temperature. More generally, equipartition can be applied to any classical system in thermal equilibrium, no matter how complicated. It can be used to derive the ideal gas law, and the Dulong–Petit law for the specific heat capacities of solids. The equipartition theorem can also be used to predict the properties of stars, even white dwarfs and neutron stars, since it holds even when relativistic effects are considered.


title: Equipartition theorem

text: Although the equipartition theorem makes accurate predictions in certain conditions, it is inaccurate when quantum effects are significant, such as at low temperatures. When the thermal energy is smaller than the quantum energy spacing in a particular degree of freedom, the average energy and heat capacity of this degree of freedom are less than the values predicted by equipartition. Such a degree of freedom is said to be "frozen out" when the thermal energy is much smaller than this spacing. For example, the heat capacity of a solid decreases at low temperatures as various types of motion become frozen out, rather than remaining constant as predicted by equipartition. Such decreases in heat capacity were among the first signs to physicists of the 19th century that classical physics was incorrect and that a new, more subtle, scientific model was required. Along with other evidence, equipartition's failure to model black-body radiation—also known as the ultraviolet catastrophe—led Max Planck to suggest that energy in the oscillators in an object, which emit light, were quantized, a revolutionary hypothesis that spurred the development of quantum mechanics and quantum field theory.


title: Equipartition theorem

text: The name "equipartition" means "equal division," as derived from the Latin "equi" from the antecedent, æquus ("equal or even"), and partition from the noun, "partitio" ("division, portion"). The original concept of equipartition was that the total kinetic energy of a system is shared equally among all of its independent parts, "on the average", once the system has reached thermal equilibrium. Equipartition also makes quantitative predictions for these energies. For example, it predicts that every atom of an inert noble gas, in thermal equilibrium at temperature , has an average translational kinetic energy of , where is the Boltzmann constant. As a consequence, since kinetic energy is equal to (mass)(velocity), the heavier atoms of xenon have a lower average speed than do the lighter atoms of helium at the same temperature. Figure 2 shows the Maxwell–Boltzmann distribution for the speeds of the atoms in four noble gases.


title: Equipartition theorem

text: In this example, the key point is that the kinetic energy is quadratic in the velocity. The equipartition theorem shows that in thermal equilibrium, any degree of freedom (such as a component of the position or velocity of a particle) which appears only quadratically in the energy has an average energy of and therefore contributes to the system's heat capacity. This has many applications.


title: Equipartition theorem

text: where , and are the Cartesian components of the velocity . Here, is short for Hamiltonian, and used henceforth as a symbol for energy because the Hamiltonian formalism plays a central role in the most general form of the equipartition theorem.


title: Equipartition theorem

text: Since the kinetic energy is quadratic in the components of the velocity, by equipartition these three components each contribute to the average kinetic energy in thermal equilibrium. Thus the average kinetic energy of the particle is , as in the example of noble gases above.


title: Equipartition theorem

text: More generally, in a monatomic ideal gas the total energy consists purely of (translational) kinetic energy: by assumption, the particles have no internal degrees of freedom and move independently of one another. Equipartition therefore predicts that the total energy of an ideal gas of particles is .


title: Equipartition theorem

text: It follows that the heat capacity of the gas is and hence, in particular, the heat capacity of a mole of such gas particles is , where "N" is the Avogadro constant and "R" is the gas constant. Since "R" ≈ 2 cal/(mol·K), equipartition predicts that the molar heat capacity of an ideal gas is roughly 3 cal/(mol·K). This prediction is confirmed by experiment when compared to monatomic gases.


title: Equipartition theorem

text: The mean kinetic energy also allows the root mean square speed of the gas particles to be calculated:


title: Equipartition theorem

text: where is the mass of a mole of gas particles. This result is useful for many applications such as Graham's law of effusion, which provides a method for enriching uranium.


title: Equipartition theorem

text: A similar example is provided by a rotating molecule with principal moments of inertia , and . The rotational energy of such a molecule is given by


title: Equipartition theorem

text: where , , and are the principal components of the angular velocity. By exactly the same reasoning as in the translational case, equipartition implies that in thermal equilibrium the average rotational energy of each particle is . Similarly, the equipartition theorem allows the average (more precisely, the root mean square) angular speed of the molecules to be calculated.


title: Equipartition theorem

text: The tumbling of rigid molecules—that is, the random rotations of molecules in solution—plays a key role in the relaxations observed by nuclear magnetic resonance, particularly protein NMR and residual dipolar couplings. Rotational diffusion can also be observed by other biophysical probes such as fluorescence anisotropy, flow birefringence and dielectric spectroscopy.


title: Equipartition theorem

text: Equipartition applies to potential energies as well as kinetic energies: important examples include harmonic oscillators such as a spring, which has a quadratic potential energy


title: Equipartition theorem

text: where the constant describes the stiffness of the spring and is the deviation from equilibrium. If such a one-dimensional system has mass , then its kinetic energy is


title: Equipartition theorem

text: where and denote the velocity and momentum of the oscillator. Combining these terms yields the total energy


title: Equipartition theorem

text: This result is valid for any type of harmonic oscillator, such as a pendulum, a vibrating molecule or a passive electronic oscillator. Systems of such oscillators arise in many situations; by equipartition, each such oscillator receives an average total energy and hence contributes to the system's heat capacity. This can be used to derive the formula for Johnson–Nyquist noise and the Dulong–Petit law of solid heat capacities. The latter application was particularly significant in the history of equipartition.


title: Equipartition theorem

text: An important application of the equipartition theorem is to the specific heat capacity of a crystalline solid. Each atom in such a solid can oscillate in three independent directions, so the solid can be viewed as a system of independent simple harmonic oscillators, where denotes the number of atoms in the lattice. Since each harmonic oscillator has average energy , the average total energy of the solid is , and its heat capacity is .


title: Equipartition theorem

text: By taking to be the Avogadro constant , and using the relation between the gas constant and the Boltzmann constant , this provides an explanation for the Dulong–Petit law of specific heat capacities of solids, which stated that the specific heat capacity (per unit mass) of a solid element is inversely proportional to its atomic weight. A modern version is that the molar heat capacity of a solid is "3R" ≈ 6 cal/(mol·K).


title: Equipartition theorem

text: However, this law is inaccurate at lower temperatures, due to quantum effects; it is also inconsistent with the experimentally derived third law of thermodynamics, according to which the molar heat capacity of any substance must go to zero as the temperature goes to absolute zero. A more accurate theory, incorporating quantum effects, was developed by Albert Einstein (1907) and Peter Debye (1911).


title: Equipartition theorem

text: Many other physical systems can be modeled as sets of coupled oscillators. The motions of such oscillators can be decomposed into normal modes, like the vibrational modes of a piano string or the resonances of an organ pipe. On the other hand, equipartition often breaks down for such systems, because there is no exchange of energy between the normal modes. In an extreme situation, the modes are independent and so their energies are independently conserved. This shows that some sort of mixing of energies, formally called "ergodicity", is important for the law of equipartition to hold.


title: Equipartition theorem

text: Potential energies are not always quadratic in the position. However, the equipartition theorem also shows that if a degree of freedom contributes only a multiple of (for a fixed real number ) to the energy, then in thermal equilibrium the average energy of that part is .


title: Equipartition theorem

text: There is a simple application of this extension to the sedimentation of particles under gravity. For example, the haze sometimes seen in beer can be caused by clumps of proteins that scatter light. Over time, these clumps settle downwards under the influence of gravity, causing more haze near the bottom of a bottle than near its top. However, in a process working in the opposite direction, the particles also diffuse back up towards the top of the bottle. Once equilibrium has been reached, the equipartition theorem may be used to determine the average position of a particular clump of buoyant mass . For an infinitely tall bottle of beer, the gravitational potential energy is given by


title: Equipartition theorem

text: where is the height of the protein clump in the bottle and "g" is the acceleration due to gravity. Since , the average potential energy of a protein clump equals . Hence, a protein clump with a buoyant mass of 10 MDa (roughly the size of a virus) would produce a haze with an average height of about 2 cm at equilibrium. The process of such sedimentation to equilibrium is described by the Mason–Weaver equation.


title: Equipartition theorem

text: The equipartition of kinetic energy was proposed initially in 1843, and more correctly in 1845, by John James Waterston. In 1859, James Clerk Maxwell argued that the kinetic heat energy of a gas is equally divided between linear and rotational energy. In 1876, Ludwig Boltzmann expanded on this principle by showing that the average energy was divided equally among all the independent components of motion in a system. Boltzmann applied the equipartition theorem to provide a theoretical explanation of the Dulong–Petit law for the specific heat capacities of solids.


title: Equipartition theorem

text: The history of the equipartition theorem is intertwined with that of specific heat capacity, both of which were studied in the 19th century. In 1819, the French physicists Pierre Louis Dulong and Alexis Thérèse Petit discovered that the specific heat capacities of solid elements at room temperature were inversely proportional to the atomic weight of the element. Their law was used for many years as a technique for measuring atomic weights. However, subsequent studies by James Dewar and Heinrich Friedrich Weber showed that this Dulong–Petit law holds only at high temperatures; at lower temperatures, or for exceptionally hard solids such as diamond, the specific heat capacity was lower.


