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https://en.wikipedia.org/wiki/Object%20file | An object file is a computer file containing object code, that is, machine code output of an assembler or compiler. The object code is usually relocatable, and not usually directly executable. There are various formats for object files, and the same machine code can be packaged in different object file formats. An object file may also work like a shared library.
In addition to the object code itself, object files may contain metadata used for linking or debugging, including: information to resolve symbolic cross-references between different modules, relocation information, stack unwinding information, comments, program symbols, debugging or profiling information. Other metadata may include the date and time of compilation, the compiler name and version, and other identifying information.
The term "object program" dates from at least the 1950s:
A computer programmer generates object code with a compiler or assembler. For example, under Linux, the GNU Compiler Collection compiler will generate files with a .o extension which use the ELF format. Compilation on Windows generates files with a .obj extension which use the COFF format. A linker is then used to combine the object code into one executable program or library pulling in precompiled system libraries as needed.
Object file formats
There are many different object file formats; originally each type of computer had its own unique format, but with the advent of Unix and other portable operating systems, some formats, such as ELF and COFF, have been defined and used on different kinds of systems. It is possible for the same format to be used both as linker input and output, and thus as the library and executable file format. Some formats can contain machine code for different processors, with the correct one chosen by the operating system when the program is loaded.
Some systems make a distinction between formats which are directly executable and formats which require processing by the linker. For example, OS/ |
https://en.wikipedia.org/wiki/Safety%20data%20sheet | A safety data sheet (SDS), material safety data sheet (MSDS), or product safety data sheet (PSDS) is a document that lists information relating to occupational safety and health for the use of various substances and products. SDSs are a widely used system for cataloguing information on chemicals, chemical compounds, and chemical mixtures. SDS information may include instructions for the safe use and potential hazards associated with a particular material or product, along with spill-handling procedures. The older MSDS formats could vary from source to source within a country depending on national requirements; however, the newer SDS format is internationally standardized.
An SDS for a substance is not primarily intended for use by the general consumer, focusing instead on the hazards of working with the material in an occupational setting. There is also a duty to properly label substances on the basis of physico-chemical, health, or environmental risk. Labels can include hazard symbols such as the European Union standard symbols. The same product (e.g. paints sold under identical brand names by the same company) can have different formulations in different countries. The formulation and hazards of a product using a generic name may vary between manufacturers in the same country.
Globally Harmonized System
The Globally Harmonized System of Classification and Labelling of Chemicals contains a standard specification for safety data sheets. The SDS follows a 16 section format which is internationally agreed and for substances especially, the SDS should be followed with an Annex which contains the exposure scenarios of this particular substance. The 16 sections are:
SECTION 1: Identification of the substance/mixture and of the company/undertaking
1.1. Product identifier
1.2. Relevant identified uses of the substance or mixture and uses advised against
1.3. Details of the supplier of the safety data sheet
1.4. Emergency telephone number
SECTION 2: Hazards identificat |
https://en.wikipedia.org/wiki/Domain%20Name%20System%20Security%20Extensions | The Domain Name System Security Extensions (DNSSEC) are a suite of extension specifications by the Internet Engineering Task Force (IETF) for securing data exchanged in the Domain Name System (DNS) in Internet Protocol (IP) networks. The protocol provides cryptographic authentication of data, authenticated denial of existence, and data integrity, but not availability or confidentiality.
Overview
The original design of the Domain Name System did not include any security features. It was conceived only as a scalable distributed system. The Domain Name System Security Extensions (DNSSEC) attempt to add security, while maintaining backward compatibility. documents some of the known threats to the DNS, and their solutions in DNSSEC.
DNSSEC was designed to protect applications using DNS from accepting forged or manipulated DNS data, such as that created by DNS cache poisoning. All answers from DNSSEC protected zones are digitally signed. By checking the digital signature, a DNS resolver is able to check if the information is identical (i.e. unmodified and complete) to the information published by the zone owner and served on an authoritative DNS server. While protecting IP addresses is the immediate concern for many users, DNSSEC can protect any data published in the DNS, including text records (TXT) and mail exchange records (MX), and can be used to bootstrap other security systems that publish references to cryptographic certificates stored in the DNS such as Certificate Records (CERT records, ), SSH fingerprints (SSHFP, ), IPSec public keys (IPSECKEY, ), TLS Trust Anchors (TLSA, ), or Encrypted Client Hello (SVCB/HTTPS records for ECH ).
DNSSEC does not provide confidentiality of data; in particular, all DNSSEC responses are authenticated but not encrypted. DNSSEC does not protect against DoS attacks directly, though it indirectly provides some benefit (because signature checking allows the use of potentially untrustworthy parties).
Other standards (not DNSSEC) a |
https://en.wikipedia.org/wiki/Raoul%20Bott | Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.
Early life
Bott was born in Budapest, Hungary, the son of Margit Kovács and Rudolph Bott. His father was of Austrian descent, and his mother was of Hungarian Jewish descent; Bott was raised a Catholic by his mother and stepfather. Bott grew up in Czechoslovakia and spent his working life in the United States. His family emigrated to Canada in 1938, and subsequently he served in the Canadian Army in Europe during World War II.
Career
Bott later went to college at McGill University in Montreal, where he studied electrical engineering. He then earned a PhD in mathematics from Carnegie Mellon University in Pittsburgh in 1949. His thesis, titled Electrical Network Theory, was written under the direction of Richard Duffin. Afterward, he began teaching at the University of Michigan in Ann Arbor. Bott continued his study at the Institute for Advanced Study in Princeton. He was a professor at Harvard University from 1959 to 1999. In 2005 Bott died of cancer in San Diego.
With Richard Duffin at Carnegie Mellon, Bott studied existence of electronic filters corresponding to given positive-real functions. In 1949 they proved a fundamental theorem of filter synthesis. Duffin and Bott extended earlier work by Otto Brune that requisite functions of complex frequency s could be realized by a passive network of inductors and capacitors. The proof relied on induction on the sum of the degrees of the polynomials in the numerator and denominator of the rational function.
In his 2000 interview with Allyn Jackson of the American Mathematical Society, he explained that he sees "networks as discrete versions of harmonic theory", so his experience with network synthesis and electroni |
https://en.wikipedia.org/wiki/Composite%20data%20type | In computer science, a composite data type or compound data type is any data type which can be constructed in a program using the programming language's primitive data types and other composite types. It is sometimes called a structure or aggregate type, although the latter term may also refer to arrays, lists, etc. The act of constructing a composite type is known as composition. Composite data types are often contrasted with scalar variables.
C/C++ structures and classes
A struct is C's and C++'s notion of a composite type, a datatype that composes a fixed set of labeled fields or members. It is so called because of the struct keyword used in declaring them, which is short for structure or, more precisely, user-defined data structure.
In C++, the only difference between a struct and a class is the default access level, which is private for classes and public for structs.
Note that while classes and the class keyword were completely new in C++, the C programming language already had a raw type of structs. For all intents and purposes, C++ structs form a superset of C structs: virtually all valid C structs are valid C++ structs with the same semantics.
Declaration
A struct declaration consists of a list of fields, each of which can have any type. The total storage required for a struct object is the sum of the storage requirements of all the fields, plus any internal padding.
For example:
struct Account {
int account_number;
char *first_name;
char *last_name;
float balance;
};
defines a type, referred to as struct Account. To create a new variable of this type, we can write struct Account myAccount;
which has an integer component, accessed by myAccount.account_number, and a floating-point component, accessed by myAccount.balance, as well as the first_name and last_name components. The structure myAccount contains all four values, and all four fields may be changed independently.
Since writing struct Account repeatedly in code becomes cumbe |
https://en.wikipedia.org/wiki/BurgerTime | originally released as in Japan, is a 1982 arcade video game developed by Data East, initially for its DECO Cassette System. The player is chef Peter Pepper, who must walk over hamburger ingredients in a maze of platforms and ladders while avoiding anthropomorphic hot dogs, fried eggs, and pickles which are in pursuit.
In the United States, Data East USA licensed BurgerTime for distribution by Bally Midway as a standard dedicated arcade game. Data East also released its own version of BurgerTime in the United States through its DECO Cassette System. The Data East and Midway versions are distinguished by the manufacturer's name on the title screen and by the marquee and cabinet artworks, as the game itself is identical. The game's original Japanese title Hamburger changed outside of Japan to BurgerTime, reportedly to avoid potential trademark issues. In addition to all releases in the Western world, BurgerTime also became the title used for the Japanese ports and sequels.
The first home port of BurgerTime was released for the Intellivision console in 1983, followed by versions for other systems. There have been multiple sequels for both the arcade and home.
When Data East went bankrupt in 2003, G-Mode bought most of Data East's intellectual properties, including BurgerTime, BurgerTime Deluxe, Super BurgerTime, and Peter Pepper's Ice Cream Factory.
Gameplay
The object of the game is to build a number of hamburgers while avoiding enemy foods. The player controls the protagonist, chef Peter Pepper, with a four-position joystick and a "pepper" button.
Each level is a maze of platforms and ladders in which giant burger ingredients (bun, meat patty, tomato, lettuce) are arranged. When Peter walks the full length of an ingredient, it falls to the level below, knocking down any ingredient that happens to be there. A burger is completed when all of its vertically aligned ingredients have been dropped out of the maze and onto a waiting plate. The player must complete a |
https://en.wikipedia.org/wiki/Table%20%28information%29 | A table is an arrangement of information or data, typically in rows and columns, or possibly in a more complex structure. Tables are widely used in communication, research, and data analysis. Tables appear in print media, handwritten notes, computer software, architectural ornamentation, traffic signs, and many other places. The precise conventions and terminology for describing tables vary depending on the context. Further, tables differ significantly in variety, structure, flexibility, notation, representation and use. Information or data conveyed in table form is said to be in tabular format (adjective). In books and technical articles, tables are typically presented apart from the main text in numbered and captioned floating blocks.
Basic description
A table consists of an ordered arrangement of rows and columns. This is a simplified description of the most basic kind of table. Certain considerations follow from this simplified description:
the term row has several common synonyms (e.g., record, k-tuple, n-tuple, vector);
the term column has several common synonyms (e.g., field, parameter, property, attribute, stanchion);
a column is usually identified by a name;
a column name can consist of a word, phrase or a numerical index;
the intersection of a row and a column is called a cell.
The elements of a table may be grouped, segmented, or arranged in many different ways, and even nested recursively. Additionally, a table may include metadata, annotations, a header, a footer or other ancillary features.
Simple table
The following illustrates a simple table with three columns and nine rows. The first row is not counted, because it is only used to display the column names. This is called a "header row".
Multi-dimensional table
The concept of dimension is also a part of basic terminology. Any "simple" table can be represented as a "multi-dimensional"
table by normalizing the data values into ordered hierarchies. A common example of such a table is a mult |
https://en.wikipedia.org/wiki/List%20of%20calculus%20topics | This is a list of calculus topics.
Limits
Limit (mathematics)
Limit of a function
One-sided limit
Limit of a sequence
Indeterminate form
Orders of approximation
(ε, δ)-definition of limit
Continuous function
Differential calculus
Derivative
Notation
Newton's notation for differentiation
Leibniz's notation for differentiation
Simplest rules
Derivative of a constant
Sum rule in differentiation
Constant factor rule in differentiation
Linearity of differentiation
Power rule
Chain rule
Local linearization
Product rule
Quotient rule
Inverse functions and differentiation
Implicit differentiation
Stationary point
Maxima and minima
First derivative test
Second derivative test
Extreme value theorem
Differential equation
Differential operator
Newton's method
Taylor's theorem
L'Hôpital's rule
General Leibniz rule
Mean value theorem
Logarithmic derivative
Differential (calculus)
Related rates
Regiomontanus' angle maximization problem
Rolle's theorem
Integral calculus
Antiderivative/Indefinite integral
Simplest rules
Sum rule in integration
Constant factor rule in integration
Linearity of integration
Arbitrary constant of integration
Cavalieri's quadrature formula
Fundamental theorem of calculus
Integration by parts
Inverse chain rule method
Integration by substitution
Tangent half-angle substitution
Differentiation under the integral sign
Trigonometric substitution
Partial fractions in integration
Quadratic integral
Proof that 22/7 exceeds π
Trapezium rule
Integral of the secant function
Integral of secant cubed
Arclength
Solid of revolution
Shell integration
Special functions and numbers
Natural logarithm
e (mathematical constant)
Exponential function
Hyperbolic angle
Hyperbolic function
Stirling's approximation
Bernoulli numbers
Absolute numerical
See also list of numerical analysis topics
Rectangle method
Trapezoidal rule
Simpson's rule
Newton–Cotes formulas
Gaussian quadrature
Lists and tables |
https://en.wikipedia.org/wiki/Dihedral%20angle | A dihedral angle is the angle between two intersecting planes or half-planes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge. In higher dimensions, a dihedral angle represents the angle between two hyperplanes.
The planes of a flying machine are said to be at positive dihedral angle when both starboard and port main planes (commonly called "wings") are upwardly inclined to the lateral axis; when downwardly inclined they are said to be at a negative dihedral angle.
Mathematical background
When the two intersecting planes are described in terms of Cartesian coordinates by the two equations
the dihedral angle, between them is given by:
and satisfies
Alternatively, if and are normal vector to the planes, one has
where is the dot product of the vectors and is the product of their lengths.
