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https://en.wikipedia.org/wiki/Behavior-driven%20development | In software engineering, behavior-driven development (BDD) is a software development process that goes well with agile software development process that encourages collaboration among developers, quality assurance experts, and customer representatives in a software project. It encourages teams to use conversation and concrete examples to formalize a shared understanding of how the application should behave. It emerged from test-driven development (TDD). Behavior-driven development combines the general techniques and principles of TDD with ideas from domain-driven design and object-oriented analysis and design to provide software development and management teams with shared tools and a shared process to collaborate on software development.
Although BDD is principally an idea about how software development should be managed by both business interests and technical insight, the practice of BDD does assume the use of specialized software tools to support the development process. Although these tools are often developed specifically for use in BDD projects, they can be seen as specialized forms of the tooling that supports test-driven development. The tools serve to add automation to the ubiquitous language that is a central theme of BDD.
BDD is largely facilitated through the use of a simple domain-specific language (DSL) using natural-language constructs (e.g., English-like sentences) that can express the behaviour and the expected outcomes. Test scripts have long been a popular application of DSLs with varying degrees of sophistication. BDD is considered an effective technical practice especially when the "problem space" of the business problem to solve is complex.
History
Behavior-driven development, an extension of test-driven development, is a development process that makes use of a simple DSL. These DSLs convert structured natural language statements into executable tests. The result is a closer relationship to acceptance criteria for a given function and the |
https://en.wikipedia.org/wiki/CDC%203000%20series | The CDC 3000 series ("thirty-six hundred" or "thirty-one hundred") are a family of mainframe computers from Control Data Corporation (CDC). The first member, the CDC 3600, was a 48-bit system introduced in 1963. The same basic design led to the cut-down CDC 3400 of 1964, and then the 24-bit CDC 3300, 3200 and 3100 introduced between 1964 and 1965. The 3000 series replaced the earlier CDC 1604 and CDC 924 systems.
The line was a great success and became CDC's cash cow through the 1960s. The series significantly outsold the much faster and more expensive machines in the CDC 6000 series, but the performance of the 3000's relative to other vendors quickly eroded. The line was phased out of production in the early 1970s in favour of new members of the 6000 series, and then the CDC Cyber series, initially based on the 6600 design but spanning a wide range of performance.
Specifications
Upper 3000 series
The upper 3000 series used a 48-bit word size. The first 3000 machine to be produced was the CDC 3600; first delivered in June 1963. First deliveries of the CDC 3400 and CDC 3800 were in December 1965. These machines were designed for scientific computing applications; they were the upgrade path for users of the CDC 1604 machines. However these machines were overshadowed by the upcoming 60-bit CDC 6000 series machines when the CDC 6600 was introduced in December 1964 and delivered in 1965. Some high-end computer labs purchased these machines as stopgaps, while waiting for delivery of their 6600 machine. (CDC had indicated that the 6600 machines would use the same assembler language.)
Lower 3000 series
The lower 3000 series used a 24-bit word size. They were based on the earlier CDC 924 - a 24-bit version of the (48-bit) CDC 1604. The first lower 3000 to be released was the CDC 3200 (May 1964), followed by the smaller CDC 3100 (February 1965), and the CDC 3300 (December 1965). The final machine in the series, the CDC 3500, was released in March 1967 and used |
https://en.wikipedia.org/wiki/241%20%28number%29 | 241 (two hundred [and] forty-one) is the natural number between 240 and 242. It is also a prime number.
241 is the larger of the twin primes (239, 241). Twin primes are pairs of primes separated by 2.
241 is a regular prime and a lucky prime.
Since 241 = 15 × 24 + 1, it is a Proth prime.
241 is a repdigit in base 15 (111).
241 is the only known Lucas–Wieferich prime to (U, V) = (3, −1). |
https://en.wikipedia.org/wiki/Outer%20billiards | Outer billiards is a dynamical system based on a convex shape in the plane. Classically, this system is defined for the Euclidean plane but one can also consider the system in the hyperbolic plane or in other spaces that suitably generalize the plane. Outer billiards differs from a usual dynamical billiard in that it deals with a discrete sequence of moves outside the shape rather than inside of it.
Definitions
The outer billiards map
Let P be a convex shape in the plane.
Given a point x0 outside P, there is typically a unique
point x1 (also outside P) so that the line segment connecting x0 to x1 is tangent to P at its midpoint and
a person walking from x0 to x1 would see P on the right. (See Figure.) The map
F: x0 -> x1 is called the outer billiards map.
The inverse (or backwards) outer billiards map is also defined, as the map x1 -> x0.
One gets the inverse map simply by replacing the word right by the word left in the definition given above.
The figure shows the situation in the Euclidean plane, but the definition in the
hyperbolic plane is essentially the same.
Orbits
An outer billiards orbit is the set of all iterations
of the point, namely ... x0 <--> x1 <--> x2 <--> x3 ... That is, start at x0 and
iteratively apply both the outer billiards map and the backwards outer billiards map.
When P is a strictly convex shape, such as an ellipse,
every point in the exterior of P has a well defined orbit. When P
is a polygon, some points might not have well-defined orbits, on account of the
potential ambiguity of choosing the midpoint of the relevant tangent line. Nevertheless, in
the polygonal case, almost every point has a well-defined orbit.
An orbit is called periodic if it eventually repeats.
An orbit is called aperiodic (or non-periodic) if it is not periodic.
An orbit is called bounded (or stable) if some bounded region in the plane contains the whole orbit.
An orbit is called unbounded (or unstable) if it is not bounded.
Higher-dimensional spaces
De |
https://en.wikipedia.org/wiki/Engel%20expansion | The Engel expansion of a positive real number x is the unique non-decreasing sequence of positive integers such that
For instance, Euler's number e has the Engel expansion
1, 1, 2, 3, 4, 5, 6, 7, 8, ...
corresponding to the infinite series
Rational numbers have a finite Engel expansion, while irrational numbers have an infinite Engel expansion. If x is rational, its Engel expansion provides a representation of x as an Egyptian fraction. Engel expansions are named after Friedrich Engel, who studied them in 1913.
An expansion analogous to an Engel expansion, in which alternating terms are negative, is called a Pierce expansion.
Engel expansions, continued fractions, and Fibonacci
observe that an Engel expansion can also be written as an ascending variant of a continued fraction:
They claim that ascending continued fractions such as this have been studied as early as Fibonacci's Liber Abaci (1202). This claim appears to refer to Fibonacci's compound fraction notation in which a sequence of numerators and denominators sharing the same fraction bar represents an ascending continued fraction:
If such a notation has all numerators 0 or 1, as occurs in several instances in Liber Abaci, the result is an Engel expansion. However, Engel expansion as a general technique does not seem to be described by Fibonacci.
Algorithm for computing Engel expansions
To find the Engel expansion of x, let
and
where is the ceiling function (the smallest integer not less than r).
If for any i, halt the algorithm.
Iterated functions for computing Engel expansions
Another equivalent method is to consider the map
and set
where
and
Yet another equivalent method, called the modified Engel expansion calculated by
and
The transfer operator of the Engel map
The Frobenius–Perron transfer operator of the Engel map acts on functions with
since
and the inverse of the n-th component is which is found by solving for .
Relation to the Riemann ζ function
The Mellin tran |
https://en.wikipedia.org/wiki/Scleritis | Scleritis is a serious inflammatory disease that affects the white outer coating of the eye, known as the sclera. The disease is often contracted through association with other diseases of the body, such as granulomatosis with polyangiitis or rheumatoid arthritis. There are three types of scleritis: diffuse scleritis (the most common), nodular scleritis, and necrotizing scleritis (the most severe). Scleritis may be the first symptom of onset of connective tissue disease.
Episcleritis is inflammation of the episclera, a less serious condition that seldom develops into scleritis.
Signs and symptoms
Symptoms of scleritis include:
Redness of the sclera and conjunctiva, sometimes changing to a purple hue
Severe ocular pain, which may radiate to the temple or jaw. The pain is often described as deep or boring.
Photophobia and tearing
Decrease in visual acuity, possibly leading to blindness
The pain of episcleritis is less severe than in scleritis. In hyperemia, there is a visible increase in the blood flow to the sclera (hyperaemia), which accounts for the redness of the eye. Unlike in conjunctivitis, this redness will not move with gentle pressure to the conjunctiva.
Complications
Secondary keratitis or uveitis may occur with scleritis. The most severe complications are associated with necrotizing scleritis.
Pathophysiology
Most of the time, scleritis is not caused by an infectious agent. Histopathological changes are that of a chronic granulomatous disorder, characterized by fibrinoid necrosis, infiltration by polymorphonuclear cells, lymphocytes, plasma cells and macrophages. The granuloma is surrounded by multinucleated epitheloid giant cells and new vessels, some of which may show evidence of vasculitis.
Diagnosis
Scleritis is best detected by examining the sclera in daylight; retracting the lids helps determine the extent of involvement. Other aspects of the eye exam (i.e. visual acuity testing, slit lamp examination, etc.) may be normal. Scleritis |
https://en.wikipedia.org/wiki/Alar%20ligament | In anatomy, the alar ligaments are ligaments which connect the dens (a bony protrusion on the second cervical vertebra) to tubercles on the medial side of the occipital condyle.
They are short, tough, fibrous cords that attach on the skull and on the axis, and function to check side-to-side movements of the head when it is turned. Because of their function, the alar ligaments are also known as the "check ligaments of the odontoid".
Structure
The alar ligaments are two strong, rounded cords of about 0.5 cm in diameter that run from the sides of the foramen magnum of the skull to the dens of the axis, the second cervical vertebra. They span almost horizontally, creating an angle between them of at least 140°.
Development
The alar ligaments, along with the transverse ligament of the atlas, derive from the axial component of the first cervical sclerotome.
Function
The function of the alar ligaments is to limit the amount of rotation of the head, and by their action on the dens of the axis, they attach the skull to the axis, the second cervical vertebra.
Clinical significance
The alar ligaments are prone to tearing if a force is applied when the head is flexed and in rotation. If an alar ligament is ruptured, the range of rotation of the head relative to the neck increases beyond the normal limit of 20 degrees. |
https://en.wikipedia.org/wiki/Single%20address%20space%20operating%20system | In computer science, a single address space operating system (or SASOS) is an operating system that provides only one globally shared address space for all processes. In a single address space operating system, numerically identical (virtual memory) logical addresses in different processes all refer to exactly the same byte of data.
Single address-space operating systems offer certain advantages. In a traditional OS with private per-process address space, memory protection is based on address space boundaries ("address space isolation"). Single address-space operating systems use a different approach for memory protection that is just as strong. One advantage is that the same virtual-to-physical map page table can be used with every process (and in some SASOS, the kernel as well). This makes context switches on a SASOS faster than on operating systems that must change the page table and flush the TLB caches on every context switch.
SASOS projects include the following:
Amiga family – AmigaOS, AROS and MorphOS
Angel
BareMetal
Br1X
Genera by Symbolics
IBM i (formerly called OS/400)
Iguana at NICTA, Australia
JX a research Java OS
IncludeOS
Mungi at NICTA, Australia
Nemesis
Opal
OS-9
Phantom OS
RTEMS
Scout
Singularity
Sombrero
TempleOS
Theseus OS
Torsion
VxWorks
Zephyr
See also
Exokernel
Hybrid kernel
Kernel
Microkernel
Nanokernel
Unikernel
Flat memory model
Virtual memory |
https://en.wikipedia.org/wiki/Doomguy | The Doomguy (also spelled Doom Guy, as well as referred to as the Doom Marine, Doom Slayer or just the Slayer in 2016's Doom and Doom Eternal) is a fictional character and the protagonist of the Doom video game franchise of first-person shooters created by id Software. He was created by American video game designer John Romero. He was introduced as the player character in the original 1993 video game Doom. Within the Doom series, Doomguy is a demon hunter space marine dressed in green combat armor who rarely speaks onscreen, and his personality and backstory were intentionally vague to reinforce his role as a player avatar. In Doom Eternal, he is voiced by American voice actor Matthew Waterson, while Jason Kelley voices the character in that game's downloadable content The Ancient Gods: Part Two. He has appeared in several other games developed by id Software, including Quake Champions and Quake III Arena.
He has been featured in several other game franchises, including his likeness as a customizable skin for the Mii Gunner character in Super Smash Bros. Ultimate, being added as an outfit in Fall Guys, and an outfit in Fortnite. He received mainly positive reviews, with some critics praising him for being a competent protagonist.
Concept and creation
The Marine is not referred to by name in the original game. Romero described this choice as increasing player immersion: "There was never a name for the [Doom] marine because it's supposed to be YOU [the player]". The character sprites were created by Adrian Carmack, based on an initial sketch and clay model he made. In 2017, John Romero stated that he was the original model of the character for the cover box art. In 2020, Romero revealed that the real name of the character is Doomguy. In 2021, Doom Eternal director Hugo Martin revealed that the female Doomguy was nearly added, but scrapped due to how much of an endeavor it would have been.
Tom Hall's original design draft, "The Doom Bible", described several planned |
https://en.wikipedia.org/wiki/Weil%20reciprocity%20law | In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K(C) of an algebraic curve C over an algebraically closed field K. Given functions f and g in K(C), i.e. rational functions on C, then
f((g)) = g((f))
where the notation has this meaning: (h) is the divisor of the function h, or in other words the formal sum of its zeroes and poles counted with multiplicity; and a function applied to a formal sum means the product (with multiplicities, poles counting as a negative multiplicity) of the values of the function at the points of the divisor. With this definition there must be the side-condition, that the divisors of f and g have disjoint support (which can be removed).
In the case of the projective line, this can be proved by manipulations with the resultant of polynomials.
To remove the condition of disjoint support, for each point P on C a local symbol
(f, g)P
is defined, in such a way that the statement given is equivalent to saying that the product over all P of the local symbols is 1. When f and g both take the values 0 or ∞ at P, the definition is essentially in limiting or removable singularity terms, by considering (up to sign)
fagb
with a and b such that the function has neither a zero nor a pole at P. This is achieved by taking a to be the multiplicity of g at P, and −b the multiplicity of f at P. The definition is then
(f, g)P = (−1)ab fagb.
See for example Jean-Pierre Serre, Groupes algébriques et corps de classes, pp. 44–46, for this as a special case of a theory on mapping algebraic curves into commutative groups.
There is a generalisation of Serge Lang to abelian varieties (Lang, Abelian Varieties). |
https://en.wikipedia.org/wiki/FFTW | The Fastest Fourier Transform in the West (FFTW) is a software library for computing discrete Fourier transforms (DFTs) developed by Matteo Frigo and Steven G. Johnson at the Massachusetts Institute of Technology.
FFTW is one of the fastest free software implementations of the fast Fourier transform (FFT). It implements the FFT algorithm for real and complex-valued arrays of arbitrary size and dimension.
Library
FFTW expeditiously transforms data by supporting a variety of algorithms and choosing the one (a particular decomposition of the transform into smaller transforms) it estimates or measures to be preferable in the particular circumstances. It works best on arrays of sizes with small prime factors, with powers of two being optimal and large primes being worst case (but still O(n log n)). To decompose transforms of composite sizes into smaller transforms, it chooses among several variants of the Cooley–Tukey FFT algorithm (corresponding to different factorizations and/or different memory-access patterns), while for prime sizes it uses either Rader's or Bluestein's FFT algorithm. Once the transform has been broken up into subtransforms of sufficiently small sizes, FFTW uses hard-coded unrolled FFTs for these small sizes that were produced (at compile time, not at run time) by code generation; these routines use a variety of algorithms including Cooley–Tukey variants, Rader's algorithm, and prime-factor FFT algorithms.
For a sufficiently large number of repeated transforms it is advantageous to measure the performance of some or all of the supported algorithms on the given array size and platform. These measurements, which the authors refer to as "wisdom", can be stored in a file or string for later use.
FFTW has a "guru interface" that intends "to expose as much as possible of the flexibility in the underlying FFTW architecture". This allows, among other things, multi-dimensional transforms and multiple transforms in a single call (e.g., where the data is in |
https://en.wikipedia.org/wiki/Thrinaxodon | Thrinaxodon is an extinct genus of cynodonts, including the species T. liorhinus which lived in what are now South Africa and Antarctica during the Early Triassic. Thrinaxodon lived just after the Permian–Triassic mass extinction event, its survival during the extinction may have been due to its burrowing habits.
Similar to other therapsids, Thrinaxodon adopted a semi-sprawling posture, an intermediary form between the sprawling position of basal tetrapods (still observed in modern Crocodilia) and the more upright posture present in current mammals. Thrinaxodon is prevalent in the fossil record in part because it was one of the few carnivores of its time, and was of a larger size than similar cynodont carnivores.
Description
Thrinaxodon was a small synapsid roughly the size of a fox and possibly covered in hair. The dentition suggests that it was a carnivore, focusing its diet mostly on insects, small herbivores and invertebrates. Their unique secondary palate successfully separated the nasal passages from the rest of the mouth, allowing the Thrinaxodon to continue mastication without interrupting to breathe, an adaptation important for digestion.
Skull
The nasals of Thrinaxodon are pitted with a large number of foramina. The nasals narrow anteriorly and expand anteriorly and articulate directly with the frontals, pre-frontals and lacrimals; however, there is no interaction with the jugals or the orbitals. The maxilla of Thrinaxodon is also heavily pitted with foramina. The arrangement of foramina on the snout of Thrinaxodon resembles lizards such as Tupinambis more than mammals, which bear a single large infraorbital foramen. As such, Thrinaxodon would have had non-muscular lips like those of lizards, not mobile, muscular ones like those of mammals. Without the infraorbital foramen and its associated facial flexibility, it is unlikely that Thrinaxodon would have had whiskers.