title: Equipartition theorem

text: Experimental observations of the specific heat capacities of gases also raised concerns about the validity of the equipartition theorem. The theorem predicts that the molar heat capacity of simple monatomic gases should be roughly 3 cal/(mol·K), whereas that of diatomic gases should be roughly 7 cal/(mol·K). Experiments confirmed the former prediction, but found that molar heat capacities of diatomic gases were typically about 5 cal/(mol·K), and fell to about 3 cal/(mol·K) at very low temperatures. Maxwell noted in 1875 that the disagreement between experiment and the equipartition theorem was much worse than even these numbers suggest; since atoms have internal parts, heat energy should go into the motion of these internal parts, making the predicted specific heats of monatomic and diatomic gases much higher than 3 cal/(mol·K) and 7 cal/(mol·K), respectively.


title: Equipartition theorem

text: A third discrepancy concerned the specific heat of metals. According to the classical Drude model, metallic electrons act as a nearly ideal gas, and so they should contribute to the heat capacity by the equipartition theorem, where "N" is the number of electrons. Experimentally, however, electrons contribute little to the heat capacity: the molar heat capacities of many conductors and insulators are nearly the same.


title: Equipartition theorem

text: Several explanations of equipartition's failure to account for molar heat capacities were proposed. Boltzmann defended the derivation of his equipartition theorem as correct, but suggested that gases might not be in thermal equilibrium because of their interactions with the aether. Lord Kelvin suggested that the derivation of the equipartition theorem must be incorrect, since it disagreed with experiment, but was unable to show how. In 1900 Lord Rayleigh instead put forward a more radical view that the equipartition theorem and the experimental assumption of thermal equilibrium were "both" correct; to reconcile them, he noted the need for a new principle that would provide an "escape from the destructive simplicity" of the equipartition theorem. Albert Einstein provided that escape, by showing in 1906 that these anomalies in the specific heat were due to quantum effects, specifically the quantization of energy in the elastic modes of the solid. Einstein used the failure of equipartition to argue for the need of a new quantum theory of matter. Nernst's 1910 measurements of specific heats at low temperatures supported Einstein's theory, and led to the widespread acceptance of quantum theory among physicists.


title: Equipartition theorem

text: The most general form of the equipartition theorem states that under suitable assumptions (discussed below), for a physical system with Hamiltonian energy function and degrees of freedom , the following equipartition formula holds in thermal equilibrium for all indices and :


title: Equipartition theorem

text: Here is the Kronecker delta, which is equal to one if and is zero otherwise. The averaging brackets formula_8 is assumed to be an ensemble average over phase space or, under an assumption of ergodicity, a time average of a single system.


title: Equipartition theorem

text: The general equipartition theorem holds in both the microcanonical ensemble, when the total energy of the system is constant, and also in the canonical ensemble, when the system is coupled to a heat bath with which it can exchange energy. Derivations of the general formula are given later in the article.


title: Equipartition theorem

text: If a degree of freedom "x" appears only as a quadratic term "ax" in the Hamiltonian "H", then the first of these formulae implies that


title: Equipartition theorem

text: which is twice the contribution that this degree of freedom makes to the average energy formula_15. Thus the equipartition theorem for systems with quadratic energies follows easily from the general formula. A similar argument, with 2 replaced by "s", applies to energies of the form "ax".


title: Equipartition theorem

text: The degrees of freedom "x" are coordinates on the phase space of the system and are therefore commonly subdivided into generalized position coordinates "q" and generalized momentum coordinates "p", where "p" is the conjugate momentum to "q". In this situation, formula 1 means that for all "k",


title: Equipartition theorem

text: The general equipartition theorem is an extension of the virial theorem (proposed in 1870), which states that


title: Equipartition theorem

text: where "t" denotes time. Two key differences are that the virial theorem relates "summed" rather than "individual" averages to each other, and it does not connect them to the temperature "T". Another difference is that traditional derivations of the virial theorem use averages over time, whereas those of the equipartition theorem use averages over phase space.


title: Equipartition theorem

text: Ideal gases provide an important application of the equipartition theorem. As well as providing the formula


title: Equipartition theorem

text: for the average kinetic energy per particle, the equipartition theorem can be used to derive the ideal gas law from classical mechanics. If q = ("q", "q", "q") and p = ("p", "p", "p") denote the position vector and momentum of a particle in the gas, and


title: Equipartition theorem

text: where the first equality is Newton's second law, and the second line uses Hamilton's equations and the equipartition formula. Summing over a system of "N" particles yields


title: Equipartition theorem

text: By Newton's third law and the ideal gas assumption, the net force on the system is the force applied by the walls of their container, and this force is given by the pressure "P" of the gas. Hence


title: Equipartition theorem

text: where is the infinitesimal area element along the walls of the container. Since the divergence of the position vector is


title: Equipartition theorem

text: where is the number of moles of gas and is the gas constant. Although equipartition provides a simple derivation of the ideal-gas law and the internal energy, the same results can be obtained by an alternative method using the partition function.


title: Equipartition theorem

text: A diatomic gas can be modelled as two masses, and , joined by a spring of stiffness , which is called the "rigid rotor-harmonic oscillator approximation". The classical energy of this system is


title: Equipartition theorem

text: where and are the momenta of the two atoms, and is the deviation of the inter-atomic separation from its equilibrium value. Every degree of freedom in the energy is quadratic and, thus, should contribute to the total average energy, and to the heat capacity. Therefore, the heat capacity of a gas of "N" diatomic molecules is predicted to be : the momenta and contribute three degrees of freedom each, and the extension contributes the seventh. It follows that the heat capacity of a mole of diatomic molecules with no other degrees of freedom should be and, thus, the predicted molar heat capacity should be roughly 7 cal/(mol·K). However, the experimental values for molar heat capacities of diatomic gases are typically about 5 cal/(mol·K) and fall to 3 cal/(mol·K) at very low temperatures. This disagreement between the equipartition prediction and the experimental value of the molar heat capacity cannot be explained by using a more complex model of the molecule, since adding more degrees of freedom can only "increase" the predicted specific heat, not decrease it. This discrepancy was a key piece of evidence showing the need for a quantum theory of matter.


title: Equipartition theorem

text: Equipartition was used above to derive the classical ideal gas law from Newtonian mechanics. However, relativistic effects become dominant in some systems, such as white dwarfs and neutron stars, and the ideal gas equations must be modified. The equipartition theorem provides a convenient way to derive the corresponding laws for an extreme relativistic ideal gas. In such cases, the kinetic energy of a single particle is given by the formula


title: Equipartition theorem

text: where the last equality follows from the equipartition formula. Thus, the average total energy of an extreme relativistic gas is twice that of the non-relativistic case: for particles, it is .


title: Equipartition theorem

text: In an ideal gas the particles are assumed to interact only through collisions. The equipartition theorem may also be used to derive the energy and pressure of "non-ideal gases" in which the particles also interact with one another through conservative forces whose potential depends only on the distance between the particles. This situation can be described by first restricting attention to a single gas particle, and approximating the rest of the gas by a spherically symmetric distribution. It is then customary to introduce a radial distribution function such that the probability density of finding another particle at a distance from the given particle is equal to , where is the mean density of the gas. It follows that the mean potential energy associated to the interaction of the given particle with the rest of the gas is


title: Equipartition theorem

text: The total mean potential energy of the gas is therefore formula_34, where is the number of particles in the gas, and the factor is needed because summation over all the particles counts each interaction twice.


title: Equipartition theorem

text: An anharmonic oscillator (in contrast to a simple harmonic oscillator) is one in which the potential energy is not quadratic in the extension (the generalized position which measures the deviation of the system from equilibrium). Such oscillators provide a complementary point of view on the equipartition theorem. Simple examples are provided by potential energy functions of the form


title: Equipartition theorem

text: More generally, a typical energy function of a one-dimensional system has a Taylor expansion in the extension :


title: Equipartition theorem

text: for non-negative integers . There is no term, because at the equilibrium point, there is no net force and so the first derivative of the energy is zero. The term need not be included, since the energy at the equilibrium position may be set to zero by convention. In this case, the law of equipartition predicts that


title: Equipartition theorem

text: The equipartition theorem can be used to derive the Brownian motion of a particle from the Langevin equation. According to that equation, the motion of a particle of mass with velocity is governed by Newton's second law


title: Equipartition theorem

text: where is a random force representing the random collisions of the particle and the surrounding molecules, and where the time constant τ reflects the drag force that opposes the particle's motion through the solution. The drag force is often written ; therefore, the time constant equals .


