title: Tetrasomy X

text: The psychological and behavioural phenotype of tetrasomy X is understudied. Some reports describe girls and women with tetrasomy X as generally placid and pleasant, while others report emotional lability and inappropriate behaviour. Family background and environment has a significant impact on behaviour, and cases with severe behavioural dysfunction frequently have similarly dysfunctional unaffected relatives. Expressive language delays and executive dysfunction are common heralds of behavioural issues, due to the difficulties they cause for educational, vocational, and social functioning. In both men and women X-chromosome polysomy is known to be associated with psychosis, and a case is known of a girl with tetrasomy X and childhood-onset schizophrenia. Parent reports describe children and young adults who are generally pleasant and affectionate yet shy, and have issues relating to temper tantrums, mood swings, and frustration at an inability to communicate.


title: Tetrasomy X

text: Tetrasomy X can interfere with pubertal development. Of the adult women recorded with tetrasomy X, half have had normal pubertal development with menarche at an appropriate age, while the other half have had some form of pubertal dysfunction such as primary amenorrhea, irregular menstrual cycles, or incomplete development of secondary sex characteristics. Premature ovarian failure, or early menopause, has been recorded. In trisomy X, premature menopause has occurred between the ages of 19 and 40, while in tetrasomy X, it has been recorded as young as 15. In tetrasomy X as for other causes of premature menopause or incomplete puberty, some writers have recommended hormone replacement therapy. Fertility in tetrasomy X is possible. In the first discussion of the phenomenon, three cases have been reported of women bearing children. One woman had two children, one with a normal chromosome complement and the other with Down syndrome. Two women had one child each; one had a daughter with normal chromosomes, while the other had a stillbirth with an omphalocele. An additional woman was reported as having three children, all with normal chromosomes.


title: Tetrasomy X

text: Tetrasomy X, like other aneuploidy disorders, is caused by a process called nondisjunction. Nondisjunction occurs when homologous chromosomes or sister chromatids fail to separate properly during meiosis, the process that produces gametes (eggs or sperm), and result in gametes with too many or too few chromosomes. In the specific case of sex chromosome tetrasomy and pentasomy, nondisjunction occurs multiple times with the same parent; for tetrasomy X specifically, all known cases have inherited either three maternal X chromosomes and one paternal, or four maternal X chromosomes with no paternal contribution. The cause of this specific pattern of inheritance is unclear. An early research group proposed that due to the gap in prevalence between the related conditions 49,XXXXY, which has a similar prevalence to tetrasomy X, and pentasomy X, which is far rarer, the paternal X chromosomes may frequently be lost in high-level aneuploidy. More recently, speculation has been based in genomic imprinting, with the suggestion that a similarly high number of paternal X-chromosomes would be incompatible with life. Nondisjunction can also occur after conception, which frequently results in a mosaic karyotype.


title: Tetrasomy X

text: Nondisjunction is related to advanced maternal age. In common aneuploidies such as Down syndrome, the relationship with maternal age is extensively studied. In Klinefelter syndrome, the most common and most studied sex chromosome aneuploidy, incidence increases substantially as maternal age rises. Less is understood about the role of maternal age in sex chromosome tetrasomy and pentasomy conditions, primarily due to their rarity, and no clear relationship has been established.


title: Tetrasomy X

text: Tetrasomy X is generally a random occurrence and does not recur in the same family. In rare cases, it may be related to a mother having trisomy X, mosaic or otherwise. It is not caused by environmental factors.


title: Tetrasomy X

text: Chromosome aneuploidies such as tetrasomy X are diagnosed via karyotype, the process in which chromosomes are tested from blood, bone marrow, amniotic fluid, or placental cells. Due to significant differential diagnosis potential, diagnosis cannot be made on the basis of phenotype alone.


title: Tetrasomy X

text: Tetrasomy X has many possibilities for differential diagnosis, with multiple other conditions overlapping with the phenotype. One differential diagnosis is trisomy X, in which a female has three copies of the X chromosome. The two conditions have overlapping phenotypes with a broad range of severity. Both are associated with hypotonia, mild facial anomalies such as hypertelorism and epicanthic folds, increased height, premature ovarian failure, and some reduction in intelligence. However, the phenotype of tetrasomy X is generally more severe than that of trisomy X. In addition, while both are associated to some degree with tall stature, the association is much stronger for trisomy X. The clinical portrait is made more complex by the possibility of mosaicism, where both 47,XXX and 48,XXXX cell lines are present; such cases frequently, but not certainly, present closer to the tetrasomy than trisomy profile. As well as simple 47,XXX/48,XXXX mosaicism, complex 46,XX/47,XXX/48,XXXX mosaicism has been reported.


title: Tetrasomy X

text: Pentasomy X, a karyotype of five X chromosomes, is another major differential diagnosis. The phenotype of pentasomy X is similar but on average more severe. Intellectual disability is more severe, with an average IQ of 50, and pubertal delay or incomplete puberty appears more common. Unlike other X-chromosome polysomies, pentasomy X is associated with short stature. Similarly, pentasomy X is commonly associated with findings that are infrequent in tetrasomy X such as microcephaly and intrauterine growth restriction. Cases of 48,XXXX/49,XXXXX mosaicism have been reported, and are often categorized as cases of pentasomy X. More complex mosaics have been reported, such as 47,XXX/48,XXXX/49,XXXXX and 45,X0/46,XX/47,XXX/48,XXXX/49,XXXXX.


title: Tetrasomy X

text: An additional differential diagnosis in some cases is Down syndrome. Some cases of tetrasomy X have been described as having "a false air of trisomy 21" (the underlying chromosomal aneuploidy in Down's), and karyotyping resulting in a diagnosis of tetrasomy X has been performed due to suspicion of Down syndrome. However, this is only a differential diagnosis for a subset of cases, while others have more normal phenotypes or abnormalities inconsistent with the Down's profile. The matter is complicated by the observation that a number of women with X chromosome polysomy, including tetrasomy X, have had children with Down syndrome.


title: Tetrasomy X

text: The long-term prognosis for tetrasomy X appears generally good. While life expectancy is unclear, patients have been diagnosed in their 50s and 60s, and long-term follow-up of individual cases shows healthy aging with good physical health. Some women live fully independent lives, while others require more persistent support from parents and caregivers, consistent with other intellectual disability syndromes of comparable severity. Many are able to work part-time, and some full-time; some young women attend tertiary education, mostly vocational. Girls and women with tetrasomy X and good outcomes are typified by supportive family environments and strong personal advocacy for their success; "[t]he children have been exposed to many varied activities and experiences and are praised for their strengths, while their limitations and delays are minimised".


title: Tetrasomy X

text: Tetrasomy X is estimated to occur in around 1 in 50,000 females. Considering the variable phenotype, tetrasomy X support organizations and researchers think it likely there are many cases that have not come to medical attention. This is common to all sex chromosome aneuploidies, which have very low diagnosis rates compared to their overall population prevalence. Overall, sex chromosome tetrasomy and pentasomy disorders occur in 1 in 18,000 to 1 in 100,000 male live births, and are somewhat rarer in females.


title: Tetrasomy X

text: Tetrasomy X only occurs in females, as the Y chromosome is in most cases necessary for male sexual development.


title: Tetrasomy X

text: Tetrasomy X was first recorded in 1961 in two intellectually disabled women residing in an institution. The late 1950s and early 1960s were a period of frequent ascertainment of previously unknown sex chromosome aneuploidies, with the discovery of the 48,XXXX karyotype being alongside that of 45,X0, 47,XXY, and 47,XXX in 1959, 48,XXYY in 1960, and 47,XYY the same year. One of the two women first diagnosed with tetrasomy X was followed up twenty-six years later in her late fifties, by which time she had left the institution and was living semi-independently with her sister; she was in good physical health, had experienced menarche and menopause at typical ages (14 and 50), and showed no signs of cognitive decline.


title: Tetrasomy X

text: Much of the medical literature for tetrasomy X dates to the 1960s and 1970s, an era of particular interest in and research on sex chromosome aneuploidy. Early reports were frequently discovered during chromosome screenings in institutions for the intellectually disabled. The early preference for diagnosis of sex chromosome aneuploidy in selected samples, such as institution residents and prisoners, led to a biased perspective on the conditions that painted an unduly negative portrait of their phenotypes and prognoses. Further research on sex chromosome aneuploidy via unselected samples such as newborn screening allowed for major conditions such as XYY syndrome, Klinefelter syndrome, and trisomy X to be re-defined by more representative phenotypes; however, rarer conditions such as tetrasomy X were not ascertained in any such studies, and therefore the medical literature continues to describe cases that were diagnosed due to developmental or behavioural issues. Aspects of the early studies remain accepted; a 1969 proposal that each supernumerary X chromosome reduces IQ by an average of 15 points is still used as a rule of thumb.


title: Tetrasomy X

text: Sex chromosome tetrasomy and pentasomy conditions have consistently received little attention compared to the more common trisomy conditions. Research into conditions such as tetrasomy X has been stymied by biased samples, outdated information, and a lack of publications above the case report level. Dedicated patient and family support groups, such as Unique and the Tetrasomy and Pentasomy X Support Group, began to appear online in the early 2000s. A patient registry in the United Kingdom was established in 2004, amidst concerns that little serious research had been conducted on tetrasomy X for many years.


title: Tetrasomy X

text: Diagnosis of sex chromosome aneuploidies is increasing, as is the number of supports available for families. The rarity of and variation in tetrasomy X limits the amount of specific support available, but major chromosome disorder organizations serve the condition and have members who are or are associates of people with it.


title: Adela Noriega

text: Adela Amalia Noriega Méndez (; born October 24, 1969), professionally known as Adela Noriega, is a Mexican retired actress. She came to prominence after starring in many teen-oriented coming-of-age telenovelas produced by Televisa, including "Quinceañera" (1987–1988) and "Dulce desafío" (1988–1989).


title: Adela Noriega

text: Some of her most notable works include "María Bonita" (1995–1996), "María Isabel" (1997–1998), "El Privilegio de Amar" (1998–1999), "El Manantial" (2001–2002), "Amor real" (2003), "La esposa virgen" (2005) and "Fuego en la sangre" (2008). Noriega's success as a leading lady has led her to be known as one of the "Queens" of the genre.