On the skull roof of Thrinaxodon, the fronto-nasal suture represents an arrow shape |
https://en.wikipedia.org/wiki/EcoHealth%20Alliance | EcoHealth Alliance is a US-based non-governmental organization with a stated mission of protecting people, animals, and the environment from emerging infectious diseases. The nonprofit is focused on research that aims to prevent pandemics and promote conservation in hotspot regions worldwide.
The EcoHealth Alliance focuses on diseases caused by deforestation and increased interaction between humans and wildlife. The organization has researched the emergence of diseases such as severe acute respiratory syndrome (SARS), Nipah virus, Middle East respiratory syndrome (MERS), Rift Valley fever, the Ebola virus, and COVID-19.
EcoHealth Alliance also advises the World Organization for Animal Health (OIE), the International Union for Conservation of Nature (IUCN), the United Nations Food and Agriculture Organization (FAO), and the World Health Organization (WHO) on global wildlife trade, threats of disease, and the environmental damage posed by these.
Following the outbreak of the COVID-19 pandemic, EcoHealth's ties with the Wuhan Institute of Virology were put into question in relation to investigations into the origin of COVID-19. Citing these concerns, the National Institutes of Health (NIH) withdrew funding to the organization in April 2020. Significant criticism followed this decision, including a joint letter signed by 77 Nobel laureates and 31 scientific societies. The NIH later reinstated funding to the organization as one of 11 institutions partnering in the Centers for Research in Emerging Infectious Diseases (CREID) initiative in August 2020, but all activities funded by the grant remain suspended.
In 2022, the NIH terminated the EcoHealth Alliance grant, stating that "EcoHealth Alliance had not been able to hand over lab notebooks and other records from its Wuhan partner that relate to controversial experiments involving modified bat viruses, despite multiple requests." In 2023, an audit by the Office of Inspector General of the Department of Health and Hum |
https://en.wikipedia.org/wiki/Beam%20emittance | In accelerator physics, emittance is a property of a charged particle beam. It refers to the area occupied by the beam in a position-and-momentum phase space.
Each particle in a beam can be described by its position and momentum along each of three orthogonal axes, for a total of six position and momentum coordinates. When the position and momentum for a single axis are plotted on a two dimensional graph, the average spread of the coordinates on this plot are the emittance. As such, a beam will have three emittances, one along each axis, which can be described independently. As particle momentum along an axis is usually described as an angle relative to that axis, an area on a position-momentum plot will have dimensions of length × angle (for example, millimeters × milliradian).
Emittance is important for analysis of particle beams. As long as the beam is only subjected to conservative forces, Liouville's Theorem shows that emittance is a conserved quantity. If the distribution over phase space is represented as a cloud in a plot (see figure), emittance is the area of the cloud. A variety of more exact definitions handle the fuzzy borders of the cloud and the case of a cloud that does not have an elliptical shape. In addition, the emittance along each axis is independent unless the beam passes through beamline elements (such as solenoid magnets) which correlate them.
A low-emittance particle beam is a beam where the particles are confined to a small distance and have nearly the same momentum, which is a desirable property for ensuring that the entire beam is transported to its destination. In a colliding beam accelerator, keeping the emittance small means that the likelihood of particle interactions will be greater resulting in higher luminosity. In a synchrotron light source, low emittance means that the resulting x-ray beam will be small, and result in higher brightness.
Definitions
The coordinate system used to describe the motion of particles in an ac |
https://en.wikipedia.org/wiki/Radiation%20damping | Radiation damping in accelerator physics is a way of reducing the beam emittance of a high-velocity charged particle beam by synchrotron radiation.
The two main ways of using radiation damping to reduce the emittance of a particle beam are the use of undulators and damping rings (often containing undulators), both relying on the same principle of inducing synchrotron radiation to reduce the particles' momentum, then replacing the momentum only in the desired direction of motion.
Damping rings
As particles are moving in a closed orbit, the lateral acceleration causes them to emit synchrotron radiation, thereby reducing the size of their momentum vectors (relative to the design orbit) without changing their orientation (ignoring quantum effects for the moment). In longitudinal direction, the loss of particle impulse due to radiation is replaced by accelerating sections (RF cavities) that are installed in the beam path so that an equilibrium is reached at the design energy of the accelerator. Since this is not happening in transverse direction, where the emittance of the beam is only increased by the quantization of radiation losses (quantum effects), the transverse equilibrium emittance of the particle beam will be smaller with large radiation losses, compared to small radiation losses.
Because high orbit curvatures (low curvature radii) increase the emission of synchrotron radiation, damping rings are often small. If long beams with many particle bunches are needed to fill a larger storage ring, the damping ring may be extended with long straight sections.
Undulators and wigglers
When faster damping is required than can be provided by the turns inherent in a damping ring, it is common to add undulator or wiggler magnets to induce more synchrotron radiation. These are devices with periodic magnetic fields that cause the particles to oscillate transversely, equivalent to many small tight turns. These operate using the same principle as damping rings and this osci |
https://en.wikipedia.org/wiki/Einstein%20relation%20%28kinetic%20theory%29 | In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation in the classical case is
where
is the diffusion coefficient;
is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, ;
is the Boltzmann constant;
is the absolute temperature.
This equation is an early example of a fluctuation-dissipation relation.
Note that the equation above describes the classical case and should be modified when quantum effects are relevant.
Two frequently used important special forms of the relation are:
Einstein–Smoluchowski equation, for diffusion of charged particles:
Stokes–Einstein equation, for diffusion of spherical particles through a liquid with low Reynolds number:
Here
is the electrical charge of a particle;
is the electrical mobility of the charged particle;
is the dynamic viscosity;
is the radius of the spherical particle.
Special cases
Electrical mobility equation (classical case)
For a particle with electrical charge , its electrical mobility is related to its generalized mobility by the equation . The parameter is the ratio of the particle's terminal drift velocity to an applied electric field. Hence, the equation in the case of a charged particle is given as
where
is the diffusion coefficient ().
is the electrical mobility ().
is the electric charge of particle (C, coulombs)
is the electron temperature or ion temperature in plasma (K).
If the temperature is given in Volt, which is more common for plasma:
where
is the Charge number of particle (unitless)
is electron temperature or ion temperature in plasma (V).
Electrical mobility equation (quantum case)
For the case of Fermi gas (Fermi liquid), relevant for the electron mobility in normal metals, |
https://en.wikipedia.org/wiki/Added%20value | Added value in financial analysis of shares is to be distinguished from value added. It is used as a measure of shareholder value, calculated using the formula:
Added Value = The selling price of a product - the cost of bought-in materials and components
Added Value can also be defined as the difference between a particular product's final selling price and the direct and indirect input used in making that particular product. Also it can be said to be the process of increasing the perceived value of the product in the eyes of the consumers (formally known as the value proposition).
The difference is profit for the firm and its shareholders after all the costs and taxes owed by the business have been paid for that financial year. Value added or any related measure may help investors decide if this is a business that is worthwhile investing on, or that there are other and better opportunities (fixed deposits, debentures).
Example
A jewelry business could display products in an attractive display or offer a gift wrapping service. These changes could make customers more willing to pay a higher price for products that appear to be of higher quality.
Other consultancy measures
For other consultancy measures for shareholder value, see
Economic value added
Market value added |
https://en.wikipedia.org/wiki/Putto | A putto (; plural putti ) is a figure in a work of art depicted as a chubby male child, usually naked and very often winged. Originally limited to profane passions in symbolism, the putto came to represent a sort of baby angel in religious art, often called cherubs (plural cherubim), though in traditional Christian theology a cherub is actually one of the most senior types of angel.
The same figures were also seen in representations of classical myth, and increasingly in general decorative art. In Baroque art the putto came to represent the omnipresence of God. A putto representing a cupid is also called an amorino (plural amorini) or amoretto (plural amoretti).
Etymology
The more commonly found form putti is the plural of the Italian word putto. The Italian word comes from the Latin word putus, meaning "boy" or "child". Today, in Italian, putto means either toddler winged angel or, rarely, toddler boy. It may have been derived from the same Indo-European root as the Sanskrit word "putra" (meaning "boy child", as opposed to "son"), Avestan puθra-, Old Persian puça-, Pahlavi (Middle Persian) pus and pusar, all meaning "son", and the New Persian pesar "boy, son".
History
Putti, in the ancient classical world of art, were winged infants that were believed to influence human lives. In Renaissance art, the form of the putto was derived in various ways including the Greek Eros or Roman Amor/Cupid, the god of love and companion of Aphrodite or Venus; the Roman, genius, a type of guardian spirit; or sometimes the Greek, daemon, a type of messenger spirit, being halfway between the realms of the human and the divine.
Revival of the putto in the Renaissance
Putti are a classical motif found primarily on child sarcophagi of the 2nd century, where they are depicted fighting, dancing, participating in bacchic rites, playing sports, etc.
The putto disappeared during the Middle Ages and was revived during the Quattrocento. The revival of the figure of the putto is genera |
https://en.wikipedia.org/wiki/Johnjoe%20McFadden | Johnjoe McFadden (born 17 May 1956) is an Anglo-Irish scientist, academic and writer. He is Professor of Molecular Genetics at the University of Surrey, United Kingdom.
Life
McFadden was born in Donegal, Ireland but raised in the UK. He holds joint British and Irish Nationality. He obtained his BSc in Biochemistry University of London in 1977 and his PhD at Imperial College London in 1982. He went on to work on human genetic diseases and then infectious diseases, at St Mary's Hospital Medical School, London (1982–84) and St George's Hospital Medical School, London (1984–88) and then at the University of Surrey in Guildford, UK.
For more than a decade, McFadden has researched the genetics of microbes such as the agents of tuberculosis and meningitis and invented a test for the diagnosis of meningitis. He has published more than 100 articles in scientific journals on subjects as wide-ranging as bacterial genetics, tuberculosis, idiopathic diseases and computer modelling of evolution. He has contributed to more than a dozen books and has edited a book on the genetics of mycobacteria. He produced a widely reported artificial life computer model which modelled evolution in organisms.
McFadden has lectured extensively in the UK, Europe, the US and Japan and his work has been featured on radio, television and national newspaper articles particularly for the Guardian. His present post, which he has held since 2001, is Professor of Molecular Genetics at the University of Surrey. Living in London, he is married and has one son.
Quantum evolution
McFadden wrote the popular science book, Quantum Evolution. The book examines the role of quantum mechanics in life, evolution and consciousness. The book has been described as offering an alternative evolutionary mechanism, beyond the neo-Darwinian framework.
The book received positive reviews by Kirkus Reviews and Publishers Weekly. It was negatively reviewed in the journal Heredity by evolutionary biologist Wallace Arthur.
W |
https://en.wikipedia.org/wiki/Lufenuron | Lufenuron is the active ingredient in the veterinary flea control medication Program, and one of the two active ingredients in the flea, heartworm, ringworm and anthelmintic medicine milbemycin oxime/lufenuron (Sentinel).
Lufenuron is stored in the animal's body fat and transferred to adult fleas through the host's blood when they feed. Adult fleas transfer it to their growing eggs through their blood, and to hatched larvae feeding on their excrement. It does not kill adult fleas.
Lufenuron, a benzoylurea pesticide, inhibits the production of chitin in insects. Without chitin, a larval flea will never develop a hard outer shell (exoskeleton). With its inner organs exposed to air, the insect dies from dehydration soon after hatching or molting (shedding its old, smaller shell).
Lufenuron is also used to fight fungal infections, since fungus cell walls are about one third chitin.
Lufenuron is also sold as an agricultural pesticide for use against lepidopterans, eriophyid mites, and western flower thrips. It is an effective antifungal in plants. |
https://en.wikipedia.org/wiki/Radiant%20flux | In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiant flux is the watt (W), one joule per second (), while that of spectral flux in frequency is the watt per hertz () and that of spectral flux in wavelength is the watt per metre ()—commonly the watt per nanometre ().
Mathematical definitions
Radiant flux
Radiant flux, denoted ('e' for "energetic", to avoid confusion with photometric quantities), is defined as
where
is the time;
is the radiant energy flux of the field out of a closed surface ;
is the Poynting vector, representing the current density of radiant energy;
is the normal vector of a point on ;
represents the area of .
But the time-average of the norm of the Poynting vector is used instead, because in radiometry it is the only quantity that radiation detectors are able to measure:
where is the time-average, and is the angle between and
Spectral flux
Spectral flux in frequency, denoted Φe,ν, is defined as
where is the frequency.
Spectral flux in wavelength, denoted , is defined as
where is the wavelength.
SI radiometry units
See also
Luminous flux
Heat flux
Power (physics)
Radiosity (heat transfer) |
https://en.wikipedia.org/wiki/Extravasation%20%28intravenous%29 | Extravasation is the leakage of intravenously (IV) infused, and potentially damaging, medications into the extravascular tissue around the site of infusion. The leakage can occur through brittle veins in the elderly, through previous venipuncture access, or through direct leakage from wrongly positioned venous access devices. When the leakage is not of harmful consequence it is known as infiltration. Extravasation of medication during intravenous therapy is an adverse event related to therapy that, depending on the medication, amount of exposure, and location, can potentially cause serious injury and permanent harm, such as tissue necrosis. Milder consequences of extravasation include irritation, characterized by symptoms of pain and inflammation, with the clinical signs of warmth, erythema, or tenderness.
Medications
Complications related to extravasation are possible with any medication. Since vesicants are blistering agents, extravasation may lead to irreversible tissue injury.
Extravasation is particularly serious during chemotherapy, since chemotherapy medications are highly toxic.
Treatment
The best "treatment" of extravasation is prevention. Depending on the medication that has extravasated, there are potential management options and treatments that aim to minimize damage, although the effectiveness of many of these treatments has not been well studied. In cases of tissue necrosis, surgical debridement and reconstruction may be necessary. The following steps are typically involved in managing extravasation:
Stop infusion immediately. Put on sterile gloves.
Replace infusion lead with a disposable syringe. While doing this, do not exert pressure on the extravasation area.
Slowly aspirate back blood back from the arm, preferably with as much of the infusion solution as possible.
Remove the original cannula or other IV access carefully from the arm (removal of the original cannula is not advised by all healthcare institutions, as access to the original cann |
https://en.wikipedia.org/wiki/Van%20Deemter%20equation | The van Deemter equation in chromatography, named for Jan van Deemter, relates the variance per unit length of a separation column to the linear mobile phase velocity by considering physical, kinetic, and thermodynamic properties of a separation. These properties include pathways within the column, diffusion (axial and longitudinal), and mass transfer kinetics between stationary and mobile phases. In liquid chromatography, the mobile phase velocity is taken as the exit velocity, that is, the ratio of the flow rate in ml/second to the cross-sectional area of the ‘column-exit flow path.’ For a packed column, the cross-sectional area of the column exit flow path is usually taken as 0.6 times the cross-sectional area of the column. Alternatively, the linear velocity can be taken as the ratio of the column length to the dead time. If the mobile phase is a gas, then the pressure correction must be applied. The variance per unit length of the column is taken as the ratio of the column length to the column efficiency in theoretical plates. The van Deemter equation is a hyperbolic function that predicts that there is an optimum velocity at which there will be the minimum variance per unit column length and, thence, a maximum efficiency. The van Deemter equation was the result of the first application of rate theory to the chromatography elution process.
Van Deemter equation
The van Deemter equation relates height equivalent to a theoretical plate (HETP) of a chromatographic column to the various flow and kinetic parameters which cause peak broadening, as follows:
Where
HETP = a measure of the resolving power of the column [m]
A = Eddy-diffusion parameter, related to channeling through a non-ideal packing [m]
B = diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion [m2 s−1]
C = Resistance to mass transfer coefficient of the analyte between mobile and stationary phase [s]
u = speed [m s−1]
In open tubular capillar |
https://en.wikipedia.org/wiki/Trudinger%27s%20theorem | In mathematical analysis, Trudinger's theorem or the Trudinger inequality (also sometimes called the Moser–Trudinger inequality) is a result of functional analysis on Sobolev spaces. It is named after Neil Trudinger (and Jürgen Moser).
It provides an inequality between a certain Sobolev space norm and an Orlicz space norm of a function. The inequality is a limiting case of Sobolev imbedding and can be stated as the following theorem:
Let be a bounded domain in satisfying the cone condition. Let and . Set
Then there exists the embedding
where
The space
is an example of an Orlicz space. |
https://en.wikipedia.org/wiki/Transudate | Transudate is extravascular fluid with low protein content and a low specific gravity (< 1.012). It has low nucleated cell counts (less than 500 to 1000 /microliter) and the primary cell types are mononuclear cells: macrophages, lymphocytes and mesothelial cells. For instance, an ultrafiltrate of blood plasma is transudate. It results from increased fluid pressures or diminished colloid oncotic forces in the plasma.
Transudate vs. exudate
There is an important distinction between transudates and exudates. Transudates are caused by disturbances of hydrostatic or colloid osmotic pressure, not by inflammation. They have a low protein content in comparison to exudates and thus appear clearer.
Levels of lactate dehydrogenase (LDH) or a Rivalta test can be used to distinguish transudate from exudate.
Their main role in nature is to protect elements of the skin and other subcutaneous substances against the contact effects of external climate and the environment and other substances – it also plays a role in integumental hygiene.