title: Equipartition theorem

text: for Brownian motion (since the random force is uncorrelated with the position ). Using the mathematical identities


title: Equipartition theorem

text: The above differential equation for formula_48 (with suitable initial conditions) may be solved exactly:


title: Equipartition theorem

text: On small time scales, with , the particle acts as a freely moving particle: by the Taylor series of the exponential function, the squared distance grows approximately "quadratically":


title: Equipartition theorem

text: However, on long time scales, with , the exponential and constant terms are negligible, and the squared distance grows only "linearly":


title: Equipartition theorem

text: This describes the diffusion of the particle over time. An analogous equation for the rotational diffusion of a rigid molecule can be derived in a similar way.


title: Equipartition theorem

text: The equipartition theorem and the related virial theorem have long been used as a tool in astrophysics. As examples, the virial theorem may be used to estimate stellar temperatures or the Chandrasekhar limit on the mass of white dwarf stars.


title: Equipartition theorem

text: The average temperature of a star can be estimated from the equipartition theorem. Since most stars are spherically symmetric, the total gravitational potential energy can be estimated by integration


title: Equipartition theorem

text: where is the mass within a radius and is the stellar density at radius ; represents the gravitational constant and the total radius of the star. Assuming a constant density throughout the star, this integration yields the formula


title: Equipartition theorem

text: where is the number of particles in the star. Since most stars are composed mainly of ionized hydrogen, equals roughly , where is the mass of one proton. Application of the equipartition theorem gives an estimate of the star's temperature


title: Equipartition theorem

text: Substitution of the mass and radius of the Sun yields an estimated solar temperature of "T" = 14 million kelvins, very close to its core temperature of 15 million kelvins. However, the Sun is much more complex than assumed by this model—both its temperature and density vary strongly with radius—and such excellent agreement (≈7% relative error) is partly fortuitous.


title: Equipartition theorem

text: The same formulae may be applied to determining the conditions for star formation in giant molecular clouds. A local fluctuation in the density of such a cloud can lead to a runaway condition in which the cloud collapses inwards under its own gravity. Such a collapse occurs when the equipartition theorem—or, equivalently, the virial theorem—is no longer valid, i.e., when the gravitational potential energy exceeds twice the kinetic energy


title: Equipartition theorem

text: Substituting the values typically observed in such clouds (, ) gives an estimated minimum mass of 17 solar masses, which is consistent with observed star formation. This effect is also known as the Jeans instability, after the British physicist James Hopwood Jeans who published it in 1902.


title: Equipartition theorem

text: The original formulation of the equipartition theorem states that, in any physical system in thermal equilibrium, every particle has exactly the same average translational kinetic energy, . However, this is true only for ideal gas, and the same result can be derived from the Maxwell–Boltzmann distribution. First, we choose to consider only the Maxwell–Boltzmann distribution of velocity of the z-component


title: Equipartition theorem

text: Since different components of velocity are independent of each other, the average translational kinetic energy is given by


title: Equipartition theorem

text: Notice, the Maxwell–Boltzmann distribution should not be confused with the Boltzmann distribution, which the former can be derived from the latter by assuming the energy of a particle is equal to its translational kinetic energy.


title: Equipartition theorem

text: As stated by the equipartition theorem. The same result can also be obtained by averaging the particle energy using the probability of finding the particle in certain quantum energy state.


title: Equipartition theorem

text: More generally, the equipartition theorem states that any degree of freedom which appears in the total energy only as a simple quadratic term , where is a constant, has an average energy of in thermal equilibrium. In this case the equipartition theorem may be derived from the partition function , where is the canonical inverse temperature. Integration over the variable yields a factor


title: Equipartition theorem

text: General derivations of the equipartition theorem can be found in many statistical mechanics textbooks, both for the microcanonical ensemble and for the canonical ensemble.


title: Equipartition theorem

text: To explain these derivations, the following notation is introduced. First, the phase space is described in terms of generalized position coordinates together with their conjugate momenta . The quantities completely describe the configuration of the system, while the quantities together completely describe its state.


title: Equipartition theorem

text: of the phase space is introduced and used to define the volume of the portion of phase space where the energy of the system lies between two limits, and :


title: Equipartition theorem

text: In this expression, is assumed to be very small, . Similarly, is defined to be the total volume of phase space where the energy is less than :


title: Equipartition theorem

text: where is the density of states. By the usual definitions of statistical mechanics, the entropy equals , and the temperature is defined by


title: Equipartition theorem

text: In the canonical ensemble, the system is in thermal equilibrium with an infinite heat bath at temperature (in kelvins). The probability of each state in phase space is given by its Boltzmann factor times a normalization factor formula_70, which is chosen so that the probabilities sum to one


title: Equipartition theorem

text: where , i.e., the first integration is not carried out over . Performing the first integral between two limits and and simplifying the second integral yields the equation


title: Equipartition theorem

text: The first term is usually zero, either because is zero at the limits, or because the energy goes to infinity at those limits. In that case, the equipartition theorem for the canonical ensemble follows immediately


title: Equipartition theorem

text: Here, the averaging symbolized by formula_75 is the ensemble average taken over the canonical ensemble.


title: Equipartition theorem

text: In the microcanonical ensemble, the system is isolated from the rest of the world, or at least very weakly coupled to it. Hence, its total energy is effectively constant; to be definite, we say that the total energy is confined between and . For a given energy and spread , there is a region of phase space in which the system has that energy, and the probability of each state in that region of phase space is equal, by the definition of the microcanonical ensemble. Given these definitions, the equipartition average of phase-space variables (which could be either or ) and is given by


title: Equipartition theorem

text: where the last equality follows because is a constant that does not depend on . Integrating by parts yields the relation


title: Equipartition theorem

text: since the first term on the right hand side of the first line is zero (it can be rewritten as an integral of "H" − "E" on the hypersurface where ).


title: Equipartition theorem

text: The law of equipartition holds only for ergodic systems in thermal equilibrium, which implies that all states with the same energy must be equally likely to be populated. Consequently, it must be possible to exchange energy among all its various forms within the system, or with an external heat bath in the canonical ensemble. The number of physical systems that have been rigorously proven to be ergodic is small; a famous example is the hard-sphere system of Yakov Sinai. The requirements for isolated systems to ensure ergodicity—and, thus equipartition—have been studied, and provided motivation for the modern chaos theory of dynamical systems. A chaotic Hamiltonian system need not be ergodic, although that is usually a good assumption.


title: Equipartition theorem

text: A commonly cited counter-example where energy is "not" shared among its various forms and where equipartition does "not" hold in the microcanonical ensemble is a system of coupled harmonic oscillators. If the system is isolated from the rest of the world, the energy in each normal mode is constant; energy is not transferred from one mode to another. Hence, equipartition does not hold for such a system; the amount of energy in each normal mode is fixed at its initial value. If sufficiently strong nonlinear terms are present in the energy function, energy may be transferred between the normal modes, leading to ergodicity and rendering the law of equipartition valid. However, the Kolmogorov–Arnold–Moser theorem states that energy will not be exchanged unless the nonlinear perturbations are strong enough; if they are too small, the energy will remain trapped in at least some of the modes.


title: Equipartition theorem

text: Another way ergodicity can be broken is by the existence of nonlinear soliton symmetries. In 1953, Fermi, Pasta, Ulam and Tsingou conducted computer simulations of a vibrating string that included a non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third). They found that the behavior of the system was quite different from what intuition based on equipartition would have led them to expect. Instead of the energies in the modes becoming equally shared, the system exhibited a very complicated quasi-periodic behavior. This puzzling result was eventually explained by Kruskal and Zabusky in 1965 in a paper which, by connecting the simulated system to the Korteweg–de Vries equation led to the development of soliton mathematics.


title: Equipartition theorem

text: The law of equipartition breaks down when the thermal energy is significantly smaller than the spacing between energy levels. Equipartition no longer holds because it is a poor approximation to assume that the energy levels form a smooth continuum, which is required in the derivations of the equipartition theorem above. Historically, the failures of the classical equipartition theorem to explain specific heats and blackbody radiation were critical in showing the need for a new theory of matter and radiation, namely, quantum mechanics and quantum field theory.


title: Equipartition theorem

text: To illustrate the breakdown of equipartition, consider the average energy in a single (quantum) harmonic oscillator, which was discussed above for the classical case. Neglecting the irrelevant zero-point energy term, its quantum energy levels are given by , where is the Planck constant, is the fundamental frequency of the oscillator, and is an integer. The probability of a given energy level being populated in the canonical ensemble is given by its Boltzmann factor


title: Equipartition theorem

text: At high temperatures, when the thermal energy is much greater than the spacing between energy levels, the exponential argument is much less than one and the average energy becomes , in agreement with the equipartition theorem (Figure 10). However, at low temperatures, when , the average energy goes to zero—the higher-frequency energy levels are "frozen out" (Figure 10). As another example, the internal excited electronic states of a hydrogen atom do not contribute to its specific heat as a gas at room temperature, since the thermal energy (roughly 0.025 eV) is much smaller than the spacing between the lowest and next higher electronic energy levels (roughly 10 eV).


