Properties.

NGC 1275 consists of two galaxies, a central type-cD galaxy in the Perseus Cluster, and a so-called "high velocity system" (HVS) which lies in front of it. The HVS is moving at 3000 km/s towards the dominant system, and is believed to be merging with the Perseus Cluster. The HVS is not affecting the cD galaxy as it lies at least 200 thousand light years from it. however tidal interactions are disrupting it and ram-pressure stripping produced by its interaction with the intracluster medium of Perseus is stripping its gas as well as producing large amounts of star formation within it  The central cluster galaxy contains a massive network of spectral line emitting filaments, which apparently are being dragged out by rising bubbles of relativistic plasma generated by the central active galactic nucleus. Long gaseous filaments made up of threads of gas stretch out beyond the galaxy, into the multimillion-degree, X-ray–emitting gas that fills the cluster. The amount of gas contained in a typical thread is approximately one million times the mass of the Sun. They are only 200 light-years wide, are often very straight, and extend for up to 20,000 light-years.  The existence of the filaments poses a problem. As they are much cooler than the surrounding intergalactic cloud, it is unclear how they have existed for such a long time, or why they have not warmed, dissipated or collapsed to form stars. One possibility is that weak magnetic fields (about one-ten-thousandth the strength of Earth's field) exert enough force on the ions within the threads to keep them together.  NGC 1275 contains 13 billion solar masses of molecular hydrogen that seems to be infalling from Perseus' intracluster medium in a cooling flow, both feeding its active nucleus and fueling significant amounts of star formation  The presence of an active nucleus demonstrates that a supermassive black hole is present in NGC 1275's center. The black hole is surrounded by a rotating disk of molecular gas. High-resolution observations of the rotation of this disk obtained using adaptive optics at the Gemini North telescope indicate a central mass of approximately 800 million Solar masses, including both the mass of the black hole and of the inner core of the gas disk.

NGC 1275 (also known as Perseus A or Caldwell 24) is a type 1.5 Seyfert galaxy located around 237 million light-years away in the direction of the constellation Perseus. NGC 1275 corresponds to the radio galaxy Perseus A and is situated near the center of the large Perseus Cluster of galaxies.

NGC 1275 (také známá jako Perseus A nebo Caldwell 24) je pekuliární galaxie v souhvězdí Persea vzdálená od Země přibližně 204 milionů světelných let. Je hlavním členem Kupy galaxií v Perseovi a nachází se blízko jejího středu, kde je umístěn i silný zdroj rádiových vln Perseus A. Na obloze se nachází ve střední části souhvězdí, 2° severovýchodně od hvězdy Algol s magnitudou 2,1. Je to Seyfertova galaxie typu 1.5, i když je někdy označována jako typ 1 i 2.


Early life.

Saliha Sultan was born 16 June 1811 in the Topkapı Palace. Her father was Sultan Mahmud II, and her mother was Aşubcan Kadın.

Marriage.

In 1834, when Saliha was twenty three years old, her father arranged her marriage to Damat Gürcü Halil Rifat Pasha. The marriage took place on Saturday, 24 May 1834 in the Beşiktaş Waterfront Palace. The bridal procession of Saliha Sultan left this palace on Thursday, conveying the bride to Fındıklı Palace. The ladies of the marriage procession rode in carriages and coaches decorated with stars. Julia Pardoe, who observed the marriage from a caique on the Bosphorus noted the illumination of the waterfront palace of Esma Sultan. She writes that, "there must have been many hundred caiques wedged together in front of her terrace, and less than fifty of them contained musicians."  The wedding ceremony was covered in the first official Ottoman newspaper "Takvim-i Vekayi". Saliha Sultan's beachfront palace and Tophane and Beşiktaş palace were flooded by rafts and boats, various descriptions were put on the rafts, and small ships, fish paintings, small cars and castles were built.  The couple owned the Neşatabad Palace located in Ortaköy Defterdarburnu and the Fındıklı Palace.  The two together had one son named Sultanzade Abdul Hamid Bey, born on 22 March 1835, who died young in 1837.

Death.

Saliha Sultan died on 6 February 1843 in the Fındıklı Palace, and was buried in the mausoleum of her father in Divanyolu, Istanbul.

Issue.

Together with Damat Gürcü Halil Rifat, Saliha had one son:

Saliha Sultan (; 16 June 1811 – 6 February 1843) was an Ottoman princess, the daughter of Sultan Mahmud II and Aşubcan Kadın. She was the half-sister of Sultans Abdulmejid I and Abdulaziz.

Saliha Sultan (16. června 1811 – 19. února 1843) byla osmanská princezna, dcera sultána Mahmuda II. a jeho konkubíny Aşubican Kadınefendi. Byla nevlastní sestrou sultánů Abdülmecida I. a Abdülazize.


History.

The first academic description of the principles of a solar cooker is by the Swiss geologist, meteorologist, physicist, mountaineer and Alpine explorer Horace-Bénédict de Saussure, in 1767. The principle of cooking meals from the sun was largely developed in the French Foreign Legion, in the 1870s.

Working Principles.

1) Concentrating sunlight: A mirrored surface with high specular reflection is used to concentrate light from the sun into a small cooking area. Depending on the geometry of the surface, sunlight could be concentrated by several orders of magnitude producing temperatures high enough to melt salt and metal. For most household solar cooking applications, such high temperatures are not really required. Solar cooking products are typically designed to achieve temperatures of (baking temperatures) to (grilling/searing temperatures) on a sunny day.  2) Converting light energy to heat energy: Solar cookers concentrate sunlight onto a receiver such as a cooking pan. The interaction between the light energy and the receiver material converts light to heat and this is called conduction. This conversion is maximized by using materials that conduct and retain heat. Pots and pans used on solar cookers should be matte black in color to maximize the absorption.  3) Trapping heat energy: It is important to reduce convection by isolating the air inside the cooker from the air outside the cooker. Simply using a glass lid on your pot enhances light absorption from the top of the pan and provides a greenhouse effect that improves heat retention and minimizes convection loss. This "glazing" transmits incoming visible sunlight but is opaque to escaping infrared thermal radiation. In resource constrained settings, a high-temperature plastic bag can serve a similar function, trapping air inside and making it possible to reach temperatures on cold and windy days similar to those possible on hot days. Below is the basic science for solar panel cookers and solar box cookers. Another style of solar cooker is a parabolic solar cooker. They typically require more frequent reorientation to the sun, but will cook more quickly at higher temperatures, and can fry foods. Evacuated tube solar cookers use a highly insulated double-wall glass tube for the cooking chamber, and do not require large reflectors

Operation.

Different kinds of solar cookers (more than 300 models of solar cooker had been made so far) use somewhat different methods of cooking, but most follow the same basic principles.  Food is prepared as if for an oven or stove top. However, because food cooks faster when it is in smaller pieces, food placed inside a solar cooker is usually cut into smaller pieces than it might otherwise be. For example, potatoes are usually cut into bite-sized pieces rather than roasted whole. For very simple cooking, such as melting butter or cheese, a lid may not be needed and the food may be placed on an uncovered tray or in a bowl. If several foods are to be cooked separately, then they are placed in different containers.  The container of food is placed inside the solar cooker, which may be elevated on a brick, rock, metal trivet, or other heat sink, and the solar cooker is placed in direct sunlight. Foods that cook quickly may be added to the solar cooker later. Rice for a mid-day meal might be started early in the morning, with vegetables, cheese, or soup added to the solar cooker in the middle of the morning. Depending on the size of the solar cooker and the number and quantity of cooked foods, a family may use one or more solar cookers.  A solar oven is turned towards the sun and left until the food is cooked. Unlike cooking on a stove or over a fire, which may require more than an hour of constant supervision, food in a solar oven is generally not stirred or turned over, both because it is unnecessary and because opening the solar oven allows the trapped heat to escape and thereby slows the cooking process. If wanted, the solar oven may be checked every one to two hours, to turn the oven to face the sun more precisely and to ensure that shadows from nearby buildings or plants have not blocked the sunlight. If the food is to be left untended for many hours during the day, then the solar oven is often turned to face the point where the sun will be when it is highest in the sky, instead of towards its current position.  The cooking time depends primarily on the equipment being used, the amount of sunlight at the time, and the quantity of food that needs to be cooked. Air temperature, wind, and latitude also affect performance. Food cooks faster in the two hours before and after the local solar noon than it does in either the early morning or the late afternoon. Large quantities of food, and food in large pieces, take longer to cook. As a result, only general figures can be given for cooking time. With a small solar panel cooker, it might be possible to melt butter in 15 minutes, to bake cookies in 2 hours, and to cook rice for four people in 4 hours. With a high performing parabolic solar cooker, you may be able to grill a steak in minutes. However, depending on local conditions and the solar cooker type, these projects could take half as long, or twice as long.  It is difficult to burn food in a solar cooker. Food that has been cooked even an hour longer than necessary is usually indistinguishable from minimally cooked food. The exception to this rule is some green vegetables, which quickly change from a perfectly cooked bright green to olive drab, while still retaining the desirable texture.  For most foods, such as rice, the typical person would be unable to tell how it was cooked from looking at the final product. There are some differences, however: Bread and cakes brown on their tops instead of on the bottom. Compared to cooking over a fire, the food does not have a smoky flavor.

Box and panel designs.

A box cooker has a transparent glass or plastic top, and it may have additional reflectors to concentrate sunlight into the box. The top can usually be removed to allow dark pots containing food to be placed inside. One or more reflectors of shiny metal or foil-lined material may be positioned to bounce extra light into the interior of the oven chamber. Cooking containers and the inside bottom of the cooker should be dark-colored or black. Inside walls should be reflective to reduce radiative heat loss and bounce the light towards the pots and the dark bottom, which is in contact with the pots. The box should have insulated sides. Thermal insulation for the solar box cooker must be able to withstand temperatures up to 150 °C (300 °F) without melting or out-gassing. Crumpled newspaper, wool, rags, dry grass, sheets of cardboard, etc. can be used to insulate the walls of the cooker. Metal pots and/or bottom trays can be darkened either with flat-black spray paint (one that is non-toxic when warmed), black tempera paint, or soot from a fire. The solar box cooker typically reaches a temperature of 150 °C (300 °F). This is not as hot as a standard oven, but still hot enough to cook food over a somewhat longer period of time. Panel solar cookers are inexpensive solar cookers that use reflective panels to direct sunlight to a cooking pot that is enclosed in a clear plastic bag.  Solar Oven science experiments are regularly done as projects in high schools and colleges, such as the "Solar Oven Throwdown" at the University of Arizona. These projects prove that it is possible to both achieve high temperatures, as well as predict the high temperatures using mathematical models.