Pathology
The most common causes of pathologic transudate include conditions that :
Increase hydrostatic pressure in vessels : left ventricular heart failure,
Decrease oncotic pressure in blood vessels :
Cirrhosis (Cirrhosis leads to hypoalbuminemia and decreasing of colloid oncotic pressure in plasma that causes edema)
Nephrotic syndrome (also due to hypoalbuminemia caused by proteinuria).
Malnutrition (hypoalbuminism)
See also
Exudate |
https://en.wikipedia.org/wiki/Wabun%20code | is a form of Morse code used to send Japanese language in kana characters. Unlike International Morse Code, which represents letters of the Latin script, in Wabun each symbol represents a Japanese kana. For this reason, Wabun code is also sometimes called Kana code.
When Wabun code is intermixed with International Morse code, the prosign DO () is used to announce the beginning of Wabun, and the prosign SN () is used to announce the return to International Code.
Chart
Kana in Iroha order.
Expanded chart |
https://en.wikipedia.org/wiki/Dimensional%20transmutation | In particle physics, dimensional transmutation is a physical mechanism providing a linkage between a dimensionless parameter and a dimensionful parameter.
In classical field theory, such as gauge theory in four-dimensional spacetime, the coupling constant is a dimensionless constant. However, upon quantization, logarithmic divergences in one-loop diagrams of perturbation theory imply that this "constant" actually depends on the typical energy scale of the processes under considerations, called the renormalization group (RG) scale. This "running" of the coupling is specified by the beta-function of the renormalization group.
Consequently, the interaction may be characterised by a dimensionful parameter , namely the value of the RG scale at which the coupling constant diverges. In the case of quantum chromodynamics, this energy scale is called the QCD scale, and its value 220 MeV supplants the role of the original dimensionless coupling constant in the form of the logarithm (at one-loop) of the ratio and . Perturbation theory, which produced this type of running formula, is only valid for a (dimensionless) coupling ≪ 1. In the case of QCD, the energy scale is an infrared cutoff, such that implies , with the RG scale.
On the other hand, in the case of theories such as QED, is an ultraviolet cutoff, such that implies .
This is also a way of saying that the conformal symmetry of the classical theory is anomalously broken upon quantization, thereby setting up a mass scale. See conformal anomaly.
Quantum field theory
Renormalization group |
https://en.wikipedia.org/wiki/Momentum%20transfer | In particle physics, wave mechanics, and optics, momentum transfer is the amount of momentum that one particle gives to another particle. It is also called the scattering vector as it describes the transfer of wavevector in wave mechanics.
In the simplest example of scattering of two colliding particles with initial momenta , resulting in final momenta , the momentum transfer is given by
where the last identity expresses momentum conservation. Momentum transfer is an important quantity because is a better measure for the typical distance resolution of the reaction than the momenta themselves.
Wave mechanics and optics
A wave has a momentum and is a vectorial quantity. The difference of the momentum of the scattered wave to the incident wave is called momentum transfer. The wave number k is the absolute of the wave vector and is related to the wavelength . Momentum transfer is given in wavenumber units in reciprocal space
Diffraction
The momentum transfer plays an important role in the evaluation of neutron, X-ray, and electron diffraction for the investigation of condensed matter. Laue-Bragg diffraction occurs on the atomic crystal lattice, conserves the wave energy and thus is called elastic scattering, where the wave numbers final and incident particles, and , respectively, are equal and just the direction changes by a reciprocal lattice vector with the relation to the lattice spacing . As momentum is conserved, the transfer of momentum occurs to crystal momentum.
The presentation in reciprocal space is generic and does not depend on the type of radiation and wavelength used but only on the sample system, which allows to compare results obtained from many different methods. Some established communities such as powder diffraction employ the diffraction angle as the independent variable, which worked fine in the early years when only a few characteristic wavelengths such as Cu-K were available. The relationship to -space is
with and basically states tha |
https://en.wikipedia.org/wiki/Tunnel%20injection | Tunnel injection is a field electron emission effect; specifically a quantum process called Fowler–Nordheim tunneling, whereby charge carriers are injected to an electric conductor through a thin layer of an electric insulator.
It is used to program NAND flash memory. The process used for erasing is called tunnel release. This injection is achieved by creating a large voltage difference between the gate and the body of the MOSFET. When VGB >> 0, electrons are injected into the floating gate. When VGB << 0, electrons are forced out of the floating gate.
An alternative to tunnel injection is the spin injection.
See also
Hot carrier injection |
https://en.wikipedia.org/wiki/Quenched%20approximation | In lattice field theory, the quenched approximation is an approximation often used in lattice gauge theory in which the quantum loops of fermions in Feynman diagrams are neglected. Equivalently, the corresponding one-loop determinants are set to one. This approximation is often forced upon the physicists because the calculation with the Grassmann numbers is computationally very difficult in lattice gauge theory.
In particular, quenched QED is QED without dynamical electrons, and quenched QCD is QCD without dynamical quarks.
Recent calculations typically avoid the quenched approximation. |
https://en.wikipedia.org/wiki/Split%20supersymmetry | In particle physics, split supersymmetry is a proposal for physics beyond the Standard Model.
History
It was proposed separately in three papers. The first by James Wells in June 2003 in a more modest form that mildly relaxed the assumption about naturalness in the Higgs potential. In May 2004 Nima Arkani-Hamed and Savas Dimopoulos argued that naturalness in the Higgs sector may not be an accurate guide to propose new physics beyond the Standard Model and argued that supersymmetry may be realized in a different fashion that preserved gauge coupling unification and has a dark matter candidate. In June 2004 Gian Giudice and Andrea Romanino argued from a general point of view that if one wants gauge coupling unification and a dark matter candidate, that split supersymmetry is one amongst a few theories that exists.
Overview
The new light (~TeV) particles in Split Supersymmetry (beyond the Standard Models particles) are
The Lagrangian for Split Supersymmetry is constrained from the existence of high energy supersymmetry. There are five couplings in Split Supersymmetry: the Higgs quartic coupling and four Yukawa couplings between the Higgsinos, Higgs and gauginos. The couplings are set by one parameter, , at the scale where the supersymmetric scalars decouple. Beneath the supersymmetry breaking scale, these five couplings evolve through the renormalization group equation down to the TeV scale. At a future Linear collider, these couplings could be measured at the 1% level and then renormalization group evolved up to high energies to show that the theory is supersymmetric at an exceedingly high scale.
Long Lived Gluinos
The striking feature of split supersymmetry is that the gluino becomes a quasi-stable particle with a lifetime that could be up to 100 seconds long. A gluino that lived longer than this would disrupt Big Bang nucleosynthesis or would have been observed as an additional source of cosmic gamma rays. The gluino is long lived because it can only de |
https://en.wikipedia.org/wiki/Penetron | The penetron, short for penetration tube, is a type of limited-color television used in some military applications. Unlike a conventional color television, the penetron produces a limited color gamut, typically two colors and their combination. Penetrons, and other military-only cathode ray tubes (CRTs), have been replaced by LCDs in modern designs.
History
Basic television
A conventional black and white television (B&W) uses a tube that is uniformly coated with a phosphor on the inside face. When excited by high-speed electrons, the phosphor gives off light, typically white but other colors are also used in certain circumstances. An electron gun at the back of the tube provides a beam of high-speed electrons, and a set of electromagnets arranged near the gun allow the beam to be moved about the display. The television signal is sent as a series of stripes, each one of which is displayed as a separate line on the display. The strength of the signal increases or decreases the current in the beam, producing bright or dark points on the display as the beam sweeps across the tube.
In a color display, the uniform coating of white phosphor is replaced by dots or lines of three colored phosphors, producing red, green or blue light (RGB) when excited. These primary colors mix in the human eye to produce a single apparent color. This presents a problem for conventional electron guns, which cannot be focussed or positioned accurately enough to hit these much smaller individual patterns. A number of companies were working on various solutions to this problem in the late 1940s, using three separate tubes or a single white-output with colored filters placed in front of it. None of these proved practical and this was a field of considerable development interest.
Penetron
The penetron was original designed by Koller and Williams while working at General Electric (GE). It was initially developed as a novel way to build a single-gun color television with the simplicity of a co |
https://en.wikipedia.org/wiki/Penrose%20graphical%20notation | In mathematics and physics, Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions or tensors proposed by Roger Penrose in 1971. A diagram in the notation consists of several shapes linked together by lines.
The notation widely appears in modern quantum theory, particularly in matrix product states and quantum circuits. In particular, Categorical quantum mechanics which includes ZX-calculus is a fully comprehensive reformulation of quantum theory in terms of Penrose diagrams, and is now widely used in quantum industry.
The notation has been studied extensively by Predrag Cvitanović, who used it, along with Feynman's diagrams and other related notations in developing "birdtracks", a group-theoretical diagram to classify the classical Lie groups. Penrose's notation has also been generalized using representation theory to spin networks in physics, and with the presence of matrix groups to trace diagrams in linear algebra.
Interpretations
Multilinear algebra
In the language of multilinear algebra, each shape represents a multilinear function. The lines attached to shapes represent the inputs or outputs of a function, and attaching shapes together in some way is essentially the composition of functions.
Tensors
In the language of tensor algebra, a particular tensor is associated with a particular shape with many lines projecting upwards and downwards, corresponding to abstract upper and lower indices of tensors respectively. Connecting lines between two shapes corresponds to contraction of indices. One advantage of this notation is that one does not have to invent new letters for new indices. This notation is also explicitly basis-independent.
Matrices
Each shape represents a matrix, and tensor multiplication is done horizontally, and matrix multiplication is done vertically.
Representation of special tensors
Metric tensor
The metric tensor is represented by a U-shaped loop or an upside- |
https://en.wikipedia.org/wiki/Diffeomorphism%20constraint | In theoretical physics, it is often important to study theories with the diffeomorphism symmetry such as general relativity. These theories are invariant under arbitrary coordinate transformations. Equations of motion are generally derived from the requirement that the action is stationary. There are special variations that are equivalent to spatial diffeomorphisms. The invariance of the action under these variations implies non-dynamical equations of motion i.e. constraints. These equations must be satisfied or, at least, they must annihilate the physical states in a quantum version of the theory.
See also
Wheeler–DeWitt equation
Quantum gravity
Diffeomorphisms |
https://en.wikipedia.org/wiki/Cosmological%20natural%20selection | Cosmological natural selection, also called the fecund universes, is a hypothesis proposed by Lee Smolin intended as a scientific alternative to the anthropic principle. It addresses the problem of complexity in our universe, which is largely unexplained. The hypothesis suggests that a process analogous to biological natural selection applies at the grandest of scales. Smolin published the idea in 1992 and summarized it in a book aimed at a lay audience called The Life of the Cosmos.
Hypothesis
Black holes have a role in natural selection. In fecund theory a collapsing black hole causes the emergence of a new universe on the "other side", whose fundamental constant parameters (masses of elementary particles, Planck constant, elementary charge, and so forth) may differ slightly from those of the universe where the black hole collapsed. Each universe thus gives rise to as many new universes as it has black holes. The theory contains the evolutionary ideas of "reproduction" and "mutation" of universes, and so is formally analogous to models of population biology.
Alternatively, black holes play a role in cosmological natural selection by reshuffling only some matter affecting the distribution of elementary quark universes. The resulting population of universes can be represented as a distribution of a landscape of parameters where the height of the landscape is proportional to the numbers of black holes that a universe with those parameters will have. Applying reasoning borrowed from the study of fitness landscapes in population biology, one can conclude that the population is dominated by universes whose parameters drive the production of black holes to a local peak in the landscape. This was the first use of the notion of a landscape of parameters in physics.
Leonard Susskind, who later promoted a similar string theory landscape, stated:
I'm not sure why Smolin's idea didn't attract much attention. I actually think it deserved far more than it got.
Howe |
https://en.wikipedia.org/wiki/Higgs%20phase | In theoretical physics, it is often important to consider gauge theory that admits many physical phenomena and "phases", connected by phase transitions, in which the vacuum may be found.
Global symmetries in a gauge theory may be broken by the Higgs mechanism. In more general theories such as those relevant in string theory, there are often many Higgs fields that transform in different representations of the gauge group.
If they transform in the adjoint representation or a similar representation, the original gauge symmetry is typically broken to a product of U(1) factors. Because U(1) describes electromagnetism including the Coulomb field, the corresponding phase is called a Coulomb phase.
If the Higgs fields that induce the spontaneous symmetry breaking transform in other representations, the Higgs mechanism often breaks the gauge group completely and no U(1) factors are left. In this case, the corresponding vacuum expectation values describe a Higgs phase.
Using the representation of a gauge theory in terms of a D-brane, for example D4-brane combined with D0-branes, the Coulomb phase describes D0-branes that have left the D4-branes and carry their own independent U(1) symmetries. The Higgs phase describes D0-branes dissolved in the D4-branes as instantons. |
https://en.wikipedia.org/wiki/Computer%20facial%20animation | Computer facial animation is primarily an area of computer graphics that encapsulates methods and techniques for generating and animating images or models of a character face. The character can be a human, a humanoid, an animal, a legendary creature or character, etc. Due to its subject and output type, it is also related to many other scientific and artistic fields from psychology to traditional animation. The importance of human faces in verbal and non-verbal communication and advances in computer graphics hardware and software have caused considerable scientific, technological, and artistic interests in computer facial animation.
Although development of computer graphics methods for facial animation started in the early-1970s, major achievements in this field are more recent and happened since the late 1980s.
The body of work around computer facial animation can be divided into two main areas: techniques to generate animation data, and methods to apply such data to a character. Techniques such as motion capture and keyframing belong to the first group, while morph targets animation (more commonly known as blendshape animation) and skeletal animation belong to the second. Facial animation has become well-known and popular through animated feature films and computer games but its applications include many more areas such as communication, education, scientific simulation, and agent-based systems (for example online customer service representatives). With the recent advancements in computational power in personal and mobile devices, facial animation has transitioned from appearing in pre-rendered content to being created at runtime.
History
Human facial expression has been the subject of scientific investigation for more than one hundred years. Study of facial movements and expressions started from a biological point of view. After some older investigations, for example by John Bulwer in the late 1640s, Charles Darwin's book The Expression of the Emotions in Men |
https://en.wikipedia.org/wiki/Myocardial%20contractility | Myocardial contractility represents the innate ability of the heart muscle (cardiac muscle or myocardium) to contract. The ability to produce changes in force during contraction result from incremental degrees of binding between different types of tissue, that is, between filaments of myosin (thick) and actin (thin) tissue. The degree of binding depends upon the concentration of calcium ions in the cell.
Within an in vivo intact heart, the action/response of the sympathetic nervous system is driven by precisely timed releases of a catecholamine, which is a process that determines the concentration of calcium ions in the cytosol of cardiac muscle cells. The factors causing an increase in contractility work by causing an increase in intracellular calcium ions (Ca++) during contraction.
Mechanisms for altering contractility
Increasing contractility is done primarily through increasing the influx of calcium or maintaining higher calcium levels in the cytosol of cardiac myocytes during an action potential. This is done by a number of mechanisms:
Sympathetic activation. Increased circulating levels of catecholamines (which can bind to β-Adrenergic activation) as well as stimulation by sympathetic nerves (which can release norepinepherine that binds to β1-adrenoceptors on myocytes) causes the Gs subunit of the receptor to render adenylate cyclase activated, resulting in increase of cAMP - which has a number of effects including phosphorylating phospholamban (via Protein kinase A).
Phosphorylating phospholamban. When phospholamban is not phosphorylated, it inhibits the calcium pumps that pump calcium back into the sarcoplasmic reticulum. When it's phosphorylated by PKA, levels of calcium stored in the sarcoplasmic reticulum are increased, allowing a higher rate of calcium being released at the next contraction. However, the increased rate of calcium sequestration also leads to an increase in lusitropy.
Sensitizing troponin-C to the effects of calcium.
Phosphorylating |
https://en.wikipedia.org/wiki/Idempotent%20matrix | In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix is idempotent if and only if . For this product to be defined, must necessarily be a square matrix. Viewed this way, idempotent matrices are idempotent elements of matrix rings.
Example
Examples of idempotent matrices are:
Examples of idempotent matrices are:
Real 2 × 2 case
If a matrix is idempotent, then
implying so or
implying so or
Thus, a necessary condition for a matrix to be idempotent is that either it is diagonal or its trace equals 1.
For idempotent diagonal matrices, and must be either 1 or 0.
If , the matrix will be idempotent provided so a satisfies the quadratic equation
or
which is a circle with center (1/2, 0) and radius 1/2. In terms of an angle θ,
is idempotent.
However, is not a necessary condition: any matrix
with is idempotent.
Properties
Singularity and regularity
The only non-singular idempotent matrix is the identity matrix; that is, if a non-identity matrix is idempotent, its number of independent rows (and columns) is less than its number of rows (and columns).
This can be seen from writing , assuming that has full rank (is non-singular), and pre-multiplying by to obtain .
When an idempotent matrix is subtracted from the identity matrix, the result is also idempotent. This holds since
If a matrix is idempotent then for all positive integers n, . This can be shown using proof by induction. Clearly we have the result for , as . Suppose that . Then, , since is idempotent. Hence by the principle of induction, the result follows.