title: Adela Noriega

text: Adela Amalia Noriega Méndez was born on October 24, 1969, in Mexico City, Mexico. Her father died when she was in her early adolescence and her mother died in 1995, after a battle with cancer. She has two siblings; an older sister, Reyna, and a younger brother, Alejandro,


title: Adela Noriega

text: Noriega was discovered as a child, at the age of twelve she was scouted in a shopping centre while she was walking with her mother. Shortly after, she began to work as a fashion model and started appearing in TV commercials and music videos.


title: Adela Noriega

text: After being spotted on a shooting of a commercial by Patty de Llano, wife of the producer Luis de Llano Macedo, she began working as a teen actress. She made her television debut at the age of fourteen in the telenovela "Principessa" and shortly after she participated in "Juana Iris". In both shows she interpreted antagonists. She also guest starred on the comic show "Cachún cachún ra ra!" for a few years.


title: Adela Noriega

text: Noriega made her debut as a leading actress in 1986, at the age of sixteen, when she was cast for her first lead role in "Yesenia", a historical telenovela. The telenovela was adapted from Yolanda Vargas Dulché's comic book of the same name, which centers around a young Romani woman and her caravan. From then on she began to work solely as a leading actress of many successful telenovelas with an international distribution.


title: Adela Noriega

text: She rose to greater prominence in 1987 when she obtained the leading role in the iconic "Quinceañera", telenovela portraying coming-of-age topics. "Quinceañera" was the first telenovela that geared towards adolescents and revealed the problems they face in this transitional period from childhood to adulthood. Topics such as substance abuse, date rape, teenage pregnancy, juvenile delinquency, gangs and self-acceptance were being explored for the first time in this genre. This teen classic had a great impact in Mexico and other countries worldwide. In 2008, it was included on the Associated Press' "10 Most Influential Telenovelas of Latin America" list, "because it represented a precedent in this genre and has had an influence on the collective imaginary."


title: Adela Noriega

text: One year after, she returned to television in another successful teen-oriented telenovela; "Dulce desafío", directed by Arturo Ripstein. In this teen drama, she played the central character, Lucero Sandoval, a teenage girl who rebels against her emotionally distant father and gets romantically involved with her teacher (Eduardo Yáñez).


title: Adela Noriega

text: Noriega obtained a contract with the rival network Telemundo in 1993 and played the leading role in "Guadalupe". For signing a contract with a different company, she was banned from her previous network, Televisa. "Guadalupe" resulted to be an international success and was well received in the Arab world to such an extent that she was invited to be the guest of honour of the King of Morocco in 1994.


title: Adela Noriega

text: In 1995, she moved to Colombia and joined RTI, starring in "María Bonita", where she interpreted the title character, a singer who stays trapped on a Caribbean island.


title: Adela Noriega

text: She returned to Televisa in 1997 and collaborated with the producer Carla Estrada in four consecutive productions. The same year, she appeared as the lead character of "María Isabel", interpreting a young indigenous woman faced with discrimination and lack of opportunities because of her origin. The telenovela presented the iconography of the tribe Huichol, based on indigenous folk beliefs and traditional symbols, and dealt with racial, cultural and class themes. For her characterization of the lead female character, Noriega received TVyNovelas Award for "Best Young Actress in a Leading Role".


title: Adela Noriega

text: A year later, she starred in "El privilegio de amar", adaptation of "Cristal", opposite Helena Rojo in a story that revolved around the world of fashion industry and show business. "El privilegio de amar" is officially the highest-rated television program in Mexico to date, according to . The show was internationally successful as well.


title: Adela Noriega

text: In 2001, she starred in "El Manantial", under the direction of Mónica Miguel and Adriana Barraza, co-starring Mauricio Islas. For her performance as the lead female character Alfonsina Valdes Rivero, she received another TVyNovelas Award, among others.


title: Adela Noriega

text: She returned to television in 2003, in the highly acclaimed historical telenovela, "Amor real", in a story that was set in the Mexican post-independence period of the mid-19th century. This costume drama registered very high records of audience in Mexico and at the time of its airing on Univision, it occasionally managed to beat leading U.S. networks in the ratings. In 2005, "Amor real" was released on DVD and due to its success, it became the first telenovela to be released with English subtitles. Noriega received various recognitions for her portrayal of the aristocrat, Matilde Peñalver y Beristáin.


title: Adela Noriega

text: In 2005, she portrayed the leading character of the telenovela "La esposa virgen", opposite Jorge Salinas. The telenovela was an adaptation of Caridad Bravo Adams' novel, "Tormenta de pasiones". Her most recent starring role was as the lead female character Sofía Elizondo in the telenovela "Fuego en la sangre", from 2008. Despite receiving mostly bad reviews, the telenovela was a big success in Mexico and the U.S.


title: Adela Noriega

text: Noriega has been honoured with multiple awards for her work in the television industry, and the wide acceptance of her work throughout the years has established her reputation as a "Telenovela Queen".


title: Dynamo theory

text: In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field. The dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time scales. A dynamo is thought to be the source of the Earth's magnetic field and the magnetic fields of Mercury and the Jovian planets.


title: Dynamo theory

text: When William Gilbert published "de Magnete" in 1600, he concluded that the Earth is magnetic and proposed the first hypothesis for the origin of this magnetism: permanent magnetism such as that found in lodestone. In 1919, Joseph Larmor proposed that a dynamo might be generating the field. However, even after he advanced his hypothesis, some prominent scientists advanced alternative explanations. Einstein believed that there might be an asymmetry between the charges of the electron and proton so that the Earth's magnetic field would be produced by the entire Earth. The Nobel Prize winner Patrick Blackett did a series of experiments looking for a fundamental relation between angular momentum and magnetic moment, but found none.


title: Dynamo theory

text: Walter M. Elsasser, considered a "father" of the presently accepted dynamo theory as an explanation of the Earth's magnetism, proposed that this magnetic field resulted from electric currents induced in the fluid outer core of the Earth. He revealed the history of the Earth's magnetic field through pioneering the study of the magnetic orientation of minerals in rocks.


title: Dynamo theory

text: In order to maintain the magnetic field against ohmic decay (which would occur for the dipole field in 20,000 years), the outer core must be convecting. The convection is likely some combination of thermal and compositional convection. The mantle controls the rate at which heat is extracted from the core. Heat sources include gravitational energy released by the compression of the core, gravitational energy released by the rejection of light elements (probably sulfur, oxygen, or silicon) at the inner core boundary as it grows, latent heat of crystallization at the inner core boundary, and radioactivity of potassium, uranium and thorium.


title: Dynamo theory

text: At the dawn of the 21st century, numerical modeling of the Earth's magnetic field has not been successfully demonstrated. Initial models are focused on field generation by convection in the planet's fluid outer core. It was possible to show the generation of a strong, Earth-like field when the model assumed a uniform core-surface temperature and exceptionally high viscosities for the core fluid. Computations which incorporated more realistic parameter values yielded magnetic fields that were less Earth-like, but indicated that model refinements may ultimately lead to an accurate analytic model. Slight variations in the core-surface temperature, in the range of a few millikelvins, result in significant increases in convective flow and produce more realistic magnetic fields.


title: Dynamo theory

text: Dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid acts to maintain a magnetic field. This theory is used to explain the presence of anomalously long-lived magnetic fields in astrophysical bodies. The conductive fluid in the geodynamo is liquid iron in the outer core, and in the solar dynamo is ionized gas at the tachocline. Dynamo theory of astrophysical bodies uses magnetohydrodynamic equations to investigate how the fluid can continuously regenerate the magnetic field.


title: Dynamo theory

text: It was once believed that the dipole, which comprises much of the Earth's magnetic field and is misaligned along the rotation axis by 11.3 degrees, was caused by permanent magnetization of the materials in the earth. This means that dynamo theory was originally used to explain the Sun's magnetic field in its relationship with that of the Earth. However, this hypothesis, which was initially proposed by Joseph Larmor in 1919, has been modified due to extensive studies of magnetic secular variation, paleomagnetism (including polarity reversals), seismology, and the solar system's abundance of elements. Also, the application of the theories of Carl Friedrich Gauss to magnetic observations showed that Earth's magnetic field had an internal, rather than external, origin.


title: Dynamo theory

text: In the case of the Earth, the magnetic field is induced and constantly maintained by the convection of liquid iron in the outer core. A requirement for the induction of field is a rotating fluid. Rotation in the outer core is supplied by the Coriolis effect caused by the rotation of the Earth. The Coriolis force tends to organize fluid motions and electric currents into columns (also see Taylor columns) aligned with the rotation axis. Induction or creation of magnetic field is described by the induction equation:


title: Dynamo theory

text: where u is velocity, B is magnetic field, "t" is time, and formula_2 is the magnetic diffusivity with formula_3 electrical conductivity and formula_4 permeability. The ratio of the second term on the right hand side to the first term gives the magnetic Reynolds number, a dimensionless ratio of advection of magnetic field to diffusion.


title: Dynamo theory

text: Tidal forces between celestial orbiting bodies cause friction that heats up their interiors. This is known as tidal heating, and it helps keep the interior in a liquid state. A liquid interior that can conduct electricity is required to produce a dynamo. Saturn's Enceladus and Jupiter's Io have enough tidal heating to liquify their inner cores, but they may not create a dynamo because they cannot conduct electricity. Mercury, despite its small size, has a magnetic field, because it has a conductive liquid core created by its iron composition and friction resulting from its highly elliptical orbit. It is theorized that the Moon once had a magnetic field, based on evidence from magnetized lunar rocks, due to its short-lived closer distance to Earth creating tidal heating. An orbit and rotation of a planet helps provide a liquid core, and supplements kinetic energy that supports a dynamo action.


title: Dynamo theory

text: In kinematic dynamo theory the velocity field is "prescribed", instead of being a dynamic variable: The model makes no provision for the flow distorting in response to the magnetic field. This method cannot provide the time variable behaviour of a fully nonlinear chaotic dynamo, but can be used to study how magnetic field strength varies with the flow structure and speed.


title: Dynamo theory

text: Using Maxwell's equations simultaneously with the curl of Ohm's law, one can derive what is basically a linear eigenvalue equation for magnetic fields (), which can be done when assuming that the magnetic field is independent from the velocity field. One arrives at a critical "magnetic Reynolds number", above which the flow strength is sufficient to amplify the imposed magnetic field, and below which the magnetic field dissipates.