title: Equipartition theorem

text: Similar considerations apply whenever the energy level spacing is much larger than the thermal energy. This reasoning was used by Max Planck and Albert Einstein, among others, to resolve the ultraviolet catastrophe of blackbody radiation. The paradox arises because there are an infinite number of independent modes of the electromagnetic field in a closed container, each of which may be treated as a harmonic oscillator. If each electromagnetic mode were to have an average energy , there would be an infinite amount of energy in the container. However, by the reasoning above, the average energy in the higher-frequency modes goes to zero as "ν" goes to infinity; moreover, Planck's law of black body radiation, which describes the experimental distribution of energy in the modes, follows from the same reasoning.


title: Equipartition theorem

text: Other, more subtle quantum effects can lead to corrections to equipartition, such as identical particles and continuous symmetries. The effects of identical particles can be dominant at very high densities and low temperatures. For example, the valence electrons in a metal can have a mean kinetic energy of a few electronvolts, which would normally correspond to a temperature of tens of thousands of kelvins. Such a state, in which the density is high enough that the Pauli exclusion principle invalidates the classical approach, is called a degenerate fermion gas. Such gases are important for the structure of white dwarf and neutron stars. At low temperatures, a fermionic analogue of the Bose–Einstein condensate (in which a large number of identical particles occupy the lowest-energy state) can form; such superfluid electrons are responsible for superconductivity.


title: Sally Bowles

text: Sally Bowles () is a fictional character created by English-American novelist Christopher Isherwood and based upon 19-year-old cabaret singer Jean Ross. The character debuted in Isherwood's 1937 novella "Sally Bowles" published by Hogarth Press, and commentators have described the novella as "one of Isherwood's most accomplished pieces of writing." The work was republished in the 1939 novel "Goodbye to Berlin" and in the 1945 anthology "The Berlin Stories".


title: Sally Bowles

text: In the 1937 novella, Sally is a British flapper who moonlights as a cabaret singer in Weimar-era Berlin during the twilight of the Jazz Age. She is depicted by Isherwood as a "self-indulgent upper-middle-class British tourist who could escape Berlin whenever she chose." By day, she is an aspiring film actress hoping to work for the UFA GmbH, the German film production company. By night, she is a mediocre chanteuse at an underground club called "The Lady Windermere" located near the Tauentzienstraße. She aspires to be a serious actress or, as an alternative, to ensnare a wealthy man to keep her as his mistress. Unsuccessful at both, Sally departs Berlin on the eve of Adolf Hitler's ascension as Chancellor of Germany and is last heard from in the form of a postcard sent from Rome, Italy, with no return address.


title: Sally Bowles

text: Following the tremendous popularity of the Sally Bowles character in subsequent decades, Jean Ross was hounded by reporters seeking information about her colourful past in Weimar-era Berlin. She believed her popular association with the naïve character of Bowles occluded her lifelong work as a political writer and social activist. According to her daughter Sarah Caudwell, Ross never "felt any sense of identity with the character of Sally Bowles, which in many respects she thought more closely modeled on" Isherwood's gay friends, many of whom "fluttered around town exclaiming how sexy the storm troopers looked in their uniforms".


title: Sally Bowles

text: Sally Bowles is a central character in the 1951 John Van Druten stage play "I Am a Camera", the 1955 film of the same name, the 1966 musical stage adaptation "Cabaret" and the 1972 film adaptation of the musical. The character of Sally Bowles inspired Truman Capote's Holly Golightly in his novella "Breakfast at Tiffany's", and the character also has appeared in novels by other authors. In June 1979, critic Howard Moss of "The New Yorker" commented upon the peculiar resiliency of the character: "It is almost fifty years since Sally Bowles shared the recipe for a Prairie oyster with Herr Issyvoo in a vain attempt to cure a hangover" and yet the character in subsequent permutations lives on "from story to play to movie to musical to movie-musical."


title: Sally Bowles

text: Sally Bowles is based on Jean Ross, a vivacious British flapper and later an ardent Stalinist, whom Isherwood knew while sojourning in Weimar-era Berlin during the twilight of the Jazz Age. Belying her humble circumstances in Berlin, the 19-year-old Ross was the offspring of a wealthy Scottish cotton merchant and came from a privileged background. She had "a long, thin handsome face, aristocratic nose, glossy dark hair" with large brown eyes.


title: Sally Bowles

text: Isherwood noted that the teenage Ross was "more essentially British than Sally; she grumbled like a true Englishwoman, with her "grin-and-bear-it" grin. And she was tougher. She never struck Christopher as being sentimental or the least bit sorry for herself. Like Sally, she boasted continually about her lovers." According to Isherwood, Ross was a sexually liberated young woman who once claimed to have had sex with another performer in view of the audience during Max Reinhardt's production of "Tales of Hoffmann" circa Winter 1931:


title: Sally Bowles

text: When crafting the "divinely decadent" Sally Bowles as a literary character, Isherwood purloined the surname "Bowles" from American writer Paul Bowles whom he had likewise met in Berlin in 1931 and to whom he was sexually attracted. Explaining his choice, he wrote, "[I] liked the sound of it and also the looks of its owner." Isherwood famously introduces Sally in his 1937 novella by writing:


title: Sally Bowles

text: Isherwood described Ross' singing talent as mediocre: "She had a surprisingly deep, husky voice. She sang badly, without any expression, her hands hanging down at her sides—yet her performance was, in its own way, effective because of her startling appearance and her air of not caring a curse of what people thought of her." Likewise, acquaintance Stephen Spender recalled that Ross' singing ability was underwhelming and forgettable: "In my mind's eye, I can see her now in some dingy bar standing on a platform and singing so inaudibly that I could not hear her from the back of the room where I was discreetly seated."


title: Sally Bowles

text: In the 1937 novella, Sally is a British flapper who is the wayward daughter of a Lancashire mill-owner and an heiress. She is a "self-indulgent upper-middle-class British tourist who could escape Berlin whenever she chose." By day, she is an aspiring film actress hoping to work for the UFA GmbH, the German film production company. By night, she is a chanteuse at an underground club called "The Lady Windermere" located near the Tauentzienstraße. She aspires to be a serious actress or, as an alternative, to ensnare a wealthy man to keep her as his mistress. Unsuccessful at both, Sally departs Berlin on the eve of Adolf Hitler's ascension as Chancellor of Germany and is last heard from in the form of a postcard sent from Rome, Italy, with no return address.


title: Sally Bowles

text: After Hitler's ascension as Chancellor of Germany on 30 January 1933, Isherwood began to notice the sinister developments occurring in the country. "Adolf, with his rectangular black moustache, has come to stay and brought all his friends," he wrote to a friend, "Nazis are to be enrolled as 'auxiliary police,' which means that one must now not only be murdered but that it is illegal to offer any resistance." Two weeks after Hitler passed the Enabling Act which cemented his power, Isherwood fled Germany and returned to England on 5 April 1933.


title: Sally Bowles

text: In late Spring 1933, while in an extended period of uncertainty and dire financial straits, Isherwood began drafting the nucleus that would become the novella "Sally Bowles" (1937). He wrote to Ross' friend and later companion Olive Mangeot in July 1933 that he had written a first draft. He continued to revise the manuscript over the next three years, completing his final draft on 21 June, 1936. In a letter to editor John Lehmann dated 16 January, 1936, Isherwood briefly outlined the piece, envisioning it as part of his unfinished novel "The Lost" which became "Mr Norris Changes Trains". He described it as akin to the work of Anthony Hope and as "an attempt to satirize the romance-of-prostitution racket. Good heter stuff."


title: Sally Bowles

text: Later in 1936, Isherwood submitted the piece to Lehmann for publication in his literary magazine, "New Writing". Lehmann liked the piece but felt that it was too lengthy for his magazine. He also was concerned about the inclusion in the manuscript of Sally's abortion, fearing both that his printers might refuse to typeset it and that Jean Ross might file a libel action. In a January 1937 letter, Isherwood expressed his conviction that, without the abortion incident, Sally would be reduced to a "little capricious bitch" and that the omission would leave the novella without a climax.


title: Sally Bowles

text: After his correspondence with Lehmann, Isherwood likewise feared a libel suit by Jean Ross and sought her permission to publish the novella. Ross hesitated in giving her consent as she feared the novella's abortion episode—which was factual and a painful memory—would strain her relations with her powerful family. Ross ultimately relented and gave her permission, and Hogarth published the volume in October 1937.


title: Sally Bowles

text: The 1937 novella received favorable reviews from literary critics, and later commentators described the novella as "one of Isherwood's most accomplished pieces of writing." Following the tremendous popularity of the Sally Bowles character in subsequent decades, Ross regretted her decision to allow the work to be published. For the remainder of her life, Ross believed her popular association with the naïve character of Bowles occluded her lifelong work as a professional journalist, political writer, and social activist.


title: Sally Bowles

text: Although Isherwood never publicly revealed that Ross was the inspiration for Sally until after her death in April 1973, other mutual acquaintances were less discreet, and many individuals who knew Ross had little difficulty in identifying her as the character's genesis. Ross claimed that her former partner, journalist Claud Cockburn, was the first person to reveal her identity to his gossiping friends in the British press.