Eigenvalues
An idempotent matrix is always diagonalizable. Its eigenvalues are either 0 or 1: if is a non-zero eigenvector of some idempotent matrix and its associated eigenvalue, then which implies This further implies that the determinant of an idempotent matrix is always 0 or 1. As stated above, if the determinant is equal to one, the matrix is i |
https://en.wikipedia.org/wiki/Belling-Lee%20connector | The Belling-Lee connector (also type 9,52, but largely only in the context of its specification, IEC 61169, Part 2: Radio-frequency coaxial connector of type 9,52) is commonly used in Europe, parts of South-East Asia, and Australia, to connect coaxial cables with each other and with terrestrial VHF/UHF roof antennas, antenna signal amplifiers, CATV distribution equipment, TV sets, and FM and DAB radio receivers. In these countries, it is known colloquially as a PAL antenna connector, IEC antenna connector, or simply as a TV aerial plug. It is one of the oldest coaxial connectors still commonly used in consumer devices. For television signals, the convention is that the source has a male connector and the receptor has a female connector. For FM radio signals, the convention is that the source has a female connector and the receptor has a male connector. This is more or less universally adopted with TV signals, while it's not uncommon for FM radio receivers to deviate from this, especially FM radio receivers from companies not based in the areas that use this kind of connector.
It was invented at Belling & Lee Ltd in Enfield, United Kingdom around 1922 at the time of the first BBC broadcasts. Originally intended for use only at MF frequencies (up to 1.6 MHz) when adopted for Television they were used for frequencies as high as 957 MHz. Belling Lee Limited still exists as a wholly owned subsidiary of Dialight, since 1992.
In type 9,52, the 9,52, in French SI style, refers to the 9.525mm (, or 0.375in) male external and female internal connector body diameter.
In their most common form the connectors just slide together. There is, however, also a screw-coupled variant which is specified to have an M14×1 thread.
There is also a miniature Belling-Lee connector which was used for internal connections inside some equipment (including BBC RC5/3 Band II receiver and the STC AF101 Radio Telephone). The miniature version is only about in diameter.
See also
List of RF c |
https://en.wikipedia.org/wiki/Dependence%20relation | In mathematics, a dependence relation is a binary relation which generalizes the relation of linear dependence.
Let be a set. A (binary) relation between an element of and a subset of is called a dependence relation, written , if it satisfies the following properties:
if , then ;
if , then there is a finite subset of , such that ;
if is a subset of such that implies , then implies ;
if but for some , then .
Given a dependence relation on , a subset of is said to be independent if for all If , then is said to span if for every is said to be a basis of if is independent and spans
Remark. If is a non-empty set with a dependence relation , then always has a basis with respect to Furthermore, any two bases of have the same cardinality.
Examples
Let be a vector space over a field The relation , defined by if is in the subspace spanned by , is a dependence relation. This is equivalent to the definition of linear dependence.
Let be a field extension of Define by if is algebraic over Then is a dependence relation. This is equivalent to the definition of algebraic dependence.
See also
matroid
Linear algebra
Binary relations |
https://en.wikipedia.org/wiki/Kolmogorov%27s%20inequality | In probability theory, Kolmogorov's inequality is a so-called "maximal inequality" that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound.
Statement of the inequality
Let X1, ..., Xn : Ω → R be independent random variables defined on a common probability space (Ω, F, Pr), with expected value E[Xk] = 0 and variance Var[Xk] < +∞ for k = 1, ..., n. Then, for each λ > 0,
where Sk = X1 + ... + Xk.
The convenience of this result is that we can bound the worst case deviation of a random walk at any point of time using its value at the end of time interval.
Proof
The following argument employs discrete martingales.
As argued in the discussion of Doob's martingale inequality, the sequence is a martingale.
Define as follows. Let , and
for all .
Then is also a martingale.
For any martingale with , we have that
Applying this result to the martingale , we have
where the first inequality follows by Chebyshev's inequality.
This inequality was generalized by Hájek and Rényi in 1955.
See also
Chebyshev's inequality
Etemadi's inequality
Landau–Kolmogorov inequality
Markov's inequality
Bernstein inequalities (probability theory) |
https://en.wikipedia.org/wiki/Superradiance | In physics, superradiance is the radiation enhancement effects in several contexts including quantum mechanics, astrophysics and relativity.
Quantum optics
In quantum optics, superradiance is a phenomenon that occurs when a group of N emitters, such as excited atoms, interact with a common light field. If the wavelength of the light is much greater than the separation of the emitters, then the emitters interact with the light in a collective and coherent fashion. This causes the group to emit light as a high-intensity pulse (with rate proportional to N2). This is a surprising result, drastically different from the expected exponential decay (with rate proportional to N) of a group of independent atoms (see spontaneous emission). Superradiance has since been demonstrated in a wide variety of physical and chemical systems, such as quantum dot arrays and J-aggregates. This effect has been used to produce a superradiant laser.
Rotational superradiance
Rotational superradiance is associated with the acceleration or motion of a nearby body (which supplies the energy and momentum for the effect). It is also sometimes described as the consequence of an "effective" field differential around the body (e.g. the effect of tidal forces). This allows a body with a concentration of angular or linear momentum to move towards a lower energy state, even when there is no obvious classical mechanism for this to happen. In this sense, the effect has some similarities with quantum tunnelling (e.g. the tendency of waves and particles to "find a way" to exploit the existence of an energy potential, despite the absence of an obvious classical mechanism for this to happen).
In classical physics, the motion or rotation of a body in a particulate medium will normally be expected to result in momentum and energy being transferred to the surrounding particles, and there is then an increased statistical likelihood of particles being discovered following trajectories that imply removal of m |
https://en.wikipedia.org/wiki/Penrose%20process | The Penrose process (also called Penrose mechanism) is theorised by Sir Roger Penrose as a means whereby energy can be extracted from a rotating black hole. The process takes advantage of the ergosphere – a region of spacetime around the black hole dragged by its rotation faster than the speed of light, meaning that from the point of an outside observer any matter inside is forced to move in the direction of the rotation of the black hole.
In the process, a working body falls (black thick line in the figure) into the ergosphere (gray region). At its lowest point (red dot) the body fires a propellant backwards; however, to a faraway observer both seem to continue to move forward due to frame-dragging (albeit at different speeds). The propellant, being slowed, falls (thin gray line) to the event horizon of the black hole (black disk). The remains of the body, being sped up, fly away (thin black line) with an excess of energy (that more than offsets the loss of the propellant and the energy used to shoot it).
The maximum amount of energy gain possible for a single particle decay via the original (or classical) Penrose process is 20.7% of its mass in the case of an uncharged black hole (assuming the best case of maximal rotation of the black hole). The energy is taken from the rotation of the black hole, so there is a limit on how much energy one can extract by Penrose process and similar strategies (for an uncharged black hole no more than 29% of its original mass; larger efficiencies are possible for charged rotating black holes).
Details of the ergosphere
The outer surface of the ergosphere is the surface at which light that moves in the direction opposite to the rotation of the black hole remains at a fixed angular coordinate, according to an external observer. Since massive particles necessarily travel slower than light, massive particles will necessarily move along with the black hole's rotation. The inner boundary of the ergosphere is the event horizon, the s |
https://en.wikipedia.org/wiki/Trust%20region | In mathematical optimization, a trust region is the subset of the region of the objective function that is approximated using a model function (often a quadratic). If an adequate model of the objective function is found within the trust region, then the region is expanded; conversely, if the approximation is poor, then the region is contracted.
The fit is evaluated by comparing the ratio of expected improvement from the model approximation with the actual improvement observed in the objective function. Simple thresholding of the ratio is used as the criterion for expansion and contraction—a model function is "trusted" only in the region where it provides a reasonable approximation.
Trust-region methods are in some sense dual to line-search methods: trust-region methods first choose a step size (the size of the trust region) and then a step direction, while line-search methods first choose a step direction and then a step size.
The general idea behind trust region methods is known by many names; the earliest use of the term seems to be by Sorensen (1982). A popular textbook by Fletcher (1980) calls these algorithms restricted-step methods. Additionally, in an early foundational work on the method, Goldfeld, Quandt, and Trotter (1966) refer to it as quadratic hill-climbing.
Example
Conceptually, in the Levenberg–Marquardt algorithm, the objective function is iteratively approximated by a quadratic surface, then using a linear solver, the estimate is updated. This alone may not converge nicely if the initial guess is too far from the optimum. For this reason, the algorithm instead restricts each step, preventing it from stepping "too far". It operationalizes "too far" as follows. Rather than solving for , it solves , where is the diagonal matrix with the same diagonal as A, and λ is a parameter that controls the trust-region size. Geometrically, this adds a paraboloid centered at to the quadratic form, resulting in a smaller step.
The trick is to change the t |
https://en.wikipedia.org/wiki/Three%20men%20make%20a%20tiger | "Three men make a tiger" () is a Chinese proverb or chengyu (four-character idiom). "Three men make a tiger" refers to an individual's tendency to accept absurd information as long as it is repeated by enough people. It refers to the idea that if an unfounded premise or urban legend is mentioned and repeated by many individuals, the premise will be erroneously accepted as the truth. This concept is related to communal reinforcement or the fallacy of argumentum ad populum and argumentum ad nauseam.
Origin
The proverb came from the story of an alleged speech by Pang Cong (), an official of the state of Wei in the Warring States period (475 BC – 221 BC) in Chinese History. According to the Warring States Records, or Zhan Guo Ce, before he left on a trip to the state of Zhao, Pang Cong asked the King of Wei whether he would hypothetically believe in one civilian's report that a tiger was roaming the markets in the capital city, to which the King replied no. Pang Cong asked what the King thought if two people reported the same thing, and the King said he would begin to wonder. Pang Cong then asked, "what if three people all claimed to have seen a tiger?" The King replied that he would believe in it. Pang Cong reminded the King that the notion of a live tiger in a crowded market was absurd, yet when repeated by numerous people, it seemed real.
Since Pang Cong, as a high-ranking official, had more than three opponents and critics, he was in fact urging the King to pay no attention to those who would spread rumors about him (Pang Cong) while he was away. "I understand", the King replied, and Pang Cong left for Zhao. Yet, slanderous talk took place. When Pang Cong returned to Wei, the King indeed stopped seeing him.
Cognitive biases
The tendency to accept absurd information is caused by certain cognitive biases. The first of which is the motivated reasoning concept, which is an emotion-biased decision-making phenomenon. It is the idea that humans are motivated to b |
https://en.wikipedia.org/wiki/Distribution%20%28differential%20geometry%29 | In differential geometry, a discipline within mathematics, a distribution on a manifold is an assignment of vector subspaces satisfying certain properties. In the most common situations, a distribution is asked to be a vector subbundle of the tangent bundle .
Distributions satisfying a further integrability condition give rise to foliations, i.e. partitions of the manifold into smaller submanifolds. These notions have several applications in many fields of mathematics, e.g. integrable systems, Poisson geometry, non-commutative geometry, sub-Riemannian geometry, differential topology, etc.
Even though they share the same name, distributions presented in this article have nothing to do with distributions in the sense of analysis.
Definition
Let be a smooth manifold; a (smooth) distribution assigns to any point a vector subspace in a smooth way. More precisely, consists in a collection of vector subspaces with the following property. Around any there exist a neighbourhood and a collection of vector fields such that, for any point , span
The set of smooth vector fields is also called a local basis of . Note that the number may be different for different neighbourhoods. The notation is used to denote both the assignment and the subset .
Regular distributions
Given an integer , a smooth distribution on is called regular of rank if all the subspaces have the same dimension. Locally, this amounts to ask that every local basis is given by linearly independent vector fields.
More compactly, a regular distribution is a vector subbundle of rank (this is actually the most commonly used definition). A rank distribution is sometimes called an -plane distribution, and when , one talks about hyperplane distributions.
Special classes of distributions
Unless stated otherwise, by "distribution" we mean a smooth regular distribution (in the sense explained above).
Involutive distributions
Given a distribution , its sections consist of the vector fields w |
https://en.wikipedia.org/wiki/Harnack%27s%20inequality | In mathematics, Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by . Harnack's inequality is used to prove Harnack's theorem about the convergence of sequences of harmonic functions. , and generalized Harnack's inequality to solutions of elliptic or parabolic partial differential equations. Such results can be used to show the interior regularity of weak solutions.
Perelman's solution of the Poincaré conjecture uses a version of the Harnack inequality, found by , for the Ricci flow.
The statement
Harnack's inequality applies to a non-negative function f defined on a closed ball in Rn with radius R and centre x0. It states that, if f is continuous on the closed ball and harmonic on its interior, then for every point x with |x − x0| = r < R,
In the plane R2 (n = 2) the inequality can be written:
For general domains in the inequality can be stated as follows: If is a bounded domain with , then there is a constant such that
for every twice differentiable, harmonic and nonnegative function . The constant is independent of ; it depends only on the domains and .
Proof of Harnack's inequality in a ball
By Poisson's formula
where ωn − 1 is the area of the unit sphere in Rn and r = |x − x0|.
Since
the kernel in the integrand satisfies
Harnack's inequality follows by substituting this inequality in the above integral and using the fact that the average of a harmonic function over a sphere equals its value at the center of the sphere:
Elliptic partial differential equations
For elliptic partial differential equations, Harnack's inequality states that the supremum of a positive solution in some connected open region is bounded by some constant times the infimum, possibly with an added term containing a functional norm of the data:
The constant depends on the ellipticity of the equation and the connected open region.
Parabolic partial differential equations
There is a version of Har |
https://en.wikipedia.org/wiki/Equivariant%20cohomology | In mathematics, equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a group action. It can be viewed as a common generalization of group cohomology and an ordinary cohomology theory. Specifically, the equivariant cohomology ring of a space with action of a topological group is defined as the ordinary cohomology ring with coefficient ring of the homotopy quotient :
If is the trivial group, this is the ordinary cohomology ring of , whereas if is contractible, it reduces to the cohomology ring of the classifying space (that is, the group cohomology of when G is finite.) If G acts freely on X, then the canonical map is a homotopy equivalence and so one gets:
Definitions
It is also possible to define the equivariant cohomology
of with coefficients in a
-module A; these are abelian groups.
This construction is the analogue of cohomology with local coefficients.
If X is a manifold, G a compact Lie group and is the field of real numbers or the field of complex numbers (the most typical situation), then the above cohomology may be computed using the so-called Cartan model (see equivariant differential forms.)
The construction should not be confused with other cohomology theories,
such as Bredon cohomology or the cohomology of invariant differential forms: if G is a compact Lie group, then, by the averaging argument, any form may be made invariant; thus, cohomology of invariant differential forms does not yield new information.
Koszul duality is known to hold between equivariant cohomology and ordinary cohomology.
Relation with groupoid cohomology
For a Lie groupoid equivariant cohomology of a smooth manifold is a special example of the groupoid cohomology of a Lie groupoid. This is because given a -space for a compact Lie group , there is an associated groupoidwhose equivariant cohomology groups can be computed using the Cartan complex which is the totalization of the d |
https://en.wikipedia.org/wiki/Maria%20Klawe | Maria Margaret Klawe ( ; born 1951) is a computer scientist and the fifth president of Harvey Mudd College (since July 1, 2006). Born in Toronto in 1951, she became a naturalized U.S. citizen in 2009. She was previously Dean of the School of Engineering and Applied Science at Princeton University. She is known for her advocacy for women in STEM fields.
Biography
Klawe was born in Toronto, Ontario. She lived in Scotland from ages 4 to 12, and then returned to Canada, living with her family in Edmonton, Alberta.
Klawe studied at the University of Alberta, dropped out to travel the world, and returned to earn her B.Sc. in 1973. She stayed at Alberta for her graduate studies, and in 1977 she earned her Ph.D. there in mathematics. She joined the mathematics faculty at Oakland University as an assistant professor in 1977 but only stayed for a year. She started a second Ph.D., in computer science, at the University of Toronto, but was offered a faculty position there before completing the degree. When she made the decision to get a PhD in computer science she had never studied the subject before. There weren't many undergraduate classes at the time so she enrolled in upper-level courses and studied about 16 hours a day to do well. She spent eight years in industry, serving at IBM's Almaden Research Center in San Jose, California, first as a research scientist, then as manager of the Discrete Mathematics Group and manager of the Mathematics and Related Computer Science Department. She and her husband Nick Pippenger then moved to the University of British Columbia, where she stayed for 15 years and served as head of the Department of Computer Science from 1988 to 1995, vice president of student and academic services from 1995 to 1998, and dean of science from 1998 to 2002.
From UBC she moved to Princeton and then Harvey Mudd College, where she is the first woman president. When she arrived at Mudd only about 30% of students and faculty were female. Today about 50% of the |
https://en.wikipedia.org/wiki/European%20Physical%20Journal | The European Physical Journal (or EPJ) is a joint publication of EDP Sciences, Springer Science+Business Media, and the Società Italiana di Fisica. It arose in 1998 as a merger and continuation of Acta Physica Hungarica, Anales de Física, Czechoslovak Journal of Physics, Il Nuovo Cimento, Journal de Physique, Portugaliae Physica and Zeitschrift für Physik. The journal is published in various sections, covering all areas of physics.
History
In the late 1990s, Springer and EDP Sciences decided to merge Zeitschrift für Physik and Journal de Physique. With the addition of Il Nuovo Cimento from the Societa Italiana di Fisica, the European Physical Journal commenced publication in January 1998. Now EPJ is a merger and continuation of Acta Physica Hungarica, Anales de Fisica, Czechoslovak Journal of Physics, Il Nuovo Cimento, Journal de Physique, Portugaliae Physica and Zeitschrift für Physik.
The short-lived open-access journal family PhysMath Central was merged in 2011 into the European Physical Journal, which has offered an open-access option since 2006.
