source stringlengths 31 227 | text stringlengths 9 2k |
|---|---|
https://en.wikipedia.org/wiki/SHEEP%20%28symbolic%20computation%20system%29 | SHEEP is one of the earliest interactive symbolic computation systems. It is specialized for computations with tensors, and was designed for the needs of researchers working with general relativity and other theories involving extensive tensor calculus computations.
SHEEP is a freeware package (copyrighted, but free for educational and research use).
The name "SHEEP" is pun on the Lisp Algebraic Manipulator or LAM on which SHEEP is based. The package was written by Inge Frick, using earlier work by Ian Cohen and Ray d'Inverno, who had written ALAM - Atlas LISP Algebraic Manipulation in earlier (designed in 1970). SHEEP was an interactive computer package whereas LAM and ALAM were batch processing languages.
Jan E. Åman wrote an important package in SHEEP to carry out the Cartan-Karlhede algorithm. A more recent version of SHEEP, written by Jim Skea, runs under Cambridge Lisp, which is also used for REDUCE.
See also
GRTensorII
Notes
External links
SHEEP download directory at Queen Mary, University of London
Some sources of info on Sheep
Review article by M.A.H.MacCallum in "Workshop on Dynamical Spacetimes and Numerical Relativity" edited by Joan Centrella
Tensors |
https://en.wikipedia.org/wiki/European%20Society%20of%20Human%20Reproduction%20and%20Embryology | The European Society of Human Reproduction and Embryology (ESHRE) was founded in 1985 by Robert Edwards (University of Cambridge) and J. Cohen (Paris), who felt that the study and research in the field of reproduction needed to be encouraged and recognized. It is currently headquartered in Belgium.
Aims
The aims of the society are:
to promote the understanding of reproductive biology and embryology
to facilitate research and the subsequent dissemination of research findings to the public, scientists, clinicians and patient associations
to inform politicians and policy makers in Europe.
The society further engages in medical education activities, the development of data registries, and the implementation of methods to improve safety and quality in clinical and laboratory procedures.
Structure
The society consists of:
General Assembly, comprising all its members, made up of diverse sub-special interest groups, such as andrology, reproductive genetics, ethics and law, and paramedics;
Executive Committee, comprising 13 members or more, and having various sub-committees, such as the Finance Subcommittee, Training Subcommittee, Annual Meeting Subcommittee, the Committee of National Representatives, and the Communications Committee.
Medical journal
The official journal of the society is Human Reproduction. It is made up of three individual publications: Human Reproduction, Human Reproduction Update and Molecular Human Reproduction.
See also
American Society for Reproductive Medicine
Human Fertilisation and Embryology Authority
Assisted Human Reproduction Canada |
https://en.wikipedia.org/wiki/GRTensorII | GRTensorII is a Maple package designed for tensor computations, particularly in general relativity.
This package was developed at Queen's University in Kingston, Ontario by Peter Musgrave, Denis Pollney and Kayll Lake. While there are many packages which perform tensor computations (including a standard Maple package), GRTensorII is particularly well suited for carrying out routine computations of useful quantities when working with (or searching for) exact solutions in general relativity. Its principal advantages include
convenience of definition of new spacetimes and tensor expression
efficient computation with frames
efficient computation of Ricci and Weyl spinor components and of Petrov classification
efficient computation of the Carminati-McLenaghan invariants and other curvature invariants
Currently, GRTensorII does have some drawbacks:
Maple is expensive
valuable subpackages for perturbation and junction computations have not been updated
no subpackage is yet publicly available in GRTensorII for executing the Cartan-Karlhede algorithm
sharing information with standard Maple packages can sometimes become awkward |
https://en.wikipedia.org/wiki/Philosophical%20presentism | Philosophical presentism is the view that only present entities exist (or, equivalently, that everything is present). According to presentism, there are no past or future entities. In a sense, the past and the future do not exist for presentists—past events have happened (have existed) and future events will happen (will exist), but neither exist at all since they do not exist now. Presentism is a view about temporal ontology that contrasts with eternalism—the view that past, present and future entities exist (that is, the ontological thesis of the 'block universe')—and with no-futurism—the view that only past and present entities exist (that is, the ontological thesis of the 'growing block universe').
Historical antecedents
Augustine of Hippo proposed that the present is analogous to a knife edge placed exactly between the perceived past and the imaginary future and does not include the concept of time. Proponents claim this should be self-evident because, if the present is extended, it must have separate parts—but these must be simultaneous if they are truly a part of the present. According to early philosophers, time cannot be simultaneously past and present and hence not extended. Contrary to Saint Augustine, some philosophers propose that conscious experience is extended in time. For instance, William James said that time is "the short duration of which we are immediately and incessantly sensible". Other early presentist philosophers include the Indian Buddhist tradition. Fyodor Shcherbatskoy, a leading scholar of the modern era on Buddhist philosophy, has written extensively on Buddhist presentism: "Everything past is unreal, everything future is unreal, everything imagined, absent, mental... is unreal. Ultimately, real is only the present moment of physical efficiency [i.e., causation]."
According to J. M. E. McTaggart's "The Unreality of Time", there are two ways of referring to events: the 'A Series' (or 'tensed time': yesterday, today, tomorrow) and the |
https://en.wikipedia.org/wiki/Net%20positive%20suction%20head | In a hydraulic circuit, net positive suction head (NPSH) may refer to one of two quantities in the analysis of cavitation:
The Available NPSH (NPSHA): a measure of how close the fluid at a given point is to flashing, and so to cavitation. Technically it is the absolute pressure head minus the vapour pressure of the liquid.
The Required NPSH (NPSHR): the head value at the suction side (e.g. the inlet of a pump) required to keep the fluid away from cavitating (provided by the manufacturer).
NPSH is particularly relevant inside centrifugal pumps and turbines, which are parts of a hydraulic system that are most vulnerable to cavitation. If cavitation occurs, the drag coefficient of the impeller vanes will increase drastically—possibly stopping flow altogether—and prolonged exposure will damage the impeller.
NPSH in a pump
In a pump, cavitation will first occur at the inlet of the impeller. Denoting the inlet by i, the NPSHA at this point is defined as:
where is the absolute pressure at the inlet, is the average velocity at the inlet, is the fluid density, is the acceleration of gravity and is the vapor pressure of the fluid. Note that NPSH is equivalent to the sum of both the static and dynamic heads – that is, the stagnation head – minus the equilibrium vapor pressure head, hence "net positive suction head".
Applying the Bernoulli's equation for the control volume enclosing the suction free surface 0 and the pump inlet i, under the assumption that the kinetic energy at 0 is negligible, that the fluid is inviscid, and that the fluid density is constant:
Using the above application of Bernoulli to eliminate the velocity term and local pressure terms in the definition of NPSHA:
This is the standard expression for the available NPSH at a point. Cavitation will occur at the point i when the available NPSH is less than the NPSH required to prevent cavitation (NPSHR). For simple impeller systems, NPSHR can be derived theoretically, but very often it is determin |
https://en.wikipedia.org/wiki/Superparasitism | Superparasitism is a form of parasitism in which the host (typically an insect larva such as a caterpillar) is attacked more than once by a single species of parasitoid. Multiparasitism or coinfection, on the other hand, occurs when the host has been parasitized by more than one species. Host discrimination, whereby parasitoids can identify a host with parasites from an unparasitized host, is present in certain species of parasitoids and is used to avoid superparasitism and thus competition from other parasites.
Superparasitism can result in transmission of viruses, and viruses may influence a parasitoid's behavior in favor of infecting already infected hosts, as is the case with Leptopilina boulardi.
Examples
One example of superparasitism is seen in Rhagoletis juglandis, also known as the walnut husk fly. During oviposition, female flies lacerate the tissue of the inner husk of the walnut and creative a cavity for her eggs. The female flies oviposit and reinfest the same walnuts and even the same oviposition sites created by conspecifics. |
https://en.wikipedia.org/wiki/Patoruz%C3%BA | Patoruzú is a comic character created in 1928 by Dante Quinterno and is considered the most popular hero of Argentine comics. Patoruzú is a wealthy Tehuelche cacique with great estate properties in Patagonia, and possesses both superhuman physical strength and a charitable yet naive heart. He was originally only a side character in Quinterno's series "Don Gil Contento", but became so popular with readers that the comic was renamed after him.
History
Patoruzú first appeared on October 19, 1928, in the Las Aventuras de Don Gil Contento strip in the Crítica newspaper, under the name of Curugua Curuguagüigua; last cacique of the giant Tehuelches, of whom Don Gil becomes tutor. The name was deemed too difficult to pronounce and was soon changed to Patoruzú, after the then-popular candy Pasta de Orozú. Nevertheless, the strip was canceled by the newspaper after only a few days.
Later that year Dante Quinterno started working for La Razón newspaper with the strip Don Julián de Monte Pío (predecessor of another of Quinterno's popular characters: the playboy Isidoro Cañones). In September 1930, Patoruzú was again introduced into the strip when Don Julián became his tutor. Slowly, Patoruzú assumed greater importance in the strip, which on December 11, 1931, was renamed to Patoruzú.
In 1935 Quinterno sold the publication rights to El Mundo newspaper, and the first compilation of the adventures of the cacique was published. The strip was also published in newspapers in other Argentine cities outside of Buenos Aires.
In November 1936 the first Patoruzú monthly magazine was released and completely sold out the same day. The magazine was then published fortnightly, and then weekly. The magazine reached a record circulation of 300,000 copies, soon requiring a team to create its scripts and drawings, under the supervision of Quinterno.
On April 30, 1977, the 2,045th and last issue of Patoruzú was released. Slightly adapted versions of the original have been published, as well |
https://en.wikipedia.org/wiki/DJ%20mixer | A DJ mixer is a type of audio mixing console used by disc jockeys (DJs) to control and manipulate multiple audio signals. Some DJs use the mixer to make seamless transitions from one song to another when they are playing records at a dance club. Hip hop DJs and turntablists use the DJ mixer to play record players like a musical instrument and create new sounds. DJs in the disco, house music, electronic dance music and other dance-oriented genres use the mixer to make smooth transitions between different sound recordings as they are playing. The sources are typically record turntables, compact cassettes, CDJs, or DJ software on a laptop. DJ mixers allow the DJ to use headphones to preview the next song before playing it to the audience. Most low- to mid-priced DJ mixers can only accommodate two turntables or CD players, but some mixers (such as the ones used in larger nightclubs) can accommodate up to four turntables or CD players. DJs and turntablists in hip hop music and nu metal use DJ mixers to create beats, loops and so-called scratching sound effects.
Description
DJ mixers are usually much smaller than other mixing consoles used in sound reinforcement systems and sound recording. Whereas a typical nightclub mixer will have 24 inputs and a professional recording studio's huge mixer may have 48, 72 or even 96 inputs, a typical DJ mixer may have only two to four inputs. The key feature that differentiates a DJ mixer from other types of larger audio mixers is the ability to redirect (cue) the sounds of a non-playing source to headphones, so the DJ can find the desired part of a song or track.
A crossfader has the same engineering design as fader, in that it is a sliding control, but unlike faders, which are usually vertical, crossfaders are usually horizontal. To understand the function of a crossfader, one can think of the crossfader in three key positions. For a DJ mixer that has two sound sources connected, such as two record turntables, when the crossfader is |
https://en.wikipedia.org/wiki/Hickenia | Hickenia is the name of two genera of flowering plants, both named after Cristóbal María Hicken:
Hickenia Lillo, a genus of Apocynaceae containing one species now reclassified as Morrenia scalae (Hicken) Goyder
Hickenia Britton & Rose, a genus of Cactaceae which included species now classified as Parodia
The second of these, having been published in Britton and Rose's Cactaceae (1922) is an illegitimate homonym of the former, which was published three years earlier in Physis (Buenos Aires) 4: 422. |
https://en.wikipedia.org/wiki/Sim4 | Sim4 is a nucleotide sequence alignment program akin to BLAST but specifically tailored to DNA to cDNA/EST (Expressed Sequence Tag) alignment (as opposed to DNA–DNA or protein–protein alignment). It was written by Florea et al.
External links
A Computer Program for Aligning a cDNA Sequence with a Genomic DNA Sequence
Download
Phylogenetics software |
https://en.wikipedia.org/wiki/Topological%20algebra | In mathematics, a topological algebra is an algebra and at the same time a topological space, where the algebraic and the topological structures are coherent in a specified sense.
Definition
A topological algebra over a topological field is a topological vector space together with a bilinear multiplication
,
that turns into an algebra over and is continuous in some definite sense. Usually the continuity of the multiplication is expressed by one of the following (non-equivalent) requirements:
joint continuity: for each neighbourhood of zero there are neighbourhoods of zero and such that (in other words, this condition means that the multiplication is continuous as a map between topological spaces or
stereotype continuity: for each totally bounded set and for each neighbourhood of zero there is a neighbourhood of zero such that and , or
separate continuity: for each element and for each neighbourhood of zero there is a neighbourhood of zero such that and .
(Certainly, joint continuity implies stereotype continuity, and stereotype continuity implies separate continuity.) In the first case is called a "topological algebra with jointly continuous multiplication", and in the last, "with separately continuous multiplication".
A unital associative topological algebra is (sometimes) called a topological ring.
History
The term was coined by David van Dantzig; it appears in the title of his doctoral dissertation (1931).
Examples
1. Fréchet algebras are examples of associative topological algebras with jointly continuous multiplication.
2. Banach algebras are special cases of Fréchet algebras.
3. Stereotype algebras are examples of associative topological algebras with stereotype continuous multiplication.
Notes
External links |
https://en.wikipedia.org/wiki/Rub%20el%20Hizb | The Rub-el-Hizb (, ) is an Islamic symbol in the shape of an octagram, represented as two overlapping squares. It has been found on a number of emblems and flags. The main purpose of this dividing system is to facilitate the recitation of the Quran.
Etymology
In Arabic, rubʻ means "one-fourth" or "quarter," while ḥizb (plural aḥzāb) translates to "a group." Initially, it was used in the Quran, which is divided into 60 aḥzāb (groups of roughly equal length); Rubʿ el Hizb further divides each ḥizb into four. A ḥizb is one half of a juz'. In total, there are thus 240 divisions.
History
It was the symbol with which the Tartessos, since remote Neolithic times, made offerings to the Sun and represented it with eight rays.
Later, with Al-Andalus in the Iberian Peninsula, he already defined it as a cultural symbol, coining it in the first coins. In addition, the use of it in so many areas led to its name being changed to the star of Abd al-Rahman I. From al Al-Andalus it was exported to the rest of the Arab culture.
It has been used extensively in Turkic Islamic culture and history.
The symbol in question, consisting of two concentric circles with a defined punctual center, connected by eight radial sectors, is similar to the Islamic symbol when the two lines of the East-West orientation are combined, thus resulting in a hexagon with a circular symmetry.
Contemporary use
Former flags
The first country to use the Rubʾ el-Hizb was the Marinid Sultanate in 1258.
Current flags
Emblems
Variants
See also
Sujud |
https://en.wikipedia.org/wiki/Data%20farming | Data farming is the process of using designed computational experiments to “grow” data, which can then be analyzed using statistical and visualization techniques to obtain insight into complex systems. These methods can be applied to any computational model.
Data farming differs from Data mining, as the following metaphors indicate:
Miners seek valuable nuggets of ore buried in the earth, but have no control over what is out there or how hard it is to extract the nuggets from their surroundings. ... Similarly, data miners seek to uncover valuable nuggets of information buried within massive amounts of data. Data-mining techniques use statistical and graphical measures to try to identify interesting correlations or clusters in the data set.
Farmers cultivate the land to maximize their yield. They manipulate the environment to their advantage using irrigation, pest control, crop rotation, fertilizer, and more. Small-scale designed experiments let them determine whether these treatments are effective. Similarly, data farmers manipulate simulation models to their advantage, using large-scale designed experimentation to grow data from their models in a manner that easily lets them extract useful information. ...the results can reveal root cause-and-effect relationships between the model input factors and the model responses, in addition to rich graphical and statistical views of these relationships.
A NATO modeling and simulation task group has documented the data farming process in the Final Report of MSG-088.
Here, data farming uses collaborative processes in combining rapid scenario prototyping, simulation modeling, design of experiments, high performance computing, and analysis and visualization in an iterative loop-of-loops .
History
The science of Design of Experiments (DOE) has been around for over a century, pioneered by R.A. Fisher for agricultural studies. Many of the classic experiment designs can be used in simulation studies. However, computation |
https://en.wikipedia.org/wiki/Large%20gauge%20transformation | Given a topological space M, a topological group G and a principal G-bundle over M, a global section of that principal bundle is a gauge fixing and the process of replacing one section by another is a gauge transformation. If a gauge transformation isn't homotopic to the identity, it is called a large gauge transformation.
In theoretical physics, M often is a manifold and G is a Lie group.
See also
Large diffeomorphism
Global anomaly
Gauge theories
Anomalies (physics) |
https://en.wikipedia.org/wiki/Ground%20bounce | In electronic engineering, ground bounce is a phenomenon associated with transistor switching where the gate voltage can appear to be less than the local ground potential, causing the unstable operation of a logic gate.
Description
Ground bounce is usually seen on high density VLSI where insufficient precautions have been taken to supply a logic gate with a sufficiently low impedance connection (or sufficiently high capacitance) to ground. In this phenomenon, when the base of an NPN transistor is turned on, enough current flows through the emitter-collector circuit that the silicon in the immediate vicinity of the emitter-ground connection is pulled partially high, sometimes by several volts, thus raising the local ground, as perceived at the gate, to a value significantly above true ground. Relative to this local ground, the base voltage can go negative, thus shutting off the transistor. As the excess local charge dissipates, the transistor turns back on, possibly causing a repeat of the phenomenon, sometimes up to a half-dozen bounces.
Ground bounce is one of the leading causes of "hung" or metastable gates in modern digital circuit design. This happens because the ground bounce puts the input of a flip flop effectively at voltage level that is neither a one nor a zero at clock time, or causes untoward effects in the clock itself. A similar voltage sag phenomenon may be seen on the collector side, called supply voltage sag (or VCC sag), where VCC is pulled unnaturally low. As a whole, ground bounce is a major issue in nanometer range technologies in VLSI.
Ground bounce can also occur when the circuit board has poorly designed ground paths. Improper ground or VCC can lead to local variations in the ground level between various components. This is most commonly seen in circuit boards that have ground and VCC paths on the surfaces of the board.
Reduction
Ground bounce may be reduced by placing a 10–30-ohm resistor in series to each of the switching outputs |
https://en.wikipedia.org/wiki/Starlink%20Project | The Starlink Project, referred to by users as Starlink and by developers as simply The Project, was a UK astronomical computing project which supplied general-purpose data reduction software. Until the late 1990s, it also supplied computing hardware and system administration personnel to UK astronomical institutes. In the former respect, it was analogous to the US IRAF project.