The absolute value is required in above formulas, as the planes are not changed when changing all coefficient signs in one equation, or replacing one normal vector by its opposite.
However the absolute values can be and should be avoided when considering the dihedral angle of two half planes whose boundaries are the same line. In this case, the half planes can be described by a point of their intersection, and three vectors , and such that , and belong respectively to the intersection line, the first half plane, and the second half plane. The dihedral angle of these two half planes is defined by
,
and satisfies In this case, switching the two half-planes gives the same result, and so does replacing with In chemistry (see below), we define a dihedral angle such that replacing with changes the sign of the angle, which can be between and .
In polymer physics
In some scientific areas such as polymer physics, one may consider a chain of points and links between consecutive point |
https://en.wikipedia.org/wiki/Plateau%27s%20problem | In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who experimented with soap films. The problem is considered part of the calculus of variations. The existence and regularity problems are part of geometric measure theory.
History
Various specialized forms of the problem were solved, but it was only in 1930 that general solutions were found in the context of mappings (immersions) independently by Jesse Douglas and Tibor Radó. Their methods were quite different; Radó's work built on the previous work of René Garnier and held only for rectifiable simple closed curves, whereas Douglas used completely new ideas with his result holding for an arbitrary simple closed curve. Both relied on setting up minimization problems; Douglas minimized the now-named Douglas integral while Radó minimized the "energy". Douglas went on to be awarded the Fields Medal in 1936 for his efforts.
In higher dimensions
The extension of the problem to higher dimensions (that is, for -dimensional surfaces in -dimensional space) turns out to be much more difficult to study. Moreover, while the solutions to the original problem are always regular, it turns out that the solutions to the extended problem may have singularities if . In the hypersurface case where , singularities occur only for . An example of such singular solution of the Plateau problem is the Simons cone, a cone over in that was first described by Jim Simons and was shown to be an area minimizer by Bombieri, De Giorgi and Giusti. To solve the extended problem in certain special cases, the theory of perimeters (De Giorgi) for codimension 1 and the theory of rectifiable currents (Federer and Fleming) for higher codimension have been developed. The theory guarantees existence of codimension 1 solutions that are smooth away from a closed set of Hausdorff dimension . In the case of highe |
https://en.wikipedia.org/wiki/Hasse%20diagram | In order theory, a Hasse diagram (; ) is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set one represents each element of as a vertex in the plane and draws a line segment or curve that goes upward from one vertex to another vertex whenever covers (that is, whenever , and there is no distinct from and with ). These curves may cross each other but must not touch any vertices other than their endpoints. Such a diagram, with labeled vertices, uniquely determines its partial order.
Hasse diagrams are named after Helmut Hasse (1898–1979); according to Garrett Birkhoff, they are so called because of the effective use Hasse made of them. However, Hasse was not the first to use these diagrams. One example that predates Hasse can be found in . Although Hasse diagrams were originally devised as a technique for making drawings of partially ordered sets by hand, they have more recently been created automatically using graph drawing techniques.
The phrase "Hasse diagram" may also refer to the transitive reduction as an abstract directed acyclic graph, independently of any drawing of that graph, but this usage is eschewed here.
Diagram design
Although Hasse diagrams are simple, as well as intuitive, tools for dealing with finite posets, it turns out to be rather difficult to draw "good" diagrams. The reason is that, in general, there are many different possible ways to draw a Hasse diagram for a given poset. The simple technique of just starting with the minimal elements of an order and then drawing greater elements incrementally often produces quite poor results: symmetries and internal structure of the order are easily lost.
The following example demonstrates the issue. Consider the power set of a 4-element set ordered by inclusion . Below are four different Hasse diagrams for this partial order. Each subset has a node labelled with a binar |
https://en.wikipedia.org/wiki/Value%20%28computer%20science%29 | In computer science and software programming, a value is the representation of some entity that can be manipulated by a program. The members of a type are the values of that type.
The "value of a variable" is given by the corresponding mapping in the environment. In languages with assignable variables, it becomes necessary to distinguish between the r-value (or contents) and the l-value (or location) of a variable.
In declarative (high-level) languages, values have to be referentially transparent. This means that the resulting value is independent of the location of the expression needed to compute the value. Only the contents of the location (the bits, whether they are 1 or 0) and their interpretation are significant.
Value category
Despite its name, in the C++ language standards this terminology is used to categorize expressions, not values.
Assignment: l-values and r-values
Some languages use the idea of l-values and r-values, deriving from the typical mode of evaluation on the left and right-hand side of an assignment statement. An l-value refers to an object that persists beyond a single expression. An r-value is a temporary value that does not persist beyond the expression that uses it.
The notion of l-values and r-values was introduced by Combined Programming Language (CPL). The notions in an expression of r-value, l-value, and r-value/l-value are analogous to the parameter modes of input parameter (has a value), output parameter (can be assigned), and input/output parameter (has a value and can be assigned), though the technical details differ between contexts and languages.
R-values and addresses
In many languages, notably the C family, l-values have storage addresses that are programmatically accessible to the running program (e.g., via some address-of operator like "&" in C/C++), meaning that they are variables or de-referenced references to a certain memory location. R-values can be l-values (see below) or non-l-values—a term only used to distin |
https://en.wikipedia.org/wiki/Long%20line%20%28topology%29 | In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer". It behaves locally just like the real line, but has different large-scale properties (e.g., it is neither Lindelöf nor separable). Therefore, it serves as an important counterexample in topology. Intuitively, the usual real-number line consists of a countable number of line segments laid end-to-end, whereas the long line is constructed from an uncountable number of such segments.
Definition
The closed long ray is defined as the Cartesian product of the first uncountable ordinal with the half-open interval equipped with the order topology that arises from the lexicographical order on . The open long ray is obtained from the closed long ray by removing the smallest element
The long line is obtained by "gluing" together two long rays, one in the positive direction and the other in the negative direction. More rigorously, it can be defined as the order topology on the disjoint union of the reversed open long ray (“reversed” means the order is reversed) (this is the negative half) and the (not reversed) closed long ray (the positive half), totally ordered by letting the points of the latter be greater than the points of the former. Alternatively, take two copies of the open long ray and identify the open interval of the one with the same interval of the other but reversing the interval, that is, identify the point (where is a real number such that ) of the one with the point of the other, and define the long line to be the topological space obtained by gluing the two open long rays along the open interval identified between the two. (The former construction is better in the sense that it defines the order on the long line and shows that the topology is the order topology; the latter is better in the sense that it uses gluing along an open set, which is clearer from the topological point of view.)
Intuitively, the clos |
https://en.wikipedia.org/wiki/Humoral%20immunity | Humoral immunity is the aspect of immunity that is mediated by macromolecules - including secreted antibodies, complement proteins, and certain antimicrobial peptides - located in extracellular fluids. Humoral immunity is named so because it involves substances found in the humors, or body fluids. It contrasts with cell-mediated immunity. Humoral immunity is also referred to as antibody-mediated immunity.
The study of the molecular and cellular components that form the immune system, including their function and interaction, is the central science of immunology. The immune system is divided into a more primitive innate immune system and an acquired or adaptive immune system of vertebrates, each of which contain both humoral and cellular immune elements.
Humoral immunity refers to antibody production and the coinciding processes that accompany it, including: Th2 activation and cytokine production, germinal center formation and isotype switching, and affinity maturation and memory cell generation. It also refers to the effector functions of antibodies, which include pathogen and toxin neutralization, classical complement activation, and opsonin promotion of phagocytosis and pathogen elimination.
History
The concept of humoral immunity developed based on the analysis of antibacterial activity of the serum components. Hans Buchner is credited with the development of the humoral theory. In 1890, Buchner described alexins as "protective substances" that exist in the blood serum and other bodily fluids and are capable of killing microorganisms. Alexins, later redefined as "complements" by Paul Ehrlich, were shown to be the soluble components of the innate response that leads to a combination of cellular and humoral immunity. This discovery helped to bridge the features of innate and acquired immunity.
Following the 1888 discovery of the bacteria that cause diphtheria and tetanus, Emil von Behring and Kitasato Shibasaburō showed that disease need not be caused by microo |
https://en.wikipedia.org/wiki/Radon%E2%80%93Nikodym%20theorem | In mathematics, the Radon–Nikodym theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable space. A measure is a set function that assigns a consistent magnitude to the measurable subsets of a measurable space. Examples of a measure include area and volume, where the subsets are sets of points; or the probability of an event, which is a subset of possible outcomes within a wider probability space.
One way to derive a new measure from one already given is to assign a density to each point of the space, then integrate over the measurable subset of interest. This can be expressed as
where is the new measure being defined for any measurable subset and the function is the density at a given point. The integral is with respect to an existing measure , which may often be the canonical Lebesgue measure on the real line or the n-dimensional Euclidean space (corresponding to our standard notions of length, area and volume). For example, if represented mass density and was the Lebesgue measure in three-dimensional space , then would equal the total mass in a spatial region .
The Radon–Nikodym theorem essentially states that, under certain conditions, any measure can be expressed in this way with respect to another measure on the same space. The function is then called the Radon–Nikodym derivative and is denoted by . An important application is in probability theory, leading to the probability density function of a random variable.
The theorem is named after Johann Radon, who proved the theorem for the special case where the underlying space is in 1913, and for Otto Nikodym who proved the general case in 1930. In 1936 Hans Freudenthal generalized the Radon–Nikodym theorem by proving the Freudenthal spectral theorem, a result in Riesz space theory; this contains the Radon–Nikodym theorem as a special case.
A Banach space is said to have the Radon–Nikodym property if the generalization of the Radon |
https://en.wikipedia.org/wiki/Back-side%20bus | In personal computer microprocessor architecture, a back-side bus (BSB), or backside bus, was a computer bus used on early Intel platforms to connect the CPU to CPU cache memory, usually off-die L2. If a design utilizes it along with a front-side bus (FSB), it is said to use a dual-bus architecture, or in Intel's terminology Dual Independent Bus (DIB) architecture. The back-side bus architecture evolved when newer processors like the second-generation Pentium III began to incorporate on-die L2 cache, which at the time was advertised as Advanced Transfer Cache, but Intel continued to refer to the Dual Independent Bus till the end of Pentium III.
History
BSB is an improvement over the older practice of using a single system bus, because a single bus typically became a severe bottleneck as CPUs and memory speeds increased. Due to its dedicated nature, the back-side bus can be optimized for communication with cache, thus eliminating protocol overheads and additional signals that are required on a general-purpose bus. Furthermore, since a BSB operates over a shorter distance, it can typically operate at higher clock speeds, increasing the computer's overall performance.
Cache connected with a BSB was initially external to the microprocessor die, but now is usually on-die. In the latter case, the BSB clock frequency is typically equal to the processor's, and the back-side bus can also be made much wider (256-bit, 512-bit) than either off-chip or on-chip FSB.
The dual-bus architecture was used in a number of designs, including the IBM and Freescale (formerly the semiconductor division of Motorola) PowerPC processors (certain PowerPC 604 models, the PowerPC 7xx family, and the Freescale 7xxx line), as well as the Intel Pentium Pro, Pentium II and early Pentium III processors,
which used it to access their L2 cache (earlier Intel processors accessed the L2 cache over the FSB, while later processors moved it on-chip).
See also
CPU cache
Bus (computing)
Front-side |
https://en.wikipedia.org/wiki/Exponential%20family | In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman–Darmois family. The terms "distribution" and "family" are often used loosely: specifically, an exponential family is a set of distributions, where the specific distribution varies with the parameter; however, a parametric family of distributions is often referred to as "a distribution" (like "the normal distribution", meaning "the family of normal distributions"), and the set of all exponential families is sometimes loosely referred to as "the" exponential family. They are distinct because they possess a variety of desirable properties, most importantly the existence of a sufficient statistic.
The concept of exponential families is credited to E. J. G. Pitman, G. Darmois, and B. O. Koopman in 1935–1936. Exponential families of distributions provide a general framework for selecting a possible alternative parameterisation of a parametric family of distributions, in terms of natural parameters, and for defining useful sample statistics, called the natural sufficient statistics of the family.
Definition
Most of the commonly used distributions form an exponential family or subset of an exponential family, listed in the subsection below. The subsections following it are a sequence of increasingly more general mathematical definitions of an exponential family. A casual reader may wish to restrict attention to the first and simplest definition, which corresponds to a single-parameter family of discrete or continuous probabilit |
https://en.wikipedia.org/wiki/Points%20of%20the%20compass | The points of the compass are a set of horizontal, radially arrayed compass directions (or azimuths) used in navigation and cartography. A compass rose is primarily composed of four cardinal directions—north, east, south, and west—each separated by 90 degrees, and secondarily divided by four ordinal (intercardinal) directions—northeast, southeast, southwest, and northwest—each located halfway between two cardinal directions. Some disciplines such as meteorology and navigation further divide the compass with additional azimuths. Within European tradition, a fully defined compass has 32 'points' (and any finer subdivisions are described in fractions of points).
Compass points are valuable in that they allow a user to refer to a specific azimuth in a colloquial fashion, without having to compute or remember degrees.