Topics covered
The EPJ is published in the following sections:
European Physical Journal A: Hadrons and Nuclei
: Applied Metamaterials
: Applied Physics
European Physical Journal B: Condensed Matter and Complex Systems
European Physical Journal C: Particles and Fields
European Physical Journal D: Atomic, Molecular, Optical and Plasma Physics
: Data Science
European Physical Journal E: Soft Matter and Biological Physics
European Physical Journal H: Historical Perspectives on Contemporary Physics
: Nuclear Sciences and Technologies
: Nonlinear Biomedical Physics
: Photovoltaics
: Quantum Technology
: Special Topics
: Techniques and Instrumentation
: Web of Conferences: journal of conference proceedings
Controversies
In 2023, editors retracted a journal article published in 2022 in European Physical Journal Plus that claimed to have found no evidence of climate change.
The article was widely shared |
https://en.wikipedia.org/wiki/Ball%20flower | The ball-flower (also written ballflower) is an architectural ornament in the form of a ball inserted in the cup of a flower. It came into use in the latter part of the 13th century in England and became one of the chief ornaments of the 14th century, in the period known as Decorated Gothic.
Ball-flowers were generally placed in rows at equal distances in the hollow of a moulding, frequently by the sides of mullions. Examples are found in many churches of the period including Gloucester Cathedral; St Mary's Church, Bloxham; St. Michael's Church, Swaton ( 1300); and Tewkesbury Abbey ( 1330). The presence of ball-flowers on the west part of Salisbury Cathedral has helped date this facade to the 14th century. |
https://en.wikipedia.org/wiki/Hartogs%20number | In mathematics, specifically in axiomatic set theory, a Hartogs number is an ordinal number associated with a set. In particular, if X is any set, then the Hartogs number of X is the least ordinal α such that there is no injection from α into X. If X can be well-ordered then the cardinal number of α is a minimal cardinal greater than that of X. If X cannot be well-ordered then there cannot be an injection from X to α. However, the cardinal number of α is still a minimal cardinal not less than or equal to the cardinality of X. (If we restrict to cardinal numbers of well-orderable sets then that of α is the smallest that is not not less than or equal to that of X.) The map taking X to α is sometimes called Hartogs's function. This mapping is used to construct the aleph numbers, which are all the cardinal numbers of infinite well-orderable sets.
The existence of the Hartogs number was proved by Friedrich Hartogs in 1915, using Zermelo–Fraenkel set theory alone (that is, without using the axiom of choice).
Hartogs's theorem
Hartogs's theorem states that for any set X, there exists an ordinal α such that ; that is, such that there is no injection from α to X. As ordinals are well-ordered, this immediately implies the existence of a Hartogs number for any set X. Furthermore, the proof is constructive and yields the Hartogs number of X.
Proof
See .
Let be the class of all ordinal numbers β for which an injective function exists from β into X.
First, we verify that α is a set.
X × X is a set, as can be seen in Axiom of power set.
The power set of X × X is a set, by the axiom of power set.
The class W of all reflexive well-orderings of subsets of X is a definable subclass of the preceding set, so it is a set by the axiom schema of separation.
The class of all order types of well-orderings in W is a set by the axiom schema of replacement, as
(Domain(w), w) (β, ≤)
can be described by a simple formula.
But this last set is exactly α. Now, because a transitive set |
https://en.wikipedia.org/wiki/Friedrich%20Hartogs | Friedrich Moritz "Fritz" Hartogs (20 May 1874 – 18 August 1943) was a German-Jewish mathematician, known for his work on set theory and foundational results on several complex variables.
Life
Hartogs was the son of the merchant Gustav Hartogs and his wife Elise Feist and grew up in Frankfurt am Main.
He studied at the Königliche Technische Hochschule Hannover, at the Technische Hochschule Charlottenburg, at the University of Berlin, and at the Ludwig Maximilian University of Munich, graduating with a doctorate in 1903 (supervised by Alfred Pringsheim). He did his Habilitation in 1905 and was Privatdozent and Professor in Munich (from 1910 to 1927 extraordinary professor and since 1927 ordinary professor).
As a Jew, he suffered greatly under the Nazi regime: he was fired in 1935, was mistreated and briefly interned in KZ Dachau in 1938, and eventually committed suicide in 1943.
Work
Hartogs main work was in several complex variables where he is known for
Hartogs's theorem, Hartogs's lemma (also known as Hartogs's principle or Hartogs's extension theorem) and the concepts of holomorphic hull and domain of holomorphy.
In set theory, he contributed to the theory of wellorders and proved what is also known as Hartogs's theorem: for every set x there is a wellordered set that cannot be injectively embedded in x.
The smallest such set is known as the Hartogs number or Hartogs Aleph of x. |
https://en.wikipedia.org/wiki/Conjugation%20of%20isometries%20in%20Euclidean%20space | In a group, the conjugate by g of h is ghg−1.
Translation
If h is a translation, then its conjugation by an isometry can be described as applying the isometry to the translation:
the conjugation of a translation by a translation is the first translation
the conjugation of a translation by a rotation is a translation by a rotated translation vector
the conjugation of a translation by a reflection is a translation by a reflected translation vector
Thus the conjugacy class within the Euclidean group E(n) of a translation is the set of all translations by the same distance.
The smallest subgroup of the Euclidean group containing all translations by a given distance is the set of all translations. So, this is the conjugate closure of a singleton containing a translation.
Thus E(n) is a direct product of the orthogonal group O(n) and the subgroup of translations T, and O(n) is isomorphic with the quotient group of E(n) by T:
O(n) E(n) / T
Thus there is a partition of the Euclidean group with in each subset one isometries that keeps the origins fixed, and its combination with all translations.
Each isometry is given by an orthogonal matrix A in O(n) and a vector b:
and each subset in the quotient group is given by the matrix A only.
Similarly, for the special orthogonal group SO(n) we have
SO(n) E+(n) / T
Inversion
The conjugate of the inversion in a point by a translation is the inversion in the translated point, etc.
Thus the conjugacy class within the Euclidean group E(n) of inversion in a point is the set of inversions in all points.
Since a combination of two inversions is a translation, the conjugate closure of a singleton containing inversion in a point is the set of all translations and the inversions in all points. This is the generalized dihedral group dih (Rn).
Similarly { I, −I } is a normal subgroup of O(n), and we have:
E(n) / dih (Rn) O(n) / { I, −I }
For odd n we also have:
O(n) SO(n) × { I, −I }
and hence not only
O(n) / SO(n) { I, −I |
https://en.wikipedia.org/wiki/Cycloamylose | Cycloamyloses are cyclic α-1,4 linked glucans comprising dozens or hundreds of glucose units. Chemically they are similar to the much smaller cyclodextrins, which are typically composed of 6, 7 or 8 glucose units.
Discovery
Cycloamyloses were discovered as a result of studies of the function of 4-α-glucanotransferase, also known as disproportionating enzyme or D-enzyme (EC 2.4.1.25) isolated from potato.
Synthesis
Upon incubation of D-enzyme with high molecular weight amylose, a product was obtained with decreased ability to form a blue complex with iodine, without reducing or non-reducing ends, and resistant to hydrolysis by glucoamylase (an exoamylase). Takaha and Smith deduced that the product was a cyclic polymer, which they confirmed by mass spectrometry and acid hydrolysis, and showed that it comprised between 17 and several hundred glucose units. It was subsequently shown that D-enzyme could create complex cycloglucans from amylopectin. Similar 4-α-glucanotransferases from bacteria and other organisms have also been shown to produce cycloglucans upon incubation with amylose or amylopectin.
Structure
While the structures of cyclodextrins are planar circles, the structure of cycloamyloses with 10 to 14 glucose units were determined to be circular with strain-induced band-flips and kinks. In contrast the structure of a larger cycloamylose with 26 glucose units was determined to comprise two short left-handed V-amylose helices in antiparallel arrangement.
Applications
Cycloamyloses contain cavities in the helices which are capable of accommodating guest molecules, which suggested applications in chemical technologies. Cycloamylose is used in artificial chaperone technology for the refolding of denatured proteins. Cycloglucans have physicochemical properties that make them useful in food and manufacturing. |
https://en.wikipedia.org/wiki/Cytochemistry | Cytochemistry is the branch of cell biology dealing with the detection of cell constituents by means of biochemical analysis and visualization techniques. This is the study of the localization of cellular components through the use of staining methods. The term is also used to describe a process of identification of the biochemical content of cells. Cytochemistry is a science of localizing chemical components of cells and cell organelles on thin histological sections by using several techniques like enzyme localization, micro-incineration, micro-spectrophotometry, radioautography, cryo-electron microscopy, X-ray microanalysis by energy-dispersive X-ray spectroscopy, immunohistochemistry and cytochemistry, etc.
Freeze Fracture Enzyme Cytochemistry
Freeze fracture enzyme cytochemistry was initially mentioned in the study of Pinto de silva in 1987. It is a technique that allows the introduction of cytochemistry into a freeze fracture cell membrane. immunocytochemistry is used in this technique to label and visualize the cell membrane's molecules. This technique could be useful in analyzing the ultrastructure of cell membranes. The combination of immunocytochemistry and freeze fracture enzyme technique, research can identify and have a better understanding of the structure and distribution of a cell membrane.
Origin
Jean Brachet's research in Brussel demonstrated the localization and relative abundance between RNA and DNA in the cells of both animals and plants opened up the door into the research of cytochemistry. The work by Moller and Holter in 1976 about endocytosis which discussed the relationship between a cell's structure and function had established the needs of cytochemical research.
Aims
Cytochemical research aims to study individual cells that may contain several cell types within a tissue. It takes a nondestructive approach to study the localization of the cell. By remaining the cell components intact, researcher are able to study the intact cell activ |
https://en.wikipedia.org/wiki/Extended%20Enterprise%20Modeling%20Language | Extended Enterprise Modeling Language (EEML) in software engineering is a modelling language used for Enterprise modelling across a number of layers.
Overview
Extended Enterprise Modeling Language (EEML) is a modelling language which combines structural modelling, business process modelling, goal modelling with goal hierarchies and resource modelling. It was intended to bridge the gap between goal modelling and other modelling approaches. According to Johannesson and Söderström (2008) "the process logic in EEML is mainly expressed through nested structures of tasks and decision points. The sequencing of tasks is expressed by the flow relation between decision points. Each task has an input port and the output port being decision points for modeling process logic".
EEML was designed as a simple language, making it easy to update models. In addition to capturing tasks and their interdependencies, models show which roles perform each task, and the tools, services and information they apply.
History
Extended Enterprise Modeling Language (EEML) is from the late 1990s, developed in the EU project EXTERNAL as extension of the Action Port Model (APM) by S. Carlsen (1998). The EXTERNAL project aimed to "facilitate inter-organisational cooperation in knowledge intensive industries. The project worked on the hypothesis that interactive process models form a suitable framework for tools and methodologies for dynamically networked organisations. In the project EEML (Extended Enterprise Modelling Language) was first constructed as a common metamodel, designed to enable syntactic and semantic interoperability".
It was further developed in the EU projects Unified Enterprise Modelling Language (UEML) from 2002 to 2003 and the ongoing ATHENA project.
The objectives of the UEML Working group were to "define, to validate and to disseminate a set of core language constructs to support a Unified Language for Enterprise Modelling, named UEML, to serve as a basis for interoperability |
https://en.wikipedia.org/wiki/ISO%207001 | ISO 7001 ("public information symbols") is a standard published by the International Organization for Standardization that defines a set of pictograms and symbols for public information. The latest version, ISO 7001:2023, was published in February 2023.
The set is the result of extensive testing in several countries and different cultures and have met the criteria for comprehensibility set up by the ISO. The design process and testing of ISO 7001 symbols is governed by ISO 22727:2007, Graphical symbols — Creation and design of public information symbols — Requirements. Common examples of public information symbols include those representing toilets, car parking, and information, and the International Symbol of Access.
History
ISO 7001 was first released in October 1980, with a single amendment in 1985. The second edition was released in February 1990, with one amendment in 1993. The third edition, the latest edition was released in November 2007, and has received four amendments in 2013, 2015, 2016 and 2017. The use of the symbols of ISO 7001 is recommended by the European standard EN 17210.
Implementation
ISO 7001 sets out some general guidelines for how symbols should be utilized, though large aspects are left up to the decision of the individual or entity designing signage for their facility.
Symbols were created with the goal of being able to stand alone, without any accompanying text. However, text can be used to further aid in communicating the message, particularly in a situation where a custom symbol has been designed for a unique situation not covered by standard ISO 7001 symbols. Specific sizes for symbols are not provided in ISO 7001, though symbols are designed with the goal of being clearly understood regardless placed on something as small as a floor plan of a building or as a large as a giant sign hanging from a ceiling in a large open space.
While symbols are intended and recommended to be reproduced as presented in ISO 7001, the ISO acknowled |
https://en.wikipedia.org/wiki/Cathodic%20arc%20deposition | Cathodic arc deposition or Arc-PVD is a physical vapor deposition technique in which an electric arc is used to vaporize material from a cathode target. The vaporized material then condenses on a substrate, forming a thin film. The technique can be used to deposit metallic, ceramic, and composite films.
History
Industrial use of modern cathodic arc deposition technology originated in Soviet Union around 1960–1970.
By the late 70's Soviet government released the use of this technology to the West.
Among many designs in USSR at that time the design by L. P. Sablev, et al., was allowed to be used outside the USSR.
Process
The arc evaporation process begins with the striking of a high current, low voltage arc on the surface of a cathode (known as the target) that gives rise to a small (usually a few micrometres wide), highly energetic emitting area known as a cathode spot. The localised temperature at the cathode spot is extremely high (around 15000 °C), which results in a high velocity (10 km/s) jet of vapourised cathode material, leaving a crater behind on the cathode surface. The cathode spot is only active for a short period of time, then it self-extinguishes and re-ignites in a new area close to the previous crater. This behaviour causes the apparent motion of the arc.
As the arc is basically a current carrying conductor it can be influenced by the application of an electromagnetic field, which in practice is used to rapidly move the arc over the entire surface of the target, so that the total surface is eroded over time.
The arc has an extremely high power density resulting in a high level of ionization (30-100%), multiple charged ions, neutral particles, clusters and macro-particles (droplets). If a reactive gas is introduced during the evaporation process, dissociation, ionization and excitation can occur during interaction with the ion flux and a compound film will be deposited.
One downside of the arc evaporation process is that if the cathode spot stay |
https://en.wikipedia.org/wiki/Terayon | Terayon Communication Systems, Inc. was a company that vended equipment to broadband service providers for delivering broadband voice, video and data services to residential and business subscribers.
History
Terayon was founded by Israeli brothers Zaki Rakib and Shlomo Rakib in 1993; both brothers graduated from high school at age 16 and went on to university. Shlomo studied electrical engineering, and Zaki did a PhD in mechanical engineering and post-doctorate studies in applied mathematics. He taught for a while at Tel Aviv University’s computer science faculty, and then joined Helios. After Helios was sold to Cadence Design Systems, Zaki moved to the US, and urged his brother to join him and set up the company. Terayon held an IPO on NASDAQ in August 1998.
In 1999, the company initiated a strategy to expand its offerings to the telecommunication and satellite industries but later refocused its business on the cable industry in 2000. During 1999 and 2000 the company acquired seven other companies, including: Imedia, a video processing startup founded by Efi Arazi (founder of Scitex) for $100m; Radwiz for $64m from the Rad Group, Teledata Networks (which was later sold) and Ultracom Communications for $32m in March 2000.
In 2004, Terayon recentered its strategy on digital video solutions, marketing to television broadcasters, telecom carriers and satellite television providers. Terayon also decided to phase out equipment for home access, such as cable modems and home networking devices.
In April 2006, Terayon was delisted from NASDAQ due to outstanding financial reports. Motorola Inc. acquired Terayon for $140 million in June 2007.
See also
Motorola Inc. |
https://en.wikipedia.org/wiki/Normalization%20%28statistics%29 | In statistics and applications of statistics, normalization can have a range of meanings. In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment. In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution. A different approach to normalization of probability distributions is quantile normalization, where the quantiles of the different measures are brought into alignment.
In another usage in statistics, normalization refers to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets in a way that eliminates the effects of certain gross influences, as in an anomaly time series. Some types of normalization involve only a rescaling, to arrive at values relative to some size variable. In terms of levels of measurement, such ratios only make sense for ratio measurements (where ratios of measurements are meaningful), not interval measurements (where only distances are meaningful, but not ratios).
In theoretical statistics, parametric normalization can often lead to pivotal quantities – functions whose sampling distribution does not depend on the parameters – and to ancillary statistics – pivotal quantities that can be computed from observations, without knowing parameters.
Examples
There are different types of normalizations in statistics – nondimensional ratios of errors, residuals, means and standard deviations, which are hence scale invariant – some of which may be summarized as follows. Note that in terms of levels of measurement, these ratios only make sense for ratio me |
https://en.wikipedia.org/wiki/Hartogs%27s%20theorem%20on%20separate%20holomorphicity | In mathematics, Hartogs's theorem is a fundamental result of Friedrich Hartogs in the theory of several complex variables. Roughly speaking, it states that a 'separately analytic' function is continuous. More precisely, if is a function which is analytic in each variable zi, 1 ≤ i ≤ n, while the other variables are held constant, then F is a continuous function.
A corollary is that the function F is then in fact an analytic function in the n-variable sense (i.e. that locally it has a Taylor expansion). Therefore, 'separate analyticity' and 'analyticity' are coincident notions, in the theory of several complex variables.