title: Sally Bowles

text: Despite this public unmasking, Ross did not seek any benefit or publicity from her association with the character. According to her daughter Sarah Caudwell, Ross never "felt any sense of identity with the character of Sally Bowles, which in many respects she thought more closely modeled on" Isherwood's gay friends, many of whom "fluttered around town exclaiming how sexy the storm troopers looked in their uniforms".


title: Sally Bowles

text: When "Cabaret" was first launched as a musical in 1966, Ross was badgered by reporters and declined all invitations to see the show. Ross was purportedly vexed by the lack of political awareness demonstrated by the tabloid reporters—particularly those from the "Daily Mail"—who stalked her and hounded her with invasive questions about her colourful past. She declared: "They say they want to know about Berlin in the Thirties, but they don't want to know about the unemployment or the poverty or the Nazis marching through the streets. All they want to know is how many men I went to bed with."


title: Sally Bowles

text: American actress Julie Harris originated the role of Sally Bowles in John Van Druten's 1951 play "I Am a Camera", for which she received the 1952 Tony Award for Best Performance by a Leading Actress in a Play.


title: Sally Bowles

text: In his memoirs, Isherwood recounts how "when Julie Harris was rehearsing for the part of Sally in the American production of "I Am a Camera", [director] John van Druten and Christopher discussed with her the possibility that nearly all of Sally's sex life is imaginary; and they agreed that the part should be played so that the audience wouldn't be able to make up its mind, either." Isherwood, in particular, was adamant that Sally not be portrayed as "a tart"—an avaricious prostitute. In a letter to John Van Druten, Isherwood explained that Sally "is a little girl who has listened to what the grown-ups had said about tarts, and who was trying to copy those things."


title: Sally Bowles

text: Following the play's critical acclaim, Isherwood ascribed the success entirely to Harris' performance as the insouciant Sally Bowles. Isherwood later described Harris' performance as "more essentially Sally Bowles than the Sally of my book, and much more like Sally than the real girl [Ross] who long ago gave me the idea for my character". Barbara Baxley took over the role when Harris departed. Harris recreated the role for the heavily censored and bowdlerized 1955 film adaptation, also titled "I Am a Camera". Later, Dorothy Tutin starred as Sally in a successful 1954 British stage production.


title: Sally Bowles

text: In his diary from October 1958, Isherwood records that a composer named Don Parks had expressed interest in writing a musical based on Sally but that Isherwood planned to deny him permission. When "I Am a Camera" was finally adapted into the musical "Cabaret" in 1966, Jill Haworth originated the role of Sally. As the run continued, Penny Fuller, Anita Gillette and Melissa Hart also played the part. "Cabaret" was revived on Broadway in 1987 with Alyson Reed playing Sally.


title: Sally Bowles

text: The musical was revived again in 1998 with Natasha Richardson as Sally. Richardson won the 1998 Tony Award for Best Actress in a Musical. As the run continued, actresses including Tina Arena, Jennifer Jason Leigh, Susan Egan, Joely Fisher, Gina Gershon, Deborah Gibson, Teri Hatcher, Melina Kanakaredes, Jane Leeves, Molly Ringwald, Brooke Shields, Lea Thompson, and Vanna White appeared in the role. The 2014 Broadway revival starred Michelle Williams as Sally, with Emma Stone and Sienna Miller as subsequent replacements.


title: Sally Bowles

text: "Cabaret" debuted on the West End in 1968 with Judi Dench in the role of Sally. A West End revival at The Strand Theatre in October 1986 featured Kelly Hunter as Sally Bowles and was the subject of printed criticism by both Jean Ross and her daughter Sarah Caudwell. Later West End revivals starred Toyah Willcox (1987), Jane Horrocks (1993), Anna Maxwell Martin (2006) and Jessie Buckley (2021) playing the part. Samantha Barks portrayed the role in the 2008–2009 UK National Tour.


title: Sally Bowles

text: In 1972, the stage musical adaptation was in turn adapted as a film directed by Bob Fosse. The 1972 film's depiction of Sally significantly differs from earlier incarnations in that she is not British but American. According to unaccredited screenwriter Hugh Wheeler, he was tasked by ABC Pictures with bowdlerizing the source material and was forced to change Sally's nationality as well as to transform her into a noble heroine in order to increase the film's commercial appeal. Key dialogue was likewise altered to make Sally appear more bisexual.


title: Sally Bowles

text: For her performance as Sally in the film, Liza Minnelli reinterpreted the character and—at the explicit suggestion of her father stage director Vincente Minnelli—she deliberately imitated film actress Louise Brooks, a flapper icon and sex symbol of the Jazz Age. Minnelli later recalled:


title: Sally Bowles

text: In particular, Minnelli drew upon Brooks' "Lulu makeup and helmet-like coiffure." Brooks, like the character of Sally in the 1972 film, was an aspiring actress and American expat who went to Weimar-era Berlin in search of stardom. Ultimately, Minnelli won the Academy Award for Best Actress for her portrayal of Sally.


title: Sally Bowles

text: In a 1986 newspaper article published long after Jean Ross' death, her daughter Sarah Caudwell indicated that Ross disapproved of Minnelli's depiction of Sally Bowles in the 1972 film: "In the transformations of the novel for stage and cinema the characterisation of Sally has become progressively cruder" and, consequently, the literary character originally based on Ross had been transmogrified into a freakish vamp.


title: Sally Bowles

text: Isherwood himself was highly critical of the 1972 film adaptation due to its negative portrayal of homosexuality: "In the film of "Cabaret", the male lead is called Brian Roberts. He is a bisexual Englishman; he has an affair with Sally and, later, with one of Sally's lovers, a German baron... Brian's homosexual tendency is treated as an indecent but comic weakness to be snickered at, like bed-wetting."


title: Sally Bowles

text: In June 1979, critic Howard Moss of "The New Yorker" noted the peculiar resiliency of the character: "It is almost fifty years since Sally Bowles shared the recipe for a Prairie oyster with Herr Issyvoo in a vain attempt to cure a hangover" and yet the character in subsequent permutations lives on "from story to play to movie to musical to movie-musical."


title: Sally Bowles

text: Sally Bowles' life after the events of "Goodbye to Berlin" was imagined in "After the Cabaret" (1998) by British writer Hilary Bailey. The plot follows a young American academic Greg Peters who seeks to piece together the missing details of Sally's life for a new biography.


title: Sally Bowles

text: According to literary critics, the character of Sally Bowles inspired Truman Capote's Holly Golightly in his novella "Breakfast at Tiffany's". Critics have alleged that both scenes and dialogue in Capote's 1958 novella have direct equivalencies in Isherwood's earlier 1937 work. Capote had befriended Isherwood in New York in the late 1940s, and Capote was an admirer of Isherwood's novels.


title: Shameless (season 7)

text: The seventh season of "Shameless", based on the British series of the same name by Paul Abbott, is an American comedy-drama television series with executive producers John Wells, Christopher Chulack, Krista Vernoff, Etan Frankel, Nancy M. Pimental and Sheila Callaghan. The season premiered on October 2, 2016, the first time the series has debuted in autumn. Showtime premiered a free preview of the season premiere online on September 23, 2016, ahead of the October 2 broadcast.


title: Shameless (season 7)

text: One month after Fiona's failed wedding, Frank wakes up in a coma and is disowned by his family. Fiona is finally trying to take control of her life, having become the manager of Patsy's Pies. She revamps the diner in order to increase its audience. When a local laundromat building goes up for sale, Fiona buys the laundromat after speaking with the senile owner, Etta, who has Alzheimer's. With the help of Frank and Kevin, Fiona revamps the laundromat and, forgiving her father, lets Frank stay with Etta in her apartment. Though business at the revamped laundromat initially goes well, Fiona sells the building for a major profit and subsequently sends Etta to live at a nursing home.


title: Shameless (season 7)

text: Lip, still struggling with alcoholism, begins a relationship with Sierra, a single mother whom Fiona hires as a waitress at Patsy's. Raising her young son alone, Sierra has left her ex-boyfriend, Charlie, due to his drug addiction. Debbie, wanting to provide Franny with a home life, gets engaged to Sierra's handicapped brother Neil, though both Sierra and Lip are disapproving of the relationship. Following his college expulsion, Lip attends an appeal at his college that Professor Youens had orchestrated. However, the committee refuses to expunge Lip's disciplinary record and refuses to let him re-enroll. This culminates in Lip relapsing back to alcohol, and when he drunkenly attacks Charlie, Sierra breaks up with him, not wanting her son to deal with two addicts. Meanwhile, Kevin and Veronica are forced to find new jobs after Svetlana manipulates them into giving her full ownership of the Alibi. Feeling betrayed, Kevin and Veronica cut off their romantic relationship with Svetlana. Carl receives a scholarship for military school and decides to attend; the school changes his personality for the better.