The project was formally started in 1980, though the funding had been agreed, and some work begun, a year earlier. It was closed down when its funding was withdrawn by the Particle Physics and Astronomy Research Council in 2005. In 2006, the Joint Astronomy Centre released its own updated version of Starlink and took over maintenance; the task was passed again in mid-2015 to the East Asian Observatory. The latest version was released on 2018 July 19.
Part of the software is relicensed under the GNU GPL while some of it remain under the original custom licence.
History
From its beginning, the project aimed to cope with the ever-increasing data volumes which astronomers had to handle. A 1982 paper exclaimed that astronomers were returning from observing runs (a week or so of observations at a remote telescope) with more than 10 Gigabits of data on tape; at the end of its life the project was rolling out libraries to handle data of more than 4 Gigabytes per single image.
The project provided centrally-purchased (and thus discounted) hardware, professional system administrators, and the developers to write astronomical data-reduction applications for the UK astronomy community and beyond. At its peak size in the late 1980s and early 1990s, the project had a presence at around 30 sites, located at most of the UK universities with an astronomy department, plus facilities at the Joint Astronomy Centre, the home of UKIRT and the James Clerk Maxwell Telescope in Hawaii. The number of active developers fluctuated between five and more than a dozen.
By 1982, the project had a staff of 17, servin |
https://en.wikipedia.org/wiki/DRTE%20Computer | The DRTE Computer was a transistorized computer built at the Defence Research Telecommunications Establishment (DRTE), part of the Canadian Defence Research Board. It was one of the earlier fully transistorized machines, running in prototype form in 1957, and fully developed form in 1960. Although the performance was quite good, equal to that of contemporary machines like the PDP-1, no commercial vendors ever took up the design, and the only potential sale to the Canadian Navy's Pacific Naval Laboratories, fell through. The machine is currently part of the Canadian national science and technology collection housed at the Canada Science and Technology Museum.
Transistor research
In the early 1950s transistors had not yet replaced vacuum tubes in most electronics. Tubes varied widely in their actual characteristics from tube to tube even of the same model. Engineers had developed techniques to ensure that the overall circuit was not overly sensitive to these changes so they could be replaced without causing trouble. The same techniques had not yet been developed for transistor-based systems, they were simply too new. While smaller circuits could be "hand tuned" to work, larger systems using many transistors were not well understood. At the same time transistors were still expensive; a tube cost about $0.75 while a similar transistor cost about $8. This limited the amount of experimentation most companies were able to perform.
DRTE was originally formed to improve communications systems, and to this end, they started a research program into using transistors in complex circuits in a new Electronics Lab under the direction of Norman Moody. Between 1950 and 1960, the Electronics Lab became a major center of excellence in the field of transistors, and through an outreach program, the Electronic Component Research and Development Committee, were able to pass on their knowledge to visiting engineers from major Canadian electronics firms who were entering the transistor fi |
https://en.wikipedia.org/wiki/Agnes%20Pockels | Agnes Luise Wilhelmine Pockels (14 February 1862 – 21 November 1935) was a German chemist whose research was fundamental in establishing the modern discipline known as surface science, which describes the properties of liquid and solid surfaces and interfaces.
Pockels became interested in fundamental research in surface science through observations of soaps and soapy water in her own home while washing dishes. She devised a surface film balance technique to study the behavior of molecules such as soaps and surfactants at air-liquid interfaces. From these studies, Pockels defined the "Pockels Point" which is the minimum area that a single molecule can occupy in monomolecular films.
Pockels was an autodidact. She was not a paid, professional scientist and had no institutional affiliation and so is an example of a citizen scientist.
Early life and education
Pockels was born in Venice, Austrian Empire, in 1862. At the time, Venice was under Austrian rule, and Pockels' father served in the Austrian Army. When he fell sick, the family moved in 1871 to Brunswick, which was part of the nascent German Empire. There, Pockels attended the Municipal High School for Girls. Agnes was interested in chemistry as a child. However, women were not allowed to enter universities to study. Pockels stated that "I had a passionate interest in natural science, especially physics, and would have liked to study.“ (Agnes Pockels, as translated by Giles from Autobiographical Notes in W. Ostwald, 1932.)
As a child, Pockels was interested in science, especially physics. In those days, women in Germany had no access to universities. Pockels studied science at home while caring for her parents. Pockels' younger brother Friedrich Carl Alwin Pockels studied physics at the University of Göttingen, completing his degree there. Friedrich shared textbooks from the university with Agnes Pockels in order to help her study from home. He later shared academic literature with Agnes Pockels to advance her |
https://en.wikipedia.org/wiki/Red%20clump | The red clump is a clustering of red giants in the Hertzsprung–Russell diagram at around 5,000 K and absolute magnitude (MV) +0.5, slightly hotter than most red-giant-branch stars of the same luminosity. It is visible as a denser region of the red-giant branch or a bulge towards hotter temperatures. It is prominent in many galactic open clusters, and it is also noticeable in many intermediate-age globular clusters and in nearby field stars (e.g. the Hipparcos stars).
The red clump giants are cool horizontal branch stars, stars originally similar to the Sun which have undergone a helium flash and are now fusing helium in their cores.
Properties
Red clump stellar properties vary depending on their origin, most notably on the metallicity of the stars, but typically they have early K spectral types and effective temperatures around 5,000 K. The absolute visual magnitude of red clump giants near the sun has been measured at an average of +0.81 with metallicities between −0.6 and +0.4 dex.
There is a considerable spread in the properties of red clump stars even within a single population of similar stars such as an open cluster. This is partly due to the natural variation in temperatures and luminosities of horizontal branch stars when they form and as they evolve, and partly due to the presence of other stars with similar properties. Although red clump stars are generally hotter than red-giant-branch stars, the two regions overlap and the status of individual stars can only be assigned with a detailed chemical abundance study.
Evolution
Modelling of the horizontal branch has shown that stars have a strong tendency to cluster at the cool end of the zero age horizontal branch (ZAHB). This tendency is weaker in low metallicity stars, so the red clump is usually more prominent in metal-rich clusters. However, there are other effects, and there are well-populated red clumps in some metal-poor globular clusters.
Stars with a similar mass to the sun evolve towards |
https://en.wikipedia.org/wiki/Static%20library | In computer science, a static library or statically-linked library is a set of routines, external functions and variables which are resolved in a caller at compile-time and copied into a target application by a compiler, linker, or binder, producing an object file and a stand-alone executable. This executable and the process of compiling it are both known as a static build of the program. Historically, libraries could only be static. Static libraries are either merged with other static libraries and object files during building/linking to form a single executable or loaded at run-time into the address space of their corresponding executable at a static memory offset determined at compile-time/link-time.
Advantages and disadvantages
There are several advantages to statically linking libraries with an executable instead of dynamically linking them. The most significant advantage is that the application can be certain that all its libraries are present and that they are the correct version. This avoids dependency problems, known colloquially as DLL Hell or more generally dependency hell. Static linking can also allow the application to be contained in a single executable file, simplifying distribution and installation.
With static linking, it is enough to include those parts of the library that are directly and indirectly referenced by the target executable (or target library). With dynamic libraries, the entire library is loaded, as it is not known in advance which functions will be invoked by applications. Whether this advantage is significant in practice depends on the structure of the library.
In static linking, the size of the executable becomes greater than in dynamic linking, as the library code is stored within the executable rather than in separate files. But if library files are counted as part of the application then the total size will be similar, or even smaller if the compiler eliminates the unused symbols.
Environment specific
On Microsoft Windows |
https://en.wikipedia.org/wiki/Dielectric%20reluctance | Dielectric reluctance is a scalar measurement of a passive dielectric circuit (or element within that circuit) dependent on voltage and electric induction flux, and this is determined by deriving the ratio of their amplitudes. The units of dielectric reluctance are F−1 (inverse farads—see daraf) [Ref. 1-3].
As seen above, dielectric reluctance is represented as lowercase z epsilon.
For a dielectric in a dielectric circuit to have no energy losses, the imaginary part of its dielectric reluctance is zero. This constitutes a lossless "resistance" to electric induction flux, and is therefore real, not complex. This formality is similar to Ohm's Law for a resistive circuit. In dielectric circuits, a dielectric material has a "lossless" dielectric reluctance equal to:
Where:
is the circuit length
is the cross-section of the circuit element
is the dielectric permeability
See also
Dielectric
Dielectric complex reluctance — General definition of dielectric reluctance that accounts for energy loss |
https://en.wikipedia.org/wiki/Topological%20quantum%20number | In physics, a topological quantum number (also called topological charge) is any quantity, in a physical theory, that takes on only one of a discrete set of values, due to topological considerations. Most commonly, topological quantum numbers are topological invariants associated with topological defects or soliton-type solutions of some set of differential equations modeling a physical system, as the solitons themselves owe their stability to topological considerations. The specific "topological considerations" are usually due to the appearance of the fundamental group or a higher-dimensional homotopy group in the description of the problem, quite often because the boundary, on which the boundary conditions are specified, has a non-trivial homotopy group that is preserved by the differential equations. The topological quantum number of a solution is sometimes called the winding number of the solution, or, more precisely, it is the degree of a continuous mapping.
Recent ideas about the nature of phase transitions indicates that topological quantum numbers, and their associated solutions, can be created or destroyed during a phase transition.
Particle physics
In particle physics, an example is given by the Skyrmion, for which the baryon number is a topological quantum number. The origin comes from the fact that the isospin is modelled by SU(2), which is isomorphic to the 3-sphere and inherits the group structure of SU(2) through its bijective association, so the isomorphism is in the category of topological groups. By taking real three-dimensional space, and closing it with a point at infinity, one also gets a 3-sphere. Solutions to Skyrme's equations in real three-dimensional space map a point in "real" (physical; Euclidean) space to a point on the 3-manifold SU(2). Topologically distinct solutions "wrap" the one sphere around the other, such that one solution, no matter how it is deformed, cannot be "unwrapped" without creating a discontinuity in the solution. |
https://en.wikipedia.org/wiki/Magnetic%20reluctance | Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux, and depends on the geometry and composition of an object.
Magnetic reluctance in a magnetic circuit is analogous to electrical resistance in an electrical circuit in that resistance is a measure of the opposition to the electric current. The definition of magnetic reluctance is analogous to Ohm's law in this respect. However, magnetic flux passing through a reluctance does not give rise to dissipation of heat as it does for current through a resistance. Thus, the analogy cannot be used for modelling energy flow in systems where energy crosses between the magnetic and electrical domains. An alternative analogy to the reluctance model which does correctly represent energy flows is the gyrator–capacitor model.
Magnetic reluctance is a scalar extensive quantity. The unit for magnetic reluctance is inverse henry, H−1.
History
The term reluctance was coined in May 1888 by Oliver Heaviside. The notion of "magnetic resistance" was first mentioned by James Joule in 1840. The idea for a magnetic flux law, similar to Ohm's law for closed electric circuits, is attributed to Henry Augustus Rowland in an 1873 paper. Rowland is also responsible for coining the term magnetomotive force in 1880, also coined, apparently independently, a bit later in 1883 by Bosanquet.
Reluctance is usually represented by a cursive capital .
Definitions
In both AC and DC fields, the reluctance is the ratio of the magnetomotive force (MMF) in a magnetic circuit to the magnetic flux in this circuit. In a pulsating DC or AC field, the reluctance also pulsates (see phasors).
The definition can be expressed as follows:
where
("R") is the reluctance in ampere-turns per weber (a unit that is equivalent to turns per henry). "Turns" refers to the winding number of an electric |
https://en.wikipedia.org/wiki/Pascal%20Lee | Pascal Lee (; born 1964) is co-founder and chairman of the Mars Institute, a planetary scientist at the SETI Institute, and the Principal Investigator of the Haughton-Mars Project (HMP) at NASA Ames Research Center in Mountain View, California. He holds an ME in geology and geophysics from the University of Paris, and a PhD in astronomy and space sciences from Cornell University.
Lee's research focuses on Mars, asteroids, and impact craters, in particular in connection with the history of water on planets and the possibility of extraterrestrial life. He is known internationally for his work on Moon and Mars analogs in the Arctic, Antarctica, and other extreme environments on Earth. He is the author and co-author of over 100 scientific publications, and first proposed the "Mars Always Cold, Sometimes Wet" model of Mars evolution based on field studies of the geology of Earth's polar regions.
In 1988, Lee wintered over for 402 days at Dumont d'Urville station, Adelie Land, Antarctica, where he served as the station's chief geophysicist. He also participated in five summer campaigns in Antarctica as a geologist and planetary scientist, in particular as a member of the US Antarctic Search for Meteorites (ANSMET) program.
In 1997, Lee initiated the Haughton-Mars Project (HMP), an international multidisciplinary field research project centered on science and exploration studies at the Haughton impact crater and surrounding terrain on Devon Island, Arctic Canada, viewed as an analog site for the Moon and Mars. Lee has led over 18 HMP field expeditions to date, including the "Northwest Passage Drive Expedition" in April 2009 and May 2010, and continues to serve as the HMP's Director in support of research for NASA and the Canadian Space Agency.
Pascal Lee is widely recognized for his efforts to advance the human exploration of Mars, in particular via its asteroid-like moons Phobos and Deimos.
Lee is a recipient of the United States Antarctic Service Medal and the Space |
https://en.wikipedia.org/wiki/Morse%E2%80%93Kelley%20set%20theory | In the foundations of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine and Morse is a first-order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays–Gödel set theory restricts the bound variables in the schematic formula appearing in the axiom schema of Class Comprehension to range over sets alone, Morse–Kelley set theory allows these bound variables to range over proper classes as well as sets, as first suggested by Quine in 1940 for his system ML.
Morse–Kelley set theory is named after mathematicians John L. Kelley and Anthony Morse and was first set out by and later in an appendix to Kelley's textbook General Topology (1955), a graduate level introduction to topology. Kelley said the system in his book was a variant of the systems due to Thoralf Skolem and Morse. Morse's own version appeared later in his book A Theory of Sets (1965).
While von Neumann–Bernays–Gödel set theory is a conservative extension of Zermelo–Fraenkel set theory (ZFC, the canonical set theory) in the sense that a statement in the language of ZFC is provable in NBG if and only if it is provable in ZFC, Morse–Kelley set theory is a proper extension of ZFC. Unlike von Neumann–Bernays–Gödel set theory, where the axiom schema of Class Comprehension can be replaced with finitely many of its instances, Morse–Kelley set theory cannot be finitely axiomatized.
MK axioms and ontology
NBG and MK share a common ontology. The universe of discourse consists of classes. Classes that are members of other classes are called sets. A class that is not a set is a proper class. The primitive atomic sentences involve membership or equality.
With the exception of Class Comprehension, the following axioms are the same as those for NBG, inessential details aside. The symbolic versions of the axioms employ the following notational devices:
Th |
https://en.wikipedia.org/wiki/Operating%20system%20abstraction%20layer | An operating system abstraction layer (OSAL) provides an application programming interface (API) to an abstract operating system making it easier and quicker to develop code for multiple software or hardware platforms.
OS abstraction layers deal with presenting an abstraction of the common system functionality that is offered by any Operating system by the means of providing meaningful and easy to use Wrapper functions that in turn encapsulate the system functions offered by the OS to which the code needs porting. A well designed OSAL provides implementations of an API for several real-time operating systems (such as vxWorks, eCos, RTLinux, RTEMS). Implementations may also be provided for non real-time operating systems, allowing the abstracted software to be developed and tested in a developer friendly desktop environment.
In addition to the OS APIs, the OS Abstraction Layer project may also provide a hardware abstraction layer, designed to provide a portable interface to hardware devices such as memory, I/O ports, and non-volatile memory. To facilitate the use of these APIs, OSALs generally include a directory structure and build automation (e.g., set of makefiles) to facilitate building a project for a particular OS and hardware platform.
Implementing projects using OSALs allows for development of portable embedded system software that is independent of a particular real-time operating system. It also allows for embedded system software to be developed and tested on desktop workstations, providing a shorter development and debug time.
Implementations
TnFOX
MapuSoft Technologies - provides a commercial OS Abstraction implementation allowing software to support multiple RTOS operating systems.
ClarinoxSoftFrame – middleware which provides OS abstraction targeting wireless embedded device and system development. It comprises wireless protocol stacks, development tools and memory management techniques in addition to the support of desktop and a range of r |
https://en.wikipedia.org/wiki/Point%20groups%20in%20three%20dimensions | In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of all isometries.
Symmetry groups of geometric objects are isometry groups. Accordingly, analysis of isometry groups is analysis of possible symmetries. All isometries of a bounded (finite) 3D object have one or more common fixed points. We follow the usual convention by choosing the origin as one of them.
The symmetry group of an object is sometimes also called its full symmetry group, as opposed to its proper symmetry group, the intersection of its full symmetry group with E+(3), which consists of all direct isometries, i.e., isometries preserving orientation. For a bounded object, the proper symmetry group is called its rotation group. It is the intersection of its full symmetry group with SO(3), the full rotation group of the 3D space. The rotation group of a bounded object is equal to its full symmetry group if and only if the object is chiral.
The point groups that are generated purely by a finite set of reflection mirror planes passing through the same point are the finite Coxeter groups, represented by Coxeter notation.
The point groups in three dimensions are heavily used in chemistry, especially to describe the symmetries of a molecule and of molecular orbitals forming covalent bonds, and in this context they are also called molecular point groups.
3D isometries that leave origin fixed
The symmetry group operations (symmetry operations) are the isometries of three-dimensional space R3 that leave the origin fixed, forming the group O(3). These operations can be categorized as:
The direct (orientation-preserving) symmetry operations, which form the group SO(3):
The identity op |
https://en.wikipedia.org/wiki/International%20Association%20for%20Plant%20Taxonomy | The International Association for Plant Taxonomy (IAPT) is an organization established to promote an understanding of plant biodiversity, facilitate international communication of research between botanists, and oversee matters of uniformity and stability in plant names. The IAPT was founded on July 18, 1950, at the Seventh International Botanical Congress in Stockholm, Sweden. The IAPT headquarters is located in Bratislava, Slovakia. Its president, since 2017, is Patrick S. Herendeen of the Chicago Botanic Garden; vice-president is Gonzalo Nieto Feliner of the Real Jardín Botánico, Madrid; and secretary-general is Karol Marhold of the Plant Science and Biodiversity Centre, Slovak Academy of Sciences, Bratislava.
Both the taxonomic journal Taxon and the series Regnum Vegetabile are published by the IAPT. The latter series includes the International Code of Nomenclature for algae, fungi, and plants, Index Nominum Genericorum, and Index Herbariorum.