Parabolic reflectors.

Parabolic solar cookers concentrate sunlight to a single point. When this point is focused on the bottom of a pot, it can heat the pot quickly to very high temperatures which can often be comparable with the temperatures achieved in gas and charcoal grills. These types of solar cookers are widely used in several regions of the world, most notably in China and India where hundreds of thousands of families currently use parabolic solar cookers for preparing food and heating water. Some parabolic solar cooker projects in China abate between 1–4 tons of carbon dioxide per year and receive carbon credits through the Clean Development Mechanism (CDM) and Gold Standard. Some parabolic solar cookers incorporate cutting edge materials and designs which lead to solar energy efficiencies >90%. Others are large enough to feed thousands of people each day, such as the solar bowl at Auroville in India, which makes 2 meals per day for 1,000 people.  If a reflector is axially symmetrical and shaped so its cross-section is a parabola, it has the property of bringing parallel rays of light (such as sunlight) to a point "focus". If the axis of symmetry is aimed at the sun, any object that is located at the focus receives highly concentrated sunlight, and therefore becomes very hot. This is the basis for the use of this kind of reflector for solar cooking.

Paraboloidal reflectors.

Paraboloids are compound curves, which are more difficult to make with simple equipment than single curves. Although paraboloidal solar cookers can cook as well as or better than a conventional stove, they are difficult to construct by hand. Frequently, these reflectors are made using many small segments that are all single curves which together approximate compound curves.  Although paraboloids are difficult to make from flat sheets of solid material, they can be made quite simply by rotating open-topped containers which hold liquids. The top surface of a liquid which is being rotated at constant speed around a vertical axis naturally takes the form of a paraboloid. Centrifugal force causes material to move outward from the axis of rotation until a deep enough depression is formed in the surface for the force to be balanced by the levelling effect of gravity. It turns out that the depression is an exact paraboloid. (See Liquid-mirror telescope.) If the material solidifies while it is rotating, the paraboloidal shape is maintained after the rotation stops, and can be used to make a reflector. This rotation technique is sometimes used to make paraboloidal mirrors for astronomical telescopes, and has also been used for solar cookers. Devices for constructing such paraboloids are known as rotating furnaces.  Paraboloidal reflectors generate high temperatures and cook quickly, but require frequent adjustment and supervision for safe operation. Several hundred thousand exist, mainly in China. They are especially useful for individual household and large-scale institutional cooking.  A Scheffler cooker (named after its inventor, Wolfgang Scheffler) uses a large ideally paraboloidal reflector which is rotated around an axis that is parallel with the earth's using a mechanical mechanism, turning at 15 degrees per hour to compensate for the earth's rotation. The axis passes through the reflector's centre of mass, allowing the reflector to be turned easily. The cooking vessel is located at the focus which is on the axis of rotation, so the mirror concentrates sunlight onto it all day. The mirror has to be occasionally tilted about a perpendicular axis to compensate for the seasonal variation in the sun's declination. This perpendicular axis does not pass through the cooking vessel. Therefore, if the reflector were a rigid paraboloid, its focus would not remain stationary at the cooking vessel as the reflector tilts. To keep the focus stationary, the reflector's shape has to vary. It remains paraboloidal, but its focal length and other parameters change as it tilts. The Scheffler reflector is therefore flexible, and can be bent to adjust its shape. It is often made up of a large number of small plane sections, such as glass mirrors, joined together by flexible plastic. A framework that supports the reflector includes a mechanism that can be used to tilt it and also bend it appropriately. The mirror is never exactly paraboloidal, but it is always close enough for cooking purposes.  Sometimes the rotating reflector is located outdoors and the reflected sunlight passes through an opening in a wall into an indoor kitchen, often a large communal one, where the cooking is done.  Paraboloidal reflectors that have their centres of mass coincident with their focal points are useful. They can be easily turned to follow the sun's motions in the sky, rotating about any axis that passes through the focus. Two perpendicular axes can be used, intersecting at the focus, to allow the paraboloid to follow both the sun's daily motion and its seasonal one. The cooking pot stays stationary at the focus. If the paraboloidal reflector is axially symmetrical and is made of material of uniform thickness, its centre of mass coincides with its focus if the depth of the reflector, measured along its axis of symmetry from the vertex to the plane of the rim, is 1.8478 times its focal length. The radius of the rim of the reflector is 2.7187 times the focal length. The angular radius of the rim, as seen from the focal point, is 72.68 degrees.

Parabolic troughs.

Parabolic troughs are used to concentrate sunlight for solar-energy purposes. Some solar cookers have been built that use them in the same way. Generally, the trough is aligned with its focal line horizontal and east-west. The food to be cooked is arranged along this line. The trough is pointed so its axis of symmetry aims at the sun at noon. This requires the trough to be tilted up and down as the seasons progress. At the equinoxes, no movement of the trough is needed during the day to track the sun. At other times of year, there is a period of several hours around noon each day when no tracking is needed. Usually, the cooker is used only during this period, so no automatic sun tracking is incorporated into it. This simplicity makes the design attractive, compared with using a paraboloid. Also, being a single curve, the trough reflector is simpler to construct. However, it suffers from lower efficiency.  It is possible to use two parabolic troughs, curved in perpendicular directions, to bring sunlight to a point focus as does a paraboloidal reflector.The incoming light strikes one of the troughs, which sends it toward a line focus. The second trough intercepts the converging light and focuses it to a point.  Compared with a single paraboloid, using two partial troughs has important advantages. Each trough is a single curve, which can be made simply by bending a flat sheet of metal. Also, the light that reaches the targeted cooking pot is directed approximately downward, which reduces the danger of damage to the eyes of anyone nearby. On the other hand, there are disadvantages. More mirror material is needed, increasing the cost, and the light is reflected by two surfaces instead of one, which inevitably increases the amount that is lost.  The two troughs are held in a fixed orientation relative to each other by being both fixed to a frame. The whole assembly of frame and troughs has to be moved to track the sun as it moves in the sky. Commercially made cookers that use this method are available.In practical applications (like in car-headlights), concave mirrors are of parabolic shape

Spherical reflectors.

Spherical reflectors operate much like paraboloidal reflectors, such that the axis of symmetry is pointed towards the sun so that light is concentrated to a focus. However, the focus of a spherical reflector will not be a point focus because it suffers from a phenomenon known as spherical aberration. Some concentrating dishes (such as satellite dishes) that do not require a precise focus opt for a spherical curvature over a paraboloid. If the radius of the rim of spherical reflector is small compared with the radius of curvature of its surface (the radius of the sphere of which the reflector is a part), the reflector approximates a paraboloidal one with focal length equal to half of the radius of curvature.

Vacuum tube technology.

Evacuated tube solar cookers are essentially a vacuum sealed between two layers of glass. The vacuum allows the tube to act both as a "super" greenhouse and an insulator. The central cooking tube is made from borosilicate glass, which is resistant to thermal shock, and has a vacuum beneath the surface to insulate the interior. The inside of the tube is lined with copper, stainless steel, and aluminum nitrile to better absorb and conduct heat from the sun's rays. Some vacuum tube solar cookers incorporate lightweight designs which allow great portability (such as the GoSun stove)  Portable vacuum tube cookers such as the GoSun allow users to cook freshly caught fish on the beach without needing to light a fire.

Advantages and disadvantages.

Advantages  Disadvantages

Projects.

Cardboard, aluminium foil, and plastic bags for well over 10,000 solar cookers have been donated to the Iridimi refugee camp and Touloum refugee camps in Chad by the combined efforts of the Jewish World Watch, the Dutch foundation KoZon, and Solar Cookers International. The refugees construct the cookers themselves, using the donated supplies and locally purchased Arabic gum. It has also significantly reduced the amount of time women spend tending open fires each day, with the results that they are healthier and they have more time to grow vegetables for their families and make handicrafts for export. By 2007, the Jewish World Watch had trained 4,500 women and had provided 10,000 solar cookers to refugees. The project has also reduced the number of foraging trips by as much as 70 percent, thus reducing the number of attacks.

A solar cooker is a device which uses the energy of direct sunlight to heat, cook or pasteurize drink and other food materials. Many solar cookers currently in use are relatively inexpensive, low-tech devices, although some are as powerful or as expensive as traditional stoves, and advanced, large-scale solar cookers can cook for hundreds of people. Because they use no fuel and cost nothing to operate, many nonprofit organizations are promoting their use worldwide in order to help reduce fuel costs (especially where monetary reciprocity is low) and air pollution, and to slow down the deforestation and desertification caused by gathering firewood for cooking.

Sluneční vařič je zařízení sloužící k vaření a pečení pokrmů nebo k pasterizaci vody. Princip slunečního vařiče spočívá v odrazu slunečních paprsků na nádobu s pokrmem nebo vodou, přičemž nádoba se slunečním zářením zahřívá. Existuje více typů slunečních vařičů. Nejběžnější jsou vařiče "panelové", "krabicové" a "parabolické". Sluneční vařiče lze rozdělit na "přímé", které soustředí paprsky přímo na černý hrnec, a "nepřímé", které dopravují teplo od absorbéru k potravinám prostřednictvím kapalného média. Vařiče "akumulační" umožňují pokračovat ve vaření při zatažené obloze nebo po setmění. Existují i vařiče "hybridní", které při nepříznivém počasí dohřívají potraviny z jiného zdroje (obvykle elektricky, ale lze použít např. i LPG).