Starting with the extra hypothesis that the function is continuous (or bounded), the theorem is much easier to prove and in this form is known as Osgood's lemma.
There is no analogue of this theorem for real variables. If we assume that a function
is differentiable (or even analytic) in each variable separately, it is not true that will necessarily be continuous. A counterexample in two dimensions is given by
If in addition we define , this function has well-defined partial derivatives in and at the origin, but it is not continuous at origin. (Indeed, the limits along the lines and are not equal, so there is no way to extend the definition of to include the origin and have the function be continuous there.) |
https://en.wikipedia.org/wiki/MuseWeb | MuseWeb (formerly Museums and the Web) is an annual international conference in the field of museums and their websites. It was founded and organized by Archives & Museum Informatics and has taken place each spring since 1997 in North America, along with events in other countries.
Since 2011 it has been organized by Museums and the Web LLC and Co-Chaired by Nancy Proctor and Rich Cherry, who also co-edit the proceedings.
Overview
The conference includes the GLAMi awards(The Galleries, Libraries, Archives, and Museums Innovation awards) which recognizes the best GLAM work in the sector. Projects are nominated by GLAM professionals from around the world and reviewed by a committee of peers. The conference previously included annual "Best of the Web awards" for museum-related websites in a number of different categories, as well as an overall winner.
Individual conferences
The following events have been held or are planned:
MW1997, March 16–19, 1997 — Los Angeles, California, US
MW1998, April 22–25, 1998 — Toronto, Ontario, Canada
MW1999, March 11–14, 1999 — New Orleans, Louisiana, US
MW2000, April 16–19, 2000 — Minneapolis, Minnesota, US
MW2001, March 14–17, 2001 — Seattle, Washington, US
MW2002, April 17–20, 2002 — Boston, Massachusetts, US
MW2003, March 19–22, 2003 — Charlotte, North Carolina, US
MW2004, March 31 – April 3, 2004 — Arlington, Virginia / Washington DC, US
MW2005, April 13–17, 2005 — Vancouver, British Columbia, Canada
MW2006, March 22–25, 2006 — Albuquerque, New Mexico, US
MW2007, April 11–14, 2007 — San Francisco, California, US
MW2008, April 8–12, 2008 — Montreal, Quebec, Canada
MW2009, April 14–18, 2009 — Indianapolis, Indiana, US
MW2010, April 13–17, 2010 — Denver, Colorado, US
MW2011, April 6–9, 2011 — Philadelphia, Pennsylvania, US
MW2012, April 11–14, 2012 — San Diego, California, US
MW2013, April 17–20, 2013 — Portland, Oregon, US
MWA2013, December 9–12, 2013 — Hong Kong
MWF2014, February 19–21, 2014 — Florence, Italy
|
https://en.wikipedia.org/wiki/Orange%20oil | Orange oil is an essential oil produced by cells within the rind of an orange fruit (Citrus sinensis fruit). In contrast to most essential oils, it is extracted as a by-product of orange juice production by centrifugation, producing a cold-pressed oil. It is composed of mostly (greater than 90%) d-limonene, and is often used in place of pure d-limonene. D-limonene can be extracted from the oil by distillation.
Composition
The compounds inside an orange oil vary with each different oil extraction. Composition varies as a result of regional and seasonal changes as well as the method used for extraction. Several hundred compounds have been identified with gas chromatograph-mass spectrometry. Most of the substances in the oil belong to the terpene group with limonene being the dominant one. Long chain aliphatic hydrocarbon alcohols and aldehydes like 1-octanol and octanal are second important group of substances. The presence of sinensetin, a flavone, explains the orange color.
Uses
Structural pest control
California has authorized and registered d-Limonene (Orange Oil) as an active ingredient with the EPA. and Florida for the extermination of drywood termites, Formosan termites, and other structural pests. It is the active ingredient of the popular structural termiticide XT-2000. Regarded an alternative to traditional fumigation, d-Limonene orange oil is increasing in popularity as approximately 70% of modern consumers in California prefer local structural chemical injections over traditional "tenting" or fumigation.
Biological pest control
Orange oil can be used in green pesticides for biological pest control. It can exterminate or control ants and other insects by erasing their scent-pheromone trail indicators, or dissolving their exoskeleton, eliminating the infestation or disrupting re-infestation.
Orange oil is also known to be useful to control, but not exterminate, drywood termites (Incisitermes), killing only those who come into direct contact with it.
|
https://en.wikipedia.org/wiki/Hans%20Grauert | Hans Grauert (8 February 1930 in Haren, Emsland, Germany – 4 September 2011) was a German mathematician. He is known for major works on several complex variables, complex manifolds and the application of sheaf theory in this area, which influenced later work in algebraic geometry. Together with Reinhold Remmert he established and developed the theory of complex-analytic spaces. He became professor at the University of Göttingen in 1958, as successor to C. L. Siegel. The lineage of this chair traces back through an eminent line of mathematicians: Weyl, Hilbert, Riemann, and ultimately to Gauss. Until his death, he was professor emeritus at Göttingen.
Grauert was awarded a fellowship of the Leopoldina.
Early life
Grauert attended school at the Gymnasium in Meppen before studying for a semester at the University of Mainz in 1949, and then at the University of Münster, where he was awarded his doctorate in 1954.
See also
Andreotti–Grauert theorem
Grauert's theorem
Levi problem
Publications
with Klaus Fritzsche:
with Klaus Fritzsche: |
https://en.wikipedia.org/wiki/Delta%20neutral | In finance, delta neutral describes a portfolio of related financial securities, in which the portfolio value remains unchanged when small changes occur in the value of the underlying security. Such a portfolio typically contains options and their corresponding underlying securities such that positive and negative delta components offset, resulting in the portfolio's value being relatively insensitive to changes in the value of the underlying security.
A related term, delta hedging is the process of setting or keeping the delta of a portfolio as close to zero as possible. In practice, maintaining a zero delta is very complex because there are risks associated with re-hedging on large movements in the underlying stock's price, and research indicates portfolios tend to have lower cash flows if re-hedged too frequently.
Mathematical interpretation
Delta measures the sensitivity of the value of an option to changes in the price of the underlying stock assuming all other variables remain unchanged.
Mathematically, delta is represented as partial derivative
of the option's fair value with respect to the price of the underlying security.
Delta is clearly a function of S, however Delta is also a function of strike price and time to expiry.
Therefore, if a position is delta neutral (or, instantaneously delta-hedged) its instantaneous change in value, for an infinitesimal change in the value of the underlying security, will be zero; see Hedge (finance). Since delta measures the exposure of a derivative to changes in the value of the underlying, a portfolio that is delta neutral is effectively hedged. That is, its overall value will not change for small changes in the price of its underlying instrument.
Creating the position
Delta hedging - i.e. establishing the required hedge - may be accomplished by buying or selling an amount of the underlier that corresponds to the delta of the portfolio. By adjusting the amount bought or sold on new positions, the portfolio de |
https://en.wikipedia.org/wiki/%C3%89va%20Tardos | Éva Tardos (born 1 October 1957) is a Hungarian mathematician and the Jacob Gould Schurman Professor of Computer Science at Cornell University.
Tardos's research interest is algorithms. Her work focuses on the design and analysis of efficient methods for combinatorial optimization problems on graphs or networks. She has done some work on network flow algorithms like approximation algorithms for network flows, cut, and clustering problems. Her recent work focuses on algorithmic game theory and simple auctions.
Education and career
Tardos received her Dipl. Math in 1981 and her Ph.D. 1984 from the Faculty of Sciences of the Eötvös Loránd University under her advisor András Frank. She was the Chair of the Department of Computer Science at Cornell from 2006-2010, and she is currently serving as the Associate Dean of the College of Computing and Information Science.
She was editor-in-Chief of SIAM Journal on Computing from 2004–2009, and is currently the Economics and Computation area editor of the Journal of the ACM as well as on the Board of Editors of Theory of Computing.
She has co-authored with Jon Kleinberg a textbook called Algorithm Design ().
Honors and awards
Tardos has been elected to the National Academy of Engineering (2007), the American Academy of Arts and Sciences, and the National Academy of Sciences (2013) and the American Philosophical Society (2020)
She is also an ACM Fellow (since 1998), a Fellow of INFORMS, and a Fellow of the American Mathematical Society (2013)
She is the recipient of Packard, Sloan Foundation, and Guggenheim fellowships.
She is the winner of the Fulkerson Prize (1988),
the George B. Dantzig Prize (2006),
the Van Wijngaarden Award (2011),
the Gödel Prize (2012)
and the EATCS Award (2017),
In 2018 the Association for Women in Mathematics and Society for Industrial and Applied Mathematics selected her as their annual Sonia Kovalevsky Lecturer.
In 2019 she was awarded the IEEE John von Neumann Medal.
Personal
Tardos is married |
https://en.wikipedia.org/wiki/Gyricon | Gyricon is a type of electronic paper developed at the Xerox PARC (Palo Alto Research Center). It has many of the same properties as paper: it is flexible, contains an image, and is viewable from a wide angle, but it can be erased and written thousands of times.
A Gyricon sheet is a thin layer of transparent plastic, in which millions of small beads, somewhat like toner particles, are randomly dispersed. The beads, each contained in an oil-filled cavity, are free to rotate within those cavities. The beads are "bichromal", with hemispheres of two contrasting colors (e.g. black and white, red and white), and charged, so they exhibit an electrical dipole. When voltage is applied to the surface of the sheet, the beads rotate to present one colored side to the viewer. Voltages can be applied to the surface to create images such as text and pictures. The image will persist until new voltage patterns are applied
As of December, 2005, Xerox closed down the direct subsidiary Gyricon LLC, their Gyricon e-paper display business, and is focusing on licensing the technology.
The company have said that the reason for their closure has been their inability to source backplane technology for their Gyricon frontplane at a price of less than $10 per square foot (US$100/m2). Being able to achieve a price of under $10 was said to be critical to the success of marketing their e-paper-based electronic signage products. Although the company will stop direct manufacture and sale of Gyricon e-paper display products, it will, however, still be licensing their frontplane technology to other users. |
https://en.wikipedia.org/wiki/Minkowski%E2%80%93Hlawka%20theorem | In mathematics, the Minkowski–Hlawka theorem is a result on the lattice packing of hyperspheres in dimension n > 1. It states that there is a lattice in Euclidean space of dimension n, such that the corresponding best packing of hyperspheres with centres at the lattice points has density Δ satisfying
with ζ the Riemann zeta function. Here as n → ∞, ζ(n) → 1. The proof of this theorem is indirect and does not give an explicit example, however, and there is still no known simple and explicit way to construct lattices with packing densities exceeding this bound for arbitrary n. In principle one can find explicit examples: for example, even just picking a few "random" lattices will work with high probability. The problem is that testing these lattices to see if they are solutions requires finding their shortest vectors, and the number of cases to check grows very fast with the dimension, so this could take a very long time.
This result was stated without proof by and proved by . The result is related to a linear lower bound for the Hermite constant.
Siegel's theorem
proved the following generalization of the Minkowski–Hlawka theorem. If S is a bounded set in Rn with Jordan volume vol(S) then the average number of nonzero lattice vectors in S is vol(S)/D, where the average is taken over all lattices with a fundamental domain of volume D, and similarly the average number of primitive lattice vectors in S is vol(S)/Dζ(n).
The Minkowski–Hlawka theorem follows easily from this, using the fact that if S is a star-shaped centrally symmetric body (such as a ball) containing less than 2 primitive lattice vectors then it contains no nonzero lattice vectors.
See also
Kepler conjecture |
https://en.wikipedia.org/wiki/Cryptographic%20key%20types | A cryptographic key is a string of data that is used to lock or unlock cryptographic functions, including authentication, authorization and encryption. Cryptographic keys are grouped into cryptographic key types according to the functions they perform.
Description
Consider a keyring that contains a variety of keys. These keys might be various shapes and sizes, but one thing is certain, each will generally serve a separate purpose. One key might be used to start an automobile, while another might be used to open a safe deposit box. The automobile key will not work to open the safe deposit box and vice versa. This analogy provides some insight on how cryptographic key types work. These keys are categorized in respect to how they are used and what properties they possess.
A cryptographic key is categorized according to how it will be used and what properties it has. For example, a key might have one of the following properties: Symmetric, Public or Private. Keys may also be grouped into pairs that have one private and one public key, which is referred to as an Asymmetric key pair.
Asymmetric versus symmetric keys
Asymmetric keys differ from symmetric keys in that the algorithms use separate keys for encryption and decryption, while a symmetric key’s algorithm uses a single key for both processes. Because multiple keys are used with an asymmetric algorithm, the process takes longer to produce than a symmetric key algorithm would. However, the benefits lay in the fact that an asymmetric algorithm is much more secure than a symmetric key algorithm is.
With a symmetric key, the key needs to be transmitted to the receiver, where there is always the possibility that the key could be intercepted or tampered with. With an asymmetric key, the message and/or accompanying data can be sent or received by using a public key; however, the receiver or sender would use his or her personal private key to access the message and/or accompanying data. Thus, asymmetric keys are suit |
https://en.wikipedia.org/wiki/Xerosere | Xerosere is a plant succession that is limited by water availability. It includes the different stages in a xerarch succession. Xerarch succession of ecological communities originated in extremely dry situation such as sand deserts, sand dunes, salt deserts, rock deserts etc. A xerosere may include lithoseres (on rock) and psammoseres (on sand).
Stages
Bare rocks
Bare rocks are produced when glaciers recede or volcanoes erupt. Erosion of these rocks is brought by rain water and wind loaded with soil particles. The rain water combines with atmospheric carbon dioxide that corrodes the surface of the rocks and produce crevices. Water enters these crevices, freezes and expands to separate boulders. These boulders move down under the influence of gravity and wear particles from the rocks. Also when the wind loaded with soil particles strikes against the rocks, it removes soil particles. All these processes lead to formation of a little soil at the surface of these bare rocks. Animals such as spiders which can hide between boulders or stones invade these rocks. These animals live by feeding on insects which have been blown in or flown in. Algal and fungal spores reach these rocks by air from the surrounding areas. These spores grow and form symbiotic association, the lichen, which act as pioneer species of bare rocks. The process of succession starts when autotrophic organisms start living in the rocks.
Foliose and fruticose lichen stage
Foliose lichens have leaf-like thalli, while the fruticose lichens are like small bushes. They are attached to the substratum at one point only, therefore, do not cover the soil completely. They can absorb and retain more water and are able to accumulate more dust particles. Their dead remains are decomposed to humus which mixes with soil particles and help building substratum and improving soil moisture contents further. The shallow depressions in the rocks and crevices become filled with soil and topsoil layer increases further. |
https://en.wikipedia.org/wiki/South%20African%20Computer%20Olympiad | The South African Computing Olympiad (SACO) is an annual computer programming competition for secondary school students (although at least one primary school student has participated) in South Africa. The South African team for the International Olympiad in Informatics is selected through it.
Competition rounds
The competition consists of three rounds. The first is a pen-and-paper aptitude examination at the entrant's school, testing a combination of general knowledge, computer knowledge, problem-solving and basic programming. (Entrants are often required to program an imaginary robot in a fictional Logo-like language.) Although the first round is not compulsory, it is accessible to those who do not have access to, or knowledge of, computers. 31,926 students entered it in 2006.
In the second round, actual programs must be written and executed. There are five questions, each requiring a different program to be written. Most entrants answer only a single question. The tasks usually include one basic shape-drawing program—for example, the 2004 question "TriSquare" required output such as:
*
* *
* *
*****
* *
* *
* *
*****
The top performers—those who have answered four or five questions in the second round—are invited to the final round. In prior years, between 10 and 15 students were chosen; but the introduction of a new language, and increased funding from the Shuttleworth Foundation in 2005, has increased it to between 20 and 30 students. The final round is held at the University of Cape Town, where finalists stay over a weekend. It consists of two five-hour rounds, the first on Saturday and second on Sunday. The problems are similar to those in the USACO, though somewhat easier. A prize ceremony is held that Monday.
Prizes
The top six entrants are awarded medals (one gold, two silver and three bronze). There are cash prizes, both for the winners and their schools. There were bonus prizes totalling R100,000 for using Python, due to Shuttlewor |
https://en.wikipedia.org/wiki/Focused%20ion%20beam | Focused ion beam, also known as FIB, is a technique used particularly in the semiconductor industry, materials science and increasingly in the biological field for site-specific analysis, deposition, and ablation of materials. A FIB setup is a scientific instrument that resembles a scanning electron microscope (SEM). However, while the SEM uses a focused beam of electrons to image the sample in the chamber, a FIB setup uses a focused beam of ions instead. FIB can also be incorporated in a system with both electron and ion beam columns, allowing the same feature to be investigated using either of the beams. FIB should not be confused with using a beam of focused ions for direct write lithography (such as in proton beam writing). These are generally quite different systems where the material is modified by other mechanisms.
Ion beam source
Most widespread instruments are using liquid metal ion sources (LMIS), especially gallium ion sources. Ion sources based on elemental gold and iridium are also available. In a gallium LMIS, gallium metal is placed in contact with a tungsten needle, and heated gallium wets the tungsten and flows to the tip of the needle, where the opposing forces of surface tension and electric field form the gallium into a cusp shaped tip called a Taylor cone. The tip radius of this cone is extremely small (~2 nm). The huge electric field at this small tip (greater than volts per centimeter) causes ionization and field emission of the gallium atoms.
Source ions are then generally accelerated to an energy of , and focused onto the sample by electrostatic lenses. LMIS produce high current density ion beams with very small energy spread. A modern FIB can deliver tens of nanoamperes of current to a sample, or can image the sample with a spot size on the order of a few nanometers.