Purpose
The IAPT's primary purpose is the promotion and understanding of biodiversity—the discovery, naming, classification, and systematics of plants—for both living and fossil plants. Additionally, it promotes the study and conservation of plant biodiversity, and works to raise awareness of the general public to this issue. The organization also facilitates international cooperation among botanists working in the fields of plant systematics, taxonomy, and nomenclature. This is accomplished in part through sponsorship of meetings and publication of resources, such as reference publications and journals.
The IAPT also seeks to achieve uniformity and stability in plant names. It accomplishes this through the International Code of Nomenclature for algae, fungi, and plants, previously known as the International Code of Botanical Nomenclature, and through the oversight of the International Bureau for Plant Taxonomy and Nomenclature.
Publications and online resources
The association's official journal is Taxon, the only me |
https://en.wikipedia.org/wiki/Truth-table%20reduction | In computability theory, a truth-table reduction is a reduction from one set of natural numbers to another.
As a "tool", it is weaker than Turing reduction, since not every Turing reduction between sets can be performed by a truth-table reduction, but every truth-table reduction can be performed by a Turing reduction. For the same reason it is said to be a stronger reducibility than Turing reducibility, because it implies Turing reducibility. A weak truth-table reduction is a related type of reduction which is so named because it weakens the constraints placed on a truth-table reduction, and provides a weaker equivalence classification; as such, a "weak truth-table reduction" can actually be more powerful than a truth-table reduction as a "tool", and perform a reduction which is not performable by truth table.
A Turing reduction from a set B to a set A computes the membership of a single element in B by asking questions about the membership of various elements in A during the computation; it may adaptively determine which questions it asks based upon answers to previous questions. In contrast, a truth-table reduction or a weak truth-table reduction must present all of its (finitely many) oracle queries at the same time. In a truth-table reduction, the reduction also gives a boolean function (a truth table) which, when given the answers to the queries, will produce the final answer of the reduction. In a weak truth-table reduction, the reduction uses the oracle answers as a basis for further computation which may depend on the given answers but may not ask further questions of the oracle.
Equivalently, a weak truth-table reduction is a Turing reduction for which the use of the reduction is bounded by a computable function. For this reason, they are sometimes referred to as bounded Turing (bT) reductions rather than as weak truth-table (wtt) reductions.
Properties
As every truth-table reduction is a Turing reduction, if A is truth-table reducible to B (A ≤tt B), |
https://en.wikipedia.org/wiki/Superconformal%20algebra | In theoretical physics, the superconformal algebra is a graded Lie algebra or superalgebra that combines the conformal algebra and supersymmetry. In two dimensions, the superconformal algebra is infinite-dimensional. In higher dimensions, superconformal algebras are finite-dimensional and generate the superconformal group (in two Euclidean dimensions, the Lie superalgebra does not generate any Lie supergroup).
Superconformal algebra in dimension greater than 2
The conformal group of the -dimensional space is and its Lie algebra is . The superconformal algebra is a Lie superalgebra containing the bosonic factor and whose odd generators transform in spinor representations of . Given Kac's classification of finite-dimensional simple Lie superalgebras, this can only happen for small values of and . A (possibly incomplete) list is
in 3+0D thanks to ;
in 2+1D thanks to ;
in 4+0D thanks to ;
in 3+1D thanks to ;
in 2+2D thanks to ;
real forms of in five dimensions
in 5+1D, thanks to the fact that spinor and fundamental representations of are mapped to each other by outer automorphisms.
Superconformal algebra in 3+1D
According to the superconformal algebra with supersymmetries in 3+1 dimensions is given by the bosonic generators , , , , the U(1) R-symmetry , the SU(N) R-symmetry and the fermionic generators , , and . Here, denote spacetime indices; left-handed Weyl spinor indices; right-handed Weyl spinor indices; and the internal R-symmetry indices.
The Lie superbrackets of the bosonic conformal algebra are given by
where η is the Minkowski metric; while the ones for the fermionic generators are:
The bosonic conformal generators do not carry any R-charges, as they commute with the R-symmetry generators:
But the fermionic generators do carry R-charge:
Under bosonic conformal transformations, the fermionic generators transform as:
Superconformal algebra in 2D
There are two possible algebras with minimal supersymmetry in two dimensio |
https://en.wikipedia.org/wiki/Virtual%20museum | A virtual museum is a digital entity that draws on the characteristics of a museum, in order to complement, enhance, or augment the museum experience through personalization, interactivity, and richness of content. Virtual museums can perform as the digital footprint of a physical museum, or can act independently, while maintaining the authoritative status as bestowed by the International Council of Museums (ICOM) in its definition of a museum. In tandem with the ICOM mission of a physical museum, the virtual museum is also committed to public access; to both the knowledge systems embedded in the collections and the systematic, and coherent organization of their display, as well as to their long-term preservation.
As with a traditional museum, a virtual museum can be designed around specific objects (such as an art museum or a natural history museum), or can consist of online exhibitions created from primary or secondary resources (as, for example in a science museum). Moreover, a virtual museum can refer to the mobile or World Wide Web offerings of traditional museums (e.g., displaying digital representations of its collections or exhibits); or can be born digital content such as, 3D environments, net art, virtual reality and digital art. Often, discussed in conjunction with other cultural institutions, a museum by definition, is essentially separate from its sister institutions such as a library or an archive. Virtual museums are usually, but not exclusively delivered electronically when they are denoted as online museums, hypermuseum, digital museum, cybermuseums or web museums.
Off-line pioneers (CD-ROM and digital media before 2000)
The following museums were created with digital technology before the web gained any form of popularity or mass usability. CD-ROM and postal mail distribution made these museums available world-wide, before web browsers, fast connections and ubiquitous web usage.
The Australian new media artist Jeffrey Shaw created the world’s |
https://en.wikipedia.org/wiki/Hagedorn%20temperature | The Hagedorn temperature, TH, is the temperature in theoretical physics where hadronic matter (i.e. ordinary matter) is no longer stable, and must either "evaporate" or convert into quark matter; as such, it can be thought of as the "boiling point" of hadronic matter. It was discovered by Rolf Hagedorn. The Hagedorn temperature exists because the amount of energy available is high enough that matter particle (quark–antiquark) pairs can be spontaneously pulled from vacuum. Thus, naively considered, a system at Hagedorn temperature can accommodate as much energy as one can put in, because the formed quarks provide new degrees of freedom, and thus the Hagedorn temperature would be an impassable absolute hot. However, if this phase is viewed as quarks instead, it becomes apparent that the matter has transformed into quark matter, which can be further heated.
The Hagedorn temperature, TH, is about or about , little above the mass–energy of the lightest hadrons, the pion. Matter at Hagedorn temperature or above will spew out fireballs of new particles, which can again produce new fireballs, and the ejected particles can then be detected by particle detectors. This quark matter has been detected in heavy-ion collisions at SPS and LHC in CERN (France and Switzerland) and at RHIC in Brookhaven National Laboratory (USA).
In string theory, a separate Hagedorn temperature can be defined for strings rather than hadrons. This temperature is extremely high (1030 K) and thus of mainly theoretical interest.
History
The Hagedorn temperature was discovered by German physicist Rolf Hagedorn in the 1960s while working at CERN. His work on the statistical bootstrap model of hadron production showed that because increases in energy in a system will cause new particles to be produced, an increase of collision energy will increase the entropy of the system rather than the temperature, and "the temperature becomes stuck at a limiting value".
Technical explanation
Hagedorn temperature |
https://en.wikipedia.org/wiki/Weinberg%E2%80%93Witten%20theorem | In theoretical physics, the Weinberg–Witten (WW) theorem, proved by Steven Weinberg and Edward Witten, states that massless particles (either composite or elementary) with spin j > 1/2 cannot carry a
Lorentz-covariant current, while massless particles with spin j > 1 cannot carry a Lorentz-covariant stress-energy. The theorem is usually interpreted to mean that the graviton (j = 2) cannot be a composite particle in a relativistic quantum field theory.
Background
During the 1980s, preon theories, technicolor and the like were very popular and some people speculated that gravity might be an emergent phenomenon or that gluons might be composite. Weinberg and Witten, on the other hand, developed a no-go theorem that excludes, under very general assumptions, the hypothetical composite and emergent theories. Decades later new theories of emergent gravity are proposed and some high-energy physicists are still using this theorem to try and refute such theories. Because most of these emergent theories aren't Lorentz covariant, the WW theorem doesn't apply. The violation of Lorentz covariance, however, usually leads to other problems.
Theorem
Weinberg and Witten proved two separate results. According to them, the first is due to Sidney Coleman, who did not publish it:
A 3 + 1D QFT (quantum field theory) with a conserved 4-vector current (see four-current) which is Poincaré covariant (and gauge invariant if there happens to be any gauge symmetry which hasn't been gauge-fixed) does not admit massless particles with helicity |h| > 1/2 that also have nonzero charges associated with the conserved current in question.
A 3 + 1D QFT with a non-zero conserved stress–energy tensor which is Poincaré covariant (and gauge invariant if there happens to be any gauge symmetry which hasn't been gauge-fixed) does not admit massless particles with helicity |h| > 1.
A sketch of the proof
The conserved charge Q is given by . We shall consider the matrix elements of the charge and o |
https://en.wikipedia.org/wiki/Rational%20conformal%20field%20theory | In theoretical physics, a rational conformal field theory is a special type of two-dimensional conformal field theory with a finite number of conformal primaries. In these theories, all dimensions (and the central charge) are rational numbers that can be computed from the consistency conditions of conformal field theory. The most famous examples are the so-called minimal models.
More generally, rational conformal field theory can refer to any CFT with a finite number of primary operators with respect to the action of its chiral algebra. Chiral algebras can be much larger than the Virasoro algebra. Well-known examples include (the enveloping algebra of) affine Lie algebras, relevant to the Wess–Zumino–Witten model, and W-algebras.
Conformal field theory |
https://en.wikipedia.org/wiki/Bank%20Panic | is an arcade shooter game developed by Sanritsu Denki and released by Sega in 1984. Bally-Midway manufactured the game in the US. The player assumes the part of an Old West sheriff who must protect a bank and its customers from masked robbers.
Gameplay
Controls consist of a two-position joystick and three buttons to fire at the left, center, and right positions.
The layout of the bank is implicitly a circle with twelve numbered doors and the player in the center. The player can rotate to the left or right using the joystick, viewing three doors at a time, and shoot at a door by pressing the button corresponding to its position on the screen. The doors will open to reveal one of the following:
A customer, who will make a deposit by dropping a bag of money onto the counter.
A robber, who will attempt to shoot the player.
A young boy wearing a stack of hats, which the player can rapidly shoot to gain a deposit or bonus time.
The level ends once every door has received at least one deposit. If a customer makes a deposit at a door where a bank teller is sitting, the player earns bonus points.
The status of each door is indicated by a row of numbered boxes across the top of the screen, with a red dollar sign representing a door with a completed deposit. A bar gauge above each box shows how close a person is to reaching that door. The disappearance of a dollar sign indicates that a robber has just stolen a deposit; the player must then turn to that door and shoot the robber to recover it.
At random intervals, a bomb will be placed on one of the doors and a rapid timer will count down from 99. The player must move to that door and destroy the bomb with gunfire. Shooting a customer, being shot by a robber, failing to destroy a bomb, or failing to complete the level before the overall timer runs out (shown by a bar at the bottom of the screen) costs the player one life.
Some robbers will wear white boots; these robbers need to be shot twice to be eliminated. At tim |
https://en.wikipedia.org/wiki/Collaborative%20product%20development | Collaborative product development (collaborative product design) (CPD) is a business strategy, work process and collection of software applications that facilitates different organizations to work together on the development of a product. It is also known as collaborative product definition management (cPDM).
Introduction
Collaborative Product Development helps individual users and companies manage, share and view your CAD projects without the cost and complexity of purchasing an entire PDM or PLM solution. CPD comes in the form of a Software as a service delivery model, which allows for rapid iterations and little or no downloads and installs.
Exactly what technology comes under this title does vary depending on whom one asks; however, it usually consists of the Product Lifecycle Management (PLM) areas of: Product Data Management (PDM); Product visualization; team collaboration and conferencing tools; and supplier sourcing software. It is generally accepted as not including CAD geometry tools, but does include data translation technology.
Technologies and methods used
Clearly general collaborative software such as email and chat (instant messaging) is used within the CPD process. One important technology is application and desktop sharing, allowing one person to view what another person is doing on a remote machine. For CAD and product visualization applications an ‘appshare’ product that supports OpenGL graphics is required. Another common application is Data sharing via Web based portals.
Specific to product data
With product data an important addition is the handling of high volumes of geometry and metadata. Exactly what techniques and technology is required depends on the level of collaboration being carried out and the commonality (or lack thereof) of the partner sites’ systems.
Specific to PLM and CAx collaboration
Collaboration using PLM and CAx tools requires technology to support the needs of:
People. Personnel of different disciplines and skill |
https://en.wikipedia.org/wiki/Browser%20sniffing | Browser sniffing (also known as browser detection) is a set of techniques used in websites and web applications in order to determine the web browser a visitor is using, and to serve browser-appropriate content to the visitor. It is also used to detect mobile browsers and send them mobile-optimized websites. This practice is sometimes used to circumvent incompatibilities between browsers due to misinterpretation of HTML, Cascading Style Sheets (CSS), or the Document Object Model (DOM). While the World Wide Web Consortium maintains up-to-date central versions of some of the most important Web standards in the form of recommendations, in practice no software developer has designed a browser which adheres exactly to these standards; implementation of other standards and protocols, such as SVG and XMLHttpRequest, varies as well. As a result, different browsers display the same page differently, and so browser sniffing was developed to detect the web browser in order to help ensure consistent display of content.
Sniffer methods
Client-side sniffing
Web pages can use programming languages such as JavaScript which are interpreted by the user agent, with results sent to the web server. For example:
var isIEBrowser = false;
if (window.ActiveXObject) {
isIEBrowser = true;
}
// Or, shorter:
var isIE = (window.ActiveXObject !== undefined);
This code is run by the client computer, and the results are used by other code to make necessary adjustments on client-side. In this example, the client computer is asked to determine whether the browser can use a feature called ActiveX. Since this feature was proprietary to Microsoft, a positive result will indicate that the client may be running Microsoft's Internet Explorer. This is no longer a reliable indicator since Microsoft's open-source release of the ActiveX code, however, meaning that it can be used by any browser.
Standard Browser detection method
The web server communicates with the client using a communication protoco |
https://en.wikipedia.org/wiki/158%20%28number%29 | 158 (one hundred [and] fifty-eight) is the natural number following 157 and preceding 159.
In mathematics
158 is a nontotient, since there is no integer with 158 coprimes below it. 158 is a Perrin number, appearing after 68, 90, 119.
158 is the number of digits in the decimal expansion of 100!, the product of all the natural numbers up to and including 100.
In the military
was a United States Navy during World War II
was a United States Navy during World War II
was a United States Navy during World War II
was a United States Navy following World War II
was a United States Navy during World War II
was a United States Navy Trefoil-class concrete barge during World War II
was a United States Navy during World War II
was a United States Navy converted yacht patrol vessel during World War I
In music
The song 158 by the Indie-rock band Blackbud
The song "Here We Go" (1998) from The Bouncing Souls’ Tie One On CD includes the lyrics "Me, Shal Pete and Lamar thumbed down the ramp of Exit 158"
In transportation
The Alfa Romeo 158 racecar
The Ferrari 158 racecar produced between 1964 and 1965
The British Rail Class 158 Express Sprinter is a diesel multiple unit (DMU) train, built for British Rail between 1989 and 1992
In other fields
158 is also:
The year AD 158 or 158 BC
One of a number of highways
The atomic number of an element temporarily called unpentoctium.
158 Koronis is a Main belt asteroid
In the Israeli satirical comedy Operation Grandma ("Mivtza Safta", מבצע סבתא), the number 158 is implied to be a classified high-rank officer position (Alon says: "Since you've became 158, you became all that?")
Township 158-30 is a small township in Lake of the Woods County, Minnesota
Edenwold No. 158, Saskatchewan is a rural municipality in Saskatchewan, Canada
John Irving's third novel, The 158-Pound Marriage
Financial Accounting Standards Board summary of statement No. 158 requires an employer to recognize the overfunded or underfunded s |
https://en.wikipedia.org/wiki/PC-MOS/386 | PC-MOS/386 is a multi-user, multitasking computer operating system produced by The Software Link (TSL), announced at COMDEX in November 1986 for February 1987 release. PC-MOS/386, a successor to PC-MOS, can run many MS-DOS programs on the host machine or a terminal connected to it. Unlike MS-DOS, PC-MOS/386 is optimized for the Intel 80386 processor; however early versions will run on any x86 computer. PC-MOS/386 used to be proprietary, but it was released as open-source software in 2017.
History
The last commercial version produced was v5.01, compatible with MS-DOS 5. It required a memory management unit (MMU) to support memory protection, so was not compatible with 8086 and 8088 processors.
MMU support for 286 class machines was provided using a proprietary hardware shim inserted between the processor and its socket. 386 machines did not require any special hardware.
Multi-user operation suffered from the limitations of the day including the inability of the processor to schedule and partition running processes. Typically swapping from a foreground to a background process on the same terminal used the keyboard to generate an interrupt and then swap the processes. The cost of RAM (over US$500/Mb in 1987) and the slow and expensive hard disks of the day limited performance.
PC-MOS terminals could be x86 computers running terminal emulation software communicating at 9600 or 19200 baud, connected via serial cables. However, the greatest benefit was reached when using standard, "dumb" terminals which shared the resources of the then central 386-based processor. Speeds above this required specialized hardware boards which increased cost, but the speed was not a serious limitation for interacting with text-based programs.
PC-MOS also figured prominently in the lawsuit Arizona Retail Systems, Inc. v. The Software Link, Inc., where Arizona Retail Systems claimed The Software Link violated implied warranties on PC-MOS. The case is notable because The Software Link argu |
https://en.wikipedia.org/wiki/Shotgun%20email | Shotgun email refers to an email requesting information or action that only requires the efforts of one person but is sent to multiple people in an effort to guarantee that at least one person will respond. The shotgun email often results in multiple people responding to something already accomplished, and therefore results in a loss of overall productivity. Shotgun emailing is considered poor internet etiquette.
An example would be a person of authority in a business organization sending out an email to five technicians in the information technology department of his company to let them know his printer is broken. One technician responds with an on-site call and fixes the problem. Later in the day, other technicians follow-up to fix the printer that is already back in order. Shotgun emails can also be request for information or other tasks.