Corporate rebranding.

Rebranding has become something of a fad at the turn of the millennium, with some companies rebranding several times. The rebranding of Philip Morris to Altria was done to help the company shed its negative image. Other rebrandings, such as the British Post Office's attempt to rebrand itself as Consignia, have proved such a failure that millions more had to be spent going back to square one.  In a study of 165 cases of rebranding, Muzellec and Lambkin (2006) found that, whether a rebranding follows from corporate strategy (e.g., M&A) or constitutes the actual marketing strategy (change the corporate reputation), it aims at enhancing, regaining, transferring, and/or recreating the corporate brand equity.  According to Sinclair (1999:13), business the world over acknowledges the value of brands. “Brands, it seems, alongside ownership of copyright and trademarks, computer software and specialist know-how, are now at the heart of the intangible value investors place on companies.” Companies in the 21st century may find it necessary to relook their brand in terms of its relevance to consumers and the changing marketplace. Successful rebranding projects can yield a brand better off than before.  Marketing develops the awareness and associations in the memory of customers so they know (and are reminded) of brands to serve their needs. Once in a lead position, it is marketing, consistent product or service quality, sensible pricing and effective distribution that will keep the brand ahead of the pack and provide value to its owners (Sinclair, 1999:15).

Potential reasons for corporate rebranding.

Corporations often rebrand in order to respond to external and/or internal issues. Firms commonly have rebranding cycles in order to stay current with the times or set themselves ahead of the competition. Companies also utilize rebranding as an effective marketing tool to hide malpractices of the past, thereby shedding negative connotations that could potentially affect profitability.  Corporations such as Citigroup, AOL, American Express, and Goldman Sachs all utilize third-party vendors that specialize in brand strategy and the development of corporate identity. Companies invest valuable resources into rebranding and third-party vendors because it is a way to protect them from being blackballed by customers in a very competitive market. Dr. Roger Sinclair, a leading expert on brand valuation and brand equity practice worldwide stated, “A brand is a resource acquired by an enterprise that generates future economic benefits.” Once a brand has negative connotations associated with it, it can only lead to decreased profitability and possibly complete corporate failure.

Differentiation from competitors.

Companies differentiate themselves from competitors by incorporating practices from changing their logo to going green. Differentiation from competitors is important in order to attract more customers and an effective way to draw in more desirable employees. The need to differentiate is especially prevalent in saturated markets such as the financial services industry. The factor and importance of differentiation are covered in the authoritative bestseller, Brand Intervention by rebranding expert David Brier.

Elimination of a negative image.

Organisations may rebrand intentionally to shed negative images of the past. Research suggests that "concern over external perceptions of the organisation and its activities" can function as a major driver in rebranding exercises.  In a corporate context, managers can utilize rebranding as an effective marketing strategy to hide malpractices and avoid or shed negative connotations and decreased profitability. Corporations such as Philip Morris USA, Blackwater and AIG rebranded in order to shed negative images. Philip Morris USA rebranded its name and logo to Altria on January 27, 2003 due to the negative connotations associated with tobacco products that could have had potential to affect the profitability of other Philip Morris brands such as Kraft Foods.  In 2008, AIG's image became damaged due to its need for a Federal bailout during the financial crisis. AIG was bailed out because the United States Treasury stated that AIG was too big to fail due to its size and complex relationships with financial counterparties. AIG itself is a huge international firm; however, the AIG Retirement and AIG Financial subsidiaries were left with negative connotations due to the bailout. As a result, AIG Financial Advisors and AIG Retirement respectively rebranded into Sagepoint Financial and VALIC (Variable Annuity Life Insurance Company) to shed the negative image associated with AIG.

Lost market share.

Brands often rebrand in reaction to losing market share. In these cases, the brands have become less meaningful to target audiences and, therefore, lost share to competitors.  In some cases, companies try to build on any perceived equity they believe still exists in their brand. Radio Shack, for example, rebranded itself as "the Shack" in 2008 but the rebranding never realized into an increase of market share in the retail industry. By 2017, Radio Shack had significantly reduced its physical retail presence, closing over 1,000 stores and shifted to a primarily online retail business model.

Emergent situations.

Rebranding may also occur unintentionally from emergent situations such as “Chapter 11 corporate restructuring,” or “bankruptcy.” Chapter 11 is rehabilitation or reorganization used primarily by business debtors. It’s more commonly known as corporate bankruptcy, which is a form of corporate financial reorganization that allows companies to function while they pay off their debt. Companies such as Lehman Brothers Holdings Inc, Washington Mutual and General Motors have all filed for Chapter 11 bankruptcy.  On July 1, 2009 General Motors filed for bankruptcy, which was fulfilled on July 10, 2009. General Motors decided to rebrand its entire structure by investing more in Chevrolet, Buick, GMC, and Cadillac automobiles. Furthermore, it decided to sell Saab Automobile and discontinue the Hummer, Pontiac, and Saturn brands. General Motors rebranded by stating they are reinventing and rebirthing the company as “The New GM” with “Fewer, stronger brands. Fewer, stronger models. Greater efficiencies, better fuel economy, and new technologies” as stated in their reinvention commercial. General Motors' reinvention commercial also stated that eliminating brands “isn’t about going out of business, but getting down to business.”

Staying relevant.

Companies can also choose to rebrand to remain relevant to its (new) customers and stakeholders. This could occur when a company's business has changed, for example its strategic direction and industry focus, or its brand no longer fits its (new) customer base. For example, a company might rebrand so that its name works in new market it enters, for reasons of culture or language, such as to make it easier to pronounce.  Rebranding is also a way to refresh an image to ensure its appeal to contemporary customers and stakeholders. What once looked fresh and relevant may no longer do so years later.

Product rebranding.

As for product offerings, when they are marketed separately to several target markets this is called market segmentation. When part of a market segmentation strategy involves offering significantly different products in each market, this is called product differentiation. This market segmentation/product differentiation process can be thought of as a form of rebranding. What distinguishes it from other forms of rebranding is that the process does not entail the elimination of the original brand image. Rebranding in this manner allows one set of engineering and QA to be used to create multiple products with minimal modifications and additional expense. Another form of product rebranding is the sale of a product manufactured by another company under a new name: an original design manufacturer is a company that manufactures a product, often in a location with lower operating costs, which is eventually branded by another firm for sale.  Following a merger or acquisition, companies usually rebrand newly-acquired products to keep them consistent with an existing product line, such as Symantec placing acquired security and utility software under its Norton brand (itself an offshoot of flagship product Norton Antivirus). This can also happen in reverse if an acquired brand has wider recognition in the market than that of the purchaser, such as Chemical Bank taking on the Chase branding after its merger with the company.

Small business rebranding.

Small businesses face different challenges from large corporations and must adapt their rebranding strategy accordingly.  Rather than implementing change gradually, small businesses are sometimes better served by rebranding their image in a short timeframe – especially when existing brand notoriety is low. “The powerful first impression on new clients made possible by professional brand design often outweighs an outdated or poorly-designed image’s weak brand recognition to existing clients”.  A change of image in a large corporation can have costly repercussions (updating signage in multiple locations, large quantities of existing collateral, communicating with a large number of employees, etc.), while small businesses can enjoy more mobility and implement change more quickly.  While small businesses can experience growth without necessarily having a professionally designed brand image, "rebranding becomes a critical step for a company to be considered seriously when expanding to more aggressive markets and facing competitors with more established brand images".

Impact of rebranding.

The ubiquitous nature of a company/product brand across all customer touch points makes rebranding a heavy undertaking for companies. According to the iceberg model, 80% of the impact is hidden. The level of impact of changing a brand depends on the degree to which the brand is changed.  There are several elements of a brand that can be changed in a rebranding these include the name, the logo, the legal name, and the corporate identity (including visual identity and verbal identity). Changes made only to the company logo have the lowest impact (called a logo-swap), and changes made to the name, legal name, and other identity elements will touch every part of the company and can result in high costs and impact on large complex organizations.  Rebranding affects not only marketing material but also digital channels, URLs, signage, clothing, and correspondence.

Rebranding is a marketing strategy in which a new name, term, symbol, design, concept or combination thereof is created for an established brand with the intention of developing a new, differentiated identity in the minds of consumers, investors, competitors, and other stakeholders. Often, this involves radical changes to a brand's logo, name, legal names, image, marketing strategy, and advertising themes. Such changes typically aim to reposition the brand/company, occasionally to distance itself from negative connotations of the previous branding, or to move the brand upmarket; they may also communicate a new message a new board of directors wishes to communicate.

Rebranding bývá nejčastěji definován jako změna positioningu, revitalizace či omlazení obchodní značky. V radikálním případě se může jednat o celkové znovuzrození obchodní značky.


Establishment.

Origins.

Multiple credible sources indicate that the Kurdistan Workers' Party (PKK) is the driving force behind the Syrian Kurdish People's Protection Units (YPG) and the YPG-led Syrian Democratic Forces (SDF).

Foundation.

The establishment of the SDF was announced on 11 October 2015 during a press conference in al-Hasakah. The alliance built on longstanding previous cooperation between the founding partners. While the People's Protection Units (Yekîneyên Parastina Gel, YPG) and the Women's Protection Units (Yekîneyên Parastina Jin, YPJ) had been operating throughout the regions of the Autonomous Administration of North and East Syria, the other founding partners were more geographically focused.  Geographically focused on the Euphrates Region were the YPG's partners in the Euphrates Volcano joint operations room, several mainstream Syrian rebel factions of the Free Syrian Army, who had helped defend the Kurdish town of Kobanî during the Siege of Kobanî. Liwa Thuwwar al-Raqqa was also in Euphrates Volcano, and it was expelled by the al-Nusra Front and ISIL from the city of Raqqa for being allied with the YPG since April 2014. The group participated in the capture of Tell Abyad from the Islamic State.  Geographically focused on the Jazira Region in northeast Syria were the Assyrian Syriac Military Council (Mawtbo Fulhoyo Suryoyo, MFS) and the al-Sanadid Forces of the Arab Shammar tribe, both of whom had cooperated with the YPG in fighting ISIL since 2013. The MFS is further politically aligned with the YPG via their shared secular ideology of democratic confederalism, which in the Assyrian community is known as the "Dawronoye" movement.  Geographically focused on the Manbij Region was the Army of Revolutionaries (Jaysh al-Thuwar, JAT), itself an alliance of several groups of diverse ethnic and political backgrounds, who had in common that they had been rejected by the mainstream Syrian opposition for secular, anti-Islamist views and affiliations. However, most of the JAT component groups have always used the Free Syrian Army label and continue to use it.