Designations
The names of the compass point directions follow these rules:
8-wind compass rose
The four cardinal directions are north (N), east (E), south (S), west (W), at 90° angles on the compass rose.
The four intercardinal (or ordinal) directions are formed by bisecting the above, giving: northeast (NE), southeast (SE), southwest (SW), and northwest (NW). In English and many other tongues, these are compound words. Different style guides for the four mandate spaces, dashes, or none.
In Bulgarian, Catalan, Czech, Danish, Dutch, English, Esperanto, French, Galician, German, Greek, Hungarian, Ido, Italian, Japanese (usually), Macedonian, Norwegian (both Bokmal and Nynorsk), Polish, Portuguese, Romansch, Russian, Serbian, Croatian, Spanish, Swedish, Ukrainian, and Welsh the part meaning north or south precedes the part meaning east or west.
In Chinese, Vietnamese, Gaelic, and less commonly Japanese, the part meaning east or west precedes the other.
In Estonian, Finnish, Breton, the "Italianate system", and Telugu, the intercardinals have distinct words.
The eight principal winds (or main winds) are the set union of the cardinals and intercardi |
https://en.wikipedia.org/wiki/List%20of%20real%20analysis%20topics | This is a list of articles that are considered real analysis topics.
General topics
Limits
Limit of a sequence
Subsequential limit – the limit of some subsequence
Limit of a function (see List of limits for a list of limits of common functions)
One-sided limit – either of the two limits of functions of real variables x, as x approaches a point from above or below
Squeeze theorem – confirms the limit of a function via comparison with two other functions
Big O notation – used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions
Sequences and series
(see also list of mathematical series)
Arithmetic progression – a sequence of numbers such that the difference between the consecutive terms is constant
Generalized arithmetic progression – a sequence of numbers such that the difference between consecutive terms can be one of several possible constants
Geometric progression – a sequence of numbers such that each consecutive term is found by multiplying the previous one by a fixed non-zero number
Harmonic progression – a sequence formed by taking the reciprocals of the terms of an arithmetic progression
Finite sequence – see sequenceInfinite sequence – see sequenceDivergent sequence – see limit of a sequence or divergent seriesConvergent sequence – see limit of a sequence or convergent seriesCauchy sequence – a sequence whose elements become arbitrarily close to each other as the sequence progresses
Convergent series – a series whose sequence of partial sums converges
Divergent series – a series whose sequence of partial sums diverges
Power series – a series of the form
Taylor series – a series of the form
Maclaurin series – see Taylor seriesBinomial series – the Maclaurin series of the function f given by f(x) = (1 + x) α
Telescoping series
Alternating series
Geometric series
Divergent geometric series
Harmonic series
Fourier series
Lambert series
Summation methods
Ce |
https://en.wikipedia.org/wiki/Cloning%20vector | A cloning vector is a small piece of DNA that can be stably maintained in an organism, and into which a foreign DNA fragment can be inserted for cloning purposes. The cloning vector may be DNA taken from a virus, the cell of a higher organism, or it may be the plasmid of a bacterium. The vector contains features that allow for the convenient insertion of a DNA fragment into the vector or its removal from the vector, for example through the presence of restriction sites. The vector and the foreign DNA may be treated with a restriction enzyme that cuts the DNA, and DNA fragments thus generated contain either blunt ends or overhangs known as sticky ends, and vector DNA and foreign DNA with compatible ends can then be joined by molecular ligation. After a DNA fragment has been cloned into a cloning vector, it may be further subcloned into another vector designed for more specific use.
There are many types of cloning vectors, but the most commonly used ones are genetically engineered plasmids. Cloning is generally first performed using Escherichia coli, and cloning vectors in E. coli include plasmids, bacteriophages (such as phage λ), cosmids, and bacterial artificial chromosomes (BACs). Some DNA, however, cannot be stably maintained in E. coli, for example very large DNA fragments, and other organisms such as yeast may be used. Cloning vectors in yeast include yeast artificial chromosomes (YACs).
Features of a cloning vector
All commonly used cloning vectors in molecular biology have key features necessary for their function, such as a suitable cloning site and selectable marker. Others may have additional features specific to their use. For reason of ease and convenience, cloning is often performed using E. coli. Thus, the cloning vectors used often have elements necessary for their propagation and maintenance in E. coli, such as a functional origin of replication (ori). The ColE1 origin of replication is found in many plasmids. Some vectors also include el |
https://en.wikipedia.org/wiki/Semiprime | In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes.
Examples and variations
The semiprimes less than 100 are:
Semiprimes that are not square numbers are called discrete, distinct, or squarefree semiprimes:
The semiprimes are the case of the -almost primes, numbers with exactly prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). These are:
Formula for number of semiprimes
A semiprime counting formula was discovered by E. Noel and G. Panos in 2005. Let denote the number of semiprimes less than or equal to n. Then
where is the prime-counting function and denotes the kth prime.
Properties
Semiprime numbers have no composite numbers as factors other than themselves. For example, the number 26 is semiprime and its only factors are 1, 2, 13, and 26, of which only 26 is composite.
For a squarefree semiprime (with )
the value of Euler's totient function (the number of positive integers less than or equal to that are relatively prime to ) takes the simple form
This calculation is an important part of the application of semiprimes in the RSA cryptosystem.
For a square semiprime , the formula is again simple:
Applications
Semiprimes are highly useful in the area of cryptography and number theory, most notably in public key cryptography, where they are used by RSA and pseudorandom number generators such as Blum Blum Shub. These methods rely on the fact that finding two large primes and multiplying them together (resulting in a semiprime) is computationally simple, whereas finding the original factors appears to be difficult. In the RSA Factoring Challenge, R |
https://en.wikipedia.org/wiki/Almost%20prime | In number theory, a natural number is called k-almost prime if it has k prime factors. More formally, a number n is k-almost prime if and only if Ω(n) = k, where Ω(n) is the total number of primes in the prime factorization of n (can be also seen as the sum of all the primes' exponents):
A natural number is thus prime if and only if it is 1-almost prime, and semiprime if and only if it is 2-almost prime. The set of k-almost primes is usually denoted by Pk. The smallest k-almost prime is 2k. The first few k-almost primes are:
The number πk(n) of positive integers less than or equal to n with exactly k prime divisors (not necessarily distinct) is asymptotic to:
a result of Landau. See also the Hardy–Ramanujan theorem.
Properties
The multiple of a -almost prime and a -almost prime is a -almost prime.
A -almost prime cannot have a -almost prime as a factor for all .
References
External links
Integer sequences
Prime numbers |
https://en.wikipedia.org/wiki/Frozen%20food | Freezing food preserves it from the time it is prepared to the time it is eaten. Since early times, farmers, fishermen, and trappers have preserved grains and produce in unheated buildings during the winter season. Freezing food slows decomposition by turning residual moisture into ice, inhibiting the growth of most bacterial species. In the food commodity industry, there are two processes: mechanical and cryogenic (or flash freezing). The freezing kinetics is important to preserve the food quality and texture. Quicker freezing generates smaller ice crystals and maintains cellular structure. Cryogenic freezing is the quickest freezing technology available due to the ultra low liquid nitrogen temperature .
Preserving food in domestic kitchens during modern times is achieved using household freezers. Accepted advice to householders was to freeze food on the day of purchase. An initiative by a supermarket group in 2012 (backed by the UK's Waste & Resources Action Programme) promotes the freezing of food "as soon as possible up to the product's 'use by' date". The Food Standards Agency was reported as supporting the change, provided the food had been stored correctly up to that time.
Preservatives
Frozen products do not require any added preservatives because microorganisms do not grow when the temperature of the food is below , which is sufficient on its own in preventing food spoilage. Long-term preservation of food may call for food storage at even lower temperatures. Carboxymethylcellulose (CMC), a tasteless and odorless stabilizer, is typically added to frozen food because it does not adulterate the quality of the product.
History
Natural food freezing (using winter frosts) had been in use by people in cold climates for centuries.
In 1861 Thomas Sutcliffe Mort established at Darling Harbour in Sydney, Australia, the world's first freezing works, which later became the New South Wales Fresh Food and Ice Company. Mort financed experiments by Eugene Dominic Nicol |
https://en.wikipedia.org/wiki/Vaccinia | Vaccinia virus (VACV or VV) is a large, complex, enveloped virus belonging to the poxvirus family. It has a linear, double-stranded DNA genome approximately 190 kbp in length, which encodes approximately 250 genes. The dimensions of the virion are roughly 360 × 270 × 250 nm, with a mass of approximately 5–10 fg. The vaccinia virus is the source of the modern smallpox vaccine, which the World Health Organization (WHO) used to eradicate smallpox in a global vaccination campaign in 1958–1977. Although smallpox no longer exists in the wild, vaccinia virus is still studied widely by scientists as a tool for gene therapy and genetic engineering.
Smallpox had been an endemic human disease that had a 30% fatality rate. In 1796, the British doctor Edward Jenner proved that an infection with the relatively mild cowpox virus would also confer immunity to the deadly smallpox. Jenner referred to cowpox as variolae vaccinae (smallpox of the cow). However, the origins of the smallpox vaccine became murky over time, especially after Louis Pasteur developed laboratory techniques for creating vaccines in the 19th century. Allan Watt Downie demonstrated in 1939 that the modern smallpox vaccine was serologically distinct from cowpox, and vaccinia was subsequently recognized as a separate viral species. Whole-genome sequencing has revealed that vaccinia is most closely related to horsepox, and the cowpox strains found in Great Britain are the least closely related to vaccinia.
Classification of vaccinia infections
In addition to the morbidity of uncomplicated primary vaccination, transfer of infection to other sites by scratching, and post-vaccinial encephalitis, other complications of vaccinia infections may be divided into the following types:
Generalized vaccinia
Eczema vaccinatum
Progressive vaccinia (vaccinia gangrenosum, vaccinia necrosum)
Roseola vaccinia
Origin
Vaccinia virus is closely related to the virus that causes cowpox; historically the two were often considered |
https://en.wikipedia.org/wiki/Myhill%E2%80%93Nerode%20theorem | In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1957 .
Statement
Given a language , and a pair of strings and , define a distinguishing extension to be a string such that
exactly one of the two strings and belongs to .
Define a relation on strings as if there is no distinguishing extension for and . It is easy to show that is an equivalence relation on strings, and thus it divides the set of all strings into equivalence classes.
The Myhill–Nerode theorem states that a language is regular if and only if has a finite number of equivalence classes, and moreover, that this number is equal to the number of states in the minimal deterministic finite automaton (DFA) accepting . Furthermore, every minimal DFA for the language is isomorphic to the canonical one .
Generally, for any language, the constructed automaton is a state automaton acceptor. However, it does not necessarily have finitely many states. The Myhill–Nerode theorem shows that finiteness is necessary and sufficient for language regularity.
Some authors refer to the relation as Nerode congruence, in honor of Anil Nerode.
Use and consequences
The Myhill–Nerode theorem may be used to show that a language is regular by proving that the number of equivalence classes of is finite. This may be done by an exhaustive case analysis in which, beginning from the empty string, distinguishing extensions are used to find additional equivalence classes until no more can be found. For example, the language consisting of binary representations of numbers that can be divided by 3 is regular. Given the empty string, (or ), , and are distinguishing extensions resulting in the three classes (corresponding to numbers that give remainders 0, 1 and 2 when divided by 3), but after this step there is no distinguishing extension |
https://en.wikipedia.org/wiki/Bernstein%20polynomial | In the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician Sergei Natanovich Bernstein.
Polynomials in Bernstein form were first used by Bernstein in a constructive proof for the Weierstrass approximation theorem. With the advent of computer graphics, Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves.
A numerically stable way to evaluate polynomials in Bernstein form is de Casteljau's algorithm.
Definition
Bernstein basis polynomials
The n+1 Bernstein basis polynomials of degree n are defined as
where is a binomial coefficient.
So, for example,
The first few Bernstein basis polynomials for blending 1, 2, 3 or 4 values together are:
The Bernstein basis polynomials of degree n form a basis for the vector space of polynomials of degree at most n with real coefficients.
Bernstein polynomials
A linear combination of Bernstein basis polynomials
is called a Bernstein polynomial or polynomial in Bernstein form of degree n. The coefficients are called Bernstein coefficients or Bézier coefficients.
The first few Bernstein basis polynomials from above in monomial form are:
Properties
The Bernstein basis polynomials have the following properties:
, if or
for
and where is the Kronecker delta function:
has a root with multiplicity at point (note: if , there is no root at 0).
has a root with multiplicity at point (note: if , there is no root at 1).
The derivative can be written as a combination of two polynomials of lower degree:
The k-th derivative at 0:
The k-th derivative at 1:
The transformation of the Bernstein polynomial to monomials is and by the inverse binomial transformation, the reverse transformation is
The indefinite integral is given by
The definite integral is constant for a given n:
If , then has a unique local maximum on |
https://en.wikipedia.org/wiki/Pointwise%20convergence | In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compared.
Definition
Suppose that is a set and is a topological space, such as the real or complex numbers or a metric space, for example. A net or sequence of functions all having the same domain and codomain is said to converge pointwise to a given function often written as
if (and only if)
The function is said to be the pointwise limit function of the
Sometimes, authors use the term bounded pointwise convergence when there is a constant such that .