The blind shotgun email occurs when the sender uses the blind co-copy feature of an email program to hide the fact that a shotgun email is in use. This is considered particularly deceitful.
Shotgun emails are also considered to be shotgun email marketing, in which companies which is mostly related to sending newsletter information, sometimes supporting missions on helping the poor and such messages like that.
But what is most reported is that scam emails use the method of Shotgun emails, as one must have approached to, such as winning lottery's, getting free trips to countries while you didn't sign up for and many others like that, to get access of what you are doing. |
https://en.wikipedia.org/wiki/Divine%20Proportions%3A%20Rational%20Trigonometry%20to%20Universal%20Geometry | Divine Proportions: Rational Trigonometry to Universal Geometry is a 2005 book by the mathematician Norman J. Wildberger on a proposed alternative approach to Euclidean geometry and trigonometry, called rational trigonometry. The book advocates replacing the usual basic quantities of trigonometry, Euclidean distance and angle measure, by squared distance and the square of the sine of the angle, respectively. This is logically equivalent to the standard development (as the replacement quantities can be expressed in terms of the standard ones and vice versa). The author claims his approach holds some advantages, such as avoiding the need for irrational numbers.
The book was "essentially self-published" by Wildberger through his publishing company Wild Egg. The formulas and theorems in the book are regarded as correct mathematics but the claims about practical or pedagogical superiority are primarily promoted by Wildberger himself and have received mixed reviews.
Overview
The main idea of Divine Proportions is to replace distances by the squared Euclidean distance, which Wildberger calls the quadrance, and to replace angle measures by the squares of their sines, which Wildberger calls the spread between two lines. Divine Proportions defines both of these concepts directly from the Cartesian coordinates of points that determine a line segment or a pair of crossing lines. Defined in this way, they are rational functions of those coordinates, and can be calculated directly without the need to take the square roots or inverse trigonometric functions required when computing distances or angle measures.
For Wildberger, a finitist, this replacement has the purported advantage of avoiding the concepts of limits and actual infinity used in defining the real numbers, which Wildberger claims to be unfounded. It also allows analogous concepts to be extended directly from the rational numbers to other number systems such as finite fields using the same formulas for quadrance |
https://en.wikipedia.org/wiki/Sodium%20croscarmellose | Sodium croscarmellose is an internally cross-linked sodium carboxymethylcellulose for use as a superdisintegrant in pharmaceutical formulations.
E468 is the E number of crosslinked sodium carboxymethyl cellulose, used in food as an emulsifier.
Background
The cross-linking reduces water solubility while still allowing the material to swell (like a sponge) and absorb many times its weight in water. As a result, it provides superior drug dissolution and disintegration characteristics, thus improving formulas′ subsequent bioavailability by bringing the active ingredients into better contact with bodily fluids.
Sodium croscarmellose also resolves formulators′ concerns over long-term functional stability, reduced effectiveness at high tablet hardness levels, and similar problems associated with other products developed to enhance drug dissolution. It is a very commonly used pharmaceutical additive approved by the U.S. Food and Drug Administration. Its purpose in most tablets – including dietary supplements – is to assist the tablet in disintegrating in the gastrointestinal tract promptly. If a tablet disintegrating agent is not included, the tablet could disintegrate too slowly, in the wrong part of the intestine or not at all, thereby reducing the efficacy and bioavailability of the active ingredients.
Croscarmellose is made by first soaking crude cellulose in sodium hydroxide, and then reacting the cellulose with sodium monochloroacetate to form sodium carboxymethylcellulose. Excess sodium monochloroacetate slowly hydrolyzes to glycolic acid and the glycolic acid catalyzes the cross-linkage to form sodium croscarmellose.
Chemically, it is the sodium salt of a cross-linked, partly O-(carboxymethylated) cellulose.
Sodium croscarmellose was first used as a stabilizer in horse supplements. |
https://en.wikipedia.org/wiki/Winlogon | Winlogon (Windows Logon) is the component of Microsoft Windows operating systems that is responsible for handling the secure attention sequence, loading the user profile on logon, creates the desktops for the window station, and optionally locking the computer when a screensaver is running (requiring another authentication step). In Windows Vista and later operating systems, the roles and responsibilities of Winlogon have changed significantly.
Overview
Winlogon is launched by the Session Manager Subsystem as a part of the booting process of Windows NT.
Before Windows Vista, Winlogon was responsible for starting the Service Control Manager and the Local Security Authority Subsystem Service, but since Vista these have been launched by the Windows Startup Application (wininit.exe).
The first part of the logon process Winlogon conducts is starting the process that shows the user the logon screen. Before Windows Vista this was done by GINA, but starting with Vista this is done by LogonUI. These programs are responsible for getting user credential and passing them to the Local Security Authority Subsystem Service, which authenticates the user.
After control is given back to Winlogon, it creates and opens an interactive window station, WinSta0, and creates three desktops, Winlogon, Default and ScreenSaver. Winlogon switches from the Winlogon desktop to the Default desktop when the shell indicates that it is ready to display something for the user, or after thirty seconds, whichever comes first.
The system switches back to the Winlogon desktop if the user presses Control-Alt-Delete or when a User Account Control prompt is shown. Winlogon now starts the program specified in the Userinit value which defaults to userinit.exe. This value supports multiple executables.
Responsibilities
Window station and desktop protection
Winlogon sets the protection of the window station and corresponding desktops to ensure that each is properly accessible. In general, this means t |
https://en.wikipedia.org/wiki/Substring | In formal language theory and computer science, a substring is a contiguous sequence of characters within a string. For instance, "the best of" is a substring of "It was the best of times". In contrast, "Itwastimes" is a subsequence of "It was the best of times", but not a substring.
Prefixes and suffixes are special cases of substrings. A prefix of a string is a substring of that occurs at the beginning of ; likewise, a suffix of a string is a substring that occurs at the end of .
The substrings of the string "apple" would be:
"a", "ap", "app", "appl", "apple",
"p", "pp", "ppl", "pple",
"pl", "ple",
"l", "le"
"e", ""
(note the empty string at the end).
Substring
A string is a substring (or factor) of a string if there exists two strings and such that . In particular, the empty string is a substring of every string.
Example: The string ana is equal to substrings (and subsequences) of banana at two different offsets:
banana
|||||
ana||
|||
ana
The first occurrence is obtained with b and na, while the second occurrence is obtained with ban and being the empty string.
A substring of a string is a prefix of a suffix of the string, and equivalently a suffix of a prefix; for example, nan is a prefix of nana, which is in turn a suffix of banana. If is a substring of , it is also a subsequence, which is a more general concept. The occurrences of a given pattern in a given string can be found with a string searching algorithm. Finding the longest string which is equal to a substring of two or more strings is known as the longest common substring problem.
In the mathematical literature, substrings are also called subwords (in America) or factors (in Europe).
Prefix
A string is a prefix of a string if there exists a string such that . A proper prefix of a string is not equal to the string itself; some sources in addition restrict a proper prefix to be non-empty. A prefix can be seen as a special case of a substring.
Example: The string b |
https://en.wikipedia.org/wiki/Thallium%28I%29%20sulfate | Thallium(I) sulfate (Tl2SO4) or thallous sulfate is the sulfate salt of thallium in the common +1 oxidation state, as indicated by the Roman numeral I. It is often referred to as simply thallium sulfate.
Uses
During the last two centuries, Tl2SO4 had been used for various medical treatments but was abandoned. In the later 1900s it found use mainly for rodenticides. These applications were prohibited in 1975 in the US due to the nonselective nature of its toxicity. Thallium(I) sulfate inhibits the growth of plants by preventing germination. Tl2SO4 is mostly used today as a source of Tl+ in the research laboratory. It is a precursor to thallium(I) sulfide (Tl2S), which exhibits high electrical conductivity when exposed to infrared light.
Preparation
Thallium(I) sulfate is produced by the reaction of thallium metal with sulfuric acid followed by crystallization.
Structure
Tl2SO4 adopts the same structure as K2SO4. In aqueous solution, the thallium(I) cations and the sulfate anions are separated and highly solvated. Thallium(I) sulfate crystals have a C2 symmetry.
Toxicity
Thallium(I) sulfate is soluble in water and its toxic effects are derived from the thallium(I) cation. The mean lethal dose of thallium(I) sulfate for an adult is about 1 gram. Since thallium(I) sulfate is a simple powder with indistinctive properties, it can easily be mistaken for more innocuous chemicals. It can enter the body by ingestion, inhalation, or through contact with the skin. The thallium(I) cation is very similar to potassium and sodium cations, which are essential for life. After the thallium ion enters the cell, many of the processes that transport potassium and sodium are disrupted. Due to its poisonous nature, many western countries have banned the use of thallium(I) sulfate in products for home use and many companies have also stopped using this compound.
A dosage in excess of 500 mg is reported as fatal. Thallium(I) sulfate, after entering the body, concentrates itself in the |
https://en.wikipedia.org/wiki/Philip%20Ball | Philip Ball (born 1962) is a British science writer. For over twenty years he has been an editor of the journal Nature, for which he continues to write regularly.
He is a regular contributor to Prospect magazine and a columnist for Chemistry World, Nature Materials, and BBC Future.
He has contributed to publications ranging from New Scientist to the New York Times, The Guardian, the Financial Times, and New Statesman.
He has broadcast on many occasions on radio and TV, and in June 2004 presented a three-part serial on nanotechnology, Small Worlds, on BBC Radio 4.
Life
Ball holds a degree in chemistry from Oxford and a doctorate in physics from Bristol University.
As of 2008 he lives in London.
Work
Ball's 2004 book Critical Mass: How One Thing Leads to Another won the 2005 Aventis Prize for Science Books. It examines a wide range of topics including the business cycle, random walks, phase transitions, bifurcation theory, traffic flow, Zipf's law, Small world phenomenon, catastrophe theory, the Prisoner's dilemma. The overall theme is one of applying modern mathematical models to social and economic phenomena.
In 2011, Ball published The Music Instinct in which he discusses how we make sense of sound and Music and emotion. He outlines what is known and still unknown about how music has such an emotional impact, and why it seems indispensable to humanity. He has since argued that music is emotively powerful due to its ability to mimic humans and through setting up expectations in pitch and harmony and then violating them.
Books
Designing the Molecular World: Chemistry at the Frontier (1994),
Made to Measure: New Materials for the 21st Century (1997),
The Self-made Tapestry: Pattern Formation in Nature (1999),
H2O: A Biography of Water (1999), (published in the U.S. as Life's Matrix)
Stories of the Invisible: A Guided Tour of Molecules (2001), (republished as Molecules: A Very Short Introduction (2003), OUP, )
Bright Earth: The Invention of Col |
https://en.wikipedia.org/wiki/Botanical%20nomenclature | Botanical nomenclature is the formal, scientific naming of plants. It is related to, but distinct from taxonomy. Plant taxonomy is concerned with grouping and classifying plants; botanical nomenclature then provides names for the results of this process. The starting point for modern botanical nomenclature is Linnaeus' Species Plantarum of 1753. Botanical nomenclature is governed by the International Code of Nomenclature for algae, fungi, and plants (ICN), which replaces the International Code of Botanical Nomenclature (ICBN). Fossil plants are also covered by the code of nomenclature.
Within the limits set by that code there is another set of rules, the International Code of Nomenclature for Cultivated Plants (ICNCP) which applies to plant cultivars that have been deliberately altered or selected by humans (see cultigen).
Botanical nomenclature is independent of other systems of nomenclature, for example zoological nomenclature. This implies that animals can have the same generic names as plants (e.g. there is a genus Iris in plants and a genus Iris in animals).
History and scope
Botanical nomenclature has a long history, going back beyond the period when Latin was the scientific language throughout Europe, to Theophrastus (c. 370–287 BC), Dioscorides (c. 40 – 90 AD) and other Greek writers. Many of these works have come down to us in Latin translations. The principal Latin writer on botany was Pliny the Elder (23–79 AD). From Mediaeval times, Latin became the universal scientific language (lingua franca) in Europe. Most written plant knowledge was the property of monks, particularly Benedictine, and the purpose of those early herbals was primarily medicinal rather than plant science per se. It would require the invention of the printing press (1450) to make such information more widely available.
Leonhart Fuchs, a German physician and botanist, is often considered the originator of Latin names for the rapidly increasing number of plants known to science. For |
https://en.wikipedia.org/wiki/Timeline%20of%20the%20Manhattan%20Project | The Manhattan Project was a research and development project that produced the first atomic bombs during World War II. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project was under the direction of Major General Leslie Groves of the US Army Corps of Engineers. The Army component of the project was designated the Manhattan District; "Manhattan" gradually became the codename for the entire project. Along the way, the project absorbed its earlier British counterpart, Tube Alloys. The Manhattan Project began modestly in 1939, but grew to employ more than 130,000 people and cost nearly US$2 billion (about $ in dollars). Over 90% of the cost was for building factories and producing the fissionable materials, with less than 10% for development and production of the weapons.
Two types of atomic bombs were developed during the war. A relatively simple gun-type fission weapon was made using uranium-235, an isotope that makes up only 0.7 percent of natural uranium. Since it is chemically identical to the most common isotope, uranium-238, and has almost the same mass, it proved difficult to separate. Three methods were employed for uranium enrichment: electromagnetic, gaseous and thermal. Most of this work was performed at Oak Ridge, Tennessee. In parallel with the work on uranium was an effort to produce plutonium. Reactors were constructed at Oak Ridge and Hanford, Washington, in which uranium was irradiated and transmuted into plutonium. The plutonium was then chemically separated from the uranium. The gun-type design proved impractical to use with plutonium so a more complex implosion-type nuclear weapon was developed in a concerted design and construction effort at the project's principal research and design laboratory in Los Alamos, New Mexico.
The following is a timeline of the Manhattan Project. It includes a number of events prior to the official formation of the Manhattan Project, and a number of even |
https://en.wikipedia.org/wiki/Dysdiadochokinesia | Dysdiadochokinesia (DDK) is the medical term for an impaired ability to perform rapid, alternating movements (i.e., diadochokinesia). Complete inability is called adiadochokinesia. The term is from Greek δυς dys "bad", διάδοχος diadochos "succeeding", κίνησις kinesis "movement".
Signs and symptoms
Abnormalities in diadochokinesia can be seen in the upper extremity, lower extremity and in speech. The deficits become visible in the rate of alternation, the completeness of the sequence, and in the variation in amplitude involving both motor coordination and sequencing. Average rate can be used as a measure of performance when testing for dysdiadochokinesia.
Dysdiadochokinesia is demonstrated clinically by asking the patient to tap the palm of one hand with the fingers of the other, then rapidly turn over the fingers and tap the palm with the back of them, repeatedly. This movement is known as a pronation/supination test of the upper extremity. A simpler method using this same concept is to ask the patient to demonstrate the movement of trying a doorknob or screwing in a light bulb. When testing for this condition in legs, ask the patient to tap your hand as quickly as possible with the ball of each foot in turn. Movements tend to be slow or awkward. The feet normally perform less well than the hands. When testing for dysdiadochokinesia with speech the patient is asked to repeat syllables such as /pə/, /tə/, and /kə/; variation, excess loudness, and irregular articular breakdown are signs of dysdiadochokinesia.
Causes
Dysdiadochokinesia is a feature of cerebellar ataxia and may be the result of lesions to either the cerebellar hemispheres or the frontal lobe (of the cerebrum), it can also be a combination of both. It is thought to be caused by the inability to switch on and switch off antagonising muscle groups in a coordinated fashion due to hypotonia, secondary to the central lesion.
Dysdiadochokinesia is also seen in Friedreich's ataxia and multiple sclerosis, as |
https://en.wikipedia.org/wiki/Brucella%20suis | Brucella suis is a bacterium that causes swine brucellosis, a zoonosis that affects pigs. The disease typically causes chronic inflammatory lesions in the reproductive organs of susceptible animals or orchitis, and may even affect joints and other organs. The most common symptom is abortion in pregnant susceptible sows at any stage of gestation. Other manifestations are temporary or permanent sterility, lameness, posterior paralysis, spondylitis, and abscess formation. It is transmitted mainly by ingestion of infected tissues or fluids, semen during breeding, and suckling infected animals.
Since brucellosis threatens the food supply and causes undulant fever, Brucella suis and other Brucella species (B. melitensis, B. abortus, B. ovis, B. canis) are recognized as potential agricultural, civilian, and military bioterrorism agents.
Symptoms and signs
The most frequent clinical sign following B. suis infection is abortion in pregnant females, reduced milk production, and infertility. Cattle can also be transiently infected when they share pasture or facilities with infected pigs, and B. suis can be transmitted by cow's milk.
Swine also develop orchitis (swelling of the testicles), lameness (movement disability), hind limb paralysis, or spondylitis (inflammation in joints).
Cause
Brucella suis is a Gram-negative, facultative, intracellular coccobacillus, capable of growing and reproducing inside of host cells, specifically phagocytic cells. They are also not spore-forming, capsulated, or motile. Flagellar genes, however, are present in the B. suis genome, but are thought to be cryptic remnants because some were truncated and others were missing crucial components of the flagellar apparatus. In mouse models, the flagellum is essential for a normal infectious cycle, where the inability to assemble a complete flagellum leads to severe attenuation of the bacteria.
Brucella suis is differentiated into five biovars (strains), where biovars 1–3 infect wild boar and dome |
https://en.wikipedia.org/wiki/Guitar%20Pro | Guitar Pro is a multitrack editor of guitar and bass tablature and musical scores, possessing a built-in MIDI-editor, a plotter of chords, a player, a metronome and other tools for musicians. It has versions for Windows and Mac OS X (Intel processors only) and is written by the French company Arobas Music.
History
There have been six popular public major releases of the software: versions 3–8. Guitar Pro was initially designed as a tablature editor, but has since evolved into a full-fledged score writer including support for many musical instruments other than guitar.
Until it reached version 4, the software was only available for Microsoft Windows. Later, Guitar Pro 5 (released November 2005) undertook a year-long porting effort and Guitar Pro 5 for the Mac OS X was released in July 2006. On April 5, 2010, Guitar Pro 6, a completely redesigned version, was released. This version also supports Linux, with 32-bit Ubuntu being the officially supported distribution.
On February 6, 2011, the first ever portable release of Guitar Pro (version 6) was made available on the App Store for support with the iPhone, iPod Touch, and iPad running iOS 3.0 or later. An Android version was released on December 17, 2014.
In 2011, a version was made to work with the Fretlight guitar called Guitar Pro 6 Fretlight Ready. The tablature notes being played in Guitar Pro 6 Fretlight Ready show up on the Fretlight guitar's LEDs which are encased within the guitar's fretboard to teach you the song.