Signatory groups.

The following groups signed the founding document:  On 10 December 2015, after a two-day conference, The Syrian Democratic Council was established as a political platform of the SDF. Human rights activist Haytham Manna was co-chairman at its founding. The Assembly that established the Syrian Democratic Council was made up of 13 members from specific ethnic, economic and political backgrounds.

Syrian Arab Coalition.

The Syrian Arab Coalition is called by the U.S. government as an alliance of programmatically exclusively ethnic Arab militias established during the Syrian Civil War. In this narrative, it consists of exclusively ethnic Arab component groups of the SDF alliance, such as the al-Sanadid Forces, the Deir ez-Zor Military Council, Arab units within the Army of Revolutionaries, along with smaller factions.

Size, growth and composition.

2015.

At the time of its founding in late 2015, "The Economist" described the SDF as "essentially a subsidiary of the Kurdish YPG".

2016.

With continuous growth in particular due to Arab groups and volunteers joining, in March 2016 only an estimated 60% of the men and women in the SDF fighting force were ethnic Kurds. Growth in particular of Arab, Turkmen and Assyrian participation in the SDF has since continued. In an interview on the first anniversary of the SDF's founding, spokesman Talal Silo, an ethnic Turkmen and former commander of the Seljuq Brigade, stated that "we started with 13 factions and now there are 32 factions", and that "90 percent" of the SDF growth since it began its operations were ethnic Arabs. In the context of the November 2016 Northern Raqqa offensive, "The Economist" said the SDF fighting force to be composed of "about 20,000 YPG fighters and about 10,000 Arabs". The next month in December 2016, Colonel John Dorrian, the Operation Inherent Resolve spokesman, stated that the SDF contained around 45,000 fighters, of which more than 13,000 were Arabs.

2017.

According to a March 2017 statement of the Spokesman for the International Coalition forces, U.S. Colonel John Dorrian, 75 percent of the SDF forces fighting in Operation Wrath of Euphrates to isolate ISIL's de facto capital of Raqqa were Syrian Arabs, a reflection of the demographic composition of that area. "The Syrian Democratic Forces are a multi-ethnic and multi-sectarian organization, and that is one of the reasons why we're working with them and they have continued to build the Arab element of their force." Concerning the SDF in general, Lieutenant General Stephen Townsend in the same month said that "I'm seeing what is probably a pretty broad coalition of people and the Kurds may be providing the leadership, because they have a capable leader who's stepped up to this challenge. And they are providing some of the organisational skill, but I see a large contingent about 23 to 25, 000 so far and growing, Arabs, who are marching to liberate their part of northern Syria. So, I don't see a Kurdish state. I see a multi-cultural, multi-party, multi-ethnic, multi-sectarian Syrian region being liberated from ISIS. Over."  Late June, an analysis by the Counter Terrorism Center at West Point said "growing acceptance of the SDF by Sunni Arab rebel groups" and more generally "growing legitimacy of the SDF". Another analysis as of late June described the YPG as "only one faction of many within the SDF", however that "it's the YPG that makes the SDF reliable and effective. The SDF's other components function as auxiliaries to the SDF's 'backbone', the YPG, which ensures effective, unitary command and control."

Alleged war crimes.

On 15 March 2017, a video surfaced that showed members of the Northern Sun Battalion reportedly torturing an ISIL fighter, who had been captured while planting mines. One of these mines had reportedly killed nine fighters of the battalion, leading five others to take revenge on the ISIL militant. The Manbij Military Council condemned the act, and announced that the involved Northern Sun Battalion fighters would be held for trial for violating the Geneva Conventions. The five accused were arrested on 17 March.

Ethnic cleansing and forced displacement.

In June 2015 the Turkish government and Amnesty International reported that the YPG was carrying out an ethnic cleansing of non-Kurdish populations as part of a plan to join the Jazira and Euphrates regions into a single territory.  The U.S. State Department reacted by stating they would'scrutinise' Amnesty International's accusations. The U.S. State Department stated it had to determine if there was "any veracity to the claims", but showed concern by calling for any administrator in the area to rule "with respect for all groups regardless of ethnicity". The report makes accusations of looting, coercing civilians to join their armed forces and the forced targeted displacement of 1400 families in the Turkman villages of Hammam al-Turkman, 800 Turkmen from Mela Berho and Suluk residents. The report offers unnamed witness testimony from reported victims, cross referenced with photo and video evidence, media reports, and satellite imagery to substantiate these reports.  In a report published by the United Nations' Independent International Commission of Inquiry on the Syrian Arab Republic on 10 March 2017, the Commission refuted Amnesty International's reports of ethnic cleansing, stating that "'though allegations of 'ethnic cleansing' continued to be received during the period under review, the Commission found no evidence to substantiate reports that YPG or SDF forces ever targeted Arab communities on the basis of ethnicity".  In interviews, YPG spokespersons acknowledged that a number of families were in fact displaced. However, they placed the number at no more than 25, and stated military necessity. They stated that the family members of terrorists maintained communications with them, and therefore had to be removed from areas where they might pose a danger. They further reported that ISIL was using civilians in those areas to plant car bombs or carry out other attacks on the YPG.

Recruitment of minors.

In June 2014, Human Rights Watch criticized the YPG for accepting minors into their ranks, picking up on multiple earlier reports of teenage fighters serving in the YPG, with a report by the United Nations Secretary General stating that 24 minors under age of 18 had been recruited by YPG, with 124 having been recruited by the Free Syrian Army and 5 by the Syrian Arab Army. In response, the YPG and YPJ signed the Geneva Call "Deed of Commitment" protecting children in armed conflict, prohibiting sexual violence and against gender discrimination in July 2014, and Kurdish security forces (YPG and Asayish) began receiving human rights training from Geneva Call and other international organisations with the YPG pledging publicly to demobilize all fighters under 18 within a month and began to enact disciplinary measures against commanders of the units that had involved in corruption and accepting recruit under age of 18 to their ranks. In October 2015 the YPG demobilized 21 minors from the military service in its ranks.  In response to reports issued by international organisations such as Human Rights Watch, the general command of the SDF issued a military order prohibiting the recruitment of children. On 29 June 2019 Abdi, as representative of the SDF, signed the action plan of the United Nations aiming to prevent the enlistment of child soldiers in the armed forces. The action plan was signed to address the inclusion of the YPG in the SDF.  In 2020, United Nations reported SDF as the largest faction in the Syrian civil war by the number recruited child soldiers, with 283 child soldiers followed by Hayat Tahrir al-Sham with 245 child soldiers.

The Syrian Democratic Forces (SDF; (QSD, قسد); (HSD); ) is an alliance in the Syrian Civil War composed primarily of Kurdish, Arab, and Assyrian/Syriac militias, as well as some smaller Armenian, Turkmen and Chechen forces. The SDF is militarily led by the People's Protection Units (YPG), a mostly Kurdish militia. Founded in October 2015, the SDF states its mission as fighting to create a secular, democratic and decentralized Syria. The updated December 2016 constitution of the Autonomous Administration of North and East Syria (NES) names the SDF as its official defence force.

Syrské demokratické síly (Kurdsky: Hêzên Sûriya Demokratîk, Arabsky: قوات سوريا الديمقراطي, Quwwāt Sūriyā al-Dīmuqrāṭīya), často také označované jen zkráceně jako jednotky SDF (z anglického: Syrian Democratic Forces) nebo QSD, je aliance kurdských, arabských, asyrských, arménských a turkmenských milicí založená během Syrské občanské války.


Formal definition.

Let "f" be a real or complex valued function and "g" a real valued function. Let both functions be defined on some unbounded subset of the real positive numbers, and "g"("x") be strictly positive for all large enough values of "x". One writes  if the absolute value of "f"("x") is at most a positive constant multiple of "g"("x") for all sufficiently large values of "x". That is, "f"("x") = "O"("g"("x")) if there exists a positive real number "M" and a real number "x" such that  In many contexts, the assumption that we are interested in the growth rate as the variable "x" goes to infinity is left unstated, and one writes more simply that  The notation can also be used to describe the behavior of "f" near some real number "a" (often, "a" = 0): we say  if there exist positive numbers "δ" and "M" such that  As "g"("x") is chosen to be non-zero for values of "x" sufficiently close to "a", both of these definitions can be unified using the limit superior:  if

Example.

In typical usage the "O" notation is asymptotical, that is, it refers to very large "x". In this setting, the contribution of the terms that grow "most quickly" will eventually make the other ones irrelevant. As a result, the following simplification rules can be applied: For example, let "f"("x") = 6"x" − 2"x" + 5, and suppose we wish to simplify this function, using "O" notation, to describe its growth rate as "x" approaches infinity. This function is the sum of three terms: 6"x", −2"x", and 5. Of these three terms, the one with the highest growth rate is the one with the largest exponent as a function of "x", namely 6"x". Now one may apply the second rule: 6"x" is a product of 6 and "x" in which the first factor does not depend on "x". Omitting this factor results in the simplified form "x". Thus, we say that "f"("x") is a "big-oh" of ("x"). Mathematically, we can write "f"("x") = "O"("x"). One may confirm this calculation using the formal definition: let "f"("x") = 6"x" − 2"x" + 5 and "g"("x") = "x". Applying the formal definition from above, the statement that "f"("x") = "O"("x") is equivalent to its expansion, for some suitable choice of "x" and "M" and for all "x" > "x". To prove this, let "x" = 1 and "M" = 13. Then, for all "x" > "x": so

Usage.