Properties
This concept is often contrasted with uniform convergence. To say that
means that
where is the common domain of and , and stands for the supremum. That is a stronger statement than the assertion of pointwise convergence: every uniformly convergent sequence is pointwise convergent, to the same limiting function, but some pointwise convergent sequences are not uniformly convergent. For example, if is a sequence of functions defined by then pointwise on the interval but not uniformly.
The pointwise limit of a sequence of continuous functions may be a discontinuous function, but only if the convergence is not uniform. For example,
takes the value when is an integer and when is not an integer, and so is discontinuous at every integer.
The values of the functions need not be real numbers, but may be in any topological space, in order that the concept of pointwise convergence make sense. Uniform convergence, on the other hand, does not make sense for functions taking values in topological spaces generally, but makes sense for functions taking values in metric spaces, and, more generally, in uniform spaces.
Topology
Let denote the set of all functions from some given set into some topological space
As described in the article on characterizations of the category of topological spa |
https://en.wikipedia.org/wiki/Partition%20of%20a%20set | In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.
Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a partition is sometimes called a setoid, typically in type theory and proof theory.
Definition and notation
A partition of a set X is a set of non-empty subsets of X such that every element x in X is in exactly one of these subsets (i.e., the subsets are nonempty mutually disjoint sets).
Equivalently, a family of sets P is a partition of X if and only if all of the following conditions hold:
The family P does not contain the empty set (that is ).
The union of the sets in P is equal to X (that is ). The sets in P are said to exhaust or cover X. See also collectively exhaustive events and cover (topology).
The intersection of any two distinct sets in P is empty (that is ). The elements of P are said to be pairwise disjoint or mutually exclusive. See also mutual exclusivity.
The sets in are called the blocks, parts, or cells, of the partition. If then we represent the cell containing by . That is to say, is notation for the cell in which contains .
Every partition may be identified with an equivalence relation on , namely the relation such that for any we have if and only if (equivalently, if and only if ). The notation evokes the idea that the equivalence relation may be constructed from the partition. Conversely every equivalence relation may be identified with a partition. This is why it is sometimes said informally that "an equivalence relation is the same as a partition". If P is the partition identified with a given equivalence relation , then some authors write . This notation is suggestive of the idea that the partition is the set X divided in to cells. The notation also evokes the idea that, from the equivale |
https://en.wikipedia.org/wiki/Pentagonal%20number%20theorem | In mathematics, Euler's pentagonal number theorem relates the product and series representations of the Euler function. It states that
In other words,
The exponents 1, 2, 5, 7, 12, ... on the right hand side are given by the formula for k = 1, −1, 2, −2, 3, ... and are called (generalized) pentagonal numbers . (The constant term 1 corresponds to .)
This holds as an identity of convergent power series for , and also as an identity of formal power series.
A striking feature of this formula is the amount of cancellation in the expansion of the product.
Relation with partitions
The identity implies a recurrence for calculating , the number of partitions of n:
or more formally,
where the summation is over all nonzero integers k (positive and negative) and is the kth generalized pentagonal number. Since for all , the apparently infinite series on the right has only finitely many non-zero terms, enabling an efficient calculation of p(n).
Franklin's bijective proof
The theorem can be interpreted combinatorially in terms of partitions. In particular, the left hand side is a generating function for the number of partitions of n into an even number of distinct parts minus the number of partitions of n into an odd number of distinct parts. Each partition of n into an even number of distinct parts contributes +1 to the coefficient of xn; each partition into an odd number of distinct parts contributes −1. (The article on unrestricted partition functions discusses this type of generating function.)
For example, the coefficient of x5 is +1 because there are two ways to split 5 into an even number of distinct parts (4+1 and 3+2), but only one way to do so for an odd number of distinct parts (the one-part partition 5). However, the coefficient of x12 is −1 because there are seven ways to partition 12 into an even number of distinct parts, but there are eight ways to partition 12 into an odd number of distinct parts, and 7 − 8 = −1.
This interpretation leads to a proo |
https://en.wikipedia.org/wiki/Sodium%20stearoyl%20lactylate | Sodium stearoyl-2-lactylate (sodium stearoyl lactylate or SSL) is a versatile, FDA approved food additive used to improve the mix tolerance and volume of processed foods. It is one type of a commercially available lactylate. SSL is non-toxic, biodegradable, and typically manufactured using biorenewable feedstocks. Because SSL is a safe and highly effective food additive, it is used in a wide variety of products ranging from baked goods and desserts to pet foods.
As described by the Food Chemicals Codex 7th edition, SSL is a cream-colored powder or brittle solid. SSL is currently manufactured by the esterification of stearic acid with lactic acid and partially neutralized with either food-grade soda ash (sodium carbonate) or caustic soda (concentrated sodium hydroxide). Commercial grade SSL is a mixture of sodium salts of stearoyl lactylic acids and minor proportions of other sodium salts of related acids. The HLB for SSL is 10–12. SSL is slightly hygroscopic, soluble in ethanol and in hot oil or fat, and dispersible in warm water. These properties are the reason that SSL is an excellent emulsifier for fat-in-water emulsions and can also function as a humectant.
Food labeling requirements
To be labeled as SSL for sale within the United States, the product must conform to the specifications detailed in 21 CFR 172.846 and the most recent edition of the Food Chemical Codex. In the EU, the product must conform to the specifications detailed in Regulation (EC) No 96/77. For the 7th edition of the FCC and Regulation (EC) No 96/77, these specifications are:
To be labeled as SSL for sale in other regions, the product must conform to the specifications detailed in that region's codex.
Food applications and maximum use levels
SSL finds widespread application in baked goods, pancakes, waffles, cereals, pastas, instant rice, desserts, icings, fillings, puddings, toppings, sugar confectionaries, powdered beverage mixes, creamers, cream liqueurs, dehydrated potatoes, |
https://en.wikipedia.org/wiki/Economic%20statistics | Economic statistics is a topic in applied statistics and applied economics that concerns the collection, processing, compilation, dissemination, and analysis of economic data. It is closely related to business statistics and econometrics. It is also common to call the data themselves "economic statistics", but for this usage, "economic data" is the more common term.
Overview
The data of concern to economic statistics may include those of an economy within a region, country, or group of countries. Economic statistics may also refer to a subtopic of official statistics for data produced by official organizations (e.g. national statistical services, intergovernmental organizations such as United Nations, European Union or OECD, central banks, and ministries).
Analyses within economic statistics both make use of and provide the empirical data needed in economic research, whether descriptive or econometric. They are a key input for decision making as to economic policy. The subject includes statistical analysis of topics and problems in microeconomics, macroeconomics, business, finance, forecasting, data quality, and policy evaluation. It also includes such considerations as what data to collect in order to quantify some particular aspect of an economy and of how best to collect in any given instance.
See also
Business statistics
Econometrics
Survey of production
References
Citations
Sources
Allen, R. G. D., 1956. "Official Economic Statistics," Economica, N.S., 23(92), pp. 360-365.
Crum, W. L., 1925. An Introduction to the Methods of Economic Statistics, AW Shaw Co.
Giovanini, Enrico, 2008. Understanding Economic Statistics. OECD Publishing.
Fox, Karl A., 1968. Intermediate Economic Statistics, Wiley. Description.
Kane, Edward J., 1968. Economic Statistics and Econometrics, Harper and Row.
Morgenstern, Oskar, [1950] 1963. On the Accuracy of Economic Observations. 2nd rev. ed. ("The Accuracy of Economic Observation" ch. 16). Princeton University Pr |
https://en.wikipedia.org/wiki/Freemartin | A freemartin or free-martin (sometimes martin heifer) is an infertile female cattle with masculinized behavior and non-functioning ovaries. Phenotypically, the animal appears female, but various aspects of female reproductive development are altered due to acquisition of anti-Müllerian hormone from the male twin. Genetically, the animal is chimeric: karyotypy of a sample of cells shows XX/XY chromosomes. The animal originates as a female (XX), but acquires the male (XY) component in utero by exchange of some cellular material from a male twin, via vascular connections between placentas: an example of microchimerism. The chimerism is mainly present in the hematopoietic stem cells.
History
Freemartins are known to have been described by the Roman writer Varro, who called them .
The 18th-century physician John Hunter discovered that a freemartin always has a male twin.
It was hypothesized early in the 20th century that masculinizing factors travel from the male twin to the female twin through the vascular connections of the placenta because of the vascular fusion and affect the internal anatomy of the female.
Several researchers made the discovery that a freemartin results when a female fetus has its chorion fuse in the uterus with that of a male twin. The result was published in 1916 by Tandler and Keller. The discovery was made independently by American biologist Frank R. Lillie, who published it in Science in 1916. Both teams are now credited with the discovery.
In rural areas folklore often claimed this condition was not just peculiar to cattle, but extended also to human twins; this belief perpetuated for generations, as was mentioned in the writings of Cuthbert Bede.
Etymology
The etymology of the term "freemartin" is uncertain: speculations include that "free" may indicate "willing" (referring to the freemartin's willingness to work) or "exempt from reproduction" (referring to its sterility, or to a farmer's decision to not bother trying to breed a fr |
https://en.wikipedia.org/wiki/Marcian%20Hoff | Marcian Edward "Ted" Hoff Jr. (born October 28, 1937, in Rochester, New York) is one of the inventors of the microprocessor.
Education and work history
Hoff received a bachelor's degree in electrical engineering from the Rensselaer Polytechnic Institute in 1958. He applied for his first two patents based on work done for the General Railway Signal Corp. of Rochester, New York during the summers of his undergraduate study. He received a National Science Foundation Fellowship to enroll in Stanford University, where he received his master's degree in 1959 and his Ph.D. in 1962. As part of his Ph.D. dissertation, Hoff co-invented the least mean squares filter and the ADALINE neural network with Bernard Widrow.
Hoff joined Intel in 1968 as employee number 12 as "manager of applications research", and is credited with coming up with the idea of using a "universal processor" rather than a variety of custom-designed circuits in the architectural idea and an instruction set formulated with Stanley Mazor in 1969 for the Intel 4004—the chip that started the microprocessor revolution in the early 1970s. Development of the silicon-gate design methodology and the actual chip design was done by Federico Faggin, who also led the project during 1970-1971. Masatoshi Shima from Busicom defined the logic.
In 1975 he started a group to work on large-scale integration for use in the telephone industry, resulting in various commercial products: first commercial monolithic telephone (named "CODEC"), first commercial switched-capacitor filter (for use with CODEC), a microprocessor for real-time digitizing analog signals (Intel 2920), and speech recognition hardware.
In 1980, Hoff was named the first Intel Fellow, which is the highest technical position in the company. He stayed in that position until 1983 when he left for Atari. After the video game crash of 1983, Atari was sold in 1984, and Hoff became an independent consultant. He then joined Teklicon in 1986 as an agent, and since |
https://en.wikipedia.org/wiki/Serial%20Peripheral%20Interface | Serial Peripheral Interface (SPI) is a de facto standard (with many variants) for synchronous serial communication, used primarily in embedded systems for short-distance wired communication between integrated circuits.
SPI uses a main–subnode (master/slave) architecture, where one main device orchestrates communication by providing the clock signal and chip select signal(s) which control any number of subservient peripherals.
Motorola's original specification uses four wires to perform full duplex communication. It is sometimes called a four-wire serial bus to contrast with three-wire variants which are half duplex, and with the two-wire I²C and 1-Wire serial buses.
Typical applications include interfacing microcontrollers with peripheral chips for Secure Digital cards, liquid crystal displays, analog-to-digital and digital-to-analog converters, flash and EEPROM memory, and various communication chips.
SPI may be accurately described as a synchronous serial interface, but it is different from the Synchronous Serial Interface (SSI) protocol.
Operation
(Note: Variations section describes operation of non-standard variants.)
SPI has four logic signals (which go by alternative namings):
SCLK : Serial Clock (clock signal from main)
MOSI : Main Out Sub In (data output from main)
MISO : Main In Sub Out (data output from sub)
: (active low signal from main to address subs and initiate transmission)
MOSI on a main outputs to MOSI on a sub. MISO on a sub outputs to MISO on a main.
SPI operates with a single device acting as main and with one or more sub devices.
Sub devices should use tri-state outputs so their MISO signal becomes high impedance (electrically disconnected) when the device is not selected. Subs without tri-state outputs cannot share a MISO wire with other subs without using an external tri-state buffer.
Data transmission
To begin communication, the SPI main first selects a sub device by pulling its low. (Note: the bar above indicates it is a |
https://en.wikipedia.org/wiki/Display%20Data%20Channel | The Display Data Channel, or DDC, is a collection of protocols for digital communication between a computer display and a graphics adapter that enable the display to communicate its supported display modes to the adapter and that enable the computer host to adjust monitor parameters, such as brightness and contrast.
Like modern analog VGA connectors, the DVI and DisplayPort connectors include pins for DDC, but DisplayPort only supports DDC within its optional Dual-Mode DP (DP++) feature in DVI/HDMI mode.
The standard was created by the Video Electronics Standards Association (VESA).
Overview
The DDC suite of standards aims to provide Plug and Play and DPMS power management experiences for computer displays.
DDC1 and DDC2B/Ab/B+/Bi protocols are a physical link between a monitor and a video card, which was originally carried on either two or three pins in a 15-pin analog VGA connector.