title: Dynamo theory

text: The most functional feature of kinematic dynamo theory is that it can be used to test whether a velocity field is or is not capable of dynamo action. By experimentally applying a certain velocity field to a small magnetic field, one can observe whether the magnetic field tends to grow (or not) in response to the applied flow. If the magnetic field does grow, then the system is either capable of dynamo action or is a dynamo, but if the magnetic field does not grow, then it is simply referred to as “not a dynamo”.


title: Dynamo theory

text: An analogous method called the "membrane paradigm" is a way of looking at black holes that allows for the material near their surfaces to be expressed in the language of dynamo theory.


title: Dynamo theory

text: Kinematic dynamo can be also viewed as the phenomenon of the spontaneous breakdown of the topological supersymmetry of the associated stochastic differential equation related to the flow of the background matter. Within stochastic supersymmetric theory, this supersymmetry is an intrinsic property of "all" stochastic differential equations, its interpretation is that the model’s phase space preserves continuity via continuous time flows. When the continuity of that flow spontaneously breaks down, the system is in the stochastic state of "deterministic chaos". In other words, kinematic dynamo arises because of chaotic flow in the underlying background matter.


title: Dynamo theory

text: The kinematic approximation becomes invalid when the magnetic field becomes strong enough to affect the fluid motions. In that case the velocity field becomes affected by the Lorentz force, and so the induction equation is no longer linear in the magnetic field. In most cases this leads to a quenching of the amplitude of the dynamo. Such dynamos are sometimes also referred to as "hydromagnetic dynamos".


title: Dynamo theory

text: The main idea of the theory is that any small magnetic field existing in the outer core creates currents in the moving fluid there due to Lorentz force. These currents create further magnetic field due to Ampere's law. With the fluid motion, the currents are carried in a way that the magnetic field gets stronger (as long as formula_5 is negative). Thus a "seed" magnetic field can get stronger and stronger until it reaches some value that is related to existing non-magnetic forces.


title: Dynamo theory

text: where is the Rayleigh number, the Ekman number, and the Prandtl and magnetic Prandtl number. Magnetic field scaling is often in Elsasser number units formula_23


title: Dynamo theory

text: The scalar product of the above form of Navier-Stokes equation with formula_24 gives the rate of increase of kinetic energy density, formula_25, on the left-hand side. The last term on the right-hand side is then formula_5, the local contribution to the kinetic energy due to Lorentz force.


title: Dynamo theory

text: The scalar product of the induction equation with formula_27 gives the rate of increase of the magnetic energy density, formula_28, on the left-hand side. The last term on the right-hand side is then formula_29 Since the equation is volume-integrated, this term is equivalent up to a boundary term (and with the double use of the scalar triple product identity) to formula_30 (where one of Maxwell's equations was used). This is the local contribution to the magnetic energy due to fluid motion.


title: Dynamo theory

text: Thus the term formula_31 is the rate of transformation of kinetic energy to magnetic energy. This has to be non-negative at least in part of the volume, for the dynamo to produce magnetic field.


title: Dynamo theory

text: From the diagram above, it is not clear why this term should be positive. A simple argument can be based on consideration of net effects. To create the magnetic field, the net electric current must wrap around the axis of rotation of the planet. In that case, for the term to be positive, the net flow of conducting matter must be towards the axis of rotation. The diagram only shows a net flow from the poles to the equator. However mass conservation requires an additional flow from the equator toward the poles. If that flow was along the axis of rotation, that implies the circulation would be completed by a flow from the ones shown towards the axis of rotation, producing the desired effect.


title: Dynamo theory

text: The above formula for the rate of conversion of kinetic energy to magnetic energy, is equivalent to a rate of work done by a force of formula_32 on the outer core matter, whose velocity is formula_33. This work is the result of non-magnetic forces acting on the fluid.


title: Dynamo theory

text: Of those, the gravitational force and the centrifugal force are conservative and therefore have no overall contribution to fluid moving in closed loops. Ekman number (defined above), which is the ratio between the two remaining forces, namely the viscosity and Coriolis force, is very low inside Earth's outer core, because its viscosity is low (1.2–1.5 ×10 pascal-second) due to its liquidity.


title: Dynamo theory

text: Thus the main time-averaged contribution to the work is from Coriolis force, whose size is formula_34 though this quantity and formula_35 are related only indirectly and are not in general equal locally (thus they affect each other but not in the same place and time).


title: Dynamo theory

text: The current density is itself the result of the magnetic field according to Ohm's law. Again, due to matter motion and current flow, this is not necessarily the field at the same place and time. However these relations can still be used to deduce orders of magnitude of the quantities in question.


title: Dynamo theory

text: Note that the magnetic field direction cannot be inferred from this approximation (at least not its sign) as it appears squared, and is, indeed, sometimes reversed, though in general it lies on a similar axis to that of formula_40.


title: Dynamo theory

text: For earth outer core, is approximately 10 kg/m,   = 2/day = 7.3×10/second   and     is approximately   10Ωm .


title: Dynamo theory

text: The magnetic field of a magnetic dipole has an inverse cubic dependence in distance, so its order of magnitude at the earth surface can be approximated by multiplying the above result with giving   2.5×10 Tesla, not far from to the measured value of 3×10 Tesla at the equator.


title: Dynamo theory

text: Broadly, models of the geodynamo attempt to produce magnetic fields consistent with observed data given certain conditions and equations as mentioned in the sections above. Implementing the magnetohydrodynamic equations successfully was of particular significance because they pushed dynamo models to self-consistency. Though geodynamo models are especially prevalent, dynamo models are not necessarily restricted to the geodynamo; solar and general dynamo models are also of interest. Studying dynamo models has utility in the field of geophysics as doing so can identify how various mechanisms form magnetic fields like those produced by astrophysical bodies like Earth and how they cause magnetic fields to exhibit certain features, such as pole reversals.


title: Dynamo theory

text: The equations used in numerical models of dynamo are highly complex. For decades, theorists were confined to two dimensional "kinematic dynamo" models described above, in which the fluid motion is chosen in advance and the effect on the magnetic field calculated. The progression from linear to nonlinear, three dimensional models of dynamo was largely hindered by the search for solutions to magnetohydrodynamic equations, which eliminate the need for many of the assumptions made in kinematic models and allow self-consistency.


title: Dynamo theory

text: The first "self-consistent" dynamo models, ones that determine both the fluid motions and the magnetic field, were developed by two groups in 1995, one in Japan and one in the United States. The latter was made as a model with regards to the geodynamo and received significant attention because it successfully reproduced some of the characteristics of the Earth's field. Following this breakthrough, there was a large swell in development of reasonable, three dimensional dynamo models.


title: Dynamo theory

text: Though many self-consistent models now exist, there are significant differences among the models, both in the results they produce and the way they were developed. Given the complexity of developing a geodynamo model, there are many places where discrepancies can occur such as when making assumptions involving the mechanisms that provide energy for the dynamo, when choosing values for parameters used in equations, or when normalizing equations. In spite of the many differences that may occur, most models have shared features like clear axial dipoles. In many of these models, phenomena like secular variation and geomagnetic polarity reversals have also been successfully recreated.


title: Dynamo theory

text: Many observations can be made from dynamo models. Models can be used to estimate how magnetic fields vary with time and can be compared to observed paleomagnetic data to find similarities between the model and the Earth. Due to the uncertainty of paleomagnetic observations, however, comparisons may not be entirely valid or useful. Simplified geodynamo models have shown relationships between the dynamo number (determined by variance in rotational rates in the outer core and mirror-asymmetric convection (e.g. when convection favors one direction in the north and the other in the south)) and magnetic pole reversals as well as found similarities between the geodynamo and the Sun's dynamo. In many models, it appears that magnetic fields have somewhat random magnitudes that follow a normal trend that average to zero. In addition to these observations, general observations about the mechanisms powering the geodynamo can be made based on how accurately the model reflects actual data collected from Earth.


title: Dynamo theory

text: The complexity of dynamo modelling is so great that models of the geodynamo are limited by the current power of supercomputers, particularly because calculating the Ekman and Rayleigh number of the outer core is extremely difficult and requires a vast number of computations.


title: Dynamo theory

text: Many improvements have been proposed in dynamo modelling since the self-consistent breakthrough in 1995. One suggestion in studying the complex magnetic field changes is applying spectral methods to simplify computations. Ultimately, until considerable improvements in computer power are made, the methods for computing realistic dynamo models will have to be made more efficient, so making improvements in methods for computing the model is of high importance for the advancement of numerical dynamo modelling.


title: Anne Charleston

text: Anne Charleston (born 30 December 1942) is an Australian-born actress, notable for her career locally and in the United Kingdom in theatre and television. Charleston has been a staple of the small screen since the early 1960s, starting with roles in telemovies, before making appearance in the various Crawford Productions series starting from the latter 1960s and 1970s.


title: Anne Charleston

text: She achieved recognition in 1979 for her recurring role in the internationally successful cult TV drama "Prisoner" as Lorraine Watkins, the daughter of elderly inmate "(Mum)" Jeanette Brooks (Mary Ward).


title: Anne Charleston

text: Charleston's best known role, however, was in the soap opera "Neighbours" as matriarch Madge Bishop. She subsequently appeared in the British soap "Emmerdale" as Lily Butterfield. Charleston also appeared in the "Prisoner" re-imagining series "Wentworth", broadcast on Foxtel.


title: Anne Charleston

text: Anne Charleston first became widely recognisable in Australia in the early 1970s on television, taking various guest roles in the Crawford Productions police dramas "Homicide", "Division 4" and "Matlock Police". Other appearances included guest roles in other Crawford's adventure series "Hunter" (1967) and "Ryan" (1973), and in Network Ten-produced police drama "The Long Arm" (1971).


title: Anne Charleston

text: She had continuing roles in soap operas "Bellbird" and "Class of '75", and appeared in "Number 96" as a deranged woman who kidnapped Alf and Lucy's baby in late 1975. She had also appeared in the feature film version of "Bellbird", "Country Town" (1971), playing a different character from that which she had played in the series.