More recently, instruments using plasma beams of noble gas ions, such as xenon, have become available more widely.
Principle
Focused ion beam (FIB) systems have been prod |
https://en.wikipedia.org/wiki/Immunoglobulin%20heavy%20chain | The immunoglobulin heavy chain (IgH) is the large polypeptide subunit of an antibody (immunoglobulin). In human genome, the IgH gene loci are on chromosome 14.
A typical antibody is composed of two immunoglobulin (Ig) heavy chains and two Ig light chains. Several different types of heavy chain exist that define the class or isotype of an antibody. These heavy chain types vary between different animals. All heavy chains contain a series of immunoglobulin domains, usually with one variable domain (VH) that is important for binding antigen and several constant domains (CH1, CH2, etc.). Production of a viable heavy chain is a key step in B cell maturation. If the heavy chain is able to bind to a surrogate light chain and move to the plasma membrane, then the developing B cell can begin producing its light chain.
The heavy chain doesn't always have to bind to a light chain. Pre-B lymphocytes can synthesize heavy chain in the absence of light chain, which then can allow the heavy chain to bind to a heavy-chain binding protein.
In mammals
Classes
There are five types of mammalian immunoglobulin heavy chain: γ, δ, α, μ and ε. They define classes of immunoglobulins: IgG, IgD, IgA, IgM and IgE, respectively.
Heavy chains α and γ have approximately 450 amino acids.
Heavy chains μ and ε have approximately 550 amino acids.
Regions
Each heavy chain has two regions:
a constant region (which is the same for all immunoglobulins of the same class but differs between classes).
Heavy chains γ, α and δ have a constant region composed of three tandem (in a line next to each other) immunoglobulin domains but also have a hinge region for added flexibility.
Heavy chains μ and ε have a constant region composed of four domains.
a variable region that differs between different B cells, but is the same for all immunoglobulins produced by the same B cell or B cell clone. The variable domain of any heavy chain is composed of a single immunoglobulin domain. These domains are about 1 |
https://en.wikipedia.org/wiki/Prolymphocyte | A prolymphocyte is a white blood cell with a certain state of cellular differentiation in lymphocytopoiesis. In the 20th century it was believed that a sequence of general maturation changed cells from lymphoblasts to prolymphocytes and then to lymphocytes (the lymphocytic series), with each being a precursor of the last. Today it is believed that the differentiation of cells in the lymphocyte line is not always simply chronologic but rather depends on antigen exposure, such that, for example, lymphocytes can become lymphoblasts.
The size is between 10 and 18 μm.
See also
Pluripotential hemopoietic stem cell
Prolymphocytic leukemia |
https://en.wikipedia.org/wiki/Clifford%27s%20theorem%20on%20special%20divisors | In mathematics, Clifford's theorem on special divisors is a result of on algebraic curves, showing the constraints on special linear systems on a curve C.
Statement
A divisor on a Riemann surface C is a formal sum of points P on C with integer coefficients. One considers a divisor as a set of constraints on meromorphic functions in the function field of C, defining as the vector space of functions having poles only at points of D with positive coefficient, at most as bad as the coefficient indicates, and having zeros at points of D with negative coefficient, with at least that multiplicity. The dimension of is finite, and denoted . The linear system of divisors attached to D is the corresponding projective space of dimension .
The other significant invariant of D is its degree d, which is the sum of all its coefficients.
A divisor is called special if ℓ(K − D) > 0, where K is the canonical divisor.
Clifford's theorem states that for an effective special divisor D, one has:
,
and that equality holds only if D is zero or a canonical divisor, or if C is a hyperelliptic curve and D linearly equivalent to an integral multiple of a hyperelliptic divisor.
The Clifford index of C is then defined as the minimum of taken over all special divisors (except canonical and trivial), and Clifford's theorem states this is non-negative. It can be shown that the Clifford index for a generic curve of genus g is equal to the floor function
The Clifford index measures how far the curve is from being hyperelliptic. It may be thought of as a refinement of the gonality: in many cases the Clifford index is equal to the gonality minus 2.
Green's conjecture
A conjecture of Mark Green states that the Clifford index for a curve over the complex numbers that is not hyperelliptic should be determined by the extent to which C as canonical curve has linear syzygies. In detail, one defines the invariant a(C) in terms of the minimal free resolution of the homogeneous coordinate rin |
https://en.wikipedia.org/wiki/Petriscript | PetriScript is a modeling language for Petri nets, designed by Alexandre Hamez and Xavier Renault. The CPN-AMI platform provides many tools to work on Petri nets, such as verifying and model-checking tools.
Originally, simple Petri nets were created through graphic design, but research conducted internally at LIP6 revealed that it was needed to automate such tasks. PetriScript was designed to provide some facilities in modeling places-transition and coloured Petri nets within the CPN-AMI platform. Petriscript's main purpose is to automate modeling operations on Petri nets by merging, creating, and connecting nodes. It supports almost everything needed, such as macros, loops control, lists, and string and arithmetic expressions, and blocks intervention of the user as much as possible. Its syntax is Ada-like.
The following script produces a FIFO with three sections:
define(FIFO_SIZE,3)
define(FIFO_BASE_X,100)
define(FIFO_BASE_Y,100)
define(FIFO_STEP,120)
int $wave := 0;
for $wave in 1..FIFO_SIZE loop
create place "Slot_" & '$wave' (x FIFO_BASE_X + FIFO_STEP * $wave,
y FIFO_BASE_Y);
create place "Empty_" & '$wave' (x FIFO_BASE_X + FIFO_STEP * $wave,
y FIFO_BASE_Y + 100, marking "1");
end loop;
for $wave in 1..FIFO_SIZE+1 loop
create transition "t" & '$wave -1' & "_to_" & '$wave' (x FIFO_BASE_X + FIFO_STEP * $wave - FIFO_STEP / 2,
y FIFO_BASE_Y + 50);
if $wave < FIFO_SIZE+1 then
connect "1" transition "t" &'$wave -1' & "_to_" & '$wave' to place "Slot_" & '$wave';
connect "1" place "Empty_" & '$wave' to transition "t" &'$wave -1' & "_to_" & '$wave';
end if;
if $wave > 1 then
connect "1" transition "t" &'$wave -1' & "_to_" & '$wave' to place "Empty_" & '$wave - 1';
connect "1" place "Slot_" & '$wave - 1' to transition "t" &'$wave -1' & "_to_" & '$wave';
end if;
end loop;
set transition "t0_to_1" to (name "FIFO_Start");
set transition "t" & 'FIFO_SIZE' & "_to_" & 'FIFO_SIZE + 1' to (name "FIFO_End");
Which produces the fol |
https://en.wikipedia.org/wiki/Green%20flag | A green flag has various meanings.
National flags
The Flag of the Great Socialist People's Libyan Arab Jamahiriya was a plain green flag.
The Flag of Saudi Arabia has a field of green, which represents Islam.
Irish nationalism was traditionally represented with a green flag. The current flag of Ireland is a tricolour with green representing the Irish Catholics, orange representing the Irish Protestants, and white in the middle to represent peace.
The former Flag of Mauritania.
Various green-striped American flags flew during the Revolutionary War, with green representing the 'color of hope'.
Other
A green flag is part of a set of racing flags and indicates the beginning or resumption of an auto race.
The actual flags flown in parks and gardens that have received the Green Flag Award.
On rail transport in Great Britain and Ireland, green flags are sometimes used (less often than in the past) by railway guards as a signal to engine drivers that they can proceed.
See also
White flag
Red flag (disambiguation)
Action Party (Italy) |
https://en.wikipedia.org/wiki/Linear%20hashing | Linear hashing (LH) is a dynamic data structure which implements a hash table and grows or shrinks one bucket at a time. It was invented by Witold Litwin in 1980.
It has been analyzed by Baeza-Yates and Soza-Pollman. It is the first in a number of schemes known as dynamic hashing
such as Larson's Linear Hashing with Partial Extensions, Linear Hashing with Priority Splitting, Linear Hashing with Partial Expansions and Priority Splitting, or Recursive Linear Hashing.
The file structure of a dynamic hashing data structure adapts itself to changes in the size of the file, so expensive periodic file reorganization is avoided. A Linear Hashing file expands by splitting a pre-determined bucket into two and contracts by merging two predetermined buckets into one. The trigger for a reconstruction depends on the flavor of the scheme; it could be an overflow at a bucket or load factor (i.e., the number of records divided by the number of buckets) moving outside of a predetermined range. In Linear Hashing there are two types of buckets, those that are to be split and those already split. While extendible hashing splits only overflowing buckets, spiral hashing (a.k.a. spiral storage) distributes records unevenly over the buckets such that buckets with high costs of insertion, deletion, or retrieval are earliest in line for a split.
Linear Hashing has also been made into a scalable distributed data structure, LH*. In LH*, each bucket resides at a different server. LH* itself has been expanded to provide data availability in the presence of failed buckets. Key based operations (inserts, deletes, updates, reads) in LH and LH* take maximum constant time independent of the number of buckets and hence of records.
Algorithm details
Records in LH or LH* consists of a key and a content, the latter basically all the other attributes of the record. They are stored in buckets. For example, in Ellis' implementation, a bucket is a linked list of records. The file allows the key based |
https://en.wikipedia.org/wiki/Metaplectic%20group | In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p-adic numbers. The construction covers more generally the case of an arbitrary local or finite field, and even the ring of adeles.
The metaplectic group has a particularly significant infinite-dimensional linear representation, the Weil representation. It was used by André Weil to give a representation-theoretic interpretation of theta functions, and is important in the theory of modular forms of half-integral weight and the theta correspondence.
Definition
The fundamental group of the symplectic Lie group Sp2n(R) is infinite cyclic, so it has a unique connected double cover, which is denoted Mp2n(R) and called the metaplectic group.
The metaplectic group Mp2(R) is not a matrix group: it has no faithful finite-dimensional representations. Therefore, the question of its explicit realization is nontrivial. It has faithful irreducible infinite-dimensional representations, such as the Weil representation described below.
It can be proved that if F is any local field other than C, then the symplectic group Sp2n(F) admits a unique perfect central extension with the kernel Z/2Z, the cyclic group of order 2, which is called the metaplectic group over F.
It serves as an algebraic replacement of the topological notion of a 2-fold cover used when . The approach through the notion of central extension is useful even in the case of real metaplectic group, because it allows a description of the group operation via a certain cocycle.
Explicit construction for n = 1
In the case , the symplectic group coincides with the special linear group SL2(R). This group biholomorphically acts on the complex upper half-plane by fractional-linear transformations,
where
is a real 2-by-2 matrix with the unit determinant and z is in the upper half-plane, and this action can be used to explicitly construct the metaplectic cover of SL2(R).
The elements of the |
https://en.wikipedia.org/wiki/Collision%20resistance | In cryptography, collision resistance is a property of cryptographic hash functions: a hash function H is collision-resistant if it is hard to find two inputs that hash to the same output; that is, two inputs a and b where a ≠ b but H(a) = H(b). The pigeonhole principle means that any hash function with more inputs than outputs will necessarily have such collisions; the harder they are to find, the more cryptographically secure the hash function is.
The "birthday paradox" places an upper bound on collision resistance: if a hash function produces N bits of output, an attacker who computes only 2N/2 (or ) hash operations on random input is likely to find two matching outputs. If there is an easier method to do this than brute-force attack, it is typically considered a flaw in the hash function.
Cryptographic hash functions are usually designed to be collision resistant. However, many hash functions that were once thought to be collision resistant were later broken. MD5 and SHA-1 in particular both have published techniques more efficient than brute force for finding collisions. However, some hash functions have a proof that finding collisions is at least as difficult as some hard mathematical problem (such as integer factorization or discrete logarithm). Those functions are called provably secure.
Definition
A family of functions {hk : {0, 1}m(k) → {0, 1}l(k)} generated by some algorithm G is a family of collision-resistant hash functions, if |m(k)| > |l(k)| for any k, i.e., hk compresses the input string, and every hk can be computed within polynomial time given k, but for any probabilistic polynomial algorithm A, we have
Pr [k ← G(1n), (x1, x2) ← A(k, 1n) s.t. x1 ≠ x2 but hk(x1) = hk(x2)] < negl(n),
where negl(·) denotes some negligible function, and n is the security parameter.
Weak and strong collision resistance
There are two different types of collision resistance.
A hash function has weak collision resistance when, given a hashing function H and an x, n |
https://en.wikipedia.org/wiki/Bred%20vector | In applied mathematics, bred vectors are perturbations related to Lyapunov vectors, that capture fast-growing dynamical instabilities of the solution of a numerical model. They are used, for example, as initial perturbations for ensemble forecasting in numerical weather prediction. They were introduced by Zoltan Toth and Eugenia Kalnay.
Method
Bred vectors are created by adding initially random perturbations to a nonlinear model. The control (unperturbed) and the perturbed models are integrated in time, and periodically the control solution is subtracted from the perturbed solution. This difference is the bred vector. The vector is scaled to be the same size as the initial perturbation and is then added back to the control to create the new perturbed initial condition. After a short transient period, this "breeding" process creates bred vectors dominated by the naturally fastest-growing instabilities of the evolving control solution. |
https://en.wikipedia.org/wiki/Fixed-satellite%20service | Fixed-satellite service (short: FSS | also: fixed-satellite radiocommunication service) is – according to article 1.21 of the International Telecommunication Union's (ITU) Radio Regulations (RR) – defined as A radiocommunication service between earth stations at given positions, when one or more satellites are used; the given position may be a specified fixed point or any fixed point within specified areas; in some cases this service includes satellite-to-satellite links, which may also be operated in the inter-satellite service; the fixed-satellite service may also include feeder links for other space radiocommunication services.
Classification
This radiocommunication service is classified in accordance with ITU Radio Regulations (article 1) as follows:
Fixed service (article 1.20)
Fixed-satellite service (article 1.21)
Inter-satellite service (article 1.22)
Earth exploration-satellite service (article 1.51)
Meteorological-satellite service (article 1.52)
Frequency allocation
The allocation of radio frequencies is provided according to Article 5 of the ITU Radio Regulations (most recent version, Edition of 2020).
In order to improve harmonisation in spectrum utilisation, the majority of service-allocations stipulated in this document were incorporated in national Tables of Frequency Allocations and Utilisations which is within the responsibility of the appropriate national administration. The allocation might be primary, secondary, exclusive, and shared.
primary allocation: is indicated by writing in capital letters (see example below)
secondary allocation: is indicated by small letters
exclusive or shared utilization: is within the responsibility of administrations
Example of frequency allocation
Use in North America
FSS – is as well the official classification (used chiefly in North America) for geostationary communications satellites that provide broadcast feeds to television stations, radio stations and broadcast networks. FSSs also transmit informatio |
https://en.wikipedia.org/wiki/DFI | DFI (Diamond Flower Inc) is a Taiwanese industrial computer company with headquarters in Taipei. It designs, develops, manufactures, and sells industrial motherboard, industrial PCs, System-on-Module, industrial displays, and ODM/OEM services.
DFI was founded by Y.C Lu on July 14, 1981, developing and selling electronics components and add-on cards in the beginning. However, DFI switched to the production of motherboards after searching for potential markets and deciding to focus on the strengths of DFI. Targeting the new growing market in motherboard products, DFI announced the Patent License Agreement with Intel Corporation to build partnership with Intel in 1990 and has been developing and manufacturing motherboard products since 1992. With continuous dedication, DFI quickly gained a reputation in Asia-Pacific region after five years and was awarded Top 10 Motherboard Manufacturer in CRN Magazine from the year 1997 to 1999. Starting from 1998, DFI began to follow the strategies of Intel by releasing Intel 440BX series motherboards, 810 motherboards, and 810e motherboards to worldwide markets. Since its growing advances in manufacturing motherboards, DFI was awarded the Intel Global Demo Board manufacturer award in 1998 and 1999 respectively.
Catering to the growing market of high-end motherboards, DFI developed advanced overclocking motherboards, the LanParty series, which has proven to be a valuable segment for small powerful computers that meet the requirements of end users in the 2000s. DFI introduced the junior lineup (“JR”) with two products, p45 and 790gx, in the beginning, which has since been extended with Nvidia and X58 chipsets. There are other LanParty series like LT, DK(Dark), and Lanparty UT.
With blossoming business in the market, DFI went public and launched its initial public offering (IPO) on January 15, 2000. DFI has already gained a reputation from its motherboard products and hot-selling lineup, LanParty, at that time. And aside from develo |
https://en.wikipedia.org/wiki/251%20%28number%29 | 251 (two hundred [and] fifty-one) is the natural number between 250 and 252. It is also a prime number.
In mathematics
251 is:
a Sophie Germain prime.
the sum of three consecutive primes (79 + 83 + 89) and seven consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47).
a Chen prime.
an Eisenstein prime with no imaginary part.
a de Polignac number, meaning that it is odd and cannot be formed by adding a power of two to a prime number.
the smallest number that can be formed in more than one way by summing three positive cubes:
Every 5 × 5 matrix has exactly 251 square submatrices. |
https://en.wikipedia.org/wiki/257%20%28number%29 | 257 (two hundred [and] fifty-seven) is the natural number following 256 and preceding 258.
257 is a prime number of the form specifically with n = 3, and therefore a Fermat prime. Thus a regular polygon with 257 sides is constructible with compass and unmarked straightedge. It is currently the second largest known Fermat prime.
Analogously, 257 is the third Sierpinski prime of the first kind, of the form ➜ .