In April 2017, Guitar Pro 7 was officially released with new features and dropped Linux support.
Guitar Pro 8 was released in May 2022 with a range of new features, most notably support for Apple Silicon processors.
Background
The software makes use of multiple instrument tracks which follow standard staff notation, but also shows the notes on tablature notation. It gives the musician visual access to keys (banjos, drumkits, etc.) for the song to be composed, and allows live previews of |
https://en.wikipedia.org/wiki/Audio%20leveler | An audio leveler performs an audio process similar to compression, which is used to reduce the dynamic range of a signal, so that the quietest portion of the signal is loud enough to hear and the loudest portion is not too loud.
Levelers work especially well with vocals, as there are huge dynamic differences in the human voice and levelers work in such a way as to sound very natural, letting the character of the sound change with the different levels but still maintaining a predictable and usable dynamic range.
A leveler is different from a compressor in that the ratio and threshold are controlled with a single control.
External links
TLA-100 Tube Levelling Amplifier by Summit Audio
Signal processing |
https://en.wikipedia.org/wiki/Harry%20Huskey | Harry Douglas Huskey (January 19, 1916 – April 9, 2017) was an American computer design pioneer.
Early life and career
Huskey was born in Whittier, in the Smoky Mountains region of North Carolina and grew up in Idaho. He received his bachelor's degree in mathematics and physics at the University of Idaho. He was the first member of his family to attend college. He gained his Master's and then his PhD in 1943 from the Ohio State University on Contributions to the Problem of Geöcze. Huskey taught mathematics to U.S. Navy students at the University of Pennsylvania and then worked part-time on the early ENIAC and EDVAC computers in 1945. This work represented his first formal introduction to computers, according to his obituary in The New York Times.
He visited the National Physical Laboratory (NPL) in the United Kingdom for a year and worked on the Pilot ACE computer with Alan Turing and others. He was also involved with the EDVAC and SEAC computer projects.
Huskey designed and managed the construction of the Standards Western Automatic Computer (SWAC) at the National Bureau of Standards in Los Angeles (1949–1953). He also designed the G-15 computer for Bendix Aviation Corporation, a machine, operable by one person. He had one at his home that is now in the Smithsonian Institution in Washington, D.C.
After five years at the National Bureau of Standards, Huskey joined the faculty of the University of California, Berkeley in 1954 and then University of California, Santa Cruz from 1966. He cofounded the computer and information science program at UC Santa Cruz in 1967. He became director of its computer center. In 1986, UC Santa Cruz named him professor emeritus. While at Berkeley, he supervised the research of pioneering programming language designer Niklaus Wirth, who gained his PhD in 1963. During 1963-1964 Prof. Huskey participated in establishing the Computer Center at IIT Kanpur and convened a meeting there with many pioneers of computing technology. Parti |
https://en.wikipedia.org/wiki/Antefix | An antefix (from Latin , to fasten before) is a vertical block which terminates and conceals the covering tiles of a tiled roof (see imbrex and tegula, monk and nun). It also serves to protect the join from the elements. In grand buildings, the face of each stone antefix was richly carved, often with the anthemion ornament. In less grand buildings moulded ceramic antefixes, usually terracotta, might be decorated with figures heads, either of humans, mythological creatures, or astrological iconography, especially in the Roman period. On temple roofs, maenads and satyrs were often alternated. The frightening features of the Gorgon, with its petrifying eyes and sharp teeth was also a popular motif to ward off evil. A Roman example from the Augustan period features the butting heads of two billy goats. It may have had special significance in imperial Rome since the constellation Capricorn was adopted by the emperor Augustus as his own lucky star sign and appeared on coins and legionary standards. By this time they were found on many large buildings, including private houses. The earliest examples in museum collections date back to the 7th century BCE in both Greece and Etruria.
In the garden of the Villa Giulia in Rome, that houses the National Etruscan Museum, is a reconstruction of an Etruscan temple built between 1889 and 1890 on the basis of the ruins found in Alatri. Its tiled roof is lined with antefixes.
Etymology
From Latin antefixa, pl. of antefixum, something fastened in front, from antefixus, fastened in front: ante-, ante- and fixus, fastened, past participle of figere, to fasten. |
https://en.wikipedia.org/wiki/GParted | GParted (acronym of GNOME Partition Editor) is a GTK front-end to GNU Parted and an official GNOME partition-editing application (alongside Disks). GParted is used for creating, deleting, resizing, moving, checking, and copying disk partitions and their file systems. This is useful for creating space for new operating systems, reorganizing disk usage, copying data residing on hard disks, and mirroring one partition with another (disk imaging). It can also be used to format a USB drive.
Background
GParted uses libparted to detect and manipulate devices and partition tables while several (optional) file system tools provide support for file systems not included in libparted. These optional packages will be detected at runtime and do not require a rebuild of GParted. GParted supports the following filesystems: Ext2, Ext3, Ext4, FAT16, FAT32, HFS, HFS+, JFS, Linux-swap, ReiserFS, Reiser4, UFS, XFS, and NTFS.
GParted is written in C++ and uses gtkmm to interface with GTK. The general approach is to keep the GUI as simple as possible and in conformity with the GNOME Human Interface Guidelines.
The GParted project provides a live operating system including GParted which can be written to a Live CD, a Live USB and other media. The operating system is based on Debian. GParted is also available on other Linux live CDs, including recent versions of Puppy, Knoppix, SystemRescueCd and Parted Magic. GParted is preinstalled when booting from "Try Ubuntu" mode on an Ubuntu installation media.
An alternative to this software is GNOME Disks.
Supported features
GParted supports the following operations on file systems (provided that all features were enabled at compile-time and all required tools are present on the system). The 'copy' field indicates whether GParted is capable of cloning the mentioned filesystem.
Cloning with GParted
GParted is capable of cloning by copying and pasting. GParted is not capable of cloning an entire disk, but only one partition at a time. The fi |
https://en.wikipedia.org/wiki/Congruence%20%28general%20relativity%29 | In general relativity, a congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime. Often this manifold will be taken to be an exact or approximate solution to the Einstein field equation.
Types of congruences
Congruences generated by nowhere vanishing timelike, null, or spacelike vector fields are called timelike, null, or spacelike respectively.
A congruence is called a geodesic congruence if it admits a tangent vector field with vanishing covariant derivative, .
Relation with vector fields
The integral curves of the vector field are a family of non-intersecting parameterized curves which fill up the spacetime. The congruence consists of the curves themselves, without reference to a particular parameterization.
Many distinct vector fields can give rise to the same congruence of curves, since if is a nowhere vanishing scalar function, then and give rise to the same congruence.
However, in a Lorentzian manifold, we have a metric tensor, which picks out a preferred vector field among the vector fields which are everywhere parallel to a given timelike or spacelike vector field, namely the field of tangent vectors to the curves. These are respectively timelike or spacelike unit vector fields.
Physical interpretation
In general relativity, a timelike congruence in a four-dimensional Lorentzian manifold can be interpreted as a family of world lines of certain ideal observers in our spacetime. In particular, a timelike geodesic congruence can be interpreted as a family of free-falling test particles.
Null congruences are also important, particularly null geodesic congruences, which can be interpreted as a family of freely propagating light rays.
Warning: the world line of a pulse of light moving in a fiber optic cable would not in general be a null geodesic, and light in the very early universe (t |
https://en.wikipedia.org/wiki/Sanitation%20Standard%20Operating%20Procedures | Sanitation Standard Operating Procedures is the common name, in the United States, given to the sanitation procedures in food production plants which are required by the Food Safety and Inspection Service of the USDA and regulated by 9 CFR part 416 in conjunction with 21 CFR part 178.1010. It is considered one of the prerequisite programs of HACCP.
SSOPs are generally documented steps that must be followed to ensure adequate cleaning of product contact and non-product surfaces. These cleaning procedures must be detailed enough to make certain that adulteration of product will not occur. All HACCP plans require SSOPs to be documented and reviewed periodically to incorporate changes to the physical plant. This reviewing procedure can take on many forms, from annual formal reviews to random reviews, but any review should be done by "responsible educated management". As these procedures can make their way into the public record if there are serious failures, they might be looked at as public documents because they are required by the government. SSOPs, in conjunction with the Master Sanitation Schedule and Pre-Operational Inspection Program, form the entire sanitation operational guidelines for food-related processing and one of the primary backbones of all food industry HACCP plans.
SSOPs can be very simple to extremely intricate depending on the focus. Food industry equipment should be constructed of sanitary design; however, some automated processing equipment by necessity is difficult to clean. An individual SSOP should include:
The equipment or affected area to be cleaned, identified by common name
The tools necessary to prepare the equipment or area to be cleaned
How to disassemble the area or equipment
The method of cleaning and sanitizing
SSOPs can be standalone documents, but they should also serve as work instructions as this will help ensure they are accurate.
Sanitary accessories
To assure thorough sanitation, the use of the following items (and |
https://en.wikipedia.org/wiki/Pramlintide | Pramlintide (trade name Symlin) is an injectable amylin analogue drug for diabetes (both type 1 and 2), developed by Amylin Pharmaceuticals (now a wholly owned subsidiary of AstraZeneca). Pramlintide is sold as an acetate salt.
Pharmacology
Pramlintide is an analogue of amylin, a small peptide hormone that is released into the bloodstream by the β cells of the pancreas along with insulin after a meal. Like insulin, amylin is completely absent in individuals with Type I diabetes.
In synergy with endogenous amylin, pramlintide aids in the regulation of blood glucose by slowing gastric emptying, promoting satiety via hypothalamic receptors (different receptors than for GLP-1), and inhibiting inappropriate secretion of glucagon, a catabolic hormone that opposes the effects of insulin and amylin. Pramlintide also has effects in raising the acute first-phase insulin response threshold following a meal.
Both a reduction in glycated hemoglobin and weight loss have been shown in insulin-treated patients with type 2 diabetes taking pramlintide as an adjunctive therapy.
Research Applications
In the research field, pramlintide has been experimented with and used as a potential treatment drug. Pramlintide has demonstrated its ability to decrease amyloid beta plaques in Alzheimer's disease mouse models.
Approval
Pramlintide has been approved on 3/16/2005 by the FDA, for use by type 1 and type 2 diabetic patients who use insulin. Pramlintide allows patients to use less insulin, lowers average blood sugar levels, and substantially reduces what otherwise would be a large unhealthy rise in blood sugar that occurs in diabetics right after eating.
Apart from insulin analogs, pramlintide is the only drug approved by the FDA to lower blood sugar in type 1 diabetics since insulin in the early 1920s.
Design and structure
Since native human amylin is highly amyloidogenic and potentially toxic, the strategy for designing pramlintide was to substitute residues from rat amylin, which |
https://en.wikipedia.org/wiki/Raychaudhuri%20equation | In general relativity, the Raychaudhuri equation, or Landau–Raychaudhuri equation, is a fundamental result describing the motion of nearby bits of matter.
The equation is important as a fundamental lemma for the Penrose–Hawking singularity theorems and for the study of exact solutions in general relativity, but has independent interest, since it offers a simple and general validation of our intuitive expectation that gravitation should be a universal attractive force between any two bits of mass–energy in general relativity, as it is in Newton's theory of gravitation.
The equation was discovered independently by the Indian physicist Amal Kumar Raychaudhuri and the Soviet physicist Lev Landau.
Mathematical statement
Given a timelike unit vector field (which can be interpreted as a family or congruence of nonintersecting world lines via the integral curve, not necessarily geodesics), Raychaudhuri's equation can be written
where
are (non-negative) quadratic invariants of the shear tensor
and the vorticity tensor
respectively. Here,
is the expansion tensor, is its trace, called the expansion scalar, and
is the projection tensor onto the hyperplanes orthogonal to . Also, dot denotes differentiation with respect to proper time counted along the world lines in the congruence. Finally, the trace of the tidal tensor can also be written as
This quantity is sometimes called the Raychaudhuri scalar.
Intuitive significance
The expansion scalar measures the fractional rate at which the volume of a small ball of matter changes with respect to time as measured by a central comoving observer (and so it may take negative values). In other words, the above equation gives us the evolution equation for the expansion of the timelike congruence. If the derivative (with respect to proper time) of this quantity turns out to be negative along some world line (after a certain event), then any expansion of a small ball of matter (whose center of mass follows the world lin |
https://en.wikipedia.org/wiki/Synovitis | Synovitis is the medical term for inflammation of the synovial membrane. This membrane lines joints that possess cavities, known as synovial joints. The condition is usually painful, particularly when the joint is moved. The joint usually swells due to synovial fluid collection.
Synovitis may occur in association with arthritis as well as lupus, gout, and other conditions. Synovitis is more commonly found in rheumatoid arthritis than in other forms of arthritis, and can thus serve as a distinguishing factor, although it is also present in many joints affected with osteoarthritis. In rheumatoid arthritis, the fibroblast-like synoviocytes, highly specialized mesenchymal cells found in the synovial membrane, play an active and prominent role in the synovitis. Long term occurrence of synovitis can result in degeneration of the joint.
Signs and symptoms
Synovitis causes joint tenderness or pain, swelling and hard lumps, called nodules. When associated with rheumatoid arthritis, swelling is a better indicator than tenderness. The joints in your hands and fingers feel painful when pressed and when moving or gripping anything.
Diagnosis
A rheumatologist will aim to diagnose the cause of the patient’s pain by first determining whether it is inside the joint itself, meaning true synovitis, or if it is actually caused by an inflammation of the tendons, referred to as tendonitis. Imaging, such as an MRI or musculoskeletal ultrasound is often required to make a firm diagnosis.
Treatment
Synovitis symptoms can be treated with anti-inflammatory drugs such as NSAIDs. An injection of steroids may be done, directly into the affected joint. Injection of beta-emitting radioisotopes to locally treat synovitis has been performed in people for decades and is now being applied using tin-117m in veterinary medicine to treat canine elbow synovitis. Specific treatment depends on the underlying cause of the synovitis.
See also
Tenosynovitis
Transient synovitis
Knee effusion (water on th |
https://en.wikipedia.org/wiki/Monocalcium%20phosphate | Monocalcium phosphate is an inorganic compound with the chemical formula Ca(H2PO4)2 ("AMCP" or "CMP-A" for anhydrous monocalcium phosphate). It is commonly found as the monohydrate ("MCP" or "MCP-M"), Ca(H2PO4)2·H2O. Both salts are colourless solids. They are used mainly as superphosphate fertilizers and are also popular leavening agents.
Preparation
Material of relatively high purity, as required for baking, is produced by treating calcium hydroxide with phosphoric acid:
Samples of Ca(H2PO4)2 tend to convert to dicalcium phosphate:
Applications
Use in fertilizers
Superphosphate fertilizers are produced by treatment of "phosphate rock" with acids ("acidulation"). Using phosphoric acid, fluorapatite is converted to Ca(H2PO4)2:
This solid is called triple superphosphate. Several million tons are produced annually for use as fertilizers.
Using sulfuric acid, fluorapatite is converted to a mixture of Ca(H2PO4)2 and CaSO4.
This solid is called single superphosphate.
Residual HF typically reacts with silicate minerals co-mingled with the phosphate ores to produce hexafluorosilicic acid (H2SiF6). The majority of the hexafluorosilicic acid is converted to aluminium fluoride and cryolite for the processing of aluminium. These materials are central to the conversion of aluminium ore into aluminium metal.
When sulfuric acid is used, the product contains phosphogypsum (CaSO4·2H2O) and is called single superphosphate.
Use as leavening agent
Calcium dihydrogen phosphate is used in the food industry as a leavening agent, i.e., to cause baked goods to rise. Because it is acidic, when combined with an alkali ingredient, commonly sodium bicarbonate (baking soda) or potassium bicarbonate, it reacts to produce carbon dioxide and a salt. Outward pressure of the carbon dioxide gas causes the rising effect. When combined in a ready-made baking powder, the acid and alkali ingredients are included in the right proportions such that they will exactly neutralize each other and |
https://en.wikipedia.org/wiki/Shortest%20common%20supersequence | In computer science, the shortest common supersequence of two sequences X and Y is the shortest sequence which has X and Y as subsequences. This is a problem closely related to the longest common subsequence problem. Given two sequences X = < x1,...,xm > and Y = < y1,...,yn >, a sequence U = < u1,...,uk > is a common supersequence of X and Y if items can be removed from U to produce X and Y.
A shortest common supersequence (SCS) is a common supersequence of minimal length. In the shortest common supersequence problem, two sequences X and Y are given, and the task is to find a shortest possible common supersequence of these sequences. In general, an SCS is not unique.
For two input sequences, an SCS can be formed from a longest common subsequence (LCS) easily. For example, the longest common subsequence of X and Y is Z. By inserting the non-LCS symbols into Z while preserving their original order, we obtain a shortest common supersequence U. In particular, the equation holds for any two input sequences.
There is no similar relationship between shortest common supersequences and longest common subsequences of three or more input sequences. (In particular, LCS and SCS are not dual problems.) However, both problems can be solved in time using dynamic programming, where is the number of sequences, and is their maximum length. For the general case of an arbitrary number of input sequences, the problem is NP-hard.
Shortest common superstring
The closely related problem of finding a minimum-length string which is a superstring of a finite set of strings = { 1,2,...,n } is also NP-hard. Several constant factor approximations have been proposed throughout the years, and the current best known algorithm has an approximation factor of 2.475. However, perhaps the simplest solution is to reformulate the problem as an instance of weighted set cover in such a way that the weight of the optimal solution to the set cover instance is less than twice the length of t |
https://en.wikipedia.org/wiki/Rogue%20access%20point | A rogue access point is a wireless access point that has been installed on a secure network without explicit authorization from a local network administrator, whether added by a well-meaning employee or by a malicious attacker.
Dangers
Although it is technically easy for a well-meaning employee to install a "soft access point" or an inexpensive wireless router—perhaps to make access from mobile devices easier—it is likely that they will configure this as "open", or with poor security, and potentially allow access to unauthorized parties.
If an attacker installs an access point they are able to run various types of vulnerability scanners, and rather than having to be physically inside the organization, can attack remotely—perhaps from a reception area, adjacent building, car park, or with a high gain antenna, even from several miles away.
Prevention and detection
To prevent the installation of rogue access points, organizations can install wireless intrusion prevention systems to monitor the radio spectrum for unauthorized access points.
Presence of a large number of wireless access points can be sensed in airspace of a typical enterprise facility. These include managed access points in the secure network plus access points in the neighborhood. A wireless intrusion prevention system facilitates the job of auditing these access points on a continuous basis to learn whether there are any rogue access points among them.