title: Anne Charleston

text: In the late 1970s and the 1980s she had several small roles in soap opera "Prisoner". Having briefly played the brusque daughter of released prisoner "Mum" Brooks in 1979, Charleston returned for several appearances in the serial as policewomen through the early 1980s before taking the larger recurring role of Deidre Kean, mother of prison toughie Reb Kean (Janet Andrewartha), in 1984. The role was intended to be a long term character in "Prisoner", however, in 1985, Grundy cast her in a leading regular role in new soap opera, "Possession"; however, the series was cancelled by the network later that same year due to lower than desired ratings.


title: Anne Charleston

text: Charleston had also enjoyed a busy career acting in the Australian theatre. With St. Martin's Theatre she acted in "Wrong Side of the Park", "The Irregular Verb", "To Love", "Angels in Love", "A Far Country", "The Anniversary", "Invitation to a March", "Eden House", "The Cavern", "Have you Any Dirty Washing Mother Dear", "Blithe Spirit" and "Children's Day".


title: Anne Charleston

text: She also appeared in J C Williamson's "Woman in a Dressing Gown" starring Googie Withers, "Juggler's Three" for the Melbourne Theatre Company Workshop, and "The Secretary Bird" starring Patrick Macnee. Other theatre includes "Busybody", "Port Wine", "Night of the Ding Dong", "Burst of Summer", "Murder in the Cathedral", "The Rivals", "The Tower", "Everyman", "Antigone", "The Man of Destiny", "Otherwise Engaged" and "The Shifting Heart".


title: Anne Charleston

text: In 1986, Charleston was cast as Madge Bishop (Mitchell) in the Australian soap opera "Neighbours". Madge was a new character added to the series when it switched to Network Ten. The series became popular in Australia and the United Kingdom in the years following. Through the series Charleston became internationally recognised, and won a Penguin Award in 1987 for Best Actress.


title: Anne Charleston

text: In 1992, Charleston left the series and emigrated to the Republic of Ireland. Four years later she accepted the offer to return to "Neighbours", reprising the role from 1996. In her second stint in the series, Charleston observed that Madge had been transformed from being bold and fiery to a more meek and passive character, a change that led to her ultimate decision to leave the series in 2000. Her final episode was broadcast in Australia during April 2001. She returned to "Neighbours" in 2015 alongside co-star Ian Smith to commemorate the 30th anniversary of the serial. Charleston also appeared in a documentary celebrating the anniversary titled "", which aired in Australia and the UK in March 2015.


title: Anne Charleston

text: Following the news of "Neighbours"' cancellation, Charleston reprised her role of Madge as a ghost in the show's final ever episode, which aired on 28 July 2022.


title: Anne Charleston

text: In 1989, Charleston took on the role of another 'Madge', Madge Allsop in an episode of "The Dame Edna Experience" on ITV in the UK, when Dame Edna Everage asked Doctor Christiaan Barnard to give her bridesmaid a face lift. Dame Edna did not like Madge's new face, so asked the surgeon to reverse the operation, restoring Emily Perry to the role.


title: Anne Charleston

text: In 2013, Charleston played a role in the Prisoner remake, "Wentworth". The role saw her portraying the mother-in-law of prisoner Lizzy Birdsworth.


title: Anne Charleston

text: After leaving "Neighbours" for the first time, Charleston lived in Ireland for several years, and returned there after leaving the series again in 2001. With the high levels of popularity enjoyed by "Neighbours" in the UK, Charleston has now relaunched her career there. She has undertaken theatre and radio work in the UK and Ireland since leaving "Neighbours" in 2001, and is also a regular performer in pantomime. In 2001, she appeared on "Lily Savage's Blankety Blank".


title: Anne Charleston

text: Charleston took the role of Dossa in comedy series "Dossa and Joe", and then had the regular role of Betty Waddell in the relaunched series of "Crossroads" in 2003. In 2004 she was a contestant in the second series of the Living TV reality television show, "I'm Famous and Frightened!"


title: Anne Charleston

text: In 2005, she had cosmetic surgery performed on her neck, live on British television, on the Channel 5 programme, "Cosmetic Surgery Live". In the same year, she also "regressed into a previous life", as a poor Irish farm girl, when she appeared in the programme "Have I Been Here Before?".


title: Anne Charleston

text: The 2014–15 pantomime season saw Anne playing the Fairy Godmother in "Cinderella" at the Redditch Palace Theatre.


title: Anne Charleston

text: In late 2006, Charleston joined the cast of "Emmerdale", originating the character of Lily Butterfield, the estranged sister of Edna Birch (Shirley Stelfox) who arrives to attend her great niece Eve's wedding blessing. Unbeknown to Edna and Lily, Edna's son Peter has invited them both to try to get them to make amends. However, a dark family secret will ensure their reunion does not run smoothly.


title: Anne Charleston

text: Of her new role, Charleston said: "I am over the moon to be joining one of my favourite soaps. I am delighted to be playing such a fantastic character." Series Producer Kathleen Beedles added: "We are thrilled to confirm that Anne will be playing the character of Lily. Viewers can expect to see sparks fly when Edna and Lily are reunited and we are looking forward to welcoming Anne on-set." Charleson's first taping day was on Monday 25 September 2006, and she first appeared on screen on Friday 3 November 2006. She appeared in only three episodes. The character returned in October 2007 for a four-month run, and returned again in 2008 on a regular contract. Charleston quit in April 2009 and the character was subsequently written out of the serial and made her last appearance on 3 August 2009.


title: Anne Charleston

text: Charleston has appeared in theatre roles both locally and internationally in her native Australia; her theatre credits go back to the early 1960s.


title: Anne Charleston

text: In January 2010, it was announced that Charleston would be joining the touring production of "Calendar Girls" as Jessie (Miss January).


title: Anne Charleston

text: In July 2012, it was revealed that Charleston would appear alongside Mischa Barton in an Irish stage production of "Steel Magnolias", playing Ouiser Boudreaux in the production. It was due to premiere at the Gaiety Theatre, Dublin in September, and be followed by a nationwide tour.


title: Anne Charleston

text: In 2012, Charleston toured the UK in a production of "The Cemetery Club" alongside Anita Harris, Shirley Anne Field and Peter Ellis.


title: Eagle (automobile)

text: Eagle was a brand of the Chrysler Corporation following the purchase of American Motors Corporation (AMC) in 1987 and marketed through the end of the 1998 model year. It was aimed at the enthusiast driver and promoted as more "European" than the automaker's similar models.


title: Eagle (automobile)

text: The "Eagle" name was taken by Chrysler from the four-wheel drive AMC Eagle models that were introduced for the 1980 model year. This was the last of American Motors' wholly U.S.-designed vehicles and one of the first modern mass-production crossover vehicles. The Eagle name also appeared on a number of Jeep trim packages and special models that included the J-10 pickup trucks, the wide-track Cherokee SJ, as well as the CJ-5 and CJ-7 models starting in 1976.


title: Eagle (automobile)

text: A variety of imported and domestic-built vehicles were marketed, mostly by former AMC dealers along with Jeep products, until the brand was discontinued in 1998. Though short-lived, the Eagle Vision sedan sold in respectable numbers, while the sporty Eagle Talon sold more than 115,000 units.


title: Eagle (automobile)

text: Following the introduction of General Motors' Saturn brand automobile, Chrysler promised a similar new brand designed to take Saturn on with innovative design and building methods. In a press release by then Chrysler Chairman Lee Iacocca, it was indicated that Chrysler was working on a car that would bow as the "Liberty". However, these plans never reached fruition. The name later was used for a Jeep model.


title: Eagle (automobile)

text: The main objective of Chrysler acquiring American Motors was the long established Jeep vehicles, but Renault forced the company to take on the contractual obligations of the passenger car models as part of the deal. Another major factor was that, due to state franchise laws, Chrysler could not start selling Jeeps through their existing dealer networks, nor could ex-AMC dealers begin to sell other Chrysler products. Thus, the Eagle marque was born.


title: Eagle (automobile)

text: Under new ownership, Chrysler quickly discontinued the domestic-built front-wheel drive Alliance and Encore that were developed under Renault, but continued to build the four-wheel drive AMC Eagle crossover. It was now called Eagle Wagon and marketed into the 1988 model year until production ended in December. This meant the Brampton Assembly (AMC) manufacturing capacity could be used for making more Jeeps. Moreover, Chrysler kept AMC's long established Eagle brand by continuing to import the mid-sized Renault 21 (now named Eagle Medallion) as well as starting production of the Renault 25-based full-size sedan that was developed by AMC (now named Eagle Premier).


title: Eagle (automobile)

text: To consolidate the marketing and maintain distribution through AMC dealerships following the 1987 acquisition, the Jeep/Eagle division of Chrysler Corporation was formed. Chrysler's initial problem was that unlike the Big Three, which had multiple brands under their corporate name, American Motors had sold passenger cars under its corporate initials of "AMC" since 1970. Thus, without having a separate brand from the now-defunct company, Chrysler looked to re-brand the legacy vehicles inherited through the purchase of AMC under the Eagle name instead of trying to fold those outside-designed products into Chrysler's existing branch structure (which, as mentioned, was unable to be done at the time).


title: Eagle (automobile)

text: Unlike Chrysler, Dodge, and Plymouth branded automobiles, the Eagle models lacked the Chrysler Corporation "pentastar" logo. Instead, all models prominently featured the Eagle head logo, seen at the top right.


title: Eagle (automobile)

text: Two of Eagle's first models, the Eagle Premier and the Eagle Medallion, were designed by AMC in cooperation with its former corporate partner (and 46.4 percent owner), Renault. The remainder of the brand's cars were simply rebadged versions of cars sold by other Chrysler Corporation divisions, as well as some captive imports produced by Mitsubishi Motors.


title: Eagle (automobile)

text: Throughout its history, the Eagle brand suffered from a lack of product recognition, although its Premier was technically more advanced than anything offered by Chrysler. Most of Eagle's models were offered in Chrysler-Plymouth, Dodge, and Mitsubishi dealerships under different guises. Chrysler was in the midst of financial difficulty at the end of the 1980s, and did not have the funds to spread to its new automotive division. Moreover, Jeep vehicles were quite popular and profitable, so most of the division's marketing resources flowed to the Jeep product range. Since Jeep's products had better recognition and higher profit margins, many dealers placed greater emphasis on Jeeps, and considered the Eagle line of passenger cars to be a distraction to that business. Their sales and service expertise was primarily in the four-wheel drive Jeeps and AMC's Eagle all-wheel-drive models.