It is also
a balanced prime,
an irregular prime,
a prime that is one more than a square,
and a Jacobsthal–Lucas number.
There are exactly 257 combinatorially distinct convex polyhedra with eight vertices (or polyhedral graphs with eight nodes). |
https://en.wikipedia.org/wiki/Kaup%E2%80%93Kupershmidt%20equation | The Kaup–Kupershmidt equation (named after David J. Kaup and Boris Abram Kupershmidt) is the nonlinear fifth-order partial differential equation
It is the first equation in a hierarchy of integrable equations with the Lax operator
.
It has properties similar (but not identical) to those of the better-known KdV hierarchy in which the Lax operator has order 2. |
https://en.wikipedia.org/wiki/SageTV | SageTV Media Center, now open source, was a proprietary, commercial DVR (Digital Video Recording) and HTPC (Home theater PC) software for Mac OS X, Windows and Linux. It requires that the host computer have a hardware-based TV tuner card. The SageTV software has an integrated Electronic Programming Guide (EPG) that is updated via the Internet. The program provides a television interface for DVR, music, and photos on Windows and Linux. SageTV Media Center typically records in standard MPEG2, making it possible to transfer recordings to laptops or other devices. It also has a built-in conversion feature to transcode files into other formats compatible with iPod, PSP, cell phones and other portable devices.
A "lite" version is commonly shipped as part of an OEM software bundle. Both the lite and regular versions offer a Java API.
SageTV Placeshifter allows the user to watch TV from any high speed internet connection, similar to the Slingbox. As of Version 6, the SageTV Placeshifter is available for Windows, Linux and Macintosh platforms. The SageTV Media Extender set-top allows other TVs to connect to SageTV over a home network. There is also the ability to use the Hauppauge MediaMVP with SageTV by purchasing a MediaMVP Client License.
On June 18, 2011, Jeffrey Kardatzke, CTO and founder of the company, announced in a SageTV forum post that his company had been acquired by Google. An official press release followed later the same day, and since then the SageTV products have no longer been available for purchase.
On March 9, 2015, Jeffrey Kardatzke announced that SageTV would be open-sourced "in the near future (i.e. months, not years)". Then a few months later, SageTV became open source, hosted on GitHub.
Google Fiber
After the acquisition of SageTV, LLC by Google, they began modifying and updating it to work with Google's upcoming Google Fiber TV service. SageTV v8 was the initial platform used for the Google Fiber Storage Box (DVR) and TV Box (Client). It has s |
https://en.wikipedia.org/wiki/Common%20tendinous%20ring | The common tendinous ring, also known as the annulus of Zinn, or annular tendon, is a ring of fibrous tissue surrounding the optic nerve at its entrance at the apex of the orbit. It is the common origin of the four recti muscles of the group of extraocular muscles.
It can be used to divide the regions of the superior orbital fissure.
The arteries surrounding the optic nerve form a vascular structure known as the circle of Zinn-Haller, or sometimes as the circle of Zinn.
The following structures pass through the tendinous ring (superior to inferior):
Superior division of the oculomotor nerve (CNIII)
Nasociliary nerve (branch of ophthalmic nerve)
Inferior division of the oculomotor nerve (CNIII)
Abducens nerve (CNVI)
Optic nerve
Parts
The common tendinous ring spans the superior orbital fissure and can be described as having two parts – an inferior tendon which gives origin to the inferior rectus muscle, and to part of the lateral rectus muscle; and a superior tendon which gives origin to the superior rectus muscle, and to part of the medial and lateral recti muscles.
Eponym
It is named for Johann Gottfried Zinn. It should not be confused with the zonule of Zinn, though it is named after the same person. |
https://en.wikipedia.org/wiki/1-Click | 1-Click, also called one-click or one-click buying, is the technique of allowing customers to make purchases with the payment information needed to complete the purchase having been entered by the user previously. More particularly, it allows an online shopper using an Internet marketplace to purchase an item without having to use shopping cart software. Instead of manually inputting billing and shipping information for a purchase, a user can use one-click buying to use a predefined address and credit card number to purchase one or more items. Since the expiration of Amazon's patent, there has been an advent of checkout experience platforms, such as ShopPay, Simpler, PeachPay, Zplit, and Bolt which offer similar one-click checkout flows.
Patent
The United States Patent and Trademark Office (USPTO) issued a patent for this technique to Amazon.com in September 1999. Amazon.com also owns the "1-Click" trademark.
On May 12, 2006, the USPTO ordered a reexamination of the "One-Click" patent, based on a request filed by Peter Calveley. Calveley cited as prior art an earlier e-commerce patent and the Digicash electronic cash system.
On October 9, 2007, the USPTO issued an office action in the reexamination which confirmed the patentability of claims 6 to 10 of the patent. The patent examiner, however, rejected claims 1 to 5 and 11 to 26. In November 2007, Amazon responded by amending the broadest claims (1 and 11) to restrict them to a shopping cart model of commerce. They have also submitted several hundred references for the examiner to consider. In March 2010, the reexamined and amended patent was allowed.
Amazon's U.S. patent expired on September 11, 2017.
In Europe, a patent application on 1-Click ordering was filed with the European Patent Office (EPO) but was rejected by the EPO in 2007 due to obviousness; the decision was upheld in 2011.
A related gift-ordering patent was granted in 2003, but revoked in 2007 following an opposition.
In Canada, the Federal Co |
https://en.wikipedia.org/wiki/GlueX | GlueX is a particle physics experiment located at the Thomas Jefferson National Accelerator Facility (JLab) accelerator in Newport News, Virginia. Its primary purpose is to better understand the nature of confinement in quantum chromodynamics (QCD) by identifying a spectrum of hybrid and exotic mesons generated by the excitation of the gluonic field binding the quarks. Such mesonic states are predicted to exist outside of the well-established quark model, but none have been definitively identified by previous experiments. A broad high-statistics survey of known light mesons up to and including the is also underway.
Experimental Apparatus
The experiment uses photoproduction (that is, the scattering of a real photon on a nucleon) to produce mesonic states. Unlike previous similar experiments, it uses linearly polarized photons, which allows the analysis of accumulated events for certain polarization observables that are thought to make identification of exotic states feasible.
The GlueX detector was installed in the new Hall D (the fourth such hall at JLab) as part of the accelerator's upgrade to 12 GeV energy. GlueX began its first commissioning run in 2014, and first received 12 GeV electrons in 2015, the highest energy available at the CEBAF accelerator. Publication-quality physics data was accumulated during multi-weeks runs starting in 2016, continuing into 2023 and beyond.
The detector is based on a solenoidal hermetic detector optimized for tracking of charged particles (electron, pions, kaons, and protons) and detection of neutral particles (primarily photons). Figure 1 shows the detector.
GlueX uses the coherent bremsstrahlung technique to produce a linearly polarized photon beam. In order to reach the optimal photon energy near 9 GeV for this mapping of the exotic spectrum, 12 GeV electrons are required and are provided by the CEBAF accelerator at Jefferson Lab.
In 2018, improved kaon/pion separation capability will be established with the a |
https://en.wikipedia.org/wiki/Signed%20measure | In mathematics, signed measure is a generalization of the concept of (positive) measure by allowing the set function to take negative values, i.e., to acquire sign.
Definition
There are two slightly different concepts of a signed measure, depending on whether or not one allows it to take infinite values. Signed measures are usually only allowed to take finite real values, while some textbooks allow them to take infinite values. To avoid confusion, this article will call these two cases "finite signed measures" and "extended signed measures".
Given a measurable space (that is, a set with a σ-algebra on it), an extended signed measure is a set function
such that and is σ-additive – that is, it satisfies the equality
for any sequence of disjoint sets in
The series on the right must converge absolutely when the value of the left-hand side is finite. One consequence is that an extended signed measure can take or as a value, but not both. The expression is undefined and must be avoided.
A finite signed measure (a.k.a. real measure) is defined in the same way, except that it is only allowed to take real values. That is, it cannot take or
Finite signed measures form a real vector space, while extended signed measures do not because they are not closed under addition. On the other hand, measures are extended signed measures, but are not in general finite signed measures.
Examples
Consider a non-negative measure on the space (X, Σ) and a measurable function f: X → R such that
Then, a finite signed measure is given by
for all A in Σ.
This signed measure takes only finite values. To allow it to take +∞ as a value, one needs to replace the assumption about f being absolutely integrable with the more relaxed condition
where f−(x) = max(−f(x), 0) is the negative part of f.
Properties
What follows are two results which will imply that an extended signed measure is the difference of two non-negative measures, and a finite signed measure is the difference |
https://en.wikipedia.org/wiki/Hahn%20decomposition%20theorem | In mathematics, the Hahn decomposition theorem, named after the Austrian mathematician Hans Hahn, states that for any measurable space and any signed measure defined on the -algebra , there exist two -measurable sets, and , of such that:
and .
For every such that , one has , i.e., is a positive set for .
For every such that , one has , i.e., is a negative set for .
Moreover, this decomposition is essentially unique, meaning that for any other pair of -measurable subsets of fulfilling the three conditions above, the symmetric differences and are -null sets in the strong sense that every -measurable subset of them has zero measure. The pair is then called a Hahn decomposition of the signed measure .
Jordan measure decomposition
A consequence of the Hahn decomposition theorem is the , which states that every signed measure defined on has a unique decomposition into a difference of two positive measures, and , at least one of which is finite, such that for every -measurable subset and for every -measurable subset , for any Hahn decomposition of . We call and the positive and negative part of , respectively. The pair is called a Jordan decomposition (or sometimes Hahn–Jordan decomposition) of . The two measures can be defined as
for every and any Hahn decomposition of .
Note that the Jordan decomposition is unique, while the Hahn decomposition is only essentially unique.
The Jordan decomposition has the following corollary: Given a Jordan decomposition of a finite signed measure , one has
for any in . Furthermore, if for a pair of finite non-negative measures on , then
The last expression means that the Jordan decomposition is the minimal decomposition of into a difference of non-negative measures. This is the minimality property of the Jordan decomposition.
Proof of the Jordan decomposition: For an elementary proof of the existence, uniqueness, and minimality of the Jordan measure decomposition see Fischer (2012).
Proof of |
https://en.wikipedia.org/wiki/Keyfile | A keyfile (or key-file) is a file on a computer which contains encryption or license keys.
A common use is web server software running secure socket layer (SSL) protocols. Server-specific keys issued by trusted authorities are merged into the keyfile along with the trusted root certificates. By this method keys can be updated without recompiling software or rebooting the server.
A keyfile is often part of a public key infrastructure (PKI).
Some applications use a keyfile to hold licensing information, which is periodically reviewed to ensure currency and compliance. Other applications allow users to merge multiple service-specific security settings into a single common store (for example, Apple Computer's Keychain in later Mac OS X versions, GNOME Keyring and KWallet in the GNOME and KDE environments in Linux, respectively).
See also
License manager
List of license managers
Passphrase
Encryption software
Product activation
Digital rights management
.KEY extension - Keynote (Apple presentation software)
Key management |
https://en.wikipedia.org/wiki/Character%20sum | In mathematics, a character sum is a sum of values of a Dirichlet character χ modulo N, taken over a given range of values of n. Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue modulo N. Character sums are often closely linked to exponential sums by the Gauss sums (this is like a finite Mellin transform).
Assume χ is a non-principal Dirichlet character to the modulus N.
Sums over ranges
The sum taken over all residue classes mod N is then zero. This means that the cases of interest will be sums over relatively short ranges, of length R < N say,
A fundamental improvement on the trivial estimate is the Pólya–Vinogradov inequality, established independently by George Pólya and I. M. Vinogradov in 1918, stating in big O notation that
Assuming the generalized Riemann hypothesis, Hugh Montgomery and R. C. Vaughan have shown that there is the further improvement
Summing polynomials
Another significant type of character sum is that formed by
for some function F, generally a polynomial. A classical result is the case of a quadratic, for example,
and χ a Legendre symbol. Here the sum can be evaluated (as −1), a result that is connected to the local zeta-function of a conic section.
More generally, such sums for the Jacobi symbol relate to local zeta-functions of elliptic curves and hyperelliptic curves; this means that by means of André Weil's results, for N = p a prime number, there are non-trivial bounds
The constant implicit in the notation is linear in the genus of the curve in question, and so (Legendre symbol or hyperelliptic case) can be taken as the degree of F. (More general results, for other values of N, can be obtained starting from there.)
Weil's results also led to the Burgess bound, applying to give non-trivial results beyond Pólya–Vinogradov, for R a power of N greater than 1/4.
Assume the |
https://en.wikipedia.org/wiki/Alfred%20Young%20%28mathematician%29 | Alfred Young, FRS (16 April 1873 – 15 December 1940) was a British mathematician.
He was born in Widnes, Lancashire, England, and educated at Monkton Combe School in Somerset and Clare College, Cambridge, graduating BA as 10th Wrangler in 1895. He is known for his work in the area of group theory. Both Young diagrams and Young tableaux (which he introduced in 1900) are named after him.
Young was appointed to the position of lecturer at Selwyn College, Cambridge, in 1901, transferring to Clare College in 1905. In 1902 he collaborated with John Hilton Grace on the book The Algebra of Invariants.
In 1907 he married Edith Clara née Wilson. In 1908 he became an ordained clergyman, and in 1910 became parish priest at Birdbrook in Essex, a village 25 miles east of Cambridge. He lived there for the rest of his life, but in 1926 began lecturing once again at Cambridge.
Most of his long series of papers on invariant theory and the symmetric group were written while he was a clergyman.
See also
Hyperoctahedral group
Young's lattice
Young–Fibonacci lattice
Young symmetrizer
Representation theory of the symmetric group |
https://en.wikipedia.org/wiki/Kodaira%20embedding%20theorem | In mathematics, the Kodaira embedding theorem characterises non-singular projective varieties, over the complex numbers, amongst compact Kähler manifolds. In effect it says precisely which complex manifolds are defined by homogeneous polynomials.
Kunihiko Kodaira's result is that for a compact Kähler manifold M, with a Hodge metric, meaning that the cohomology class in degree 2 defined by the Kähler form ω is an integral cohomology class, there is a complex-analytic embedding of M into complex projective space of some high enough dimension N.
The fact that M embeds as an algebraic variety follows from its compactness by Chow's theorem.
A Kähler manifold with a Hodge metric is occasionally called a Hodge manifold (named after W. V. D. Hodge), so Kodaira's results states that Hodge manifolds are projective.
The converse that projective manifolds are Hodge manifolds is more elementary and was already known.
Kodaira also proved (Kodaira 1963), by recourse to the classification of compact complex surfaces, that every compact Kähler surface is a deformation of a projective Kähler surface. This was later simplified by Buchdahl to remove reliance on the classification (Buchdahl 2008).
Kodaira embedding theorem
Let X be a compact Kähler manifold, and L a holomorphic line bundle on X. Then L is a positive line bundle if and only if there is a holomorphic embedding of X into some projective space such that for some m > 0.
See also
Fujita conjecture
Hodge structure
Moishezon manifold |
https://en.wikipedia.org/wiki/Soft%20goal | In connection with modeling languages and especially with goal-oriented modeling, a soft goal is an objective without clear-cut criteria. Soft goals can represent:
Non-functional requirements
Relations between non-functional requirements
Non-functional requirements (or quality attributes, qualities, or more colloquially "-ilities") are global qualities of a software system, such as flexibility, maintainability, usability, and so forth. Such requirements are usually stated only informally; and they are often controversial (i.e. management wants a secure system but staff desires user-friendliness). They are also often difficult to validate.
Why soft?
Normally a goal is a very strict and clear logical criterion. It is satisfied when all sub-goals are satisfied. But in non-functional requirements you often need more loosely defined criteria, like satisficeable or unsatisficeable. The term satisficing was first coined by Herbert Simon. Soft goals are goals that do not have a clear-cut criterion for their satisfaction: they are satisficed when there is sufficient positive and little negative evidence for this claim, while they are unsatisficeable in the opposite case.
Relations between soft goals
Decompositions
AND
OR
Contributions
Helps (+)
Hurts (-)
Makes (++)
Breaks (--)
Unknown |
https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s%20cat%20in%20popular%20culture | Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as absurdities in the views that other physicists had about quantum mechanics (ideas later labeled the Copenhagen interpretation), by applying them not to microscopic objects but to everyday ones. The thought experiment presents a cat that might be alive or dead, depending on an earlier random event. In the course of developing this experiment, he coined the term Verschränkung (entanglement). It was not long before science-fiction writers picked up this evocative concept, often using it in a humorous vein. Works of fiction have employed Schrödinger's thought experiment as plot device and as metaphor, in genres from apocalyptic science fiction to young-adult drama, making the cat more prominent in popular culture than in physics itself.
Schrödinger's cat has been a motive in many science fiction works, and used as a title of a number of them, including Greg Bear's "Schrödinger's Plague" (Analog, 29 March 1982), George Alec Effinger's "Schrödinger's Kitten" (Omni, September 1988), Ursula Le Guin's "Schrödinger's Cat" (in the 1974 anthology Universe 5), F. Gwynplaine MacIntyre's "Schrödinger's Cat-Sitter" (Analog, July/August 2001), Rudy Rucker's "Schrödinger's Cat" (Analog, 30 March 1981), and Robert Anton Wilson's Schrödinger's Cat Trilogy (1988), illustrating various interpretations of quantum physics. In addition to novels and short stories, Schrödinger's cat has appeared in film, poetry theatre, live-action television, cartoons, music, and webcomics. |
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