In order to detect rogue access points, two conditions need to be tested:
whether or not the access point is in the managed access point list
whether or not it is connected to the secure network
The first of the above two conditions is easy to test—compare wireless MAC address (also called as BSSID) of the access point against the managed access point BSSID list. However, automated testing of the second condition can become challenging in the light of following factors: a) Need to cover different types of access point devices such as bridging, N |
https://en.wikipedia.org/wiki/Yellow%20flag | Yellow flag may refer to:
Iris pseudacorus, an aquatic flowering plant
A flag of a yellow colour:
Yellow flag (contagion), historically displayed on ships to indicate the presence of disease or quarantine (obsolete); also used in some cities to mark a recent death in a neighborhood, regardless of cause
Racing flags, used in motor sports to indicate hazardous conditions
Penalty flag, used in various sports including American football
Yellow Flag Line, transport on the Chao Phraya River, with service indicated by the flag color
Yellow Dragon Flag, the flag of the Qing dynasty
The Yellow Flag, 1937 German drama film
Yellow Banners of the Eight Banner system
Plain Yellow Banner
Bordered Yellow Banner
Flag, yellow |
https://en.wikipedia.org/wiki/Frank%20Spitzer | Frank Ludvig Spitzer (July 24, 1926 – February 1, 1992) was an Austrian-born American mathematician who made fundamental contributions to probability theory, including the theory of random walks, fluctuation theory, percolation theory, the Wiener sausage, and especially the theory of interacting particle systems. Rare among mathematicians, he chose to focus broadly on "phenomena", rather than any one of the many specific theorems that might help to articulate a given phenomenon. His book Principles of Random Walk, first published in 1964, remains a well-cited classic.
Spitzer was born into a Jewish family in Vienna, Austria, and by the time he was twelve years old, the Nazi threat in Austria was evident. His parents were able to send him to a summer camp for Jewish children in Sweden, and, as a result, Spitzer spent all of the war years in Sweden. He lived with two Swedish families, learned Swedish, graduated from high school, and for one year attended Tekniska Hogskolan in Stockholm.
During the war years, Spitzer's parents and his sister were able to make their way to the United States by passing through the unoccupied parts of France and North Africa, and, after the war, Spitzer joined his family in their new country. Spitzer enlisted in the U.S. Army just as the war in Europe was ending. After completing his military service in 1947, Spitzer entered the University of Michigan to study mathematics. His studies went quickly, and he completed his B.A. and Ph.D. in just six years.
Spitzer's first academic appointments were at the California Institute of Technology (1953–1958), but most of his academic career was spent at Cornell University, with leaves at the Institute for Advanced Study in Princeton and the Mittag-Leffler Institute in Sweden. Among his many honors, Spitzer was a member of the National Academy of Sciences.
Publications |
https://en.wikipedia.org/wiki/Thermosiphon | Thermosiphon (or thermosyphon) is a method of passive heat exchange, based on natural convection, which circulates a fluid without the necessity of a mechanical pump. Thermosiphoning is used for circulation of liquids and volatile gases in heating and cooling applications such as heat pumps, water heaters, boilers and furnaces. Thermosiphoning also occurs across air temperature gradients such as those utilized in a wood fire chimney or solar chimney.
This circulation can either be open-loop, as when the substance in a holding tank is passed in one direction via a heated transfer tube mounted at the bottom of the tank to a distribution point—even one mounted above the originating tank—or it can be a vertical closed-loop circuit with return to the original container. Its purpose is to simplify the transfer of liquid or gas while avoiding the cost and complexity of a conventional pump.
Simple thermosiphon
Natural convection of the liquid starts when heat transfer to the liquid gives rise to a temperature difference from one side of the loop to the other. The phenomenon of thermal expansion means that a temperature difference will have a corresponding difference in density across the loop. The warmer fluid on one side of the loop is less dense and thus more buoyant than the cooler fluid on the other side. The warmer fluid will "float" above the cooler fluid, and the cooler fluid will "sink" below the warmer fluid. This phenomenon of natural convection is known by the saying "heat rises". Convection moves the heated liquid upwards in the system as it is simultaneously replaced by cooler liquid returning by gravity. A good thermosiphon has very little hydraulic resistance so that liquid can flow easily under the relatively low pressure produced by natural convection.
Heat pipes
In some situations the flow of liquid may be reduced further, or stopped, perhaps because the loop is not entirely full of liquid. In this case, the system no longer convects, so it is no |
https://en.wikipedia.org/wiki/Bed%20of%20nails%20tester | A bed of nails tester is a traditional electronic test fixture used for in-circuit testing. It has numerous pins inserted into holes in an epoxy phenolic glass cloth laminated sheet (G-10) which are aligned using tooling pins to make contact with test points on a printed circuit board and are also connected to a measuring unit by wires. Named by analogy with a real-world bed of nails, these devices contain an array of small, spring-loaded pogo pins; each pogo pin makes contact with one node in the circuitry of the DUT (device under test). By pressing the DUT down against the bed of nails, reliable contact can be quickly and simultaneously made with hundreds or even thousands of individual test points within the circuitry of the DUT. The hold-down force may be provided manually or by means of a vacuum or a mechanical presser, thus pulling the DUT downwards onto the nails.
Devices that have been tested on a bed of nails tester may show evidence of this after the process: small dimples (from the sharp tips of the Pogo pins) can often be seen on many of the soldered connections of the PCB.
Bed of nails fixtures require a mechanical assembly to hold the PCB in place. Fixtures can hold the PCB with either a vacuum or pressing down from the top of the PCB. Vacuum fixtures give better signal reading versus the press-down type. On the other hand, vacuum fixtures are expensive because of their high manufacturing complexity. Moreover, vacuum fixtures cannot be used on bed-of-nails systems that are used in automated production lines, where the board is automatically loaded to the tester by a handling mechanism.
The bed of nails or fixture, as generally termed, is used together with an in-circuit tester. Fixtures with a grid of 0.8 mm for small nails and test point diameter 0.6 mm are theoretically possible without using special constructions. But in mass production, test point diameters of 1.0 mm or higher are normally used to minimise contact failures, leading to lower rema |
https://en.wikipedia.org/wiki/Majorette%20%28toy%20manufacturer%29 | Majorette is a French toy manufacturer which mostly produces small Die-cast scale model cars, commercial vehicles, aircraft, and other vehicles, particularly in 1:64 scale. This is a normal size, thus Majorette has sometimes been called "the Matchbox of France". Traditionally, production was centered in the urban area of Lyon, but diecast models are now made in China, the Philippines, Taiwan, Thailand and Vietnam.
History
The company was founded in 1961 by Emile Véron, of the family that also created Norev (the Véron family name spelled backwards). Initially, model railways and accessories were made and the firm was known as "Rail-Route". By 1964, the first cars came to market, and in 1967, the name was changed to Majorette.
Majorette became the main French manufacturer of Matchbox-sized miniature vehicles (scale variously pegged to 3 inches long). The company soon became the largest French toy car manufacturer. The main competition was Matchbox of Hackney, London, but also German Siku and later, conceptually, Japanese Tomica. Though French cars like Peugeot and Renault were emphasized, other licensed marques included European brands, and North American vehicles from General Motors, Ford, and Chrysler. Japanese Nissan and Toyota are also represented.
At the end of 1980, Majorette purchased revered diecast producer Solido. About this same time, the Portuguese company Novacar was also purchased and Majorette production commenced in Portugal. Besides their important domestic presence, Majorette relies heavily on commercial sales to foreign markets. In 1982, Majorette USA was established in Miami, Florida, but that extension was relatively short-lived as Majorettes were not heavily retailed in the U.S. through the 1990s and 2000s. Majorette was purchased by Smoby in 2003. In 2008, there was talk that Majorette, then called Smoby-Majorette, was to be divorced from Smoby and sold to MI29, a French investment fund which owns Bigben Interactive for €3,900,000. This vent |
https://en.wikipedia.org/wiki/Bridged%20and%20paralleled%20amplifiers | Multiple electronic amplifiers can be connected such that they drive a single floating load (bridge) or a single common load (parallel), to increase the amount of power available in different situations. This is commonly encountered in audio applications.
Overview
Bridged or paralleled modes of working, normally involving audio power amplifiers, are methods of using a two or more identical amplifiers to drive the same load simultaneously. This is possible for sets of mono, stereo and multichannel amplifiers since the amplifier outputs are combined on a per load basis. Depending on the method of combining separate amplifiers, bridging or paralleling, different amplification goals can be served. The result is an amplifier that can be further combined with bridging or paralleling. This approach can be beneficial for driving loads for which using a single-ended amplifier is impossible, impractical or less cost-effective.
Bridged amplifier
A bridge-tied load (BTL), also known as bridged transformerless and bridged mono, is an output configuration for audio amplifiers, a form of impedance bridging used mainly in professional audio & car applications. The two channels of a stereo amplifier are fed the same monaural audio signal, with one channel's electrical polarity reversed. A loudspeaker is connected between the two amplifier outputs, bridging the output terminals. This doubles the available voltage swing at the load compared with the same amplifier used without bridging. The configuration is most often used for subwoofers.
For a given output voltage swing, the lower the impedance the higher the amplifier load. Bridging is used to allow an amplifier to drive low loads into higher power, because power is inversely proportional to impedance and proportional to the square of voltage, according to the equation . This equation also shows that bridging quadruples the theoretical power in an amplifier, however this is true only for low enough loads. For example, for load |
https://en.wikipedia.org/wiki/SciELO | SciELO (Scientific Electronic Library Online) is a bibliographic database, digital library, and cooperative electronic publishing model of open access journals. SciELO was created to meet the scientific communication needs of developing countries and provides an efficient way to increase visibility and access to scientific literature. Originally established in Brazil in 1997, today there are 16 countries in the SciELO network and its journal collections: Argentina, Bolivia, Brazil, Chile, Colombia, Costa Rica, Cuba, Ecuador, Mexico, Paraguay, Peru, Portugal, South Africa, Spain, Uruguay, and Venezuela.
SciELO was initially supported by the São Paulo Research Foundation (FAPESP) and the Brazilian National Council for Scientific and Technological Development (CNPq), along with the Latin American and Caribbean Center on Health Sciences Information (BIREME). SciELO provides a portal that integrates and provides access to all of the SciELO network sites. Users can search across all SciELO collections or limit the search by a single country collection, or browse by subject area, publisher, or journal title.
Database and projects
By October 2015 the database contained:
1,249 journals
39,651 issues (journal numbers)
573,525 research articles
13,005,080 citations (sum of the number of items in each article's reference list)
from different countries, universally accessible for free open access, in full-text format. The SciELO Project's stated aims are to "envisage the development of a common methodology for the preparation, storage, dissemination and evaluation of scientific literature in electronic format". All journals are published by a special software suite which implements a scientific electronic virtual library accessed via several mechanisms, including a table of titles in alphabetic and subject list, subject and author indexes and a search engine.
History
Project's launch timeline:
1997: Beginning of the development of SciELO as a FAPESP supported projec |
https://en.wikipedia.org/wiki/Dynamic-link%20library | Dynamic-link library (DLL) is Microsoft's implementation of the shared library concept in the Microsoft Windows and OS/2 operating systems. These libraries usually have the file extension DLL, OCX (for libraries containing ActiveX controls), or DRV (for legacy system drivers).
The file formats for DLLs are the same as for Windows EXE files – that is, Portable Executable (PE) for 32-bit and 64-bit Windows, and New Executable (NE) for 16-bit Windows. As with EXEs, DLLs can contain code, data, and resources, in any combination.
Data files with the same file format as a DLL, but with different file extensions and possibly containing only resource sections, can be called resource DLLs. Examples of such DLLs include icon libraries, sometimes having the extension ICL, and font files, having the extensions FON and FOT.
Background
The first versions of Microsoft Windows ran programs together in a single address space. Every program was meant to co-operate by yielding the CPU to other programs so that the graphical user interface (GUI) could multitask and be maximally responsive. All operating-system level operations were provided by the underlying operating system: MS-DOS. All higher-level services were provided by Windows Libraries "Dynamic Link Library". The Drawing API, Graphics Device Interface (GDI), was implemented in a DLL called GDI.EXE, the user interface in USER.EXE. These extra layers on top of DOS had to be shared across all running Windows programs, not just to enable Windows to work in a machine with less than a megabyte of RAM, but to enable the programs to co-operate with each other. The code in GDI needed to translate drawing commands to operations on specific devices. On the display, it had to manipulate pixels in the frame buffer. When drawing to a printer, the API calls had to be transformed into requests to a printer. Although it could have been possible to provide hard-coded support for a limited set of devices (like the Color Graphics Adapter display |
https://en.wikipedia.org/wiki/Blook | A blook is a printed book that contains or is based on content from a blog.
The first printed blook was User Interface Design for Programmers, by Joel Spolsky, published by Apress on June 26, 2001, based on his blog Joel on Software. An early blook was written by Tony Pierce in 2002 when he compiled selected posts from his one-year-old blog and turned the collection into a book called "Blook". The name came about when Pierce held a contest, asking his readers to suggest a title for the book. Jeff Jarvis of BuzzMachine won the contest and subsequently invented the term. Pierce went on to publish two other blooks, How To Blog and Stiff.
Print-on-demand publisher Lulu inaugurated the Lulu Blooker Prize for blooks, which was first awarded in 2006. The printed blook phenomenon is not limited to self-publishing. Several popular bloggers have signed book deals with major publishers to write books based on their blogs. However, some publishers are starting to realize that blog popularity does not translate to sales. Blog to book conversions via traditional publishing houses still happen, but the focus has shifted from blog popularity to content quality.
"Blook" was short-listed in 2006 for inclusion in the Oxford English Dictionary and was a runner-up for Word of the Year.
See also
Digital library
List of digital library projects
Dynabook
Elibrary
Expanded Books
Networked book
Webserial
OpenReader Consortium
Project Gutenberg |
https://en.wikipedia.org/wiki/Asteroid%20spectral%20types | An asteroid spectral type is assigned to asteroids based on their reflectance spectrum, color, and sometimes albedo. These types are thought to correspond to an asteroid's surface composition. For small bodies that are not internally differentiated, the surface and internal compositions are presumably similar, while large bodies such as Ceres and Vesta are known to have internal structure. Over the years, there has been a number of surveys that resulted in a set of different taxonomic systems such as the Tholen, SMASS and Bus–DeMeo classifications.
Taxonomic systems
In 1975, astronomers Clark R. Chapman, David Morrison, and Ben Zellner developed a simple taxonomic system for asteroids based on color, albedo, and spectral shape. The three categories were labelled "C" for dark carbonaceous objects, "S" for stony (silicaceous) objects, and "U" for those that did not fit into either C or S. This basic division of asteroid spectra has since been expanded and clarified. A number of classification schemes are currently in existence, and while they strive to retain some mutual consistency, quite a few asteroids are sorted into different classes depending on the particular scheme. This is due to the use of different criteria for each approach. The two most widely used classifications are described below:
Overview of Tholen and SMASS
S3OS2 classification
The Small Solar System Objects Spectroscopic Survey (S3OS2 or S3OS2, also known as the Lazzaro classification) observed 820 asteroids, using the former ESO 1.52-metre telescope at La Silla Observatory during 1996–2001. This survey applied both the Tholen and Bus–Binzel (SMASS) taxonomy to the observed objects, many of which had previously not been classified. For the Tholen-like classification, the survey introduced a new "Caa-type", which shows a broad absorption band associated indicating an aqueous alteration of the body's surface. The Caa class corresponds to Tholen's C-type and to the SMASS hydrated Ch-type (inclu |
https://en.wikipedia.org/wiki/ISO%208583 | ISO 8583 is an international standard for financial transaction card originated interchange messaging. It is the International Organization for Standardization standard for systems that exchange electronic transactions initiated by cardholders using payment cards.
ISO 8583 defines a message format and a communication flow so that different systems can exchange these transaction requests and responses. The vast majority of transactions made when a customer uses a card to make a payment in a store (EFTPOS) use ISO 8583 at some point in the communication chain, as do transactions made at ATMs. In particular, the Mastercard, Visa and Verve networks base their authorization communications on the ISO 8583 standard, as do many other institutions and networks.
Although ISO 8583 defines a common standard, it is not typically used directly by systems or networks. It defines many standard fields (data elements) which remain the same in all systems or networks, and leaves a few additional fields for passing network-specific details. These fields are used by each network to adapt the standard for its own use with custom fields and custom usages like Proximity Cards.
Introduction
The ISO 8583 specification has three parts:
Part 1: Messages, data elements, and code values
Part 2: Application and registration procedures for Institution Identification Codes (IIC)
Part 3: Maintenance procedures for the aforementioned messages, data elements and code values
Message format
A card-based transaction typically travels from a transaction-acquiring device, such as a point-of-sale terminal (POS) or an automated teller machine (ATM), through a series of networks, to a card issuing system for authorization against the card holder's account. The transaction data contains information derived from the card (e.g., the card number or card holder details), the terminal (e.g., the terminal number, the merchant number), the transaction (e.g., the amount), together with other data which ma |
https://en.wikipedia.org/wiki/Salsa20 | Salsa20 and the closely related ChaCha are stream ciphers developed by Daniel J. Bernstein. Salsa20, the original cipher, was designed in 2005, then later submitted to the eSTREAM European Union cryptographic validation process by Bernstein. ChaCha is a modification of Salsa20 published in 2008. It uses a new round function that increases diffusion and increases performance on some architectures.
Both ciphers are built on a pseudorandom function based on add-rotate-XOR (ARX) operations — 32-bit addition, bitwise addition (XOR) and rotation operations. The core function maps a 256-bit key, a 64-bit nonce, and a 64-bit counter to a 512-bit block of the key stream (a Salsa version with a 128-bit key also exists). This gives Salsa20 and ChaCha the unusual advantage that the user can efficiently seek to any position in the key stream in constant time. Salsa20 offers speeds of around 4–14 cycles per byte in software on modern x86 processors, and reasonable hardware performance. It is not patented, and Bernstein has written several public domain implementations optimized for common architectures.
Structure
Internally, the cipher uses bitwise addition ⊕ (exclusive OR), 32-bit addition mod 232 ⊞, and constant-distance rotation operations <<< on an internal state of sixteen 32-bit words. Using only add-rotate-xor operations avoids the possibility of timing attacks in software implementations. The internal state is made of sixteen 32-bit words arranged as a 4×4 matrix.
The initial state is made up of eight words of key (), two words of stream position (), two words of nonce (essentially additional stream position bits) (), and four fixed words ():
The constant words spell "expand 32-byte k" in ASCII (i.e. the 4 words are "expa", "nd 3", "2-by", and "te k"). This is an example of a nothing-up-my-sleeve number. The core operation in Salsa20 is the quarter-round QR(a, b, c, d) that takes a four-word input and produces a four-word output:
b ^= (a + d) <<< 7;
c ^= (b + a) < |
https://en.wikipedia.org/wiki/Composition%20operator | In mathematics, the composition operator with symbol is a linear operator defined by the rule
where denotes function composition.