title: Shameless (season 7)

text: When Frank briefly begins a short-lived homeless shelter in the neighborhood, Ian meets Trevor, a male transgender activist wanting to volunteer at the shelter. Ian and Trevor begin dating, but their relationship is tested when Ian is informed by an officer that Mickey has recently broken out of prison. Unbeknownst to Trevor, Ian reconnects with Mickey, who is on the run with another inmate; Mickey implores Ian to flee with him across the Mexican border, which forces Ian to make a hard decision. Though he initially accompanies Mickey to the border, he experiences second thoughts before crossing and refuses to go through with Mickey's plan. Heartbroken, Mickey shares a final kiss with Ian before successfully crossing the border wearing a disguise. Ian later apologizes to Trevor for cheating on him.


title: Shameless (season 7)

text: The second half of the season revolves around the reappearance of a frail Monica, who has returned to make amends with her family—however, her kids are all generally dismissive of her. Monica reconciles with Frank and reveals that she is dying with irreparable brain damage; the two resort back to their old habits. Frank and Monica eventually decide to renew their vows, and the following morning, Monica passes away in her sleep from a brain aneurysm. Indifferent to her mother's death, Fiona meets with her grandfather to prepare a small funeral, while Frank gives each family member a portion of Monica's inheritance: 70 pounds of crystal meth. Fiona buries her portion of the meth in Monica's coffin. The Gallagher family and friends host a small party following Monica's funeral: Frank is accepted by his family once again, and he shares a dance with Fiona; Lip and Sierra have a good time at the party—they remain separated, but stay on good terms.


title: Shameless (season 7)

text: The seventh season closes with a montage of the Gallaghers continuing on with their lives, some with new beginnings: Debbie has begun taking welding classes; Lip gets a new AA sponsor, Brad; Carl has returned from military school as a changed man; Fiona becomes the owner of a local apartment building.


title: Shameless (season 7)

text: Recurring actress Isidora Goreshter has been promoted to series regular with the commencement of the season. Star Emmy Rossum made her directorial debut with the fourth episode, "I Am A Storm".


title: Bakugan: Battle Planet

text: The second season, titled , premiered on February 16, 2020 in Canada, and on March 1 in the U.S. It was released exclusively online in Japan on April 3, 2020. The third season premiered on January 24, 2021 in Canada, with its first thirteen episodes streaming on Netflix in the United States starting April 15, 2021. The second half was released on Roblox's "Bakugan" hub on September 8, 2021, and on Netflix on September 15.


title: Bakugan: Battle Planet

text: The series follows preteens Dan Kouzo, Shun Kazami, Wynton Styles, Lia Venegas, and their dog Lightning. They are known as the "Awesome Ones" (later the “Awesome Brawlers”) and make videos on the website ViewTube. Eventually, they stumble across a race of battling biomechanical creatures called Bakugan. They soon befriend the Bakugan and begin to battle each other with them, all while defending their neighborhood from thugs who use the Bakugan for malicious purposes. They encounter many foes such as Philomena Dusk and the mysterious Magnus, bent on beating Dan in a Bakugan Battle to be the best brawler.


title: Bakugan: Battle Planet

text: As the Awesome Ones continue to learn more about the Bakugan, they befriend the enigmatic billionaire Benton Dusk, Philomena's brother. Benton uncovers a mysterious underground world he dubs "The Maze", where the Bakugan are enhanced. When a Bakugan hunter named Strata kidnaps several Bakugan, a Bakugan named Phaedrus escapes and warns the Awesome Ones. They go to the Maze and rescue the others, but fall even deeper into it. As they try to make their way home, the Awesome Ones encounter a strange evil Bakugan named Tiko. Drago and the others find a powerful artifact called the Core Cell within the Maze and protect it from Tiko. However, when Drago is injured by the corrupting V Virus, he and Dan retreat into the Core Cell, and Tiko makes it inside. Drago is healed and experiences a power upgrade called a Bakugan Evolution. Drago evolves into Hyper Drago and defeats Tiko. The Awesome Ones then escape the Maze. Soon after, they learn that Magnus is working with Philomina, along with several other of their old rivals, as AAAnimus' publicity team, The Exit. In order to combat them, the Awesome Ones learn, one by one, to evolve their Bakugan without going inside the Core Cell. Eventually, they defeat the Exit and they are fired. Despite their efforts, AAAnimus learns that there are more Core Cells within the Maze, and they successfully extract one. They use it to take control of the Awesome Ones' primary Bakugan. Benton creates a plan to stop them. They break into AAAnimus' headquarters, and while Benton dismantles their network, the Awesome Ones act as decoys. The plan works, and they defeat Philomina. Benton informs the Awesome Ones of his plan to make all the Core Cells open-sourced, which sets them on an adventure around the world. However, even greater threats lurk in the shadows. Tiko survived his battle in the Core Cell, and hatches a plan of his own.


title: Bakugan: Battle Planet

text: News on a relaunch of the "Bakugan" property first broke in late 2015 through an investor presentation conducted by Spin Master. Information on the project remained scarce until November 2017 when the company revealed that the new series would launch in 2018/2019. Shortly after, it was discovered that Spin Master had filed a trademark for the name "Bakugan Battle Planet". The following January, Corus Entertainment confirmed its Nelvana subsidiary would again collaborate with TMS Entertainment on the animated series.


title: Bakugan: Battle Planet

text: In preparation for the relaunch, Spin Master filed patent infringement lawsuits against Alpha Group, GuangZhou Lingdong Creative Culture Technology and Mattel for allegedly violating "Bakugan" patents in their "Screechers Wild", "Eonster Hunter", "Mecard" and "Beyblade Burst" toylines. Spin Master co-CEO Ronnen Harary stated that "Bakugan" would be reintroduced globally in 2019.


title: Bakugan: Battle Planet

text: In March 2018, Harary described the new animated series as utilizing an eleven-minute format. This was done at the request of broadcast partner Cartoon Network, who felt the original's 22-minute episode runtime would not appeal to the current generation of kids. A decision to include more comedic elements was also made. A promotional image for the reboot first surfaced in June 2018 through another Spin Master investor document.


title: Bakugan: Battle Planet

text: The company formally announced "Bakugan Battle Planet" on October 9, 2018. Spin Master revealed that the animated series would premiere the following December on Cartoon Network in the United States and Teletoon in Canada with the toys and online web-shorts following shortly after. Cartoon Network had also picked up the show for a 2019 launch in Latin America, EMEA, Australia and New Zealand. In Asia, the series would be distributed by TMS Entertainment with Takara Tomy handling the toyline.


title: Bakugan: Battle Planet

text: On October 16, 2019, it was announced that it was renewed for a second season titled "", which debuted in 2020.


title: Bakugan: Battle Planet

text: Like its predecessor, "Bakugan: Battle Planet" is an international co-production. The series is produced at TMS Entertainment with additional assistance from Nelvana Enterprises and Spin Master Entertainment. Kazuya Ichikawa directed the series. Kazuhiko Inukai as well as Man of Action Studios act as story editors. The episode scripts are primarily written in Japan, with American writers occasionally contributing. The first season consists of 100 eleven-minute episodes that are also distributed as 50 twenty-two minutes.


title: Bakugan: Battle Planet

text: "Bakugan Battle Planet" debuted in the United States on Cartoon Network on December 23, 2018, with the first 20 episodes made available on the channel's video-on-demand services in the days prior. The series then had a five-day linear premiere event before settling into its regular slot on January 12, 2019. In Canada, the series launched on Teletoon on December 31, 2018 through a similar five-day premiere stunt before the show debuted in its regular slot on January 12, 2019. Reruns began airing on sister channel YTV on the 11th. In the UK, the series premiered on Cartoon Network on 23 March 2019, with a free-to-air broadcast on Pop following on 2 September. In Australia, the pay-TV premiere occurred on Cartoon Network on 6 April 2019 with a terrestrial broadcast on 9Go! beginning on 14 July.


title: Bakugan: Battle Planet

text: The first season launched in Japan on TV Tokyo and other TX Network stations on April 1, 2019. The opening theme song is titled with the ending theme is titled "Be my story", both songs performed by HiHi Jets. The Japanese version also features an entirely different musical score composed by Yasuharu Takanashi.


title: Bakugan: Battle Planet

text: Alongside the television series, Spin Master launched a series of animated web-shorts called "Bakugan: Beyond the Brawl" on YouTube. They feature the Bakugan creatures in comedic situations.


title: Bakugan: Battle Planet

text: Spin Master has launched a new tabletop game that mixes the traditional transforming Bakugan marbles with a full-fledged trading card game. Co-designed by Justin Gary, the game is intended to appeal to both younger audiences and those wanting a competitive scene.


title: Bakugan: Battle Planet

text: The game launched in January 2019 in Canada and the United States, with additional markets set throughout the rest of the year.


title: Bakugan: Battle Planet

text: In December 2018, Spin Master launched the "Bakugan Battle Hub" app for iOS and Android devices. It offers character profiles, videos and a simplified version of the tabletop game.


title: Bakugan: Battle Planet

text: On July 10, 2020, Warner Bros. Interactive Entertainment announced the Bakugan: Champions of Vestroia action role-playing game. Developed by WayForward, it released exclusively on the Nintendo Switch in North America on November 3, 2020.