Big O notation has two main areas of application:  In both applications, the function "g"("x") appearing within the "O"(...) is typically chosen to be as simple as possible, omitting constant factors and lower order terms.  There are two formally close, but noticeably different, usages of this notation:  This distinction is only in application and not in principle, however—the formal definition for the "big O" is the same for both cases, only with different limits for the function argument.

Infinite asymptotics.

Big O notation is useful when analyzing algorithms for efficiency. For example, the time (or the number of steps) it takes to complete a problem of size "n" might be found to be "T"("n") = 4"n" − 2"n" + 2. As "n" grows large, the "n" term will come to dominate, so that all other terms can be neglected—for instance when "n" = 500, the term 4"n" is 1000 times as large as the 2"n" term. Ignoring the latter would have negligible effect on the expression's value for most purposes. Further, the coefficients become irrelevant if we compare to any other order of expression, such as an expression containing a term "n" or "n". Even if "T"("n") = 1,000,000"n", if "U"("n") = "n", the latter will always exceed the former once "n" grows larger than 1,000,000 ("T"(1,000,000) = 1,000,000= "U"(1,000,000)). Additionally, the number of steps depends on the details of the machine model on which the algorithm runs, but different types of machines typically vary by only a constant factor in the number of steps needed to execute an algorithm. So the big O notation captures what remains: we write either or and say that the algorithm has "order of n" time complexity. The sign "=" is not meant to express "is equal to" in its normal mathematical sense, but rather a more colloquial "is", so the second expression is sometimes considered more accurate (see the "Equals sign" discussion below) while the first is considered by some as an abuse of notation.

Infinitesimal asymptotics.

Big O can also be used to describe the error term in an approximation to a mathematical function. The most significant terms are written explicitly, and then the least-significant terms are summarized in a single big O term. Consider, for example, the exponential series and two expressions of it that are valid when "x" is small: The second expression (the one with "O"("x")) means the absolute-value of the error "e" − (1 + "x" + "x"/2) is at most some constant times "x" when "x" is close enough to 0.

Properties.

If the function "f" can be written as a finite sum of other functions, then the fastest growing one determines the order of "f"("n"). For example, In particular, if a function may be bounded by a polynomial in "n", then as "n" tends to "infinity", one may disregard "lower-order" terms of the polynomial. The sets "O"("n") and "O"("c") are very different. If "c" is greater than one, then the latter grows much faster. A function that grows faster than "n" for any "c" is called "superpolynomial". One that grows more slowly than any exponential function of the form "c" is called "subexponential". An algorithm can require time that is both superpolynomial and subexponential; examples of this include the fastest known algorithms for integer factorization and the function "n".  We may ignore any powers of "n" inside of the logarithms. The set "O"(log "n") is exactly the same as "O"(log("n")). The logarithms differ only by a constant factor (since log("n") = "c" log "n") and thus the big O notation ignores that. Similarly, logs with different constant bases are equivalent. On the other hand, exponentials with different bases are not of the same order. For example, 2 and 3 are not of the same order.  Changing units may or may not affect the order of the resulting algorithm. Changing units is equivalent to multiplying the appropriate variable by a constant wherever it appears. For example, if an algorithm runs in the order of "n", replacing "n" by "cn" means the algorithm runs in the order of "c""n", and the big O notation ignores the constant "c". This can be written as "c""n" = O("n"). If, however, an algorithm runs in the order of 2, replacing "n" with "cn" gives 2 = (2). This is not equivalent to 2 in general. Changing variables may also affect the order of the resulting algorithm. For example, if an algorithm's run time is "O"("n") when measured in terms of the number "n" of "digits" of an input number "x", then its run time is "O"(log "x") when measured as a function of the input number "x" itself, because "n" = "O"(log "x").

Sum.

This implies formula_18, which means that formula_19 is a convex cone.

Multiple variables.

Big "O" (and little o, Ω, etc.) can also be used with multiple variables. To define big "O" formally for multiple variables, suppose formula_22 and formula_23 are two functions defined on some subset of formula_24. We say if and only if Equivalently, the condition that formula_27 for some formula_28 can be replaced with the condition that formula_29, where formula_30 denotes the Chebyshev norm. For example, the statement asserts that there exist constants "C" and "M" such that where "g"("n","m") is defined by This definition allows all of the coordinates of formula_34 to increase to infinity. In particular, the statement (i.e., formula_36) is quite different from (i.e., formula_38).  Under this definition, the subset on which a function is defined is significant when generalizing statements from the univariate setting to the multivariate setting. For example, if formula_39 and formula_40, then formula_41 if we restrict formula_22 and formula_23 to formula_44, but not if they are defined on formula_45.  This is not the only generalization of big O to multivariate functions, and in practice, there is some inconsistency in the choice of definition.

Matters of notation.

Equals sign.

The statement ""f"("x") is "O"("g"("x"))" as defined above is usually written as "f"("x") = "O"("g"("x")). Some consider this to be an abuse of notation, since the use of the equals sign could be misleading as it suggests a symmetry that this statement does not have. As de Bruijn says, "O"("x") = "O"("x") is true but "O"("x") = "O"("x") is not. Knuth describes such statements as "one-way equalities", since if the sides could be reversed, "we could deduce ridiculous things like "n" = "n" from the identities "n" = "O"("n") and "n" = "O"("n")."  For these reasons, it would be more precise to use set notation and write "f"("x") ∈ "O"("g"("x")), thinking of "O"("g"("x")) as the class of all functions "h"("x") such that |"h"("x")| ≤ "C"|"g"("x")| for some constant "C". However, the use of the equals sign is customary. Knuth pointed out that "mathematicians customarily use the = sign as they use the word 'is' in English: Aristotle is a man, but a man isn't necessarily Aristotle."

Other arithmetic operators.

Big O notation can also be used in conjunction with other arithmetic operators in more complicated equations. For example, "h"("x") + "O"("f"("x")) denotes the collection of functions having the growth of "h"("x") plus a part whose growth is limited to that of "f"("x"). Thus, expresses the same as

Example.

Suppose an algorithm is being developed to operate on a set of "n" elements. Its developers are interested in finding a function "T"("n") that will express how long the algorithm will take to run (in some arbitrary measurement of time) in terms of the number of elements in the input set. The algorithm works by first calling a subroutine to sort the elements in the set and then perform its own operations. The sort has a known time complexity of "O"("n"), and after the subroutine runs the algorithm must take an additional 55"n" + 2"n" + 10 steps before it terminates. Thus the overall time complexity of the algorithm can be expressed as "T"("n") = 55"n" + "O"("n"). Here the terms 2"n"+10 are subsumed within the faster-growing "O"("n"). Again, this usage disregards some of the formal meaning of the "=" symbol, but it does allow one to use the big O notation as a kind of convenient placeholder.

Multiple uses.

In more complicated usage, "O"(...) can appear in different places in an equation, even several times on each side. For example, the following are true for formula_48 The meaning of such statements is as follows: for "any" functions which satisfy each "O"(...) on the left side, there are "some" functions satisfying each "O"(...) on the right side, such that substituting all these functions into the equation makes the two sides equal. For example, the third equation above means: "For any function "f"("n") = "O"(1), there is some function "g"("n") = "O"("e") such that "n" = "g"("n")." In terms of the "set notation" above, the meaning is that the class of functions represented by the left side is a subset of the class of functions represented by the right side. In this use the "=" is a formal symbol that unlike the usual use of "=" is not a symmetric relation. Thus for example "n" = "O"("e") does not imply the false statement "O"("e") = "n"

Typesetting.

Big O consists of just an uppercase "O". Unlike Greek-named Bachmann–Landau notations, it needs no special symbol. Yet, commonly used calligraphic variants, like formula_52, are available, in LaTeX and derived typesetting systems.

Orders of common functions.

Here is a list of classes of functions that are commonly encountered when analyzing the running time of an algorithm. In each case, "c" is a positive constant and "n" increases without bound. The slower-growing functions are generally listed first. The statement formula_53 is sometimes weakened to formula_54 to derive simpler formulas for asymptotic complexity. For any formula_55 and formula_56, formula_57 is a subset of formula_58 for any formula_59, so may be considered as a polynomial with some bigger order.

Related asymptotic notations.

Big "O" is the most commonly used asymptotic notation for comparing functions. Together with some other related notations it forms the family of Bachmann–Landau notations.

Little-o notation.

Intuitively, the assertion " is " (read " is little-o of ") means that grows much faster than. Let as before "f" be a real or complex valued function and "g" a real valued function, both defined on some unbounded subset of the real positive numbers, such that "g(x)" is strictly positive for all large enough values of "x". One writes if for every positive constant there exists a constant such that For example, one has  The difference between the earlier definition for the big-O notation and the present definition of little-o, is that while the former has to be true for "at least one" constant "M", the latter must hold for "every" positive constant, however small. In this way, little-o notation makes a "stronger statement" than the corresponding big-O notation: every function that is little-o of "g" is also big-O of "g", but not every function that is big-O of "g" is also little-o of "g". For example, formula_64 but formula_65  As "g"("x") is nonzero, or at least becomes nonzero beyond a certain point, the relation is equivalent to  Little-o respects a number of arithmetic operations. For example, It also satisfies a transitivity relation:

Big Omega notation.

There are two very widespread and incompatible definitions of the statement  where "a" is some real number, ∞, or −∞, where "f" and "g" are real functions defined in a neighbourhood of "a", and where "g" is positive in this neighbourhood.  The first one (chronologically) is used in analytic number theory, and the other one in computational complexity theory. When the two subjects meet, this situation is bound to generate confusion.

The Hardy–Littlewood definition.

In 1914 Godfrey Harold Hardy and John Edensor Littlewood introduced the new symbol formula_76, which is defined as follows:  Thus formula_78 is the negation of formula_79.  In 1916 the same authors introduced the two new symbols formula_80 and formula_81, defined as:  These symbols were used by Edmund Landau, with the same meanings, in 1924. After Landau, the notations were never used again exactly thus; formula_80 became formula_85 and formula_81 became formula_87.  These three symbols formula_88, as well as formula_89 (meaning that formula_90 and formula_91 are both satisfied), are now currently used in analytic number theory.