The study of composition operators is covered by AMS category 47B33.
In physics
In physics, and especially the area of dynamical systems, the composition operator is usually referred to as the Koopman operator (and its wild surge in popularity is sometimes jokingly called "Koopmania"), named after Bernard Koopman. It is the left-adjoint of the transfer operator of Frobenius–Perron.
In Borel functional calculus
Using the language of category theory, the composition operator is a pull-back on the space of measurable functions; it is adjoint to the transfer operator in the same way that the pull-back is adjoint to the push-forward; the composition operator is the inverse image functor.
Since the domain considered here is that of Borel functions, the above describes the Koopman operator as it appears in Borel functional calculus.
In holomorphic functional calculus
The domain of a composition operator can be taken more narrowly, as some Banach space, often consisting of holomorphic functions: for example, some Hardy space or Bergman space. In this case, the composition operator lies in the realm of some functional calculus, such as the holomorphic functional calculus.
Interesting questions posed in the study of composition operators often relate to how the spectral properties of the operator depend on the function space. Other questions include whether is compact or trace-class; answers typically depend on how the function behaves on the boundary of some domain.
When the transfer operator is a left-shift operator, the Koopman operator, as its adjoint, can be taken to be the right-shift operator. An appropriate basis, explicitly manifesting the shift, can often be found in the orthogonal polynomials. When these are orthogonal on the real number line, the shift is given by the Jacobi operator. When the polynomials are orthogonal o |
https://en.wikipedia.org/wiki/Network%20bridge | A network bridge is a computer networking device that creates a single, aggregate network from multiple communication networks or network segments. This function is called network bridging. Bridging is distinct from routing. Routing allows multiple networks to communicate independently and yet remain separate, whereas bridging connects two separate networks as if they were a single network. In the OSI model, bridging is performed in the data link layer (layer 2). If one or more segments of the bridged network are wireless, the device is known as a wireless bridge.
The main types of network bridging technologies are simple bridging, multiport bridging, and learning or transparent bridging.
Transparent bridging
Transparent bridging uses a table called the forwarding information base to control the forwarding of frames between network segments. The table starts empty and entries are added as the bridge receives frames. If a destination address entry is not found in the table, the frame is flooded to all other ports of the bridge, flooding the frame to all segments except the one from which it was received. By means of these flooded frames, a host on the destination network will respond and a forwarding database entry will be created. Both source and destination addresses are used in this process: source addresses are recorded in entries in the table, while destination addresses are looked up in the table and matched to the proper segment to send the frame to. Digital Equipment Corporation (DEC) originally developed the technology in the 1980s.
In the context of a two-port bridge, the forwarding information base can be seen as a filtering database. A bridge reads a frame's destination address and decides to either forward or filter. If the bridge determines that the destination host is on another segment on the network, it forwards the frame to that segment. If the destination address belongs to the same segment as the source address, the bridge filters the frame, p |
https://en.wikipedia.org/wiki/Index%20of%20software%20engineering%20articles | This is an alphabetical list of articles pertaining specifically to software engineering.
0–9
2D computer graphics —
3D computer graphics
A
Abstract syntax tree —
Abstraction —
Accounting software —
Ada —
Addressing mode —
Agile software development —
Algorithm —
Anti-pattern —
Application framework —
Application software —
Artificial intelligence —
Artificial neural network —
ASCII —
Aspect-oriented programming —
Assembler —
Assembly language —
Assertion —
Automata theory —
Automotive software —
Avionics software
B
Backward compatibility —
BASIC —
BCPL —
Berkeley Software Distribution —
Beta test —
Boolean logic —
Business software
C
C —
C++ —
C# —
CAD —
Canonical model —
Capability Maturity Model —
Capability Maturity Model Integration —
COBOL —
Code coverage —
Cohesion —
Compilers —
Complexity —
Computation —
Computational complexity theory —
Computer —
Computer-aided design —
Computer-aided manufacturing —
Computer architecture —
Computer bug —
Computer file —
Computer graphics —
Computer model —
Computer multitasking —
Computer programming —
Computer science —
Computer software —
Computer term etymologies —
Concurrent programming —
Configuration management —
Coupling —
Cyclomatic complexity
D
Data structure —
Data-structured language —
Database —
Dead code —
Decision table —
Declarative programming —
Design pattern —
Development stage —
Device driver —
Disassembler —
Disk image —
Domain-specific language
E
EEPROM —
Electronic design automation —
Embedded system —
Engineering —
Engineering model —
EPROM —
Even-odd rule —
Expert system —
Extreme programming
F
FIFO (computing and electronics) —
File system —
Filename extension —
Finite-state machine —
Firmware —
Formal methods —
Forth —
Fortran —
Forward compatibility —
Functional decomposition —
Functional design —
Functional programming
G
Game development —
Game programming —
Game tester —
GIMP Toolkit —
Graphical user interface
H
Hierarchical database —
High-level language —
Hoare logic —
Human–compute |
https://en.wikipedia.org/wiki/Nuclear%20operators%20between%20Banach%20spaces | In mathematics, nuclear operators between Banach spaces are a linear operators between Banach spaces in infinite dimensions that share some of the properties of their counter-part in finite dimension. In Hilbert spaces such operators are usually called trace class operators and one can define such things as the trace. In Banach spaces this is no longer possible for general nuclear operators, it is however possible for -nuclear operator via the Grothendieck trace theorem.
The general definition for Banach spaces was given by Grothendieck. This article presents both cases but concentrates on the general case of nuclear operators on Banach spaces.
Nuclear operators on Hilbert spaces
An operator on a Hilbert space
is compact if it can be written in the form
where and and are (not necessarily complete) orthonormal sets. Here is a set of real numbers, the set of singular values of the operator, obeying if
The bracket is the scalar product on the Hilbert space; the sum on the right hand side must converge in norm.
An operator that is compact as defined above is said to be or if
Properties
A nuclear operator on a Hilbert space has the important property that a trace operation may be defined. Given an orthonormal basis for the Hilbert space, the trace is defined as
Obviously, the sum converges absolutely, and it can be proven that the result is independent of the basis. It can be shown that this trace is identical to the sum of the eigenvalues of (counted with multiplicity).
Nuclear operators on Banach spaces
The definition of trace-class operator was extended to Banach spaces by Alexander Grothendieck in 1955.
Let and be Banach spaces, and be the dual of that is, the set of all continuous or (equivalently) bounded linear functionals on with the usual norm.
There is a canonical evaluation map
(from the projective tensor product of and to the Banach space of continuous linear maps from to ).
It is determined by sending and to the li |
https://en.wikipedia.org/wiki/Friedrich%20L.%20Bauer | Friedrich Ludwig "Fritz" Bauer (10 June 1924 – 26 March 2015) was a German pioneer of computer science and professor at the Technical University of Munich. He coined the term Software engineering
Life
Bauer earned his Abitur in 1942 and served in the Wehrmacht during World War II, from 1943 to 1945. From 1946 to 1950, he studied mathematics and theoretical physics at Ludwig-Maximilians-Universität in Munich. Bauer received his Doctor of Philosophy (Ph.D.) under the supervision of Fritz Bopp for his thesis Gruppentheoretische Untersuchungen zur Theorie der Spinwellengleichungen ("Group-theoretic investigations of the theory of spin wave equations") in 1952. He completed his habilitation thesis Über quadratisch konvergente Iterationsverfahren zur Lösung von algebraischen Gleichungen und Eigenwertproblemen ("On quadratically convergent iteration methods for solving algebraic equations and eigenvalue problems") in 1954 at the Technical University of Munich. After teaching as a privatdozent at the Ludwig Maximilian University of Munich from 1954 to 1958, he became extraordinary professor for applied mathematics at the University of Mainz. Since 1963, he worked as a professor of mathematics and (since 1972) computer science at the Technical University of Munich. He retired in 1989.
Work
Bauer's early work involved constructing computing machinery (e.g. the logical relay computer STANISLAUS from 1951–1955). In this context, he was the first to propose the widely used stack method of expression evaluation.
Bauer was a member of the committees that developed the imperative computer programming languages ALGOL 58, and its successor ALGOL 60, important predecessors to all modern imperative programming languages. For ALGOL 58, Bauer was with the German Gesellschaft für Angewandte Mathematik und Mechanik (GAMM, Society of Applied Mathematics and Mechanics) which worked with the American Association for Computing Machinery (ACM). For ALGOL 60, Bauer was with the Internation |
https://en.wikipedia.org/wiki/Shikaku | (also anglicised as Divide by Squares or Divide by Box) is a logic puzzle published by Nikoli. As of 2011, two books consisting entirely of Shikaku puzzles has been published by Nikoli.
Rules
Shikaku is played on a rectangular grid. Some of the squares in the grid are numbered. The objective is to divide the grid into rectangular and square pieces such that each piece contains exactly one number, and that number represents the area of the rectangle.
See also
List of Nikoli puzzle types
External links
Nikoli's English-language page on Shikaku
Logic puzzles |
https://en.wikipedia.org/wiki/Xerophyllum%20tenax | Xerophyllum tenax is a North American species of plants in the corn lily family. It is known by several common names, including bear grass, soap grass, quip-quip, and Indian basket grass.
Ecology
Xerophyllum tenax has flowers with six sepals and six stamens borne in a terminal raceme. The plant is a perennial herb that can grow to 15–150 cm in height. It grows in bunches with the leaves wrapped around and extending from a small stem at ground level. The leaves are 30–100 cm long and 2–6 mm wide, dull olive green with toothed edges. The slightly fragrant white flowers emerge from a tall stalk that bolts from the base. When the flowers are in bloom they are tightly packed at the tip of the stalk like an upright club. It produces small, tan coloured seeds that will germinate after a cold period of 12 to 16 weeks. The plant is found mostly in western North America from British Columbia south to California and east to Wyoming, in subalpine meadows and coastal mountains, and also on low ground in the California coastal fog belt as far south as Monterey County. It is common on the Olympic Peninsula and in the Cascades, northern Sierra Nevada and Rockies.
Xerophyllum tenax is an important part of the fire ecology of regions where it is native. It has rhizomes which survive fire that clears dead and dying plant matter from the surface of the ground. The plant thrives with periodic burns and is often the first plant to sprout in a scorched area.
Its fibrous leaves, which turn from green to white as they dry, are tough, durable, and easily dyed and manipulated into tight waterproof weaves.
Depending on site-specific and environmental conditions, plants may bloom every year or only once every decade, though back-to-back blooming of individual plants is rare. It is a common myth that beargrass blooms every seven years, but depending on conditions such as moisture and temperatures there are periodically large concentrations of blooms.
Deer and elk eat the flower and other p |
https://en.wikipedia.org/wiki/Fredholm%20kernel | In mathematics, a Fredholm kernel is a certain type of a kernel on a Banach space, associated with nuclear operators on the Banach space. They are an abstraction of the idea of the Fredholm integral equation and the Fredholm operator, and are one of the objects of study in Fredholm theory. Fredholm kernels are named in honour of Erik Ivar Fredholm. Much of the abstract theory of Fredholm kernels was developed by Alexander Grothendieck and published in 1955.
Definition
Let B be an arbitrary Banach space, and let B* be its dual, that is, the space of bounded linear functionals on B. The tensor product has a completion under the norm
where the infimum is taken over all finite representations
The completion, under this norm, is often denoted as
and is called the projective topological tensor product. The elements of this space are called Fredholm kernels.
Properties
Every Fredholm kernel has a representation in the form
with and such that and
Associated with each such kernel is a linear operator
which has the canonical representation
Associated with every Fredholm kernel is a trace, defined as
p-summable kernels
A Fredholm kernel is said to be p-summable if
A Fredholm kernel is said to be of order q if q is the infimum of all for all p for which it is p-summable.
Nuclear operators on Banach spaces
An operator : is said to be a nuclear operator if there exists an
∈ such that = . Such an operator is said to be -summable and of order if is. In general, there may be more than one associated with such a nuclear operator, and so the trace is not uniquely defined. However, if the order ≤ 2/3, then there is a unique trace, as given by a theorem of Grothendieck.
Grothendieck's theorem
If is an operator of order then a trace may be defined, with
where are the eigenvalues of . Furthermore, the Fredholm determinant
is an entire function of z. The formula
holds as well. Finally, if is parameterized by some complex-valued parameter w, that is, |
https://en.wikipedia.org/wiki/Projection%20%28relational%20algebra%29 | In relational algebra, a projection is a unary operation written as , where is a relation and are attribute names. Its result is defined as the set obtained when the components of the tuples in are restricted to the set – it discards (or excludes) the other attributes.
In practical terms, if a relation is thought of as a table, then projection can be thought of as picking a subset of its columns. For example, if the attributes are (name, age), then projection of the relation {(Alice, 5), (Bob, 8)} onto attribute list (age) yields {5,8} – we have discarded the names, and only know what ages are present.
Projections may also modify attribute values. For example, if has attributes , , , where the values of are numbers, then
is like , but with all -values halved.
Related concepts
The closely related concept in set theory (see: projection (set theory)) differs from that of relational algebra in that, in set theory, one projects onto ordered components, not onto attributes. For instance, projecting onto the second component yields 7.
Projection is relational algebra's counterpart of existential quantification in predicate logic. The attributes not included correspond to existentially quantified variables in the predicate whose extension the operand relation represents. The example below illustrates this point.
Because of the correspondence with existential quantification, some authorities prefer to define projection in terms of the excluded attributes. In a computer language it is of course possible to provide notations for both, and that was done in ISBL and several languages that have taken their cue from ISBL.
A nearly identical concept occurs in the category of monoids, called a string projection, which consists of removing all of the letters in the string that do not belong to a given alphabet.
When implemented in SQL standard the "default projection" returns a multiset instead of a set, and the projection is obtained by the addition of the DISTINCT |
https://en.wikipedia.org/wiki/Nuclear%20space | In mathematics, nuclear spaces are topological vector spaces that can be viewed as a generalization of finite dimensional Euclidean spaces and share many of their desirable properties. Nuclear spaces are however quite different from Hilbert spaces, another generalization of finite dimensional Euclidean spaces. They were introduced by Alexander Grothendieck.
The topology on nuclear spaces can be defined by a family of seminorms whose unit balls decrease rapidly in size. Vector spaces whose elements are "smooth" in some sense tend to be nuclear spaces; a typical example of a nuclear space is the set of smooth functions on a compact manifold. All finite-dimensional vector spaces are nuclear. There are no Banach spaces that are nuclear, except for the finite-dimensional ones. In practice a sort of converse to this is often true: if a "naturally occurring" topological vector space is a Banach space, then there is a good chance that it is nuclear.
Original motivation: The Schwartz kernel theorem
Much of the theory of nuclear spaces was developed by Alexander Grothendieck while investigating the Schwartz kernel theorem and published in . We now describe this motivation.
For any open subsets and the canonical map is an isomorphism of TVSs (where has the topology of uniform convergence on bounded subsets) and furthermore, both of these spaces are canonically TVS-isomorphic to (where since is nuclear, this tensor product is simultaneously the injective tensor product and projective tensor product).
In short, the Schwartz kernel theorem states that:
where all of these TVS-isomorphisms are canonical.
This result is false if one replaces the space with (which is a reflexive space that is even isomorphic to its own strong dual space) and replaces with the dual of this space.
Why does such a nice result hold for the space of distributions and test functions but not for the Hilbert space (which is generally considered one of the "nicest" TVSs)?
This question |
https://en.wikipedia.org/wiki/Topological%20tensor%20product | In mathematics, there are usually many different ways to construct a topological tensor product of two topological vector spaces. For Hilbert spaces or nuclear spaces there is a simple well-behaved theory of tensor products (see Tensor product of Hilbert spaces), but for general Banach spaces or locally convex topological vector spaces the theory is notoriously subtle.
Motivation
One of the original motivations for topological tensor products is the fact that tensor products of the spaces of smooth functions on do not behave as expected. There is an injection
but this is not an isomorphism. For example, the function cannot be expressed as a finite linear combination of smooth functions in We only get an isomorphism after constructing the topological tensor product; i.e.,
This article first details the construction in the Banach space case. is not a Banach space and further cases are discussed at the end.
Tensor products of Hilbert spaces
The algebraic tensor product of two Hilbert spaces A and B has a natural positive definite sesquilinear form (scalar product) induced by the sesquilinear forms of A and B. So in particular it has a natural positive definite quadratic form, and the corresponding completion is a Hilbert space A ⊗ B, called the (Hilbert space) tensor product of A and B.
If the vectors ai and bj run through orthonormal bases of A and B, then the vectors ai⊗bj form an orthonormal basis of A ⊗ B.
Cross norms and tensor products of Banach spaces
We shall use the notation from in this section. The obvious way to define the tensor product of two Banach spaces and is to copy the method for Hilbert spaces: define a norm on the algebraic tensor product, then take the completion in this norm. The problem is that there is more than one natural way to define a norm on the tensor product.
If and are Banach spaces the algebraic tensor product of and means the tensor product of and as vector spaces and is denoted by The algebraic tensor prod |
https://en.wikipedia.org/wiki/Selection%20%28relational%20algebra%29 | In relational algebra, a selection (sometimes called a restriction in reference to E.F. Codd's 1970 paper and not, contrary to a popular belief, to avoid confusion with SQL's use of SELECT, since Codd's article predates the existence of SQL) is a unary operation that denotes a subset of a relation.
A selection is written as
or where:
and are attribute names
is a binary operation in the set
is a value constant
is a relation
The selection denotes all tuples in for which holds between the and the attribute.
The selection denotes all tuples in for which holds between the attribute and the value .
For an example, consider the following tables where the first table gives the relation , the second table gives the result of and the third table gives the result of .
More formally the semantics of the selection is defined as
follows:
The result of the selection is only defined if the attribute names that it mentions are in the heading of the relation that it operates upon.
Generalized selection
A generalized selection is a unary operation written as where is a propositional formula that consists of atoms as allowed in the normal selection and, in addition, the logical operators ∧ (and), ∨ (or) and (negation). This selection selects all those tuples in for which holds.
For an example, consider the following tables where the first table gives the relation and the second the result of .
Formally the semantics of the generalized selection is defined as follows:
The result of the selection is only defined if the attribute names that it mentions are in the header of the relation that it operates upon.