title: ISO 26262

text: ISO 26262, titled "Road vehicles – Functional safety", is an international standard for functional safety of electrical and/or electronic systems that are installed in serial production road vehicles (excluding mopeds), defined by the International Organization for Standardization (ISO) in 2011, and revised in 2018.


title: ISO 26262

text: Functional safety features form an integral part of each automotive product development phase, ranging from the specification, to design, implementation, integration, verification, validation, and production release. The standard ISO 26262 is an adaptation of the Functional Safety standard IEC 61508 for Automotive Electric/Electronic Systems. ISO 26262 defines functional safety for automotive equipment applicable throughout the lifecycle of all automotive electronic and electrical safety-related systems.


title: ISO 26262

text: The first edition (ISO 26262:2011), published on 11 November 2011, was limited to electrical and/or electronic systems installed in "series production passenger cars" with a maximum gross weight of 3500 kg. The second edition (ISO 26262:2018), published in December 2018, extended the scope from passenger cars to all road vehicles except mopeds.


title: ISO 26262

text: The standard aims to address possible hazards caused by the malfunctioning behaviour of electronic and electrical systems in vehicles. Although entitled "Road vehicles – Functional safety" the standard relates to the functional safety of Electrical and Electronic systems as well as that of systems as a whole or of their mechanical subsystems.


title: ISO 26262

text: Like its parent standard, IEC 61508, ISO 26262 is a risk-based safety standard, where the risk of hazardous operational situations is qualitatively assessed and safety measures are defined to avoid or control systematic failures and to detect or control random hardware failures, or mitigate their effects.


title: ISO 26262

text: ISO 26262:2018 consists of twelve parts, ten normative parts (parts 1 to 9 and 12) and two guidelines (parts 10 and 11):


title: ISO 26262

text: ISO 26262 specifies a vocabulary (a Project Glossary) of terms, definitions, and abbreviations for application in all parts of the standard.


title: ISO 26262

text: Of particular importance is the careful definition of "fault", "error", and "failure" as these terms are key to the standard’s definitions of functional safety processes, particularly in the consideration that "A "fault" can manifest itself as an "error" ... and the "error" can ultimately cause a "failure"". A resulting "malfunction" that has a "hazardous" effect represents a loss of "functional safety".


title: ISO 26262

text: "Note:" In contrast to other "Functional Safety" standards and the updated ISO 26262:2018, "Fault Tolerance" was not explicitly defined in ISO 26262:2011 – since it was assumed impossible to comprehend all possible faults in a system.


title: ISO 26262

text: "Note:" ISO 26262 does not use the IEC 61508 term Safe failure fraction (SFF). The terms "single point faults metric" and "latent faults metric" are used instead."


title: ISO 26262

text: ISO 26262 provides a standard for functional safety management for automotive applications, defining standards for overall organizational safety management as well as standards for a safety life cycle for the development and production of individual automotive products. The ISO 26262 safety life cycle described in the next section operates on the following safety management concepts:


title: ISO 26262

text: Processes within the ISO 26262 "safety life cycle" identify and assess hazards (safety risks), establish specific safety requirements to reduce those risks to acceptable levels, and manage and track those safety requirements to produce reasonable assurance that they are accomplished in the delivered product. These safety-relevant processes may be viewed as being integrated or running in parallel with a managed requirements life cycle of a conventional Quality Management System:


title: ISO 26262

text: ISO 26262 defines objectives for integral processes that are supportive to the Safety Life Cycle processes, but are continuously active throughout all phases, and also defines additional considerations that support accomplishment of general process objectives.


title: ISO 26262

text: "Automotive Safety Integrity Level" refers to an abstract classification of inherent safety risk in an automotive system or elements of such a system. ASIL classifications are used within ISO 26262 to express the level of risk reduction required to prevent a specific hazard, with ASIL D representing the highest hazard level and ASIL A the lowest. The ASIL assessed for a given hazard is then assigned to the safety goal set to address that hazard and is then inherited by the safety requirements derived from that goal.


title: ISO 26262

text: The determination of ASIL is the result of "hazard analysis and risk assessment". In the context of ISO 26262, a hazard is assessed based on the relative impact of hazardous effects related to a system, as adjusted for relative likelihoods of the hazard manifesting those effects. That is, each hazardous event is assessed in terms of severity of possible injuries within the context of the relative amount of time a vehicle is exposed to the possibility of the hazard happening as well as the relative likelihood that a typical driver can act to prevent the injury.


title: ISO 26262

text: At the beginning of the safety life cycle, hazard analysis and risk assessment is performed, resulting in assessment of ASIL to all identified hazardous events and safety goals.


title: ISO 26262

text: Each "hazardous event" is classified according to the "severity" (S) of "injuries" it can be expected to cause:


title: ISO 26262

text: Risk Management recognizes that consideration of the severity of a possible injury is modified by how likely the injury is to happen; that is, for a given hazard, a hazardous event is considered a lower risk if it is less likely to happen. Within the "hazard analysis and risk assessment" process of this standard, the likelihood of an injurious hazard is further classified according to a combination of


title: ISO 26262

text: In terms of these classifications, an "Automotive Safety Integrity Level D" hazardous event (abbreviated "ASIL D") is defined as an event having reasonable possibility of causing a life-threatening (survival uncertain) or fatal injury, with the injury being physically possible in most operating conditions, and with little chance the driver can do something to prevent the injury. That is, "ASIL D" is the combination of S3, E4, and C3 classifications. For each single reduction in any one of these classifications from its maximum value (excluding reduction of C1 to C0), there is a single-level reduction in the ASIL from "D". [For example, a hypothetical uncontrollable (C3) fatal injury (S3) hazard could be classified as "ASIL A" if the hazard has a very low probability (E1).] The ASIL level below "A" is the lowest level, "QM". "QM" refers to the standard's consideration that below "ASIL A"; there is no safety relevance and only standard Quality Management processes are required.


title: ISO 26262

text: These Severity, Exposure, and Control definitions are informative, not prescriptive, and effectively leave some room for subjective variation or discretion between various automakers and component suppliers. In response, the Society for Automotive Safety Engineers (SAE) has issued "J2980 – Considerations for ISO26262 ASIL Hazard Classification" to provide more explicit guidance for assessing Exposure, Severity and Controllability for a given hazard.


title: Semaphore

text: Semaphore (; ) is the use of an apparatus to create a visual signal transmitted over distance. A semaphore can be performed with devices including: fire, lights, flags, sunlight, and moving arms. Semaphores can be used for telegraphy when arranged in visually connected networks, or for traffic signalling such as in railway systems, or traffic lights in cities.


title: Semaphore

text: The Phryctoriae were a semaphore system used in Ancient Greece for the transmission of specific prearranged messages. Towers were built on selected mountaintops, so that one tower, the "phryctoria", would be visible to the next tower, usually twenty-miles distant. Flames were lit on one tower, then the next tower would light a flame in succession.


title: Semaphore

text: The Byzantine beacon system was a semaphore developed in the 9th century during the Arab–Byzantine wars. The Byzantine Empire used a system of beacons to transmit messages from the border with the Abbasid Caliphate across Asia Minor to the Byzantine capital, Constantinople. The main line of beacons stretched over some with stations placed from to . A message could be sent along the line in approximately one hour. A bonfire was set at the first beacon and transmitted down the line to Constantinople.


title: Semaphore

text: The Lighthouse of Alexandria was a high tower in overall height with a fire on top to provide a navigation beacon for ships in ancient times. The lighthouse was built in the 2nd century BC and is considered one of the Seven Wonders of the Ancient World, which remained one of the tallest man-made structures in the world for several centuries. The Tower of Hercules at A Coruña, Spain was a Roman 2nd century lighthouse that used a large fire as a warning beacon to passing ships.


title: Semaphore

text: A smoke signal is one of the oldest forms of semaphore for long-distance communication. The smoke is used to transmit news, signal danger or gather people to a common area.


title: Semaphore

text: A signal lamp is a semaphore system using a visual signaling device, often utilizing Morse code. In the 19th century, the Royal Navy began using signal lamps. In 1867, then Captain, later Vice Admiral, Philip Howard Colomb for the first time began using dots and dashes from a signal lamp.


title: Semaphore

text: The modern lighthouse is a semaphore using a tower, building, or another type of structure designed to emit light from a system of lamps and lenses and to serve as a navigational aid for maritime pilots at sea or on inland waterways. Lighthouses mark dangerous coastlines, hazardous shoals, reefs, rocks, and safe entries to harbors; they also assist in aerial navigation. Originally lit by open fires and later candles, the Argand hollow wick lamp and parabolic reflector were introduced in the late 18th century. The source of light is called the "lamp" and the light is concentrated, by the "lens" or "optic". Whale oil was also used with wicks as the source of light. Kerosene became popular in the 1870s and electricity and carbide (acetylene gas) began replacing kerosene around the turn of the 20th century. Carbide was promoted by the Dalén light which automatically lit the lamp at nightfall and extinguished it at dawn. The advent of electrification and automatic lamp changers began to make lighthouse keepers obsolete. Improvements in maritime navigation and safety with satellite navigation systems like the Global Positioning System (GPS) have led to the phasing out of non-automated lighthouses across the world.