Simple examples.

We have  and more precisely  We have  and more precisely  however

The Knuth definition.

In 1976 Donald Knuth published a paper to justify his use of the formula_76-symbol to describe a stronger property. Knuth wrote: "For all the applications I have seen so far in computer science, a stronger requirement [...] is much more appropriate". He defined  with the comment: "Although I have changed Hardy and Littlewood's definition of formula_76, I feel justified in doing so because their definition is by no means in wide use, and because there are other ways to say what they want to say in the comparatively rare cases when their definition applies."

Family of Bachmann–Landau notations.

The limit definitions assume formula_121 for sufficiently large. The table is (partly) sorted from smallest to largest, in the sense that o, O, Θ, ∼, (Knuth's version of) Ω, ω on functions correspond to <, ≤, ≈, =, ≥, > on the real line (the Hardy-Littlewood version of Ω, however, doesn't correspond to any such description).  Computer science uses the big "O", big Theta Θ, little "o", little omega ω and Knuth's big Omega Ω notations. Analytic number theory often uses the big "O", small "o", Hardy–Littlewood's big Omega Ω (with or without the +, - or ± subscripts) and formula_122 notations. The small omega ω notation is not used as often in analysis.

Use in computer science.

Informally, especially in computer science, the big "O" notation often can be used somewhat differently to describe an asymptotic tight bound where using big Theta Θ notation might be more factually appropriate in a given context. For example, when considering a function "T"("n") = 73"n" + 22"n" + 58, all of the following are generally acceptable, but tighter bounds (such as numbers 2 and 3 below) are usually strongly preferred over looser bounds (such as number 1 below). The equivalent English statements are respectively: So while all three statements are true, progressively more information is contained in each. In some fields, however, the big O notation (number 2 in the lists above) would be used more commonly than the big Theta notation (items numbered 3 in the lists above). For example, if "T"("n") represents the running time of a newly developed algorithm for input size "n", the inventors and users of the algorithm might be more inclined to put an upper asymptotic bound on how long it will take to run without making an explicit statement about the lower asymptotic bound.

Other notation.

In their book "Introduction to Algorithms", Cormen, Leiserson, Rivest and Stein consider the set of functions "f" which satisfy  In a correct notation this set can, for instance, be called "O"("g"), where  The authors state that the use of equality operator (=) to denote set membership rather than the set membership operator (∈) is an abuse of notation, but that doing so has advantages. Inside an equation or inequality, the use of asymptotic notation stands for an anonymous function in the set "O"("g"), which eliminates lower-order terms, and helps to reduce inessential clutter in equations, for example:

Extensions to the Bachmann–Landau notations.

Another notation sometimes used in computer science is Õ (read "soft-O"): "f"("n") = "Õ"("g"("n")) is shorthand for "f"("n") = "O"("g"("n") log "g"("n")) for some "k". Essentially, it is big O notation, ignoring logarithmic factors because the growth-rate effects of some other super-logarithmic function indicate a growth-rate explosion for large-sized input parameters that is more important to predicting bad run-time performance than the finer-point effects contributed by the logarithmic-growth factor(s). This notation is often used to obviate the "nitpicking" within growth-rates that are stated as too tightly bounded for the matters at hand (since log "n" is always "o"("n") for any constant "k" and any ε > 0).  Also the L notation, defined as is convenient for functions that are between polynomial and exponential in terms of formula_130.

Generalizations and related usages.

The generalization to functions taking values in any normed vector space is straightforward (replacing absolute values by norms), where "f" and "g" need not take their values in the same space. A generalization to functions "g" taking values in any topological group is also possible. The "limiting process" "x" → "x" can also be generalized by introducing an arbitrary filter base, i.e. to directed nets "f" and "g". The "o" notation can be used to define derivatives and differentiability in quite general spaces, and also (asymptotical) equivalence of functions, which is an equivalence relation and a more restrictive notion than the relationship ""f" is Θ("g")" from above. (It reduces to lim "f" / "g" = 1 if "f" and "g" are positive real valued functions.) For example, 2"x" is Θ("x"), but 2"x" − "x" is not "o"("x").

History (Bachmann–Landau, Hardy, and Vinogradov notations).

The symbol O was first introduced by number theorist Paul Bachmann in 1894, in the second volume of his book "Analytische Zahlentheorie" ("analytic number theory"). The number theorist Edmund Landau adopted it, and was thus inspired to introduce in 1909 the notation o; hence both are now called Landau symbols. These notations were used in applied mathematics during the 1950s for asymptotic analysis. The symbol formula_76 (in the sense "is not an "o" of") was introduced in 1914 by Hardy and Littlewood. Hardy and Littlewood also introduced in 1918 the symbols formula_80 ("right") and formula_81 ("left"), precursors of the modern symbols formula_85 ("is not smaller than a small o of") and formula_87 ("is not larger than a small o of"). Thus the Omega symbols (with their original meanings) are sometimes also referred to as "Landau symbols". This notation formula_76 became commonly used in number theory at least since the 1950s. In the 1970s the big O was popularized in computer science by Donald Knuth, who introduced the related Theta notation, and proposed a different definition for the Omega notation.  Landau never used the big Theta and small omega symbols.  Hardy's symbols were (in terms of the modern "O" notation)  (Hardy however never defined or used the notation formula_140, nor formula_141, as it has been sometimes reported). Hardy introduced the symbols formula_142 and formula_143 (as well as some other symbols) in his 1910 tract "Orders of Infinity", and made use of them only in three papers (1910–1913). In his nearly 400 remaining papers and books he consistently used the Landau symbols O and o.  Hardy's notation is not used anymore. On the other hand, in the 1930s, the Russian number theorist Ivan Matveyevich Vinogradov introduced his notation formula_141, which has been increasingly used in number theory instead of the formula_145 notation. We have and frequently both notations are used in the same paper.  The big-O originally stands for "order of" ("Ordnung", Bachmann 1894), and is thus a Latin letter. Neither Bachmann nor Landau ever call it "Omicron". The symbol was much later on (1976) viewed by Knuth as a capital omicron, probably in reference to his definition of the symbol Omega. The digit zero should not be used.

Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation.

Landauova notace (též notace velké O nebo notace omikron) je notace používaná v matematice pro porovnávání asymptotického chování funkcí, tj. chování funkcí pro „velké“ hodnoty parametru. V matematické informatice se tato notace používá pro porovnání asymptotické časové nebo prostorové složitosti algoritmů, případně pro omezení složitosti algoritmu.


Organization.

Like most of the other branches of the ROC armed forces, much of the ROCAF's structure and organization is patterned after the United States Air Force. Like the USAF, the ROCAF used to have a wing → group → squadron structure. After November 2004, tactical fighter wing switch to wing → Tactical Fighter Group, with some fighter squadrons stood down, with each tactical fighter group, still pretty much the same size as a squadron, now commanded by a full colonel.

History.

Formally established in 1920 as the Aviation Ministry, the ROCAF was active during the tenure of the ROC on Mainland China. In this period, various airplanes were purchased and deployed by warlords in their struggle for power until nominal Chinese reunification in 1928. In February 1932, US Reserve Lt. Robert McCawley Short, who was transporting armed Chinese aircraft, shot down an IJN aircraft on February 19, 1932, and downed another on February 22 before he was killed (he was posthumously raised to the rank of colonel in the Chinese Air Service).  During the Second Sino-Japanese War (1937–1945), the ROCAF participated in attacks on Japanese warships on the eastern front and along the Yangtze river including support for the Battle of Shanghai in 1937. The Chinese frontline fighter aircraft initially were mainly the Curtiss Hawk II and III and the Boeing P-26 model 281, and engaged Japanese fighters in many major air battles beginning on August 14, 1937, when Imperial Japanese Navy warplanes raided Chienchiao airbase; "814" has thus become known as "Air Force Day". Chinese Boeing P-26/281 fighters engaged Japanese Mitsubishi A5M fighters in what is among the world's first aerial dogfighting between all-metal monoplane fighter aircraft. A unique mission in May 1938 saw two Chinese B-10 bombers fly a mission over Japan, but dropping only propaganda leaflets over the Japanese cities of Nagasaki and Saga, four years before 1942 Doolittle Raid on Japanese home islands. It was a war of attrition for the Chinese pilots, as many of their most experienced ace fighter pilots, such as Lieutenant Liu Tsui-Kang and Colonel Kao Chih-Hang were lost early in the war. Code breaking operations played a role in the conflict. A Japanese radio intercept unit was attached to the landing forces at Shanghai. IJN Lt. Commander Tsunezo Wachi and a Lt. Yamada, an expert in Chinese codes, enabled Japanese to make preemptive strikes against ROCAF airfields.  In the latter half of the Sino-Japanese War, part of World War II, the ROCAF was augmented by a volunteer group of American pilots (the Flying Tigers) in 1941. Throughout the war, the ROCAF was involved in attacks on Japanese air and ground forces in the Chinese theatre.  ROCAF General HQ was established in June 1946. From 1946 to 1948, during the Chinese Civil War, the ROCAF participated in combat against the People's Liberation Army engaging in air-to-air combat on at least eleven occasions in the areas surrounding the Taiwan Strait. The ROCAF reportedly enjoyed a 31:1 kill ratio against the PLA. GHQ was evacuated to Taiwan along with the rest of the ROC Government in April 1949 following the Communist victory in the Chinese Civil War. The ROCAF assisted in halting the PLA advance at the Battle of Kuningtou on Kinmen the same year.  The ROCAF regularly patrolled the Taiwan Straits and fought many engagements with its Communist counterpart (the PLAAF). The ROCAF received second hand equipment from the US at that time, such as the F-86, F-100 and F-104.  During the Cold War, the ROCAF was involved in combat air patrols over the Taiwan Strait and engaged the PLAAF and PLAN-AF on several occasions. The ROCAF was also the testbed of American technology at this time. The first successful kill scored by an air-to-air missile was accomplished by a ROCAF F-86 Sabre with then experimental AIM-9 Sidewinder. ROCAF pilots also flew U-2 recon overflights of the PRC during this time with assistance from the USAF. Known as the Black Cat Squadron they flew a total of 220 missions, with 102 missions over mainland China, losing 5 aircraft. All five were shot down by SA-2 surface-to-air missiles, the same type of surface-to-air missile that shot down Gary Powers over the USSR in 1960. The 34th "Black Bat Squadron" flew low level missions into China as part of its mapping PRC growing air defense networks, conducting ESM and ECM missions, inserting agents behind enemy lines, and air drop resupply missions.  Starting in November 1967, the ROC secretly operated a cargo transport detachment to assist the US and the ROV as part of its participation in the Vietnam War. It was based on existing formation of the 34th squadron of ROC Air force. The unit's strength included two C-123 cargo aircraft, seven flight officers and two mechanics, even though a higher number of military personnel was involved through rotation. It was tasked with air transportation, airdrop and electronic reconnaissance. Some 25 members of the unit were killed, among them 17 pilots and co-pilots, and three aircraft were lost. Other ROC involvement in Vietnam included a secret listening station, special reconnaissance and raiding squads, military advisers and civilian airline operations (which cost a further two aircraft due to Vietnamese individually operated AA missiles).  From 1979 to 1990 the ROCAF engaged in a classified military aid program in Yemen Arab Republic known as the Great Desert Program (大漠計畫). The program started after American President Jimmy Carter rushed 14 F-5s to the Yemeni Air Force who had no pilots or ground crew trained to operate the type or even western aircraft (they previously operated Mig-15s). The Americans and the Saudis (who were bankrolling the Yemen Arab Republic's military) requested military aid from Taiwan who provided 80 F-5 pilots, ground crews, early warning radars, and anti-aircraft missile batteries. All told more than a thousand ROCAF personnel deployed to Yemen.  The opposing Air Force of South Yemen was made up of Cuban Revolutionary Air and Air Defense Force pilots and maintainers with some Soviet advisors and pilots as well. The ROCAF force were actively involved in combat with the Cubans/Soviets and for all intents and purposes constitutes the Yemen Arab Republic's Air Force during this time. Taiwanese pilots scored a number of kills and the air-defense and early warning radar teams took casualties from aerial attacks. The program ended in 1990 when Saudi Arabia withdrew its diplomatic recognition of Taiwan.