title: Eagle (automobile)

text: Furthermore, following Chrysler's acquisition of AMC, there was a realignment of the dealership network. Some former AMC/Jeep dealers were consolidated with Chrysler-Plymouth franchises. Up to this point, Chrysler-Plymouth outlets did not have a sport utility vehicle (SUV) to sell, and adding the Jeep line helped dealers offer customers a range of vehicles in a rapidly growing market segment. The merger may have helped the individual dealerships that signed on, but it caused the nascent Eagle division and its largely derivative models to compete unfavorably for attention with Chrysler's and Plymouth's often similar, but longer-established and better-recognized, lines of passenger cars.


title: Eagle (automobile)

text: The Eagle brand was phased out in stages. In 1996, Chrysler discontinued the Mitsubishi Mirage-based Eagle Summit, having canceled the nearly identical Dodge Colt and Plymouth Colt models after the 1994 season. After a decade of slow sales, Chrysler announced the discontinuation of the Eagle brand in September 1997, and the last 1998 Eagle Talon rolled off the line shortly thereafter. In 1997, the Eagle Vision was discontinued at the end of its design cycle, though the similar Dodge Intrepid and Chrysler Concorde were redesigned for 1998 and continued through 2004. Only the Mitsubishi Eclipse-based Eagle Talon remained for 1998, after which it, along with the Eagle brand itself, was discontinued.


title: Eagle (automobile)

text: Chrysler had originally planned to redesign the Eagle Vision for 1999. Prototypes, called the VanCuren Eagle were even spotted wearing the Eagle logo, and Vision production continued into September 1997 to provide dealers with enough stock of the older car to carry them through to the new car's introduction. However, Chrysler executives decided to pull the plug on the Eagle brand just a few months later. The car they were working on went on to be marketed as the Chrysler 300M.


title: Eagle (automobile)

text: The AMC name disappeared with Chrysler's acquisition of the independent automaker, "but the Eagle name carried on, worn by various Renault- and Mitsubishi-sourced models through the ‘90s, when it was finally retired in 1998." Those Eagle cars failed because the automaker did not have a coherent marketing strategy for the mix of models and they also lacked effective promotional efforts in the automotive marketplace. In the end, "Chrysler wasn't fully committed to the nameplate and also left consumers confused about what an Eagle was -- if they knew the name at all."


title: Eagle (automobile)

text: The continuation of the AMC Eagle line after Chrysler acquired AMC in only the station wagon body style. Production of the crossover vehicle ended December 14, 1987. According to the National Automobile Dealers Association NADA Guide, Chrysler's "Eagle was spawned from the buyout of American Motors and their AMC Eagle model."


title: Eagle (automobile)

text: Also badged as the Renault Medallion in 1987, this car was imported and was very similar to the Renault 21.


title: Eagle (automobile)

text: Designed by AMC, the Premier was briefly badged as the Renault Premier prior to launch. Unusual (for an FWD car) in having a north–south engine mounting (to accommodate a future AWD version), it shared several parts with the Renault 25, and spawned a rebadged version named Dodge Monaco (1990–1992); this platform was the basis for the 1993 LH cars.


title: Eagle (automobile)

text: Two models were offered. The 3-door hatchback and 4-door sedan were rebadged Mitsubishi Mirages, and the station wagon (badged as either an Eagle Vista, or a Dodge/Plymouth Colt Vista) was a rebadged Mitsubishi Chariot. Sold only in Canada.


title: Eagle (automobile)

text: Coupe, sedan, and wagon models were available. The coupe and 1987-1991 sedans were rebadged Mitsubishi Mirages, while the wagon was a rebadged Mitsubishi Expo LRV. The 1991-1996 sedan was a rebadged Dodge/Plymouth Colt.


title: Eagle (automobile)

text: Similar to the Plymouth Laser and the Mitsubishi Eclipse, the Talon was Eagle's halo car and outsold its Plymouth cousin. (see also Diamond Star Motors)


title: Eagle (automobile)

text: The Eagle Optima was a 1990 concept car. It was a four-door sedan that used cab forward design and was powered by an experimental, 32-valve all-aluminum V8 engine with all-wheel drive.


title: Eagle (automobile)

text: It was one of a series of concepts (which included the 1987 Lamborghini Portofino and the 1989 Chrysler Millennium) that lead up to the 1993 LH Eagle Vision and its siblings.


title: Orientability

text: In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space is orientable if such a consistent definition exists. In this case, there are two possible definitions, and a choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable. A space is non-orientable if "clockwise" is changed into "counterclockwise" after running through some loops in it, and coming back to the starting point. This means that a geometric shape, such as , that moves continuously along such a loop is changed into its own mirror image . A Möbius strip is an example of a non-orientable space.


title: Orientability

text: Various equivalent formulations of orientability can be given, depending on the desired application and level of generality. Formulations applicable to general topological manifolds often employ methods of homology theory, whereas for differentiable manifolds more structure is present, allowing a formulation in terms of differential forms. A generalization of the notion of orientability of a space is that of orientability of a family of spaces parameterized by some other space (a fiber bundle) for which an orientation must be selected in each of the spaces which varies continuously with respect to changes in the parameter values.


title: Orientability

text: A surface "S" in the Euclidean space R is orientable if a two-dimensional figure (for example, ) cannot be moved around the surface and back to where it started so that it looks like its own mirror image (). Otherwise the surface is non-orientable. An abstract surface (i.e., a two-dimensional manifold) is orientable if a consistent concept of clockwise rotation can be defined on the surface in a continuous manner. That is to say that a loop going around one way on the surface can never be continuously deformed (without overlapping itself) to a loop going around the opposite way. This turns out to be equivalent to the question of whether the surface contains no subset that is homeomorphic to the Möbius strip. Thus, for surfaces, the Möbius strip may be considered the source of all non-orientability.


title: Orientability

text: For an orientable surface, a consistent choice of "clockwise" (as opposed to counter-clockwise) is called an orientation, and the surface is called oriented. For surfaces embedded in Euclidean space, an orientation is specified by the choice of a continuously varying surface normal n at every point. If such a normal exists at all, then there are always two ways to select it: n or −n. More generally, an orientable surface admits exactly two orientations, and the distinction between an orient"ed" surface and an orient"able" surface is subtle and frequently blurred. An orientable surface is an abstract surface that admits an orientation, while an oriented surface is a surface that is abstractly orientable, and has the additional datum of a choice of one of the two possible orientations.


title: Orientability

text: Most surfaces encountered in the physical world are orientable. Spheres, planes, and tori are orientable, for example. But Möbius strips, real projective planes, and Klein bottles are non-orientable. They, as visualized in 3-dimensions, all have just one side. The real projective plane and Klein bottle cannot be embedded in R, only immersed with nice intersections.


title: Orientability

text: Note that locally an embedded surface always has two sides, so a near-sighted ant crawling on a one-sided surface would think there is an "other side". The essence of one-sidedness is that the ant can crawl from one side of the surface to the "other" without going through the surface or flipping over an edge, but simply by crawling far enough.


title: Orientability

text: In general, the property of being orientable is not equivalent to being two-sided; however, this holds when the ambient space (such as R above) is orientable. For example, a torus embedded in


title: Orientability

text: can be one-sided, and a Klein bottle in the same space can be two-sided; here formula_2 refers to the Klein bottle.


title: Orientability

text: Any surface has a triangulation: a decomposition into triangles such that each edge on a triangle is glued to at most one other edge. Each triangle is oriented by choosing a direction around the perimeter of the triangle, associating a direction to each edge of the triangle. If this is done in such a way that, when glued together, neighboring edges are pointing in the opposite direction, then this determines an orientation of the surface. Such a choice is only possible if the surface is orientable, and in this case there are exactly two different orientations.


title: Orientability

text: If the figure can be consistently positioned at all points of the surface without turning into its mirror image, then this will induce an orientation in the above sense on each of the triangles of the triangulation by selecting the direction of each of the triangles based on the order red-green-blue of colors of any of the figures in the interior of the triangle.


title: Orientability

text: This approach generalizes to any "n"-manifold having a triangulation. However, some 4-manifolds do not have a triangulation, and in general for "n" > 4 some "n"-manifolds have triangulations that are inequivalent.


title: Orientability

text: If "H"("S") denotes the first homology group of a surface "S", then "S" is orientable if and only if "H"("S") has a trivial torsion subgroup. More precisely, if "S" is orientable then "H"("S") is a free abelian group, and if not then "H"("S") = "F" + Z/2Z where "F" is free abelian, and the Z/2Z factor is generated by the middle curve in a Möbius band embedded in "S".


title: Orientability

text: Let "M" be a connected topological "n"-manifold. There are several possible definitions of what it means for "M" to be orientable. Some of these definitions require that "M" has extra structure, like being differentiable. Occasionally, must be made into a special case. When more than one of these definitions applies to "M", then "M" is orientable under one definition if and only if it is orientable under the others.


title: Orientability

text: The most intuitive definitions require that "M" be a differentiable manifold. This means that the transition functions in the atlas of "M" are "C"-functions. Such a function admits a Jacobian determinant. When the Jacobian determinant is positive, the transition function is said to be orientation preserving. An oriented atlas on "M" is an atlas for which all transition functions are orientation preserving. "M" is orientable if it admits an oriented atlas. When , an orientation of "M" is a maximal oriented atlas. (When , an orientation of "M" is a function .)


title: Orientability

text: Orientability and orientations can also be expressed in terms of the tangent bundle. The tangent bundle is a vector bundle, so it is a fiber bundle with structure group . That is, the transition functions of the manifold induce transition functions on the tangent bundle which are fiberwise linear transformations. If the structure group can be reduced to the group of positive determinant matrices, or equivalently if there exists an atlas whose transition functions determine an orientation preserving linear transformation on each tangent space, then the manifold "M" is orientable. Conversely, "M" is orientable if and only if the structure group of the tangent bundle can be reduced in this way. Similar observations can be made for the frame bundle.