The generalized selection is expressible with other basic algebraic operations. A simulation of generalized selection using the fundamental operators is defined by the following rules:
Computer languages
In computer languages it is expected that any truth-valued expression be permitted as the selection condition rather than restrictin |
https://en.wikipedia.org/wiki/Wesson%20cooking%20oil | Wesson cooking oil is an American brand of vegetable oil manufactured in Memphis, Tennessee, and sold by Richardson International. Historically, Wesson was cottonseed oil, but as of 2009 the products sold under the Wesson brand are oil mixtures that may include canola oil, corn oil, soybean oil or sunflower oil.
History
Founding
Wesson was originally a trademark of the Southern Cotton Oil Company, named after David Wesson (1861–1934), a food chemist at the firm who, in 1899 developed a novel process for deodorizing cottonseed oil, producing the first commercial all-vegetable shortenings from cottonseeds. This new product was marketed as Snowdrift. The Savannah, Georgia, factory was erected in 1911 and torn down in 2004. In the 1920s, the vegetable oil division was spun off as the Wesson Oil & Snowdrift Company. In 1960, this firm merged with Hunt's Foods, Inc. to become Hunt-Wesson Foods, which later merged with Beatrice Foods. The brand was sold to ConAgra Foods along with many other former Beatrice brands in 1990.
Advertising lawsuit
In July 2011, two lawsuits were brought against ConAgra, arguing that it misrepresented Wesson as being "pure and natural" when it used genetically modified corn and soy in its oils. They argued that ConAgra "engaged in this misleading and deceptive campaign to charge a premium and take away market share from other similar products". In March 2019 a $27 million settlement or damages and reliefs was agreed to, pending a final hearing and approval by the courts set for October 7, 2019.
Proposed acquisition
After an antitrust lawsuit filed by the Federal Trade Commission (FTC) in early March 2018, Conagra Brands Inc. and J. M. Smucker Co. cancelled a deal for Smucker to purchase the Wesson brand. The FTC claimed that Smucker would have controlled at least 70 percent of the market for branded canola and vegetable oils.
On December 18, 2018, Conagra announced that it had reached an agreement to sell Wesson to Richardson Internatio |
https://en.wikipedia.org/wiki/Functional%20determinant | In functional analysis, a branch of mathematics, it is sometimes possible to generalize the notion of the determinant of a square matrix of finite order (representing a linear transformation from a finite-dimensional vector space to itself) to the infinite-dimensional case of a linear operator S mapping a function space V to itself. The corresponding quantity det(S) is called the functional determinant of S.
There are several formulas for the functional determinant. They are all based on the fact that the determinant of a finite matrix is equal to the product of the eigenvalues of the matrix. A mathematically rigorous definition is via the zeta function of the operator,
where tr stands for the functional trace: the determinant is then defined by
where the zeta function in the point s = 0 is defined by analytic continuation. Another possible generalization, often used by physicists when using the Feynman path integral formalism in quantum field theory (QFT), uses a functional integration:
This path integral is only well defined up to some divergent multiplicative constant. To give it a rigorous meaning it must be divided by another functional determinant, thus effectively cancelling the problematic 'constants'.
These are now, ostensibly, two different definitions for the functional determinant, one coming from quantum field theory and one coming from spectral theory. Each involves some kind of regularization: in the definition popular in physics, two determinants can only be compared with one another; in mathematics, the zeta function was used. have shown that the results obtained by comparing two functional determinants in the QFT formalism agree with the results obtained by the zeta functional determinant.
Defining formulae
Path integral version
For a positive self-adjoint operator S on a finite-dimensional Euclidean space V, the formula
holds.
The problem is to find a way to make sense of the determinant of an operator S on an infinite dimensional func |
https://en.wikipedia.org/wiki/Feline%20spongiform%20encephalopathy | Feline spongiform encephalopathy (FSE) is a disease that affects the brains of felines. It is caused by proteins called prions. FSE is thought to be related or identical to bovine spongiform encephalopathy (BSE). This disease is known to affect domestic and captive feline species. This infectious agent might be spread by both haematogenous and nervous pathways. Like BSE, this disease can take several years to develop. It is probable, but not proven, that the affected animals contract the disease by eating contaminated bovine meat.
Symptoms and signs
Clinical signs of FSE typically develop gradually in housecats. Initial signs of the condition include behavioral changes such as aggression, timidity, and hiding. Other commonly observed motor signs include gait abnormalities and ataxia, which typically affect the hind legs first. Affected cats may also display poor judgement of distance, and some cats may develop a rapid, crouching, hypermetric gait. Another common symptom is hyperesthesia. Some affected cats may exhibit an abnormal head tilt, tremors, a vacant stare, excessive salivation, decreased grooming behaviors, polyphagia, polydipsia, and dilated pupils. Once signs of FSE appear, the disease progresses and results in death within a few weeks to 3 months.
Ataxia was observed to last for about 8 weeks in the affected animals. The ultimate result is death of the infected animals.
Diagnosis
This disease can only be confirmed at the post-mortem, which includes identification of bilaterally symmetrical vacuolation of the neuropil and vacuolation in neurones. Lesions are likely to be found in basal ganglia, cerebral cortex and thalamus of the brain.
Treatment
This is a terminal condition and there is currently no specific treatment for the disease.
Epidemiology
This disease was first reported in domestic cats within the United Kingdom in 1990. Since 1990, cases have been reported in other countries and other feline species in captivity, although most affected fel |
https://en.wikipedia.org/wiki/Loop%20integral | In quantum field theory and statistical mechanics, loop integrals are the integrals which appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. These integrals are used to determine counterterms, which in turn allow evaluation of the beta function, which encodes the dependence of coupling for an interaction on an energy scale .
One-loop integral
Generic formula
A generic one-loop integral, for example those appearing in one-loop renormalization of QED or QCD may be written as a linear combination of terms in the form
where the are 4-momenta which are linear combinations of the external momenta, and the are masses of interacting particles. This expression uses Euclidean signature. In Lorentzian signature the denominator would instead be a product of expressions of the form .
Using Feynman parametrization, this can be rewritten as a linear combination of integrals of the form
where the 4-vector and are functions of the and the Feynman parameters. This integral is also integrated over the domain of the Feynman parameters. The integral is an isotropic tensor and so can be written as an isotropic tensor without dependence (but possibly dependent on the dimension ), multiplied by the integral
Note that if were odd, then the integral vanishes, so we can define .
Regularizing the integral
Cutoff regularization
In Wilsonian renormalization, the integral is made finite by specifying a cutoff scale . The integral to be evaluated is then
where is shorthand for integration over the domain . The expression is finite, but in general as , the expression diverges.
Dimensional regularization
The integral without a momentum cutoff may be evaluated as
where is the Beta function. For calculations in the renormalization of QED or QCD, takes values and .
For loop integrals in QFT, actually has a pole for relevant values of and . For example in scalar theory in 4 dimensions, the loop integral in the calculat |
https://en.wikipedia.org/wiki/Feynman%20parametrization | Feynman parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. However, it is sometimes useful in integration in areas of pure mathematics as well.
Formulas
Richard Feynman observed that:
which is valid for any complex numbers A and B as long as 0 is not contained in the line segment connecting A and B. The formula helps to evaluate integrals like:
If A(p) and B(p) are linear functions of p, then the last integral can be evaluated using substitution.
More generally, using the Dirac delta function :
This formula is valid for any complex numbers A1,...,An as long as 0 is not contained in their convex hull.
Even more generally, provided that for all :
where the Gamma function was used.
Derivation
By using the substitution ,
we have , and ,
from which we get the desired result
In more general cases, derivations can be done very efficiently using the Schwinger parametrization. For example, in order to derive the Feynman parametrized form of , we first reexpress all the factors in the denominator in their Schwinger parametrized form:
and rewrite,
Then we perform the following change of integration variables,
to obtain,
where denotes integration over the region with .
The next step is to perform the integration.
where we have defined
Substituting this result, we get to the penultimate form,
and, after introducing an extra integral, we arrive at the final form of the Feynman parametrization, namely,
Similarly, in order to derive the Feynman parametrization form of the most general case, one could begin with the suitable different Schwinger parametrization form of factors in the denominator, namely,
and then proceed exactly along the lines of previous case.
Alternative form
An alternative form of the parametrization that is sometimes useful is
This form can be derived using the change of variables .
We can use the product rule to show that , then
More generally we have
wh |
https://en.wikipedia.org/wiki/Rosewood | Rosewood is any of a number of richly hued hardwoods, often brownish with darker veining, but found in other colours. It is hard, tough, strong, and dense. True rosewoods come from trees of the genus Dalbergia, but other woods are often called rosewood. Rosewood takes a high polish and is used for luxury furniture-making, flooring, musical instruments, and turnery.
True rosewoods
Genuine rosewoods belong to the genus Dalbergia. The pre-eminent rosewood appreciated in the Western world is the wood of Dalbergia nigra. It is best known as "Brazilian rosewood", but also as "Bahia rosewood". This wood has a strong, sweet smell, which persists for many years, explaining the name rosewood.
Another classic rosewood comes from Dalbergia latifolia, known as (East) Indian rosewood or sonokeling (Indonesia). It is native to India and is also grown in plantations elsewhere in Pakistan (Chiniot).
Madagascar rosewood (Dalbergia maritima), known as bois de rose, is highly prized for its red color. It is overexploited in the wild, despite a 2010 moratorium on trade and illegal logging, which continues on a large scale.
Throughout southeast Asia, Dalbergia oliveri is harvested for use in woodworking. It has a very fragrant and dense grain near the core, but the outer sapwood is soft and porous. Dalbergia cultrata, variegated burgundy to light brown in color, is a blackwood timber sold as Burmese rosewood. Products built with rosewood-based engineered woods are sold as 'Malaysian rosewood' or as D. oliveri.
Some rosewood comes from Dalbergia retusa, also known as 'Nicaraguan rosewood' or as cocobolo. Several species are known as Guatemalan rosewood or Panama rosewood: D. tucerencis, D. tucarensis, and D. cubiquitzensis. Honduran rosewood, D. stevensonii is used for marimba keys, guitar parts, clarinets and other musical and ornamental applications.
Not all species in the large genus Dalbergia yield rosewoods; only about a dozen species do. The woods of some other species in th |
https://en.wikipedia.org/wiki/Culture24 | Culture24, originally the 24 Hour Museum, is a British charity which publishes websites, Culture24, Museum Crush and Show Me, about visual culture and heritage in the United Kingdom, as well as supplying data and support services to other cultural websites including Engaging Places.
It operates independently, and receives government funding.
Organisation
Culture24 is based in Brighton, southern England, and has ten employees. The Culture24 Director is Jane Finnis, who contributed a chapter to Learning to Live: Museums, young people and education and in March 2010 was named as one of 50 "Women to Watch" in the United Kingdom cultural and creative sectors by the Cultural Leadership Programme. Past Culture24 chairman include John Newbigin, who was named as one of Wired Magazine's top 100 people shaping the digital world in May 2010.
The charity was founded in 2001 as the 24 Hour Museum, when the website of the same name became an independent company.
The organisation changed its name to Culture24 in November 2007, and the website followed suit on 11 February 2009. Culture24 is a registered charity and is funded by the UK government through Arts Council England (ACE).
Purpose
The (now defunct) Museums, Libraries and Archives Council was working with Culture24 as one of its partners in furthering the council's digital agenda, specifically helping to deliver:
Culture24 also administered Museums at Night (UK) between 2010 and 2019, the annual weekend of late openings at museums, galleries and heritage sites.
Websites
The main Culture24 website is a guide to museums, public galleries, libraries, archives, heritage sites and science centres. It has a database of over 5,000 cultural institutions, who are able to update the information about their activities. It features daily arts, museum, history and heritage news, and exhibition reviews. News stories are available as RSS newsfeed.
Culture24 also runs a site for children, Show Me, which has online activities related |
https://en.wikipedia.org/wiki/Gross%E2%80%93Neveu%20model | The Gross–Neveu (GN) model is a quantum field theory model of Dirac fermions interacting via four-fermion interactions in 1 spatial and 1 time dimension. It was introduced in 1974 by David Gross and André Neveu as a toy model for quantum chromodynamics (QCD), the theory of strong interactions. It shares several features of the QCD: GN theory is asymptotically free thus at strong coupling the strength of the interaction gets weaker and the corresponding function of the interaction coupling is negative, the theory has a dynamical mass generation mechanism with chiral symmetry breaking, and in the large number of flavor () limit, GN theory behaves as t'Hooft's large limit in QCD.
It consists of N Dirac fermions . The Lagrangian density is
.
Einstein summation notation is used, is a two component spinor object and is the coupling constant. If the mass is nonzero, the model is massive classically, otherwise it enjoys a chiral symmetry.
This model has a U(N) global internal symmetry. If one takes N=1 (which permits only one quartic interaction) and makes no attempt to analytically continue the dimension, the model reduces to the massive Thirring model (which is completely integrable).
It is a 2-dimensional version of the 4-dimensional Nambu–Jona-Lasinio model (NJL), which was introduced 14 years earlier as a model of dynamical chiral symmetry breaking (but no quark confinement) modeled upon the BCS theory of superconductivity. The 2-dimensional version has the advantage that the 4-fermi interaction is renormalizable, which it is not in any higher number of dimensions.
Features of the theory
Gross and Neveu studied this model in the large limit, expanding the relevant parameters in a 1/N expansion. After demonstrating that this and related models are asymptotically free, they found that, in the subleading order, for small fermion masses the bifermion condensate acquires a vacuum expectation value (VEV) and as a result the fundamental fermions become mas |
https://en.wikipedia.org/wiki/Schwinger%20parametrization | Schwinger parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops.
Using the well-known observation that
Julian Schwinger noticed that one may simplify the integral:
for Re(n)>0.
Another version of Schwinger parametrization is:
which is convergent as long as and . It is easy to generalize this identity to n denominators.
See also
Feynman parametrization |
https://en.wikipedia.org/wiki/%28%E2%88%921%29F | {{DISPLAYTITLE:(−1)F}}
In a quantum field theory with fermions, (−1)F is a unitary, Hermitian, involutive operator where F is the fermion number operator. For the example of particles in the Standard Model, it is equal to the sum of the lepton number plus the baryon number, . The action of this operator is to multiply bosonic states by 1 and fermionic states by −1. This is always a global internal symmetry of any quantum field theory with fermions and corresponds to a rotation by 2π. This splits the Hilbert space into two superselection sectors. Bosonic operators commute with (−1)F whereas fermionic operators anticommute with it.
This operator really shows its utility in supersymmetric theories. Its trace is the spectral asymmetry of the fermion spectrum, and can be understood physically as the Casimir effect.
See also
Parity (physics)
Primon gas
Möbius function |
https://en.wikipedia.org/wiki/Witten%20index | In quantum field theory and statistical mechanics, the Witten index at the inverse temperature β is defined as a modification of the standard partition function:
Note the (-1)F operator, where F is the fermion number operator. This is what makes it different from the ordinary partition function. It is sometimes referred to as the spectral asymmetry.
In a supersymmetric theory, each nonzero energy eigenvalue contains an equal number of bosonic and fermionic states. Because of this, the Witten index is independent of the temperature and gives the number of zero energy bosonic vacuum states minus the number of zero energy fermionic vacuum states. In particular, if supersymmetry is spontaneously broken then there are no zero energy ground states and so the Witten index is equal to zero.
The Witten index of the supersymmetric sigma model on a manifold is given by the manifold's Euler characteristic.
It is an example of a quasi-topological quantity, which is a quantity that depends only on F-terms and not on D-terms in the Lagrangian. A more refined invariant in 2-dimensional theories, constructed using only the right-moving part of the fermion number operator together with a 2-parameter family of variations, is the elliptic genus.
See also
Supersymmetric theory of stochastic dynamics |
https://en.wikipedia.org/wiki/Tympanic%20cavity | The tympanic cavity is a small cavity surrounding the bones of the middle ear. Within it sit the ossicles, three small bones that transmit vibrations used in the detection of sound.
Structure
On its lateral surface, it abuts the external auditory meatus [ ear canal ] from which it is separated by the tympanic membrane (eardrum).
Walls
The tympanic cavity is bounded by:
Facing the inner ear, the medial wall (or labyrinthic wall, labyrinthine wall) is vertical, and has the oval window and round window, the promontory, and the prominence of the facial canal.
Facing the outer ear, the lateral wall (or membranous wall), is formed mainly by the tympanic membrane, partly by the ring of bone into which this membrane is inserted. This ring of bone is incomplete at its upper part, forming a notch (notch of Rivinus), close to which are three small apertures: the "iter chordæ posterius", the petrotympanic fissure, and the "iter chordæ anterius". The iter chordæ posterius (apertura tympanica canaliculi chordæ) is situated in the angle of junction between the mastoid and membranous wall of tympanic cavity immediately behind the tympanic membrane and on a level with the upper end of the manubrium of the malleus; it leads into a minute canal, which descends in front of the canal for the facial nerve, and ends in that canal near the stylo-mastoid foramen. Through it the chorda tympani nerve enters the tympanic cavity. The petrotympanic fissure opens just above and in front of the ring of bone into which the tympanic membrane is inserted; in this situation it is a mere slit about 2 mm. in length. It lodges the anterior process and anterior ligament of the malleus, and gives passage to the anterior tympanic branch of the internal maxillary artery. The iter chordæ anterius (canal of Huguier) is placed at the medial end of the petrotympanic fissure; through it the chorda tympani nerve leaves the tympanic cavity.
The roof of the cavity (also called the tegmental wall, tegmental roof |
https://en.wikipedia.org/wiki/Congruence%20%28manifolds%29 | In the theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold.
Congruences are an important concept in general relativity, and are also important in parts of Riemannian geometry.
A motivational example
The idea of a congruence is probably better explained by giving an example than by a definition. Consider the smooth manifold R². Vector fields can be specified as first order linear partial differential operators, such as
These correspond to a system of first order linear ordinary differential equations, in this case
where dot denotes a derivative with respect to some (dummy) parameter. The solutions of such systems are families of parameterized curves, in this case
This family is what is often called a congruence of curves, or just congruence for short.
This particular example happens to have two singularities, where the vector field vanishes. These are fixed points of the flow. (A flow is a one-dimensional group of diffeomorphisms; a flow defines an action by the one-dimensional Lie group R, having locally nice geometric properties.) These two singularities correspond to two points, rather than two curves. In this example, the other integral curves are all simple closed curves. Many flows are considerably more complicated than this. To avoid complications arising from the presence of singularities, usually one requires the vector field to be nonvanishing.
If we add more mathematical structure, our congruence may acquire new significance.
Congruences in Riemannian manifolds
For example, if we make our smooth manifold into a Riemannian manifold by adding a Riemannian metric tensor, say the one defined by the line element
our congruence might become a geodesic congruence. Indeed, in the example from the preceding section, our curves become geodesics on an ordinary round sphere (with the North pole excised). If we had added the standard Euclidean metric instead, our |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.