title: Semaphore

text: A flag semaphore is the telegraphy system conveying information at a distance by means of visual signals with hand-held flags, rods, disks, paddles, or occasionally bare or gloved hands. Information is encoded by the position of the flags. It is still used during underway replenishment at sea and is acceptable for emergency communication in daylight or using lighted wands instead of flags, at night.


title: Semaphore

text: A heliograph is a semaphore that signals by flashes of sunlight using a mirror, often in Morse code. The flashes are produced by momentarily pivoting the mirror or by interrupting the sunlight with a shutter. The heliograph was a simple but effective instrument for instantaneous optical communication over long distances during the late 19th and early 20th century. The main uses were for the military, survey and forest protection work. Heliographs were standard issue in the British and Australian armies until the 1960s and were used by the Pakistani army as late as 1975.


title: Semaphore

text: In 1792 Claude Chappe, a clergyman from France, invented a terrestrial semaphore telegraph, which uses pivoted indicator arms and conveys information according to the direction the indicators point and was popular in the late eighteenth to early nineteenth centuries. Relay towers were built with a sightline to each tower at separations of . On the top of each tower was an apparatus, which uses pivoted indicator arms and conveys information according to the direction the indicators point. An observer at each tower would watch the neighbouring tower through a telescope and when the semaphore arms began to move spelling out a message, they would pass the message on to the next tower. This early form of telegraph system was much more effective and efficient than post riders for conveying a message over long distances. The sightline between relay stations was limited by geography and weather. In addition, the visual communication would not be able cross large bodies of water.


title: Semaphore

text: An example is during the Napoleonic era, stations were constructed to send and receive messages using the coined term "Napoleonic semaphore". This form of visual communication was so effective that messages that normally took days to communicate could now be transmitted in mere hours.


title: Semaphore

text: The railway semaphore signal is one of the earliest forms of fixed railway signals. These signals display their different indications to train drivers by changing the angle of inclination of a pivoted 'arms'. A single arm that pivots is attached to a vertical post and can take one of three positions. The horizontal position indicates stop, the vertical means all clear and the inclined indicates go ahead under control, but expect to stop. Designs have altered over the intervening years and colour light signals have replaced semaphore signals in most countries.


title: Semaphore

text: A hydraulic telegraph is either of two different semaphore systems. The earliest one was developed in 4th-century BC Greece, while the other was developed in 19th-century AD Britain. The Greek system was deployed in combination with semaphoric fires, while the latter British system was operated purely by hydraulic fluid pressure.


title: Semaphore

text: In the early 1800s, the electrical telegraph was gradually invented allowing a message to be sent over a wire. In 1835, the American inventor Samuel Morse created a dots and dashes language system representing both letters and numbers, called the Morse code. In 1837, the British inventors William Fothergill Cooke and Charles Wheatstone obtained a patent for the first commercially viable telegraph. By the 1840s, with the combination of the telegraph and Morse code, the semaphore system was replaced. The telegraph continued to be used commercially for over 100 years and is still used by amateur radio enthusiasts. Telecommunication evolved replacing the electric telegraph with the advent of wireless telegraphy, teleprinter, telephone, radio, television, satellite, mobile phone, Internet and broadband.


title: Italian nationality law

text: Italian nationality law is the law of Italy governing the acquisition, transmission and loss of Italian citizenship. Like many continental European countries it is largely based on "jus sanguinis". It also incorporates many elements that are seen as favourable to the Italian diaspora. The Italian Parliament's 1992 update of Italian nationality law is Law no. 91, and came into force on 15 August 1992. Presidential decrees and ministerial directives, including several issued by the Ministry of the Interior, instruct the civil service how to apply Italy's citizenship-related laws.


title: Italian nationality law

text: Citizens of other countries descended from an ancestor (parent, grandparent, great-grandparent, etc.) born in Italy may have a claim to Italian citizenship by descent (or, in other words, by "derivation" according to "jus sanguinis" citizenship principles).


title: Italian nationality law

text: Italian citizenship is granted by birth through the paternal line, with no limit on the number of generations, or through the maternal line for individuals born on or after 1 January 1948. An Italian citizen may be born in a country whose citizenship is acquired at birth by all persons born there. That person would be born therefore with the citizenship of two (or possibly more) countries. Delays in reporting the birth of an Italian citizen abroad do not cause that person to lose Italian citizenship, and such a report might in some cases be filed by the person's descendants many years after he or she is deceased. A descendant of a deceased Italian citizen whose birth in another country was not reported to Italy may report that birth, along with his or her own birth (and possibly the births of descendants in intermediate generations), to be acknowledged as having Italian citizenship.


title: Italian nationality law

text: A person may only have acquired "jus sanguinis" Italian citizenship by birth if one or both of that person's parents was in possession of Italian citizenship on the birth date. There is a possibility in the law that the only parent who held Italian citizenship on the birth date of a child born with "jus sanguinis" Italian citizenship was the mother, who previously acquired the Italian citizenship by marriage to the father, who relinquished his own Italian citizenship before the child was born.


title: Italian nationality law

text: Under certain conditions, a child born with Italian citizenship might later have lost Italian citizenship during his or her infancy. The event could prevent a claim of Italian citizenship by his or her descendants. If the Italian parents of a minor child naturalised in another country, the child may have remained holding Italian citizenship, or else may have lost the Italian citizenship. The children who were exempt from losing their Italian citizenship upon the foreign naturalisation of their parents were in many cases (dual) citizens of other countries where they were born, by operation of the "jus soli" citizenship laws in those countries.


title: Italian nationality law

text: One must apply through the Italian consulate that has jurisdiction over their place of residence. Each consulate has slightly different procedures, requirements, and waiting times. However, the legal criteria for "jus sanguinis" citizenship are the same.


title: Italian nationality law

text: All conditions above must be met by every person in a direct lineage. There is no generational limit, except in respect to the date of 17 March 1861. Note that if an Italian ancestor naturalised as a citizen of another country independently from his or her parents, and prior to reaching legal Italian adulthood (age 21 prior to 10 March 1975, and age 18 otherwise), then often that ancestor retained Italian citizenship even after the naturalisation and could still pass citizenship on to children. Also, having one qualifying Italian parent—who except in certain situations could only have been the child's "father" if the birth occurred before 1 January 1948—is sufficient for deriving (inheriting) citizenship, even if the other Italian parent naturalised or otherwise became unable to pass on citizenship. Sometimes that qualifying parent is the foreign-born mother, because foreign women who married Italian men prior to 27 April 1983 automatically became Italian citizens and, in many cases, retained that citizenship even when their Italian husbands later naturalised.


title: Italian nationality law

text: A significant portion of "jus sanguinis" applicants are Argentines of Italian descent, as Argentina received a large number of Italian immigrants in the 1900s.


title: Italian nationality law

text: The lack of limits on the number of generations of transmission of citizenship means that up to 60 million people, mostly in the Americas, could be entitled to Italian citizenship, a number that is the same as the population of Italy. This large number and the desire for EU citizenship has led to waiting times for a "jus sanguinis" appointment of up to 20 years at some Italian consulates, particularly in Argentina and Brazil.


title: Italian nationality law

text: Many of these Italians who do receive an Italian passport then use it to live in Spain and had previously used it to live in the United Kingdom when it was still part of the European Union.


title: Italian nationality law

text: The landmark 1992 European Court of Justice case "Micheletti v. Cantabria", a case of an Argentine Italian citizen by descent living in Spain whose Italian citizenship was challenged by Spain, established that EU member states were not permitted to distinguish between traditional citizens of a fellow EU state, like Italy, and persons who only had citizenship in another EU state through descent or "jus sanguinis".


title: Italian nationality law

text: The long consular waiting lines, combined with the difficulty of locating all the required documents, the fees, and the lack of reason to obtain a second passport for many people, act as a practical limit on the numbers who will actually apply.


title: Italian nationality law

text: The Statuto Albertino, put forth in 1848 by the Kingdom of Sardinia, was the first basic legal system of the Italian state, formed in 1861. It was not a true constitution, but was essentially an outline of the fundamental principles on which the monarchic rule was based.


title: Italian nationality law

text: "All subjects, whatever be their title or rank, are equal before the law. All enjoy equally the civil and political rights, and are admissible to the civil and military offices, except under circumstances determined in the Law."


title: Italian nationality law

text: This proclaimed equality before the law referred nonetheless only to men, since women were subordinate to the authority of the "pater familias". This was held very pertinent in the matter of citizenship, as the subordination of women and also their children to the husband made it so that each event regarding the husband's citizenship would be transmitted to the family. These events could include the loss or reacquisition of citizenship. For example, the family might lose Italian citizenship if the husband naturalised in a foreign state.