Extended display identification data (EDID) is a companion standard; it defines a compact binary file format describing the monitor's capabilities and supported graphics modes, stored in a read-only memory (EEPROM) chip programmed by the manufacturer of the monitor. The format uses a description block containing 128 bytes of data, with optional extension blocks to provide additional information. The most current version is Enhanced EDID (E-EDID) Release A, v2.0.
The first version of the DDC standard was adopted in August 1994. It included the EDID 1.0 format and specified DDC1, DDC2B and DDC2Ab physical links.
DDC version 2, introduced in April 1996, split EDID into a separate standard and introduced the DDC2B+ protocol.
DDC version 3, December 1997, introduced the DDC2Bi protocol and support for VESA Plug and Display and Flat Panel Display Interface on separate device addresses, requiring them to comply with EDID 2.0.
The DDC standard has been superseded by E-DDC in 1999.
Physical link
Prior to the DDC, the VGA standard had reserved four pins in the analog VGA connector, kn |
https://en.wikipedia.org/wiki/Prodigy%20%28online%20service%29 | Prodigy Communications Corporation was an online service from 1984 to 2001 that offered its subscribers access to a broad range of networked services. It was one of the major internet service providers of the 1990s.
The company claimed it was the first consumer online service, citing its graphical user interface and basic architecture as differentiation from CompuServe, which started in 1979 and used a command-line interface. Prodigy was described by the New York Times as "family-oriented" and one of "the Big Three information services" in 1994. By 1990, it was the second-largest online service provider with 465,000 subscribers, trailing only CompuServe's 600,000. In 1993 it was the largest.
In 2001, it was acquired by SBC Communications, which in 2005 became the present iteration of AT&T. The Mexican branch of Prodigy, however, was acquired by Telmex.
Early history
The roots of Prodigy date to 1980 when broadcaster CBS and telecommunications firm AT&T Corporation formed a joint venture named Venture One in Fair Lawn, New Jersey. The company conducted a market test of 100 homes in Ridgewood, New Jersey to gauge consumer interest in a Videotex-based TV set-top device that would allow consumers to shop at home and receive news, sports, and weather. After concluding the market test, CBS and AT&T took the data and went their separate ways in pursuit of developing and profiting from this market demand.
Prodigy was founded on February 13, 1984, as Trintex, a joint venture between CBS, computer manufacturer IBM, and retailer Sears, Roebuck and Company. The company was headed by Theodore Papes, a career IBM executive, until his retirement in 1992. CBS left the venture in 1986 when CBS CEO Tom Wyman was divesting properties outside of CBS's core broadcasting business. The company's service was launched regionally in 1988 in Atlanta, Hartford, and San Francisco under the name Prodigy. The marketing roll-out plan closely followed IBM's Systems Network Architecture (S |
https://en.wikipedia.org/wiki/Nilometer | A nilometer was a structure for measuring the Nile River's clarity and water level during the annual flood season. There were three main types of nilometers, calibrated in Egyptian cubits: (1) a vertical column, (2) a corridor stairway of steps leading down to the Nile, or (3) a deep well with culvert. If the water level was low, the fertility of the floodplain would suffer. If it was too high, the flooding would be destructive. There was a specific mark that indicated how high the flood should be if the fields were to get good soil.
Nilometers originated in pharaonic times, were also built in Roman times, and were used until the Aswan Dam rendered them obsolete in the 1960s.
Description
Between July and November, the reaches of the Nile running through Egypt would burst their banks and cover the adjacent floodplain. When the waters receded, around September or October, they left behind a rich alluvial deposit of exceptionally fertile black silt over the croplands. The akhet, or Season of the Inundation, was one of the three seasons into which the ancient Egyptians divided their year.
Importance
The annual flood was of great importance to Egyptian civilization. A moderate inundation was a vital part of the agricultural cycle; however, a lighter inundation than normal would cause famine, and too much flood water would be equally disastrous, washing away much of the infrastructure built on the flood plain. Records from AD 622999 indicate that, on average, 28% of the years saw an inundation that fell short of expectations.
The ability to predict the volume of the coming inundation was part of the mystique of the Ancient Egyptian priesthood. The same skill also played a political and administrative role, since the quality of the year's flood was used to determine the levels of tax to be paid. This is where the nilometer came into play, with priests monitoring the day-to-day level of the river and announcing the awaited arrival of the summer flood.
Designs
The |
https://en.wikipedia.org/wiki/List%20of%20complex%20analysis%20topics | Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics, including hydrodynamics, thermodynamics, and electrical engineering.
Overview
Complex numbers
Complex plane
Complex functions
Complex derivative
Holomorphic functions
Harmonic functions
Elementary functions
Polynomial functions
Exponential functions
Trigonometric functions
Hyperbolic functions
Logarithmic functions
Inverse trigonometric functions
Inverse hyperbolic functions
Residue theory
Isometries in the complex plane
Related fields
Number theory
Hydrodynamics
Thermodynamics
Electrical engineering
Local theory
Holomorphic function
Antiholomorphic function
Cauchy–Riemann equations
Conformal mapping
Conformal welding
Power series
Radius of convergence
Laurent series
Meromorphic function
Entire function
Pole (complex analysis)
Zero (complex analysis)
Residue (complex analysis)
Isolated singularity
Removable singularity
Essential singularity
Branch point
Principal branch
Weierstrass–Casorati theorem
Landau's constants
Holomorphic functions are analytic
Schwarzian derivative
Analytic capacity
Disk algebra
Growth and distribution of values
Ahlfors theory
Bieberbach conjecture
Borel–Carathéodory theorem
Corona theorem
Hadamard three-circle theorem
Hardy space
Hardy's theorem
Maximum modulus principle
Nevanlinna theory
Paley–Wiener theorem
Progressive function
Value distribution theory of holomorphic functions
Contour integrals
Line integral
Cauchy's integral theorem
Cauchy's integral formula
Residue theorem
Liouville's theorem (complex analysis)
Examples of contour integration
Fundamental theorem of algebra
Simply connected
Winding number
Principle of the argument
Rouché's theorem
Bromwich integral
Morera's theorem
Mellin transform
Kramers–Kronig relation, a. k. a. |
https://en.wikipedia.org/wiki/George%20Boolos | George Stephen Boolos (; 4 September 1940 – 27 May 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.
Life
Boolos was of Greek-Jewish descent. He graduated with an A.B. in mathematics from Princeton University after completing a senior thesis, titled "A simple proof of Gödel's first incompleteness theorem", under the supervision of Raymond Smullyan. Oxford University awarded him the B.Phil. in 1963. In 1966, he obtained the first PhD in philosophy ever awarded by the Massachusetts Institute of Technology, under the direction of Hilary Putnam. After teaching three years at Columbia University, he returned to MIT in 1969, where he spent the rest of his career.
A charismatic speaker well known for his clarity and wit, he once delivered a lecture (1994b) giving an account of Gödel's second incompleteness theorem, employing only words of one syllable. At the end of his viva, Hilary Putnam asked him, "And tell us, Mr. Boolos, what does the analytical hierarchy have to do with the real world?" Without hesitating Boolos replied, "It's part of it". An expert on puzzles of all kinds, in 1993 Boolos reached the London Regional Final of The Times crossword competition. His score was one of the highest ever recorded by an American. He wrote a paper on "The Hardest Logic Puzzle Ever"—one of many puzzles created by Raymond Smullyan.
Boolos died of pancreatic cancer on 27 May 1996.
Work
Boolos coauthored with Richard Jeffrey the first three editions of the classic university text on mathematical logic, Computability and Logic. The book is now in its fifth edition, the last two editions updated by John P. Burgess.
Kurt Gödel wrote the first paper on provability logic, which applies modal logic—the logic of necessity and possibility—to the theory of mathematical proof, but Gödel never developed the subject to any significant extent. Boolos was one of its earliest proponents and pioneers, and he produced the fi |
https://en.wikipedia.org/wiki/Function%20space | In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set into a vector space has a natural vector space structure given by pointwise addition and scalar multiplication. In other scenarios, the function space might inherit a topological or metric structure, hence the name function space.
In linear algebra
Let be a vector space over a field and let be any set. The functions → can be given the structure of a vector space over where the operations are defined pointwise, that is, for any , : → , any in , and any in , define
When the domain has additional structure, one might consider instead the subset (or subspace) of all such functions which respect that structure. For example, if is also a vector space over , the set of linear maps → form a vector space over with pointwise operations (often denoted Hom(,)). One such space is the dual space of : the set of linear functionals → with addition and scalar multiplication defined pointwise.
Examples
Function spaces appear in various areas of mathematics:
In set theory, the set of functions from X to Y may be denoted {X → Y} or YX.
As a special case, the power set of a set X may be identified with the set of all functions from X to {0, 1}, denoted 2X.
The set of bijections from X to Y is denoted . The factorial notation X! may be used for permutations of a single set X.
In functional analysis, the same is seen for continuous linear transformations, including topologies on the vector spaces in the above, and many of the major examples are function spaces carrying a topology; the best known examples include Hilbert spaces and Banach spaces.
In functional analysis, the set of all functions from the natural numbers to some set X is called a sequence space. It consists of the set of all possible sequences of elements of X.
In t |
https://en.wikipedia.org/wiki/Internal%20energy | The internal energy of a thermodynamic system is the energy contained within it, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization. It excludes the kinetic energy of motion of the system as a whole and the potential energy of position of the system as a whole, with respect to its surroundings and external force fields. It includes the thermal energy, i.e., the constituent particles' kinetic energies of motion relative to the motion of the system as a whole. The internal energy of an isolated system cannot change, as expressed in the law of conservation of energy, a foundation of the first law of thermodynamics.
The internal energy cannot be measured absolutely. Thermodynamics concerns changes in the internal energy, not its absolute value. The processes that change the internal energy are transfers, into or out of the system, of matter, or of energy, as heat, or by thermodynamic work. These processes are measured by changes in the system's properties, such as temperature, entropy, volume, electric polarization, and molar constitution. The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable, a thermodynamic potential, and an extensive property.
Thermodynamics defines internal energy macroscopically, for the body as a whole. In statistical mechanics, the internal energy of a body can be analyzed microscopically in terms of the kinetic energies of microscopic motion of the system's particles from translations, rotations, and vibrations, and of the potential energies associated with microscopic forces, including chemical bonds.
The unit of energy in the International System of Units (SI) is the joule (J) |
https://en.wikipedia.org/wiki/Arlington%20Hall | Arlington Hall (also called Arlington Hall Station) is a historic building in Arlington, Virginia, originally a girls' school and later the headquarters of the United States Army's Signal Intelligence Service (SIS) cryptography effort during World War II. The site presently houses the George P. Shultz National Foreign Affairs Training Center, and the Army National Guard's Herbert R. Temple, Jr. Readiness Center. It is located on Arlington Boulevard (U.S. Route 50) between S. Glebe Road (State Route 120) and S. George Mason Drive.
History
Arlington Hall was founded in 1927 as a private post-secondary women's educational institution, which, by 1941, resided on a campus and had acquired the name "Arlington Hall Junior College for Women". The school suffered financial problems in the 1930s, and eventually became a non-profit institution in 1940. On June 10, 1942, the U.S. Army took possession of the facility under the War Powers Act for use by its Signals Intelligence Service.
During World War II, Arlington Hall was in many respects similar to Bletchley Park in England (though BP also covered naval codes), and was one of only two primary cryptography operations in Washington (the other was the Naval Communications Annex, also housed in a commandeered private girls' school). Arlington Hall concentrated its efforts on the Japanese systems (including PURPLE) while Bletchley Park concentrated on European combatants. Initially work was on Japanese diplomatic codes as Japanese army codes were not solved until April 1943, but in September 1943 with success on the Army codes they were put under Solomon Kullback in a separate branch B-II, with other mainly diplomatic work under Frank Rowlett in B-III (which also had the Bombes and Rapid Analytical Machinery). The third branch B-I translated Japanese decrypts.
The Arlington Hall effort was comparable in influence to other Anglo-American Second World War-era technological efforts, such as the cryptographic work at Bletchley |
https://en.wikipedia.org/wiki/Sparse%20matrix | In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., m × n for an m × n matrix) is sometimes referred to as the sparsity of the matrix.
Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. The concept of sparsity is useful in combinatorics and application areas such as network theory and numerical analysis, which typically have a low density of significant data or connections. Large sparse matrices often appear in scientific or engineering applications when solving partial differential equations.
When storing and manipulating sparse matrices on a computer, it is beneficial and often necessary to use specialized algorithms and data structures that take advantage of the sparse structure of the matrix. Specialized computers have been made for sparse matrices, as they are common in the machine learning field. Operations using standard dense-matrix structures and algorithms are slow and inefficient when applied to large sparse matrices as processing and memory are wasted on the zeros. Sparse data is by nature more easily compressed and thus requires significantly less storage. Some very large sparse matrices are infeasible to manipulate using standard dense-matrix algorithms.
Storing a sparse matrix |
https://en.wikipedia.org/wiki/Reporter%20gene | In molecular biology, a reporter gene (often simply reporter) is a gene that researchers attach to a regulatory sequence of another gene of interest in bacteria, cell culture, animals or plants. Such genes are called reporters because the characteristics they confer on organisms expressing them are easily identified and measured, or because they are selectable markers. Reporter genes are often used as an indication of whether a certain gene has been taken up by or expressed in the cell or organism population.