title: Orientability

text: Another way to define orientations on a differentiable manifold is through volume forms. A volume form is a nowhere vanishing section "ω" of , the top exterior power of the cotangent bundle of "M". For example, R has a standard volume form given by . Given a volume form on "M", the collection of all charts for which the standard volume form pulls back to a positive multiple of "ω" is an oriented atlas. The existence of a volume form is therefore equivalent to orientability of the manifold.


title: Orientability

text: Volume forms and tangent vectors can be combined to give yet another description of orientability. If is a basis of tangent vectors at a point "p", then the basis is said to be right-handed if . A transition function is orientation preserving if and only if it sends right-handed bases to right-handed bases. The existence of a volume form implies a reduction of the structure group of the tangent bundle or the frame bundle to . As before, this implies the orientability of "M". Conversely, if "M" is orientable, then local volume forms can be patched together to create a global volume form, orientability being necessary to ensure that the global form is nowhere vanishing.


title: Orientability

text: At the heart of all the above definitions of orientability of a differentiable manifold is the notion of an orientation preserving transition function. This raises the question of what exactly such transition functions are preserving. They cannot be preserving an orientation of the manifold because an orientation of the manifold is an atlas, and it makes no sense to say that a transition function preserves or does not preserve an atlas of which it is a member.


title: Orientability

text: This question can be resolved by defining local orientations. On a one-dimensional manifold, a local orientation around a point "p" corresponds to a choice of left and right near that point. On a two-dimensional manifold, it corresponds to a choice of clockwise and counter-clockwise. These two situations share the common feature that they are described in terms of top-dimensional behavior near "p" but not at "p". For the general case, let "M" be a topological "n"-manifold. A local orientation of "M" around a point "p" is a choice of generator of the group


title: Orientability

text: To see the geometric significance of this group, choose a chart around "p". In that chart there is a neighborhood of "p" which is an open ball "B" around the origin "O". By the excision theorem, formula_4 is isomorphic to formula_5. The ball "B" is contractible, so its homology groups vanish except in degree zero, and the space is an -sphere, so its homology groups vanish except in degrees and . A computation with the long exact sequence in relative homology shows that the above homology group is isomorphic to formula_6. A choice of generator therefore corresponds to a decision of whether, in the given chart, a sphere around "p" is positive or negative. A reflection of through the origin acts by negation on formula_7, so the geometric significance of the choice of generator is that it distinguishes charts from their reflections.


title: Orientability

text: On a topological manifold, a transition function is orientation preserving if, at each point "p" in its domain, it fixes the generators of formula_4. From here, the relevant definitions are the same as in the differentiable case. An oriented atlas is one for which all transition functions are orientation preserving, "M" is orientable if it admits an oriented atlas, and when , an orientation of "M" is a maximal oriented atlas.


title: Orientability

text: Intuitively, an orientation of "M" ought to define a unique local orientation of "M" at each point. This is made precise by noting that any chart in the oriented atlas around "p" can be used to determine a sphere around "p", and this sphere determines a generator of formula_4. Moreover, any other chart around "p" is related to the first chart by an orientation preserving transition function, and this implies that the two charts yield the same generator, whence the generator is unique.


title: Orientability

text: Purely homological definitions are also possible. Assuming that "M" is closed and connected, "M" is orientable if and only if the "n"th homology group formula_10 is isomorphic to the integers Z. An orientation of "M" is a choice of generator of this group. This generator determines an oriented atlas by fixing a generator of the infinite cyclic group formula_11 and taking the oriented charts to be those for which pushes forward to the fixed generator. Conversely, an oriented atlas determines such a generator as compatible local orientations can be glued together to give a generator for the homology group formula_11.


title: Orientability

text: A manifold "M" is orientable if and only if the first Stiefel–Whitney class formula_13 vanishes. In particular, if the first cohomology group with Z/2 coefficients is zero, then the manifold is orientable. Moreover if "M" is orientable and "w" vanishes, then formula_14 parametrizes the choices of orientations. This characterization of orientability extends to orientability of general vector bundles over "M", not just the tangent bundle.


title: Orientability

text: Around each point of "M" there are two local orientations. Intuitively, there is a way to move from a local orientation at a point to a local orientation at a nearby point : when the two points lie in the same coordinate chart , that coordinate chart defines compatible local orientations at and . The set of local orientations can therefore be given a topology, and this topology makes it into a manifold.


title: Orientability

text: More precisely, let "O" be the set of all local orientations of "M". To topologize "O" we will specify a subbase for its topology. Let "U" be an open subset of "M" chosen such that formula_15 is isomorphic to Z. Assume that α is a generator of this group. For each "p" in "U", there is a pushforward function formula_16. The codomain of this group has two generators, and α maps to one of them. The topology on "O" is defined so that


title: Orientability

text: There is a canonical map that sends a local orientation at "p" to "p". It is clear that every point of "M" has precisely two preimages under . In fact, is even a local homeomorphism, because the preimages of the open sets "U" mentioned above are homeomorphic to the disjoint union of two copies of "U". If "M" is orientable, then "M" itself is one of these open sets, so "O" is the disjoint union of two copies of "M". If "M" is non-orientable, however, then "O" is connected and orientable. The manifold "O" is called the orientation double cover.


title: Orientability

text: If "M" is a manifold with boundary, then an orientation of "M" is defined to be an orientation of its interior. Such an orientation induces an orientation of ∂"M". Indeed, suppose that an orientation of "M" is fixed. Let be a chart at a boundary point of "M" which, when restricted to the interior of "M", is in the chosen oriented atlas. The restriction of this chart to ∂"M" is a chart of ∂"M". Such charts form an oriented atlas for ∂"M".


title: Orientability

text: When "M" is smooth, at each point "p" of ∂"M", the restriction of the tangent bundle of "M" to ∂"M" is isomorphic to , where the factor of R is described by the inward pointing normal vector. The orientation of "T"∂"M" is defined by the condition that a basis of "T"∂"M" is positively oriented if and only if it, when combined with the inward pointing normal vector, defines a positively oriented basis of "T""M".


title: Orientability

text: A closely related notion uses the idea of covering space. For a connected manifold "M" take "M", the set of pairs ("x", o) where "x" is a point of "M" and "o" is an orientation at "x"; here we assume "M" is either smooth so we can choose an orientation on the tangent space at a point or we use singular homology to define orientation. Then for every open, oriented subset of "M" we consider the corresponding set of pairs and define that to be an open set of "M". This gives "M" a topology and the projection sending ("x", o) to "x" is then a 2-to-1 covering map. This covering space is called the orientable double cover, as it is orientable. "M" is connected if and only if "M" is not orientable.


title: Orientability

text: Another way to construct this cover is to divide the loops based at a basepoint into either orientation-preserving or orientation-reversing loops. The orientation preserving loops generate a subgroup of the fundamental group which is either the whole group or of index two. In the latter case (which means there is an orientation-reversing path), the subgroup corresponds to a connected double covering; this cover is orientable by construction. In the former case, one can simply take two copies of "M", each of which corresponds to a different orientation.


title: Orientability

text: A real vector bundle, which "a priori" has a GL(n) structure group, is called "orientable" when the structure group may be reduced to formula_18, the group of matrices with positive determinant. For the tangent bundle, this reduction is always possible if the underlying base manifold is orientable and in fact this provides a convenient way to define the orientability of a smooth real manifold: a smooth manifold is defined to be orientable if its tangent bundle is orientable (as a vector bundle). Note that as a manifold in its own right, the tangent bundle is "always" orientable, even over nonorientable manifolds.


title: Orientability

text: In Lorentzian geometry, there are two kinds of orientability: space orientability and time orientability. These play a role in the causal structure of spacetime. In the context of general relativity, a spacetime manifold is space orientable if, whenever two right-handed observers head off in rocket ships starting at the same spacetime point, and then meet again at another point, they remain right-handed with respect to one another. If a spacetime is time-orientable then the two observers will always agree on the direction of time at both points of their meeting. In fact, a spacetime is time-orientable if and only if any two observers can agree which of the two meetings preceded the other.


title: Orientability

text: Formally, the pseudo-orthogonal group O("p","q") has a pair of characters: the space orientation character σ and the time orientation character σ,


title: Orientability

text: Their product σ = σσ is the determinant, which gives the orientation character. A space-orientation of a pseudo-Riemannian manifold is identified with a section of the associated bundle


title: Orientability

text: where O("M") is the bundle of pseudo-orthogonal frames. Similarly, a time orientation is a section of the associated bundle


title: Chiaki J. Konaka

text: Konaka gave himself the middle initial "J", evoking the Christian name "John", due to him being born to parents who were members of the Anglican Church, but he does not identify as Christian. He began using the middle initial at the age of 12, when he began making 8 mm films; he patterned the style after Western names such as Charles M. Schulz.


title: Chiaki J. Konaka

text: Konaka's serious works generally have a dark, psychological tone. As a Cthulhu Mythos writer, he tends to add Lovecraftian elements to his works. He has cited "Ghost Hound" as his favorite screenwriting project.


title: Chiaki J. Konaka

text: The story-line of the early episodes of "Digimon Tamers" was based on one of the original scripts by Chiaki and Kazuya Konaka for "" in 1995 before the final draft by Kazunori Itō. Konaka brothers' plot was later used for "Digimon Tamers" and "Gamera the Brave" in 2006.


title: Chiaki J. Konaka

text: In 2021, Konaka wrote a stage drama for "Digimon Tamers"' 20th anniversary that was performed at DigiFes 2021, an official "Digimon" event held annually on August 1. The drama featured the cast of the show being confronted by a physical manifestation of "political correctness" that uses "cancel culture" as an attack. This brought attention to his blog meant for retrospective commentary on "Digimon Tamers", in which he also discussed conspiracy theories, and sparked international controversy. In response, Konaka posted a statement in English addressed to his overseas fans on August 8, 2021, to explain his circumstances and to apologize for triggering a divide among the fandom.


title: Female infanticide in China

text: China has a history of female infanticide spanning 2,000 years. When Christian missionaries arrived in China in the late sixteenth century, they witnessed newborns being thrown into rivers or onto rubbish piles. In the seventeenth century Matteo Ricci documented that the practice occurred in several of China's provinces and said that the primary reason for the practice was poverty. The practice continued into the 19th century and declined precipitously during the Communist era, but has reemerged as an issue since the introduction of the one-child policy in the early 1980s. The 2020 census showed a male-to-female ratio of 105.07 for mainland China, a record low since the People's Republic of China began conducting censuses.