Humanitarian operations.

The ROCAF has also taken part in numerous humanitarian operations. Some of the more major ones include the following:

Equipment and procurement.

Current ROCAF inventory includes over 400 combat aircraft, the mainstays being the AIDC F-CK-1 Ching-kuo IDF (Indigenous Defense Fighter) and F-16 while the Mirage 2000-5 provides the most formidable air-defense capabilities. Older F-5 fighters are gradually being phased out but remain in service.  The United States serves as the ROCAF's main supplier of equipment and also provides training for ROCAF and ROC Navy pilots at Luke AFB in Arizona. This base which is between Phoenix and Tucson has an instrumented flight area for training approximately the size of the State of Connecticut. German Air Force (Luftwaffe) and German Naval Aviation (Marineflieger) who used to train at Luke AFB from 1957-1983 now train at NATO facilities at CFB Goose Bay in Canada and also alongside the USAF at Holloman AFB in New Mexico. As of 2019 the US Air Force is assisting the Taiwanese Air Force in sourcing new and surplus F-5 parts.

Domestic development.

Prior to 1984, ROCAF fighters were almost exclusively American-made aircraft sold under terms of a mutual defense treaty between the Republic of China and the United States. Development of the F-CK-1 "Ching-kuo" Indigenous Defense Fighter (IDF) began in 1984 due to U.S. refusal to sell F-16s to the ROCAF as a result of changes in national policy between the U.S. and the People's Republic of China. After a successful maiden flight in 1989, the domestically produced fighter entered service in 1994. However, the ROCAF was subsequently able to obtain F-16s from the United States as well as Mirage 2000-5 fighters from France, resulting in delays to later IDF development that had been anticipated.  In response to American refusals to supply "smart bombs", Taiwan is developing their own equivalent of the Joint Direct Attack Munition for attacks against the PRC mainland in case of invasion preparations.  Taiwan is looking to replace its current fleet of AT-3 jet trainers and F-5 LIFT planes with 66 advanced trainers. In 2008 the Republic of China Air Force released a request for information (RFI) and two companies including Lockheed Martin for the T-50 and Alenia Aermacchi's M-346 responded to the request. These planes were expected to be license produced in Taiwan with a local partner firm, and the overall estimated contract value was 69 billion New Taiwan dollars (US$2.2 billion). However, after the election of President Tsai Ing-wen, who intends to make Taiwan's defense industry a cornerstone for future development, it was decided to domestically design and build 66 AIDC T-5 Brave Eagle supersonic trainers instead of selecting the T-50 or M-346. The T-5, with a program cost of NT$68.6 billion, will be a new aircraft whose design will draw upon Taiwan's expertise gained by building the domestically produced Indigenous Defense Fighter.  In 2019 the Taiwan Air Force's Air Defense and Missile Command announced a five-year, NT$80b (US$2.54b) project to build up a full force of anti-radiation UAVs made by NCSIST.

Foreign procurement.

One of the first modern jets purchased was the Northrop F-5. In 1974 a total of 308 were purchased but, lacking spare parts, the ROC has been forced to salvage them from inoperable F-5s. Taiwan is considering reusing engines from inoperable F-5s in cruise missiles.  On February 28, 2007, the US Defense Department approved an order made by the ROC for 218 AIM-120C-7 AMRAAM missiles, as well as 235 AGM-65G2 Maverick missiles, associated launchers and other equipment. The total value of this order was revealed to be US$421 million.  In June 2007, the Legislative Yuan also approved the upgrade of the existing PAC-2 batteries to PAC-3 standard, and, in November, the Pentagon notified the U.S. Congress of the Patriot upgrade order. On August 10, 2007, a shipment of Harpoon anti-ship missiles, valued at an estimated $125 million, was also authorised by the U.S. Defense Department, including 60 AGM-84L Block II missiles and 50 upgrade kits to bring the ROCAF's existing Harpoons up to Block II, Mark L standard.  On October 3, 2008, arms notifications were sent to Congress concerning, amongst other things, the sale of 330 PAC III missiles, 4 missile batteries, radar sets, ground stations and other equipment valued up to US$3.1 billion, the upgrade of 4 E-2T aircraft to the Hawkeye 2000 standard and US$334 million worth of spare parts for the ROCAF's F-16s, IDFs, F-5E/Fs and C-130s. Late in January 2010, ROCAF received the first batch of new TC-2(V) BVR missiles ordered from CSIST, believed to have new radar seeker and improved performance from the original missile which entered service over 10 years ago. The U.S. government also announced 5 notifications to Congress for additional arms sales totaling some US$6.39 Billion, under which the ROCAF will receive 3 PAC-3 batteries with 26 launchers and 114 PAC-3 missiles. On February 3, 2010, ROCAF also announced at a Singapore Airshow that it had signed a new contract for 3 EC-225 SAR (Search-And-Rescue) helicopters that was awarded to Eurocopter back in December 2009 for US$111 million, along with options for 17 more EC-225s. On November 26, 2011, the 3 EC-225 C-SAR helicopters were loaded on board an An-124 cargo aircraft and delivered to Chai-yi AB in Taiwan, and should enter service on July 1, 2012. On August 31, 2010, it was announced for next year's defense budget, ROCAF's "Medium Transport aircraft" plan to replace 12 B-1900 VIP/transport training aircraft, believed to be 6-8+ Lockheed C-27J, has been put on hold and might be axed, due to lack of budget, but will allocate 20+ million US dollars over next 4 years for quick runway repair. Other items mentioned including increases in runways from 3 to 6 at Eastern Taiwan's 3 airbases, moving 2 I-HAWK batteries to Eastern Taiwan to protect those airbases, which will double to 4 batteries, and others. On November 8, 2011, a second pair of E-2T Hawkeye AEW(s/n 2501 and 2502) were loaded on a ship and sent to the US for upgrade to the E-2C 2000 standard. The first pair of E-2T (s/n 2503 and 2504) were sent to the US in June 2010 and returned to Taiwan on December 18, 2011, and will be return to service by end of the year.  On August 15, 2011, the United States again deferred the ROCAF request to purchase 66 new F-16C/Ds but offered a retrofit package for older F-16A/B's. (originally 150 were brought in 1992) However, the US allowed the F-16A/Bs to be upgraded to the AN/APG-83 radar. Unfortunately, it was discovered the F-16A/Bs have rusting issues during the F-16V upgrade due to aging and Taiwan's climate. The $5.3 billion upgrade package for ROCAF's existing F-16A/B fighters was announced on 21 September 2011. The upgrade budget was to be spread over 12 years, though the Ministry of Defense indicated that it would try to reduce the period. In November 2011, the United States-China Economic and Security Review Commission recommended that new fighters be sold to the ROCAF. Taiwan is also balking at the cost of the radar upgrade, as it does not want to be the lead customer who pays to develop the upgrade and also because they will be unable to afford both the upgrade and the new fighters, should these be offered. In response to a U.S. vote in the House of Representatives to force the sale of the C/D models, the ROC MND said that the upgrade package offered some superior capabilities over the C/D model aircraft and some defense officials have said that in light of the PRC's increasing capabilities, only the F-35 would be sufficient.  In July 2012, Taiwan's Aerospace Industrial Development Corp. and Lockheed Martin announced plans to establish a maintenance and overhaul center to upgrade and maintain the F-16s in place without having to ship them back to the United States. In 2012 a letter of acceptance was agreed on for a US$3.8 billion deal that included the radars, electronic warfare, structural improvements and new weapons. A Pentagon report has corroborated that claim, asserting that the PRC would probably seek to destroy ROCAF airfields in the first stages of any attack, making a STOVL fighter such as the F-35B vital for effective defense. On April 10, 2019, Air Force Chief of Staff Liu Jen-yuan confirmed that the Air Force is asking for a total of new-built 66 F-16V fighter jets from the U.S. to replace its aging and nearly obsolete F-5 fighters. Previous presidents after George H.W. Bush refused to sell F-16 fighters to the ROC Airforce, including George W. Bush in 2006 after a ROC request for F-16C/Ds.  President Barack Obama also refused Taiwan's request for new F-16s in 2011. The Obama administration later allowed the ROC Airforce to upgrade its current F-16s though the upgrades did not start until 2017 and first upgraded aircraft were only delivered in 2018 during the Trump administration.  On August 20, 2019, the sale of F-16 C/D Block 70, also known as F-16V, was officially approved by the State Department and formally submitted to Congress. The 66 newly-built F-16s will be supplied with 75 General Electric F110 engines and 75 AN/APG-83 Scalable Agile Beam AESA radars. The final signing of the Letter of Offer and Acceptance (LOA) for the purchase of 66 F-16V fighter jets was confirmed on December 21st, 2019.