Common reporter genes
To introduce a reporter gene into an organism, scientists place the reporter gene and the gene of interest in the same DNA construct to be inserted into the cell or organism. For bacteria or prokaryotic cells in culture, this is usually in the form of a circular DNA molecule called a plasmid. For viruses, this is known as a viral vector. It is important to use a reporter gene that is not natively expressed in the cell or organism under study, since the expression of the reporter is being used as a marker for successful uptake of the gene of interest.
Commonly used reporter genes that induce visually identifiable characteristics usually involve fluorescent and luminescent proteins. Examples include the gene that encodes jellyfish green fluorescent protein (GFP), which causes cells that express it to glow green under blue light, the enzyme luciferase, which catalyzes a reaction with luciferin to produce light, and the red fluorescent protein from the gene . The GUS gene has been commonly used in plants but luciferase and GFP are becoming more common.
A common reporter in bacteria is the E. coli lacZ gene, which encodes the protein beta-galactosidase. This enzyme causes bacteria expressing the gene to appear blue when grown on a medium that contains the substrate analog X-gal. An example of a selectable marker which is also a reporter in bacteria is the chloramphenicol acetyltransferase (CAT) gene, which confers resistance to the antibioti |
https://en.wikipedia.org/wiki/List%20of%20functional%20analysis%20topics | This is a list of functional analysis topics.
See also: Glossary of functional analysis.
Hilbert space
Functional analysis, classic results
Operator theory
Banach space examples
Lp space
Hardy space
Sobolev space
Tsirelson space
ba space
Real and complex algebras
Topological vector spaces
Amenability
Amenable group
Von Neumann conjecture
Wavelets
Quantum theory
See also list of mathematical topics in quantum theory
Probability
Free probability
Bernstein's theorem
Non-linear
Fixed-point theorems in infinite-dimensional spaces
History
Stefan Banach (1892–1945)
Hugo Steinhaus (1887–1972)
John von Neumann (1903-1957)
Alain Connes (born 1947)
Earliest Known Uses of Some of the Words of Mathematics: Calculus & Analysis
Earliest Known Uses of Some of the Words of Mathematics: Matrices and Linear Algebra
Functional analysis |
https://en.wikipedia.org/wiki/Matrix%20similarity | In linear algebra, two n-by-n matrices and are called similar if there exists an invertible n-by-n matrix such that
Similar matrices represent the same linear map under two (possibly) different bases, with being the change of basis matrix.
A transformation is called a similarity transformation or conjugation of the matrix . In the general linear group, similarity is therefore the same as conjugacy, and similar matrices are also called conjugate; however, in a given subgroup of the general linear group, the notion of conjugacy may be more restrictive than similarity, since it requires that be chosen to lie in .
Motivating example
When defining a linear transformation, it can be the case that a change of basis can result in a simpler form of the same transformation. For example, the matrix representing a rotation in when the axis of rotation is not aligned with the coordinate axis can be complicated to compute. If the axis of rotation were aligned with the positive -axis, then it would simply be
where is the angle of rotation. In the new coordinate system, the transformation would be written as
where and are respectively the original and transformed vectors in a new basis containing a vector parallel to the axis of rotation. In the original basis, the transform would be written as
where vectors and and the unknown transform matrix are in the original basis. To write in terms of the simpler matrix, we use the change-of-basis matrix that transforms and as and :
Thus, the matrix in the original basis, , is given by . The transform in the original basis is found to be the product of three easy-to-derive matrices. In effect, the similarity transform operates in three steps: change to a new basis (), perform the simple transformation (), and change back to the old basis ().
Properties
Similarity is an equivalence relation on the space of square matrices.
Because matrices are similar if and only if they represent the same linear operator with |
https://en.wikipedia.org/wiki/The%20Analyst | The Analyst (subtitled A Discourse Addressed to an Infidel Mathematician: Wherein It Is Examined Whether the Object, Principles, and Inferences of the Modern Analysis Are More Distinctly Conceived, or More Evidently Deduced, Than Religious Mysteries and Points of Faith) is a book by George Berkeley. It was first published in 1734, first by J. Tonson (London), then by S. Fuller (Dublin). The "infidel mathematician" is believed to have been Edmond Halley, though others have speculated Sir Isaac Newton was intended.
Background and purpose
From his earliest days as a writer, Berkeley had taken up his satirical pen to attack what were then called 'free-thinkers' (secularists, skeptics, agnostics, atheists, etc.—in short, anyone who doubted the truths of received Christian religion or called for a diminution of religion in public life). In 1732, in the latest installment in this effort, Berkeley published his Alciphron, a series of dialogues directed at different types of 'free-thinkers'. One of the archetypes Berkeley addressed was the secular scientist, who discarded Christian mysteries as unnecessary superstitions, and declared his confidence in the certainty of human reason and science. Against his arguments, Berkeley mounted a subtle defense of the validity and usefulness of these elements of the Christian faith.
Alciphron was widely read and caused a bit of a stir. But it was an offhand comment mocking Berkeley's arguments by the 'free-thinking' royal astronomer Sir Edmund Halley that prompted Berkeley to pick up his pen again and try a new tack. The result was The Analyst, conceived as a satire attacking the foundations of mathematics with the same vigor and style as 'free-thinkers' routinely attacked religious truths.
Berkeley sought to take mathematics apart, claimed to uncover numerous gaps in proof, attacked the use of infinitesimals, the diagonal of the unit square, the very existence of numbers, etc. The general point was not so much to mock mathe |
https://en.wikipedia.org/wiki/Straw-bale%20construction | Straw-bale construction is a building method that uses bales of straw (commonly wheat, rice, rye and oats straw) as structural elements, building insulation, or both. This construction method is commonly used in natural building or "brown" construction projects. Research has shown that straw-bale construction is a sustainable method for building, from the standpoint of both materials and energy needed for heating and cooling.
Advantages of straw-bale construction over conventional building systems include the renewable nature of straw, cost, easy availability, naturally fire-retardant and high insulation value. Disadvantages include susceptibility to rot, difficulty of obtaining insurance coverage, and high space requirements for the straw itself. Research has been done using moisture probes placed within the straw wall in which 7 of 8 locations had moisture contents of less than 20%. This is a moisture level that does not aid in the breakdown of the straw. However, proper construction of the straw-bale wall is important in keeping moisture levels down, just as in the construction of any type of building.
History
Straw houses have been built on the African plains since the Paleolithic Era. Straw bales were used in construction 400 years ago in Germany; and straw-thatched roofs have long been used in northern Europe and Asia. When European Settlers came to North America, teepees were insulated in winter with loose straw between the inner lining and outer cover.
Straw-bale construction was greatly facilitated by the mechanical hay baler, which was invented in the 1850s and was widespread by the 1890s. It proved particularly useful in the Nebraska Sandhills. Pioneers seeking land under the 1862 Homestead Act and the 1904 Kinkaid Act found a dearth of trees over much of Nebraska. In many parts of the state, the soil was suitable for dugouts and sod houses.
However, in the Sandhills, the soil generally made poor construction sod;
in the few places where suitable sod |
https://en.wikipedia.org/wiki/Damk%C3%B6hler%20numbers | The Damköhler numbers (Da) are dimensionless numbers used in chemical engineering to relate the chemical reaction timescale (reaction rate) to the transport phenomena rate occurring in a system. It is named after German chemist Gerhard Damköhler.
The Karlovitz number (Ka) is related to the Damköhler number by Da = 1/Ka.
In its most commonly used form, the Damköhler number relates the reaction timescale to the convection time scale, volumetric flow rate, through the reactor for continuous (plug flow or stirred tank) or semibatch chemical processes:
In reacting systems that include interphase mass transport, the second Damköhler number (DaII) is defined as the ratio of the chemical reaction rate to the mass transfer rate
It is also defined as the ratio of the characteristic fluidic and chemical time scales:
Since the reaction rate determines the reaction timescale, the exact formula for the Damköhler number varies according to the rate law equation. For a general chemical reaction A → B following the Power law kinetics of n-th order, the Damköhler number for a convective flow system is defined as:
where:
k = kinetics reaction rate constant
C0 = initial concentration
n = reaction order
= mean residence time or space time
On the other hand, the second Damköhler number is defined as:
where
kg is the global mass transport coefficient
a is the interfacial area
The value of Da provides a quick estimate of the degree of conversion that can be achieved. As a rule of thumb, when Da is less than 0.1 a conversion of less than 10% is achieved, and when Da is greater than 10 a conversion of more than 90% is expected. The limit is called the Burke–Schumann limit.
Derivation for decomposition of a single species
From the general mole balance on some species , where for a CSTR steady state and perfect mixing are assumed,
Assuming a constant volumetric flow rate , which is the case for a liquid reactor or a gas phase reaction with no net generation |
https://en.wikipedia.org/wiki/Standard%20enthalpy%20of%20reaction | The standard enthalpy of reaction (denoted ) for a chemical reaction is the difference between total product and total reactant molar enthalpies, calculated for substances in their standard states. The value can be approximately interpreted in terms of the total of the chemical bond energies for bonds broken and bonds formed.
For a generic chemical reaction
the standard enthalpy of reaction is related to the standard enthalpy of formation values of the reactants and products by the following equation:
In this equation, are the stoichiometric coefficients of each product and reactant. The standard enthalpy of formation, which has been determined for a vast number of substances, is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements, with all substances in their standard states.
Standard states can be defined at any temperature and pressure, so both the standard temperature and pressure must always be specified. Most values of standard thermochemical data are tabulated at either (25°C, 1 bar) or (25°C, 1 atm).
For ions in aqueous solution, the standard state is often chosen such that the aqueous H+ ion at a concentration of exactly 1 mole/liter has a standard enthalpy of formation equal to zero, which makes possible the tabulation of standard enthalpies for cations and anions at the same standard concentration. This convention is consistent with the use of the standard hydrogen electrode in the field of electrochemistry. However, there are other common choices in certain fields, including a standard concentration for H+ of exactly 1 mole/(kg solvent) (widely used in chemical engineering) and mole/L (used in the field of biochemistry). For this reason it is important to note which standard concentration value is being used when consulting tables of enthalpies of formation.
Introduction
Two initial thermodynamic systems, each isolated in their separate states of internal thermodynamic equilibrium, can, by a |
https://en.wikipedia.org/wiki/Cantor%27s%20theorem | In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set , the set of all subsets of the power set of has a strictly greater cardinality than itself.
For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with elements has a total of subsets, and the theorem holds because for all non-negative integers.
Much more significant is Cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for infinite sets also. As a consequence, the cardinality of the real numbers, which is the same as that of the power set of the integers, is strictly larger than the cardinality of the integers; see Cardinality of the continuum for details.
The theorem is named for German mathematician Georg Cantor, who first stated and proved it at the end of the 19th century. Cantor's theorem had immediate and important consequences for the philosophy of mathematics. For instance, by iteratively taking the power set of an infinite set and applying Cantor's theorem, we obtain an endless hierarchy of infinite cardinals, each strictly larger than the one before it. Consequently, the theorem implies that there is no largest cardinal number (colloquially, "there's no largest infinity").
Proof
Cantor's argument is elegant and remarkably simple. The complete proof is presented below, with detailed explanations to follow.
By definition of cardinality, we have for any two sets and if and only if there is an injective function but no bijective function from to It suffices to show that there is no surjection from to . This is the heart of Cantor's theorem: there is no surjective function from any set to its power set. To establish this, it is enough to show that no function that maps elements in to subsets of can reach every possible subset, i.e., we just need to demonstrate the existence of a subset of that i |
https://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem%20theorem | In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem.
The precise formulation is given below. It implies that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ, and that no first-order theory with an infinite model can have a unique model up to isomorphism.
As a consequence, first-order theories are unable to control the cardinality of their infinite models.
The (downward) Löwenheim–Skolem theorem is one of the two key properties, along with the compactness theorem, that are used in Lindström's theorem to characterize first-order logic.
In general, the Löwenheim–Skolem theorem does not hold in stronger logics such as second-order logic.
Theorem
In its general form, the Löwenheim–Skolem Theorem states that for every signature σ, every infinite σ-structure M and every infinite cardinal number , there is a σ-structure N such that and such that
if then N is an elementary substructure of M;
if then N is an elementary extension of M.
The theorem is often divided into two parts corresponding to the two cases above. The part of the theorem asserting that a structure has elementary substructures of all smaller infinite cardinalities is known as the downward Löwenheim–Skolem Theorem. The part of the theorem asserting that a structure has elementary extensions of all larger cardinalities is known as the upward Löwenheim–Skolem Theorem.
Discussion
Below we elaborate on the general concept of signatures and structures.
Concepts
Signatures
A signature consists of a set of function symbols Sfunc, a set of relation symbols Srel, and a function representing the arity of function and relation symbols. (A nullary function symbol is called a constant symbol.) In the context of first-order logic, a signature is sometimes called a language. It is called countable if the set of function and r |
https://en.wikipedia.org/wiki/30%20%28number%29 | 30 (thirty) is the natural number following 29 and preceding 31.