title: Female infanticide in China

text: During the 19th century the practice was widespread. Readings from Qing texts show a prevalence of the term "ni nü" (to drown girls), and drowning was the most common method used to kill female children. Other methods used were suffocation and starvation. Exposure to the elements was another method: the child would be placed in a basket which was then placed in a tree. Buddhist nunneries created "baby towers" for people to leave a child. In 1845 in the province of Jiangxi, a missionary wrote that these children survived for up to two days while exposed to the elements, and that those passing by would ignore the screaming child. Missionary David Abeel reported in 1844 that between one fourth and one third of all female children were killed at birth or soon after.


title: Female infanticide in China

text: In 1878 French Jesuit missionary, Gabriel Palatre, collated documents from 13 provinces and the "Annales de la Sainte-Enfance" (Annals of the Holy Childhood), also found evidence of infanticide in Shanxi and Sichuan. According to the information collected by Palatre the practice was more widespread in the southeastern provinces and the Lower Yangzi River region.


title: Female infanticide in China

text: In 1930, Rou Shi, a noted member of the May Fourth Movement, wrote the short story "A Slave-Mother". In it he portrayed the extreme poverty in rural communities that was a direct cause of female infanticide.


title: Female infanticide in China

text: A white paper published by the Chinese government in 1980 stated that the practice of female infanticide was a "feudalistic evil". The state officially considers the practice a carryover from feudal times, not a result of the state's one-child policy. According to Jing-Bao Nie, it would be "inconceivable" to believe there is "no link" between the state's family planning policies and female infanticide.


title: Female infanticide in China

text: On September 25, 1980, in an "open letter", the Politburo of the Chinese Communist Party requested that members of the party, and those in the Communist Youth League, lead by example and have only one child. From the beginning of the one-child policy, there were concerns that it would lead to an imbalance in the sex ratio. Early in the 1980s, senior officials became increasingly concerned with reports of abandonment and female infanticide by parents desperate for a son. In 1984, the government attempted to address the issue by adjusting the one-child policy. Couples whose first child is a girl are allowed to have a second child.


title: Female infanticide in China

text: Many Chinese couples desire to have sons because they provide support and security to their aging parents later in life. Conversely, a daughter is expected to leave her parents upon marriage to join and care for her husband's family (parents-in-law). In rural households, which as of 2014 constitute almost half the Chinese population, males are additionally valuable for performing agricultural work and manual labor.


title: Female infanticide in China

text: A 2005 intercensus survey demonstrated pronounced differences in sex ratio across provinces, ranging from 1.04 in Tibet to 1.43 in Jiangxi. Banister (2004), in her literature review on China's shortage of girls, suggested that there has been a resurgence in the prevalence of female infanticide following the introduction of the one-child policy. On the other hand, many researchers have argued that female infanticide is rare in China today, especially since the government has outlawed the practice. Zeng and colleagues (1993), for example, contended that at least half of the nation's gender imbalance arises from the underreporting of female births.


title: Female infanticide in China

text: According to the Geneva Centre for the Democratic Control of Armed Forces (DCAF), the demographic shortfall of female babies who have died for gender related issues is in the same range as the 191 million estimated dead accounting for all conflicts in the twentieth century. In 2012, the documentary "" was released. It focused on female infanticide in India and China.


title: Female infanticide in China

text: According to China's 2020 census (the Seventh National Population Census of the People's Republic of China), the gender ratio of mainland China has improved, with the male-to-female ratio reaching a new record low of 105.07. This is the most balanced gender ratio since the PRC began conducting a census in 1953.


title: Yellowhammer

text: The yellowhammer (Emberiza citrinella) is a passerine bird in the bunting family that is native to Eurasia and has been introduced to New Zealand and Australia. Most European birds remain in the breeding range year-round, but the eastern subspecies is partially migratory, with much of the population wintering further south. The male yellowhammer has a bright yellow head, streaked brown back, chestnut rump, and yellow under parts. Other plumages are duller versions of the same pattern. The yellowhammer is common in open areas with some shrubs or trees, and forms small flocks in winter. Its song has a rhythm like "A little bit of bread and no cheese". The song is very similar to that of its closest relative, the pine bunting, with which it interbreeds.


title: Yellowhammer

text: Breeding commences mainly in April and May, with the female building a lined cup nest in a concealed location on or near the ground. The three to five eggs are patterned with a mesh of fine dark lines, giving rise to the old name for the bird of "scribble lark" or "writing lark". The female incubates the eggs for 12–14 days prior to hatching, and broods the altricial downy chicks until they fledge 11–13 days later. Both adults feed the chick in the nest and raise two or three broods each year. The nest may be raided by rodents or corvids, and the adults are hunted by birds of prey. Yellowhammers feed on the ground, usually in flocks outside the breeding season. Their diet is mainly seeds, supplemented by invertebrates in the breeding season. Changes to agricultural practices have led to population declines in western Europe, but its large numbers and huge range mean that the yellowhammer is classed as being of least concern by the International Union for Conservation of Nature.


title: Yellowhammer

text: This conspicuous yellow bird has inspired poems by Robert Burns and John Clare, and its characteristic song has influenced musical works by Beethoven and Messiaen. Children's writer Enid Blyton helped to popularise the standard English representation of the song.


title: Yellowhammer

text: The yellowhammer was described by Carl Linnaeus in his landmark 1758 10th edition of "Systema Naturae" under its current scientific name. "Emberiza" is derived from the Old German "Embritz", a bunting, and "citrinella" is the Italian for a small yellow bird. The English name is thought to have come from "Ammer", another German word for a bunting, and was first recorded in 1553 as "yelambre".


title: Yellowhammer

text: The bird family Emberizidae contains a single genus "Emberiza", with around 40 members, that are confined to the Old World. Within its genus, the yellowhammer is most closely related to the pine bunting, with which it forms a superspecies; they have at times been considered as one species. The white-capped and cirl buntings are also near relatives of the species pair. Where their ranges meet, the yellowhammer and pine bunting interbreed; the yellowhammer is dominant, and the hybrid zone is moving further east.


title: Yellowhammer

text: The yellowhammer is a large bunting, long, with a wingspan; it weighs . The male of the nominate subspecies "E. c. citrinella" has a bright yellow head, heavily streaked brown back, rufous rump, yellow under parts, and white outer tail feathers. The female is less brightly coloured, and more streaked on the crown, breast, and flanks. Both sexes are less strongly marked outside the breeding season, when the dark fringes on new feathers obscure the yellow plumage. The juvenile is much duller and less yellow than the adults, and often has a paler rump.


title: Yellowhammer

text: After breeding, adults have a complete moult, which takes at least eight weeks; males acquire more yellow in the plumage each time they moult. Juveniles have a partial moult not long after fledging, replacing the head, body, and some covert feathers.


title: Yellowhammer

text: Differences between the subspecies are small and geographically gradual. On average, the male of "E. c. caliginosa " is slightly smaller and darker than the same sex of the nominate subspecies, and also has more streaking on its back, a greenish tint to the yellow of the head and more chestnut on the flanks. The male of the eastern form, "E. c. erythrogenys", is paler and less streaked than "E. c. citrinella". Its flanks, undertail and wing bars are usually whiter, and its crown and throat are brighter yellow. Distinguishing females of the three subspecies using plumage features is not usually possible.


title: Yellowhammer

text: Females and juveniles, especially of the pale eastern subspecies, "E. c. erythrogenys", may be confused with pine buntings, but they always have a yellow tint to their plumage, a paler rufous rump, and more uniform upperparts than that species. Young and female yellowhammers can be distinguished from cirl buntings by the grey-brown rump of the latter species. Male hybrids with pine buntings are typically white-faced and have some yellow on the head, under parts or flight feathers, but females are usually indistinguishable from yellowhammers.


title: Yellowhammer

text: The song of the cock yellowhammer is a series of short notes, gradually increasing in volume and followed by one or two more protracted notes. It is often represented as "A little bit of bread and no cheese", and the full version can be confused with the almost identical song of the pine bunting. If the final notes are omitted, confusion with the cirl bunting is possible. Other vocalisations include a "zit" contact call, a "see" alarm, and a trilled "tirrr" given in flight.


title: Yellowhammer

text: Yellowhammer males learn their songs from their fathers, and over time, regional dialects have developed, with minor differences to the conclusion of the basic song; all are mutually recognised by birds from different areas. Each male has an individual repertoire of song variants within its regional dialect; females tend to mate with males that share their dialect, and prefer those with the largest repertoires.


title: Yellowhammer

text: The pine bunting and yellowhammer are so closely related that each responds to the other's song. The male yellowhammer's song is more attractive to females, and is one reason for the dominance of that species where the ranges overlap.


title: Yellowhammer

text: The yellowhammer breeds across the Palearctic between the July isotherms. It is the commonest and most widespread European bunting, although it is absent from high mountains, Arctic regions, the western Netherlands, most of Iberia and Greece, and low-lying regions of other countries adjoining the Mediterranean Sea. It breeds in Russia east to Irkutsk, and in most of Ukraine. The Asian range extends into northwest Turkey, the Caucasus, and northern Kazakhstan.


title: Yellowhammer

text: Most European yellowhammers winter within their breeding range, only the far north being vacated, although some birds move south of their breeding range in Spain, Italy, and other Mediterranean countries. Distances travelled can be up to for northern birds. Asian birds are more strongly migratory, deserting much of the north to winter in Iraq, Iran, and southern Central Asia. The yellowhammer has occurred as a vagrant in the United Arab Emirates, Egypt, Kuwait, Morocco, Malta, the Himalayas (winter vagrant from northern Afghanistan to central Nepal), the Balearic Islands, Iceland, and the Faroes.


title: Yellowhammer

text: Yellowhammers of the British and Irish race, "E. c. caliginosa", were introduced to New Zealand by local acclimatisation societies in 1862, and soon spread over the main islands. They sometimes visit New Zealand's subantarctic islands, although rarely staying to breed, and have reached Australia's Lord Howe Island on a number of occasions. At the beginning of the 20th century, this bunting was seen as a serious agricultural pest in its adopted country.