The Republic of China Air Force (ROCAF;,) is the military aviation branch of the Republic of China Armed Forces. The ROCAF's primary mission is the defense of the airspace over and around Taiwan. Priorities of the ROCAF include the development of long range reconnaissance and surveillance networks, integrating C4ISTAR systems to increase battle effectiveness, procuring counterstrike weapons, next generation fighters, and hardening airfields and other facilities to survive a surprise attack.

Letectvo Čínské republiky (Tchaj-wanu) tvoří spolu s vojskovým letectvem tchajwanské armády a námořním letectvem tchajwanského loďstva vzdušné síly Čínské republiky, jejíž území si nárokuje Čínská lidová republika. Velitelství bojových leteckých jednotek zodpovídá za letouny osmi křídel, včetně výcvikových a podpůrných jednotek. Z celkem osmi křídel je pět taktických (TFW), jedno smíšené (TCW), jedno středisko taktického výcviku a rozvoje (TTDC) a jedno křídlo dopravní a včasného varování (T/EWW).


Early life.

Nilus of Sora, a great ascetic of the Russian Church, was descended from the Maikov nobility. Before becoming a monk, Nil Sorsky worked as a scribe and was engaged in book copying. He also journeyed to Palestine and Greece early in his life and was acquainted there with the Hesychast movement.  Later in his life, he took monastic vows at the Kirillo-Belozersky Monastery, which had been known for its hostile stance towards monastic landownership. The founder of the monastery – Saint Kirill of Beloozero – was himself known for rejecting villages that had been offered to him by devout nobles.  Kirill’s followers adopted his ways and would later become known as the "startsy from out the Volga" with Nil Sorsky as their leader. Soon, he went on a journey to the Holy Land and visited Palestine, Constantinople, and Mount Athos, acquainting himself with a mystical doctrine of Hesychasm and reading patristic literature. Upon his return to Russia (between 1473 and 1489), Nil Sorsky founded a cloister on the Sora River (hence, Nil Sorsky, or Nil of Sora) not far from the Kirillo-Belozersky Monastery, where he would settle down with his followers. He wrote extensively. This travelling to the holy places made a great impression upon him and changed all his individuality. Solitude, isolation, oblivion of the world became the main features of his character.

The Novgorod heresy affair.

Nil Sorsky was involved in the Novgorod heresy affair (see "Sect of Skhariya the Jew" for details), which had stirred a lot of minds in Russia at that time. It appears that Sorsky and his closest associate Paisiy Yaroslavov were much more tolerant towards the heretics than most of the Russian clergy, led by Gennady (Archbishop of Novgorod) and Joseph Volotsky.  In 1489, Archbishop Gennady embarked on the path of fighting the heretics and asked Archbishop of Rostov to consult with the elders Nil Sorsky and Paisiy Yaroslavov (who had been living in his eparchy) and seek their assistance in this matter. Historical accounts of that period do not shed any light on the outcome of these "negotiations", but from that time on there seems to have been no interaction between Sorsky and Yaroslavov on one side and Gennady and Joseph Volotsky on the other.  The two elders, however, did not treat heresy with indifference. They were both present at the Synod of 1490, which dealt with heresy, and exerted their influence upon its final decision. Initially, the clergy unanimously spoke in support of burning all the heretics at the stake. At the conclusion of the synod, however, only a few priests were condemned and then defrocked without being executed. Later in the decade, however, several heretics were burned in both Novgorod and Moscow.

Teaching and influence.

Nil Sorsky was opposed to formality in Orthodoxy faith which were widely spread in the mids of 16 century in Russia. It was so deeply crystallized in church life of that period that such persons as Maximus the Greek and elder Artemiy who had tried to show the deep basics of Orthodoxy were considered as Heretics. His wish was to disclose the deep understanding of Orthodoxy devoting more attention to spiritual life of a soul rather than to religious rituals. He was not a bookworm but a speculator-philosopher or speculator-theorist and an uncommon spiritual freedom marked his personality. The whole life of a person - the path of incessant self-perfection and self-improvement - is based on the Holy Gospel. And the Elder showed a lot of psychological understanding of the spiritual struggle and outlined clear ways of "graceful struggle". He deeply believed that moral, inner, spiritual perfection was the ideal foundation of the active, productive life of the believer.  In his teachings, he developed mystical and ascetical ideas along the lines of Gregory Sinaite's hesychasm, asking the believers to concentrate on their inner world and personal emotional experiences of faith as means for achieving unity with God. Nil Sorsky demanded that monks participate in productive labor and spoke in support of monastic reforms on a basis of a secluded and modest lifestyle.  Nil Sorsky dedicated his efforts towards fighting against monastic landownership rights at the Synod of 1503 in Moscow. There, he raised a question about monastic estates, which comprised about one third of the territory of the whole Russian state at that time and which, in his view, had been responsible for demoralization of the Russian monastic communities. Nil Sorsky was supported by the elders of the Kirillo-Belozersky Monastery and his disciple Vassian Patrikeyev. Although he spoke in favor of Ivan III’s policy of secularization of monastic lands, Sorsky did not live long enough to see the end of this struggle. Patrikeyev and Artemius of the Trinity were Nil Sorsky’s successors.

Nil Sorsky (, also Nilus of Sora and Nil Sorski; birth name: Nikolai Maikov () (c. 1433–1508) became a leader of a tendency in the medieval Russian Orthodox Church known as the "Non-possessors" which opposed ecclesiastic landownership. The Russian Orthodox Church venerates Nil Sorsky as a saint, marking his feast day on the anniversary of his repose on May 7.

Sv. Nil Sorský (rusky Нил Сорский; 1433, Moskva – 7. května 1508) byl ruský mnich, starec a mystik, představitel hnutí nestjažatělů.


Background.

The movement is led by Mihrac Ural, a Turkish Alawite who has Syrian citizenship and is also known as "Ali Kayyali" (علي كيالي). According to "Today's Zaman", Ural was the leader of a clandestine insurgent cell in Hatay Province called the People's Liberation Party-Front of Turkey or "Acilciler" (The Urgent Ones). "Zaman" further alleged that Ural's group has sought to agitate Hatay's sizable Alawite population into confrontation with the Turkish authorities and has also recruited local Alawites to fight in Syria on behalf of the Syrian government. The group claims to also have supporters among Syria's Sunni Muslims and Christians.  Though the group openly espouses a broadly-inclusive platform of Syrian nationalism in addition to secular leftism, it has been claimed that its primary focus is the defence of the Alawite and Twelver Shi’a religious minorities of Syria. The Syrian Resistance has been accused by the Syrian opposition of being a sectarian Alawite militia, and of having carried out bombings and attacks in Turkey and on villages in Syria. However, Sheikh Muwaffaq al-Ghazal, a member of the Islamic Alawi Council, claims it has an inclusive national line regarding religion, race and gender.

History.

Founded before the Syrian Civil War's outbreak under the name "Popular Front for the Liberation of the Sanjak of Iskandarun", the militia has been most active in Latakia Governorate, where its members reportedly committed a massacre in the town of Baniyas in 2013. The Turkish government has also suspected the Syrian Resistance for carrying out the Reyhanlı bombings.  On 29 March 2016, it was falsely reported that Mihraç Ural had been killed by Ahrar al-Sham.  In late July 2016, the Syrian Resistance sent reinforcement contingents from Hama to Aleppo in order to support the pro-government forces during the 2016 Aleppo campaign. In course of the campaign, they were deployed both in the northern city at the Castello road front, as well as in the south where rebel forces launched a counter-offensive.  At some point, the "Falcons of the Jazira and Euphrates", a militia of Deir ez-Zor Governorate natives, officially joined the Syrian Resistance, though it remained operationally fully autonomous. Under the Syrian Resistance's flag, this unit took part in the central Syria campaign of mid-2017.  Jamal Trabelsi, director of the Syrian Resistance's information office, was targeted by an improvised explosive device (IED) in Aleppo in July 2017, though he survived. The group accused "Turkey-backed & hired gangs" of being behind the attack. A few days later, a female media officer of the Syrian Resistance, Duaa Hayel Sulaiman, was assassinated in Damascus.

The Syrian Resistance ("Al Muqāwamat al-Sūriyah", Arabic: المقاومة السورية), formerly known as the Popular Front for the Liberation of the Sanjak of Iskandarun (Arabic: الجبهة الشعبية لتحرير لواء اســكندرون), is a pro-government Syrian armed militia group operating in northwest Syria, claiming a Marxist–Leninist ideology.

Jednotky syrského odporu (arabsky: المقاومة السورية, Al Muqāwamat al-Sūriyah), oficiálně též Lidová fronta pro osvobození sandžaku İskenderun, je syrská provládní ozbrojená skupina operující hlavně na severozápadě Sýrie. Hnutí se hlásí k marxisticko-leninistické ideologii.