In mathematics
30 is an even, composite, pronic number. With 2, 3, and 5 as its prime factors, it is a regular number and the first sphenic number, the smallest of the form , where is a prime greater than 3. It has an aliquot sum of 42, which is the second sphenic number.
It is also:
A semiperfect number, since adding some subsets of its divisors (e.g., 5, 10 and 15) equals 30.
A primorial.
A Harshad number in decimal.
Divisible by the number of prime numbers (10) below it.
The largest number such that all coprimes smaller than itself, except for 1, are prime.
The sum of the first four squares, making it a square pyramidal number.
The number of vertices in the Tutte–Coxeter graph.
The measure of the central angle and exterior angle of a dodecagon, which is the petrie polygon of the 24-cell.
The number of sides of a triacontagon, which in turn is the petrie polygon of the 120-cell and 600-cell.
The number of edges of a dodecahedron and icosahedron, of vertices of an icosidodecahedron, and of faces of a rhombic dodecahedron.
The sum of the number of elements of a 5-cell: 5 vertices, 10 edges, 10 faces, and 5 cells.
The Coxeter number of E8.
Furthermore,
In a group , such that , where does not divide , and has a subgroup of order , 30 is the only number less than 60 that is neither a prime nor of the aforementioned form. Therefore, 30 is the only candidate for the order of a simple group less than 60, in which one needs other methods to specifically reject to eventually deduce said order.
The SI prefix for 1030 is Quetta- (Q), and for 10−30 (i.e., the reciprocal of 1030) quecto (q). These numbers are the largest and smallest number to receive an SI prefix to date.
In science
The atomic number of zinc is 30.
Astronomy
Messier object M30, a magnitude 8.5 globular cluster in the constellation Capricornus
The New General Catalogue object NGC 30, a double star in the constellation Pega |
https://en.wikipedia.org/wiki/40%20%28number%29 | 40 (forty) is the natural number following 39 and preceding 41.
Though the word is related to four (4), the spelling forty replaced fourty during the 17th century and is now the standard form.
In mathematics
Forty is the fourth octagonal number. As the sum of the first four pentagonal numbers: , it is also the fourth pentagonal pyramidal number. Forty is a repdigit in ternary, and a Harshad number in decimal.
40 is the smallest number with exactly nine solutions to the equation Euler's totient function (for values 41, 55, 75, 82, 88, 100, 110, 132, and 150 of ).
Adding up some subsets of the divisors of 40 (e.g., 1, 4, 5, 10, and 20) gives 40; hence, 40 is the ninth semiperfect number. 40 is also the ninth refactorable number.
Forty is the number of -queens problem solutions for .
Euler's lucky numbers
Swiss mathematician Leonard Euler noted forty prime numbers generated by the quadratic polynomial , with values :
41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, 1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, and 1601.
The differences between terms are 0, 2, 4, 6, 8, ..., 78 (equivalently, up through a difference of twice 39). The first such prime (41) is the thirteenth prime number, where 13 divides the largest thrice over. The last such prime (1601) is the two hundred and fifty-second prime number (where 252 is the sum between two through twenty-two, inclusive) as well as one more than the square of forty, 402 = 1600. Importantly, 41 is also the largest of six lucky numbers of Euler of the form,
These forty prime numbers are the same prime numbers that are generated using the polynomial with values of from 1 through 40, and are also known in this context as Euler's "lucky" numbers.
Given 40, the Mertens function returns 0, as with 39 — the only other smaller number to return a value of zero is 2. Adding 39 and 40 yields a prime number, the twenty- |
https://en.wikipedia.org/wiki/Square%20root%20of%202 | The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as or . It is an algebraic number, and therefore not a transcendental number. Technically, it should be called the principal square root of 2, to distinguish it from the negative number with the same property.
Geometrically, the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. The fraction (≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator.
Sequence in the On-Line Encyclopedia of Integer Sequences consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places:
History
The Babylonian clay tablet YBC 7289 (–1600 BC) gives an approximation of in four sexagesimal figures, , which is accurate to about six decimal digits, and is the closest possible three-place sexagesimal representation of :
Another early approximation is given in ancient Indian mathematical texts, the Sulbasutras (–200 BC), as follows: Increase the length [of the side] by its third and this third by its own fourth less the thirty-fourth part of that fourth. That is,
This approximation is the seventh in a sequence of increasingly accurate approximations based on the sequence of Pell numbers, which can be derived from the continued fraction expansion of . Despite having a smaller denominator, it is only slightly less accurate than the Babylonian approximation.
Pythagoreans discovered that the diagonal of a square is incommensurable with its side, or in modern language, that the square root of two is irrational. Little is known with certainty about the time or circumstances of this discovery, but the name of Hippasus of Metapontum is often mentioned. For a while, the Pythagoreans treated as an official s |
https://en.wikipedia.org/wiki/List%20of%20Lie%20groups%20topics | This is a list of Lie group topics, by Wikipedia page.
Examples
See Table of Lie groups for a list
General linear group, special linear group
SL2(R)
SL2(C)
Unitary group, special unitary group
SU(2)
SU(3)
Orthogonal group, special orthogonal group
Rotation group SO(3)
SO(8)
Generalized orthogonal group, generalized special orthogonal group
The special unitary group SU(1,1) is the unit sphere in the ring of coquaternions. It is the group of hyperbolic motions of the Poincaré disk model of the Hyperbolic plane.
Lorentz group
Spinor group
Symplectic group
Exceptional groups
G2
F4
E6
E7
E8
Affine group
Euclidean group
Poincaré group
Heisenberg group
Lie algebras
Commutator
Jacobi identity
Universal enveloping algebra
Baker-Campbell-Hausdorff formula
Casimir invariant
Killing form
Kac–Moody algebra
Affine Lie algebra
Loop algebra
Graded Lie algebra
Foundational results
One-parameter group, One-parameter subgroup
Matrix exponential
Infinitesimal transformation
Lie's third theorem
Maurer–Cartan form
Cartan's theorem
Cartan's criterion
Local Lie group
Formal group law
Hilbert's fifth problem
Hilbert-Smith conjecture
Lie group decompositions
Real form (Lie theory)
Complex Lie group
Complexification (Lie group)
Semisimple theory
Simple Lie group
Compact Lie group, Compact real form
Semisimple Lie algebra
Root system
Simply laced group
ADE classification
Maximal torus
Weyl group
Dynkin diagram
Weyl character formula
Representation theory
Representation of a Lie group
Representation of a Lie algebra
Adjoint representation of a Lie group
Adjoint representation of a Lie algebra
Unitary representation
Weight (representation theory)
Peter–Weyl theorem
Borel–Weil theorem
Kirillov character formula
Representation theory of SU(2)
Representation theory of SL2(R)
Applications
Physical theories
Pauli matrices
Gell-Mann matrices
Poisson bracket
Noether's theorem
Wigner's classification
Gauge theory
Grand unification theory
Supergroup
Lie superalgebra
Twistor theory
Anyon
Witt |
https://en.wikipedia.org/wiki/List%20of%20gene%20families | This is a list of gene families or gene complexes, i.e. sets of genes which are related ancestrally and often serve similar biological functions. These gene families typically encode functionally related proteins, and sometimes the term gene families is a shorthand for the sets of proteins that the genes encode. They may or may not be physically adjacent on the same chromosome.
Regulatory protein gene families
14-3-3 protein family
Achaete-scute complex (neuroblast formation)
FOX proteins (forkhead box proteins)
Families containing homeobox domains
DLX gene family
Hox gene family
POU family
Krüppel-type zinc finger (ZNF)
MADS-box gene family
NOTCH2NL
P300-CBP coactivator family
SOX gene family
Immune system proteins
Immunoglobulin superfamily
Major histocompatibility complex (MHC)
Motor proteins
Dynein
Kinesin
Myosin
Signal transducing proteins
G-proteins
MAP Kinase
Olfactory receptor
Peroxiredoxin
Receptor tyrosine kinases
Transporters
ABC transporters
Antiporter
Aquaporins
Other families
See also
Protein family
Housekeeping gene
F
Biological classification
Gene families |
https://en.wikipedia.org/wiki/Yamaha%20YM2612 | The YM2612, a.k.a. OPN2, is a sound chip developed by Yamaha. It is a member of Yamaha's OPN family of FM synthesis chips, and is derived from the YM2203.
The YM2612 is a six-channel FM synthesizer. It was used in several game and computer systems, most notably in Sega's Mega Drive/Genesis video game console as well as Fujitsu's FM Towns computer series.
As with the YM3438, it was used by Sega in later models of the Mega Drive/Genesis (integrated into an ASIC) as well as in various arcade game systems, including the Mega-Play and Sega System 32.
Features
The YM2612 has the following features:
Six concurrent FM synthesis channels (voices)
Four operators per channel
Two interval timers
A sine-wave low frequency oscillator
Integrated stereo output digital-to-analog converter (most other contemporary Yamaha FM chips require a separate external D/A converter chip)
Per-channel programmable stereo sound (left, right, or both left and right resulting in centre)
For channel three, operator frequencies can be set independently, making dissonant harmonics possible. (Normally, they would have a simple relation like e.g. 2× or 3× relative to a common base frequency)
Technical details
The YM2612's FM synthesis block is an extended version of the FM block featured in the YM2203, adding three FM channels and integrating a stereo output DAC. The YM2612 removes the SSG component (although retaining its envelope generators) and I/O ports found in the YM2203, YM2608 and YM2610. It was also available in CMOS form as the YM3438, a.k.a. OPN2C.
Whereas the high-end OPN chips such as the YM2608 have dedicated ADPCM channels for playing sampled audio, the YM2612 does not. However, its sixth channel can act as a basic PCM channel by means of the 'DAC Enable' register, disabling FM output for that channel but allowing it to play 8-bit pulse-code modulation sound samples. Unlike the other OPNs with ADPCM, the YM2612 does not provide any timing or buffering of samples, so all frequency con |
https://en.wikipedia.org/wiki/Center%20%28algebra%29 | The term center or centre is used in various contexts in abstract algebra to denote the set of all those elements that commute with all other elements.
The center of a group G consists of all those elements x in G such that xg = gx for all g in G. This is a normal subgroup of G.
The similarly named notion for a semigroup is defined likewise and it is a subsemigroup.
The center of a ring (or an associative algebra) R is the subset of R consisting of all those elements x of R such that xr = rx for all r in R. The center is a commutative subring of R.
The center of a Lie algebra L consists of all those elements x in L such that [x,a] = 0 for all a in L. This is an ideal of the Lie algebra L.
See also
Centralizer and normalizer
Center (category theory)
References
Abstract algebra |
https://en.wikipedia.org/wiki/Fuel%20efficiency | Fuel efficiency is a form of thermal efficiency, meaning the ratio of effort to result of a process that converts chemical potential energy contained in a carrier (fuel) into kinetic energy or work. Overall fuel efficiency may vary per device, which in turn may vary per application, and this spectrum of variance is often illustrated as a continuous energy profile. Non-transportation applications, such as industry, benefit from increased fuel efficiency, especially fossil fuel power plants or industries dealing with combustion, such as ammonia production during the Haber process.
In the context of transport, fuel economy is the energy efficiency of a particular vehicle, given as a ratio of distance traveled per unit of fuel consumed. It is dependent on several factors including engine efficiency, transmission design, and tire design. In most countries, using the metric system, fuel economy is stated as "fuel consumption" in liters per 100 kilometers (L/100 km) or kilometers per liter (km/L or kmpl). In a number of countries still using other systems, fuel economy is expressed in miles per gallon (mpg), for example in the US and usually also in the UK (imperial gallon); there is sometimes confusion as the imperial gallon is 20% larger than the US gallon so that mpg values are not directly comparable. Traditionally, litres per mil were used in Norway and Sweden, but both have aligned to the EU standard of L/100 km.
Fuel consumption is a more accurate measure of a vehicle's performance because it is a linear relationship while fuel economy leads to distortions in efficiency improvements. Weight-specific efficiency (efficiency per unit weight) may be stated for freight, and passenger-specific efficiency (vehicle efficiency per passenger) for passenger vehicles.
Vehicle design
Fuel efficiency is dependent on many parameters of a vehicle, including its engine parameters, aerodynamic drag, weight, AC usage, fuel and rolling resistance. There have been advances in all |
https://en.wikipedia.org/wiki/Touchard%20polynomials | The Touchard polynomials, studied by , also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by
where is a Stirling number of the second kind, i.e., the number of partitions of a set of size n into k disjoint non-empty subsets.
The first few Touchard polynomials are
Properties
Basic properties
The value at 1 of the nth Touchard polynomial is the nth Bell number, i.e., the number of partitions of a set of size n:
If X is a random variable with a Poisson distribution with expected value λ, then its nth moment is E(Xn) = Tn(λ), leading to the definition:
Using this fact one can quickly prove that this polynomial sequence is of binomial type, i.e., it satisfies the sequence of identities:
The Touchard polynomials constitute the only polynomial sequence of binomial type with the coefficient of x equal 1 in every polynomial.
The Touchard polynomials satisfy the Rodrigues-like formula:
The Touchard polynomials satisfy the recurrence relation
and
In the case x = 1, this reduces to the recurrence formula for the Bell numbers.