title: Yellowhammer

text: The yellowhammer is a bird of dry, open country, preferably with a range of vegetation types and some trees from which to sing. It is absent from urban areas, forests, and wetlands. Probably originally found at forest edges and large clearing, it has benefited from traditional agriculture, which created extensive open areas with hedges and clumps of trees.


title: Yellowhammer

text: Breeding normally starts in early May, but often in April in the south of the range. Yellowhammers are monogamous and breed when aged one year. The males establish territories along hedges or woodland fringes and sing from a tree or bush, often continuing well into July or August. The male displays to the female by raising his wings and running towards her. The nest is built by the female on or near the ground, and is typically well hidden in tussocks, against a bank or low in a bush. It is constructed from nearby plant material, such as leaves, dry grass, and stalks, and is lined with fine grasses and sometimes animal hair. It is across with a cup deep.


title: Yellowhammer

text: The clutch is usually three to five whitish eggs, typically patterned with a network of fine, dark lines. The eggs average in size and weigh , of which 6% is shell. The female incubates the eggs for 12–14 days to hatching, and broods the altricial, downy chicks until they fledge 11–13 days later. Both adults feed the chick in the nest and two or three broods are raised each year.


title: Yellowhammer

text: The adult annual survival rate in the UK is around 54%, and that for juveniles in their first year is 53%. The typical lifespan is three years, although records from Great Britain and Germany indicate birds surviving more than 13 years.


title: Yellowhammer

text: Foraging is mainly on the ground, and the bird's diet consists mainly of seeds. Oily seeds, such as those of brassicas, are ignored in favour of more starchy items. Typical food plants include common nettle, docks, common knotgrass, fat hen, common chickweed, and yarrow. Grasses are also important, particularly cereals, and grain makes up a significant part of the food consumed in autumn and winter, wheat and oats being preferred to barley. When not breeding, yellowhammers forage in flocks that can occasionally number hundreds of birds, and often contain other buntings and finches.


title: Yellowhammer

text: The yellowhammer adds invertebrates to its diet in the breeding season, particularly as food for its growing chicks. A wide range of species is taken, including springtails, grasshoppers, flies, beetles, caterpillars, earthworms, spiders, and snails. During the first few days, chicks are exclusively fed invertebrate prey, but from day three they are also fed cereal grains, which the chicks can digest efficiently. This is thought to be intentional by the parents to allow the nestlings to adjust their physiology to eating seed.


title: Yellowhammer

text: Predators of the yellowhammer include the sparrowhawk, northern goshawk, lesser spotted eagle, and hobby. It is not a significant host of the common cuckoo, a brood parasite, although as a ground-nesting bird, its eggs and chicks are vulnerable to predation from small mammals such as mice and other rodents. Nests are also raided by crows, Eurasian jays, and Eurasian magpies. Predation accounted for more than 60% of nest failures in a 2012 survey in Germany.


title: Yellowhammer

text: Thirteen species of fleas in the genera "Ceratophyllus" and "Dasypsyllus" have been found on this bunting, and internal parasites include "Ascaridia galli". The yellowhammer may carry haematozoan blood parasites such as "Haemoproteus coatneyi". Males with high parasite levels produced fewer offspring (there is no such effect for females), and tend to be less brightly coloured. The striking plumage of the male may therefore have arisen as a signal of fitness to breed. Yellowhammers infected with "Haemoproteus" may have lower winter survival rates due to a tendency to having shorter wings.


title: Yellowhammer

text: The International Union for Conservation of Nature estimates the European population of the yellowhammer to be from 54–93 million individuals, suggesting a Eurasian total of 73–186 million birds. Although the population appears to be in a decline, the decrease is not rapid enough to trigger their vulnerability criteria. The large numbers and huge breeding range of about 12.9 million km (5 million sq mi), mean that this bunting is classified by the IUCN as being of least concern.


title: Yellowhammer

text: Populations have declined in recent decades in western Europe, including the British Isles, Belgium, the Netherlands, Austria, and Italy. The yellowhammer is a red-list (severely declining) species in Ireland and the UK. In 2016 the species went extinct on the Isle of Man. In eastern Europe, numbers appear to be stable, although the trend in Russia is unknown. Changes to agricultural practices are thought to be responsible for reduced breeding densities. The introduced population in New Zealand has been very successful, with breeding densities much higher than in the UK.


title: Yellowhammer

text: The yellowhammer is a conspicuous, vocal, and formerly common country bird, and has attracted human interest. Yellowham Wood and Yellowham Hill, near Dorchester, both derive their names from the bird. Robbie Burns' poem "The Yellow, Yellow Yorlin'" gets its title from a Scottish name for the yellowhammer, which is given an obvious sexual connotation: "I met a pretty maid, an' unto her I said,/ 'I wad fain fin' your yellow, yellow yorlin'.' " More factual descriptions of the bird and its behaviour can be found in John Clare's "The Yellowhammer's Nest" and "The Yellowhammer", whose final lines read:


title: Yellowhammer

text: Enid Blyton helped to popularize the bird's song as ""little bit of bread and no cheese"" in books such as "The Ship of Adventure" and "Five Go Off in a Caravan", and wrote a poem called "The Yellow-hammer".


title: Yellowhammer

text: Beethoven's student, Carl Czerny, and biographer Anton Schindler, both suggested that the composer got the idea for the first four notes of his 5th symphony from the yellowhammer's call, although more likely the opening of the 4th Piano Concerto was actually the work in question. Beethoven also used the yellowhammer theme in two piano sonatas, no. 21 in C major (the "Waldstein", Op.53) and No. 23 in F minor (the "Appassionata", Op.57).


title: Yellowhammer

text: Olivier Messiaen often used birdsong as an inspiration for his music, and the yellowhammer features in "Chronochromie", "Catalogue d'oiseaux", "La fauvette des jardins" and "Méditations sur le mystère de la Sainte Trinité", appearing in four movements of the last piece.


title: Yellowhammer

text: An old legend links the yellowhammer to the devil. Its tongue was supposed to bear a drop of his blood, and the intricate pattern on the eggs was said to carry a concealed, possibly evil, message; these satanic associations sometimes led to the persecution of the bird. The unusual appearance of the eggs also led to the names of Scribble Lark or Scribble Jack, alternative titles for the bird.


title: Brad Gillis

text: Bradley Frank Gillis (born 15 June 1957) is a guitarist most famous for playing with the band Night Ranger. He was in the band Rubicon during the 1970s before Night Ranger. Since forming in 1979, Gillis and drummer Kelly Keagy are the only members to have appeared in every incarnation of the band and all studio releases. However, Keagy missed several shows for the first time in 2017. On Saturday, May 8th, 2021, Gillis was absent from a Night Ranger show for the first time in the band's history (he was recovering from rotator cuff surgery). He has also played for Ozzy Osbourne and Fiona, and has released solo albums. Gillis’s musical side projects include placing over 300 songs for ESPN’s Sports Center, The X Games, Fox Sports, Tiger Woods Sony PlayStation Games, EA Sports, The Fuse Channel and many others. He has appeared in over a dozen music videos, with TV performances on "American Bandstand", "Solid Gold", "Rock & Roll Tonight" and thousands of live concerts. He also participated in the one-time collaboration, Hear 'n Aid, for the promotional single, "Stars," which helped raise $1 million for famine relief in Africa. He was one of several lead guitarists to contribute guitar solos for the cause, including Vivian Campbell, Buck Dharma, and Neal Schon. His first solo album "Gilrock Ranch" produced a top twenty single, “Honest to God,” which was co-written and sung by Gregg Allman.


title: Brad Gillis

text: Jerry Martini formed the funk-rock band Rubicon with future Night Ranger founding members Gillis and Jack Blades. Rubicon recorded two albums on 20th Century Fox Records – "Rubicon", and "American Dreams", scoring one minor hit single entitled "I’m Gonna Take Care of Everything". Rubicon played the 1978 California Jam II rock festival before 250,000 people. Future Ozzy Osbourne bandmate Rudy Sarzo saw Gillis's Cal Jam performance and was very impressed. Rubicon broke up in 1979 and Gillis formed the short-lived club band Stereo with future Night Ranger members Blades and Kelly Keagy.


title: Brad Gillis

text: With the sudden death of guitarist Randy Rhoads in a plane crash while on tour in March 1982, Bernie Torme was quickly brought in as his replacement. After a handful of shows it became apparent that Torme's blues-based style was not a good match for Osbourne's style of music and Gillis was subsequently hired as his replacement. Osbourne, drinking heavily while still coming to terms with the loss of Rhoads, took his frustrations out on Gillis and treated him very poorly. As a result, Gillis left Osbourne's band after completing the 1982 "Diary of a Madman" tour and he returned to Night Ranger. Gillis can be heard playing lead guitar on Osbourne’s 1982 "Speak of the Devil" live album and on the DVD of the same title.


title: Brad Gillis

text: Over the course of his career, Gillis has used several different models of guitars by various brands. He has been a longtime user of his 1962 Fender Stratocaster and 1971 Gibson Les Paul, and in the 1980s played Hamer and Jackson Soloists, which he still periodically uses today. He also has an extensive collection of over 100 various vintage guitars, most notably Les Pauls, Flying V's, Martin and Gibson acoustics. Today he uses his Fernandes Brad Gillis model, along with his 1962 Stratocaster, PRS 513 model and an Atomic Guitars Red, White and Blue American flag guitar. Gillis uses Taylor acoustic guitars in the studio and live with his band Night Ranger. Gillis's amplifiers are mainly Mesa Boogie but also uses Soldano, Marshall and vintage Fender amps in the studio. Gillis uses original Floyd Rose non fine tuner tremolo bridges, Nady built-in wireless systems and metal picks by Star Access Guitar Picks.


title: Moratorium (law)

text: A moratorium is a delay or suspension of an activity or a law. In a legal context, it may refer to the temporary suspension of a law to allow a legal challenge to be carried out.


title: Moratorium (law)

text: For example, animal rights activists and conservation authorities may request fishing or hunting moratoria to protect endangered or threatened animal species. These delays, or suspensions, prevent people from hunting or fishing the animals in discussion.


title: Moratorium (law)

text: Another instance is a delay of legal obligations or payment ("debt moratorium"). A legal official can order due to extenuating circumstances, which render one party incapable of paying another.