A generalization of both this formula and the definition, is a generalization of Spivey's formula
Using the umbral notation Tn(x)=Tn(x), these formulas become:
The generating function of the Touchard polynomials is
which corresponds to the generating function of Stirling numbers of the second kind.
Touchard polynomials have contour integral representation:
Zeroes
All zeroes of the Touchard polynomials are real and negative. This fact was observed by L. H. Harper in 1967.
The absolute value of the leftmost zero is bounded from above by
although it is conjectured that the leftmost zero grows linearly with the index n.
The Mahler measure of the Touchard polynomials can be estimated as follows:
where and are the smallest of the maximum two k indices such that
and
are maximal, respectively.
Generalizations
Complete Bell polynomial may be viewed as a multivariate g |
https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion%20principle | In combinatorics, a branch of mathematics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as
where A and B are two finite sets and |S | indicates the cardinality of a set S (which may be considered as the number of elements of the set, if the set is finite). The formula expresses the fact that the sum of the sizes of the two sets may be too large since some elements may be counted twice. The double-counted elements are those in the intersection of the two sets and the count is corrected by subtracting the size of the intersection.
The inclusion-exclusion principle, being a generalization of the two-set case, is perhaps more clearly seen in the case of three sets, which for the sets A, B and C is given by
This formula can be verified by counting how many times each region in the Venn diagram figure is included in the right-hand side of the formula. In this case, when removing the contributions of over-counted elements, the number of elements in the mutual intersection of the three sets has been subtracted too often, so must be added back in to get the correct total.
Generalizing the results of these examples gives the principle of inclusion–exclusion. To find the cardinality of the union of sets:
Include the cardinalities of the sets.
Exclude the cardinalities of the pairwise intersections.
Include the cardinalities of the triple-wise intersections.
Exclude the cardinalities of the quadruple-wise intersections.
Include the cardinalities of the quintuple-wise intersections.
Continue, until the cardinality of the -tuple-wise intersection is included (if is odd) or excluded ( even).
The name comes from the idea that the principle is based on over-generous inclusion, followed by compensating exclusion.
This concept is attributed to Abraham de Moivre (1718), although it first appears in a paper of Daniel da Silva (185 |
https://en.wikipedia.org/wiki/Toyota%20Production%20System | The Toyota Production System (TPS) is an integrated socio-technical system, developed by Toyota, that comprises its management philosophy and practices. The TPS is a management system that organizes manufacturing and logistics for the automobile manufacturer, including interaction with suppliers and customers. The system is a major precursor of the more generic "lean manufacturing". Taiichi Ohno and Eiji Toyoda, Japanese industrial engineers, developed the system between 1948 and 1975.<ref>Strategos-International. [http://www.strategosinc.com/toyota_production.htm Toyota Production System and Lean Manufacturing].</ref>
Originally called "just-in-time production", it builds on the approach created by the founder of Toyota, Sakichi Toyoda, his son Kiichiro Toyoda, and the engineer Taiichi Ohno. The principles underlying the TPS are embodied in The Toyota Way.
Goals
The main objectives of the TPS are to design out overburden (muri) and inconsistency (mura), and to eliminate waste (muda). The most significant effects on process value delivery are achieved by designing a process capable of delivering the required results smoothly; by designing out "mura" (inconsistency). It is also crucial to ensure that the process is as flexible as necessary without stress or "muri" (overburden) since this generates "muda" (waste). Finally the tactical improvements of waste reduction or the elimination of muda are very valuable. There are eight kinds of muda that are addressed in the TPS:
Waste of overproduction (largest waste)
Waste of time on hand (waiting)
Waste of transportation
Waste of processing itself
Waste of excess inventory
Waste of movement
Waste of making defective products
Waste of underutilized workers
Concept
Toyota Motor Corporation published an official description of TPS for the first time in 1992; this booklet was revised in 1998. In the foreword it was said: "The TPS is a framework for conserving resources by eliminating waste. People who participate in |
https://en.wikipedia.org/wiki/Corning%20Inc. | Corning Incorporated () is an American multinational technology company that specializes in specialty glass, ceramics, and related materials and technologies including advanced optics, primarily for industrial and scientific applications. The company was named Corning Glass Works until 1989. Corning divested its consumer product lines (including CorningWare and Visions Pyroceram-based cookware, Corelle Vitrelle tableware, and Pyrex glass bakeware) in 1998 by selling the Corning Consumer Products Company subsidiary (now known as Corelle Brands) to Borden.
, Corning had five major business sectors: display technologies, environmental technologies, life sciences, optical communications, and specialty materials. Corning is involved in two joint ventures: Dow Corning and Pittsburgh Corning. Quest Diagnostics and Covance were spun off from Corning in 1996. Corning is one of the main suppliers to Apple Inc. Since working with Steve Jobs in 2007, to develop the iPhone; Corning develops and manufactures Gorilla Glass, which is used by many smartphone makers. It is one of the world's biggest glassmakers. Corning won the National Medal of Technology and Innovation four times for its product and process innovations.
History
Corning Glass Works was founded in 1851 by Amory Houghton, in Somerville, Massachusetts, originally as the Bay State Glass Co. It later moved to Williamsburg, Brooklyn, and operated as the Brooklyn Flint Glass Works. The company moved again to its ultimate home and eponym, the city of Corning, New York, in 1868, under leadership of the founder's son, Amory Houghton, Jr.
Corning continues to maintain its world headquarters at Corning, N.Y. The firm also established one of the first industrial research labs there in 1908. It continues to expand the nearby research and development facility, as well as operations associated with catalytic converters and diesel engine filter product lines. Corning has a long history of community development and has assured co |
https://en.wikipedia.org/wiki/Bilayer | A bilayer is a double layer of closely packed atoms or molecules.
The properties of bilayers are often studied in condensed matter physics, particularly in the context of semiconductor devices, where two distinct materials are united to form junctions, such as p–n junctions, Schottky junctions, etc. Layered materials, such as graphene, boron nitride, or transition metal dichalcogenides, have unique electronic properties as a bilayer system and are an active area of current research.
In biology a common example is the lipid bilayer, which describes the structure of multiple organic structures, such as the membrane of a cell.
See also
Monolayer
Non-carbon nanotube
Semiconductor
Thin film
References
Phases of matter
Thin films |
https://en.wikipedia.org/wiki/Image%20%28category%20theory%29 | In category theory, a branch of mathematics, the image of a morphism is a generalization of the image of a function.
General definition
Given a category and a morphism in , the image
of is a monomorphism satisfying the following universal property:
There exists a morphism such that .
For any object with a morphism and a monomorphism such that , there exists a unique morphism such that .
Remarks:
such a factorization does not necessarily exist.
is unique by definition of monic.
, therefore by monic.
is monic.
already implies that is unique.
The image of is often denoted by or .
Proposition: If has all equalizers then the in the factorization of (1) is an epimorphism.
Second definition
In a category with all finite limits and colimits, the image is defined as the equalizer of the so-called cokernel pair , which is the cocartesian of a morphism with itself over its domain, which will result in a pair of morphisms , on which the equalizer is taken, i.e. the first of the following diagrams is cocartesian, and the second equalizing.
Remarks:
Finite bicompleteness of the category ensures that pushouts and equalizers exist.
can be called regular image as is a regular monomorphism, i.e. the equalizer of a pair of morphisms. (Recall also that an equalizer is automatically a monomorphism).
In an abelian category, the cokernel pair property can be written and the equalizer condition . Moreover, all monomorphisms are regular.
Examples
In the category of sets the image of a morphism is the inclusion from the ordinary image to . In many concrete categories such as groups, abelian groups and (left- or right) modules, the image of a morphism is the image of the correspondent morphism in the category of sets.
In any normal category with a zero object and kernels and cokernels for every morphism, the image of a morphism can be expressed as follows:
im f = ker coker f
In an abelian category (which is in particular binormal), if |
https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker%20metric | The Friedmann–Lemaître–Robertson–Walker metric (FLRW; ) is a metric based on the exact solution of the Einstein field equations of general relativity. The metric describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the scale factor of the universe as a function of time. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker – are variously grouped as Friedmann, Friedmann–Robertson–Walker (FRW), Robertson–Walker (RW), or Friedmann–Lemaître (FL). This model is sometimes called the Standard Model of modern cosmology, although such a description is also associated with the further developed Lambda-CDM model. The FLRW model was developed independently by the named authors in the 1920s and 1930s.
General metric
The FLRW metric starts with the assumption of homogeneity and isotropy of space. It also assumes that the spatial component of the metric can be time-dependent. The generic metric which meets these conditions is
where ranges over a 3-dimensional space of uniform curvature, that is, elliptical space, Euclidean space, or hyperbolic space. It is normally written as a function of three spatial coordinates, but there are several conventions for doing so, detailed below. does not depend on t – all of the time dependence is in the function a(t), known as the "scale factor".
Reduced-circumference polar coordinates
In reduced-circumference polar coordinates the spatial metric has the form
k is a constant representing the curvature of the space. There are two common unit conventions:
k may be taken to have units of length−2, in which case r has units of length and a(t) is unitless. k is then the Gaussian curvatu |
https://en.wikipedia.org/wiki/Cousin%20prime | In number theory, cousin primes are prime numbers that differ by four. Compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six.
The cousin primes (sequences and in OEIS) below 1000 are:
(3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), (79, 83), (97, 101), (103, 107), (109, 113), (127, 131), (163, 167), (193, 197), (223, 227), (229, 233), (277, 281), (307, 311), (313, 317), (349, 353), (379, 383), (397, 401), (439, 443), (457, 461), (463,467), (487, 491), (499, 503), (613, 617), (643, 647), (673, 677), (739, 743), (757, 761), (769, 773), (823, 827), (853, 857), (859, 863), (877, 881), (883, 887), (907, 911), (937, 941), (967, 971)
Properties
The only prime belonging to two pairs of cousin primes is 7. One of the numbers will always be divisible by 3, so is the only case where all three are primes.
An example of a large proven cousin prime pair is for
which has 20008 digits. In fact, this is part of a prime triple since is also a twin prime (because is also a proven prime).
, the largest-known pair of cousin primes was found by S. Batalov and has 51,934 digits. The primes are:
It follows from the first Hardy–Littlewood conjecture that cousin primes have the same asymptotic density as twin primes. An analogue of Brun's constant for twin primes can be defined for cousin primes, called Brun's constant for cousin primes, with the initial term (3, 7) omitted, by the convergent sum:
Using cousin primes up to 242, the value of was estimated by Marek Wolf in 1996 as
This constant should not be confused with Brun's constant for prime quadruplets, which is also denoted .
The Skewes number for cousin primes is 5206837 ().
Notes
References
.
Classes of prime numbers
Unsolved problems in mathematics |
https://en.wikipedia.org/wiki/Schnirelmann%20density | In additive number theory, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is. It is named after Russian mathematician Lev Schnirelmann, who was the first to study it.
Definition
The Schnirelmann density of a set of natural numbers A is defined as
where A(n) denotes the number of elements of A not exceeding n and inf is infimum.
The Schnirelmann density is well-defined even if the limit of A(n)/n as fails to exist (see upper and lower asymptotic density).
Properties
By definition, and for all n, and therefore , and if and only if . Furthermore,
Sensitivity
The Schnirelmann density is sensitive to the first values of a set:
.
In particular,
and
Consequently, the Schnirelmann densities of the even numbers and the odd numbers, which one might expect to agree, are 0 and 1/2 respectively. Schnirelmann and Yuri Linnik exploited this sensitivity.
Schnirelmann's theorems
If we set , then Lagrange's four-square theorem can be restated as . (Here the symbol denotes the sumset of and .) It is clear that . In fact, we still have , and one might ask at what point the sumset attains Schnirelmann density 1 and how does it increase. It actually is the case that and one sees that sumsetting once again yields a more populous set, namely all of . Schnirelmann further succeeded in developing these ideas into the following theorems, aiming towards Additive Number Theory, and proving them to be a novel resource (if not greatly powerful) to attack important problems, such as Waring's problem and Goldbach's conjecture.
Theorem. Let and be subsets of . Then
Note that . Inductively, we have the following generalization.
Corollary. Let be a finite family of subsets of . Then
The theorem provides the first insights on how sumsets accumulate. It seems unfortunate that its conclusion stops short of showing being superadditive. Yet, Schnirelmann provided us with the following results, which sufficed for most of his purpose.
|
https://en.wikipedia.org/wiki/Internet2 | Internet2 is a not-for-profit United States computer networking consortium led by members from the research and education communities, industry, and government. The Internet2 consortium administrative headquarters are located in Ann Arbor, Michigan, with offices in Washington, D.C., and Emeryville, California.
As of November 2013, Internet2 has over 500 members including 251 institutions of higher education, 9 partners and 76 members from industry, over 100 research and education networks or connector organizations, and 67 affiliate members.
Internet2 operates the Internet2 Network, an Internet Protocol network using optical fiber that delivers network services for research and education, and provides a secure network testing and research environment. In late 2007, Internet2 began operating its newest dynamic circuit network, the Internet2 DCN, an advanced technology that allows user-based allocation of data circuits over the fiber-optic network.
The Internet2 Network, through its regional network and connector members, connects over 60,000 U.S. educational, research, government and "community anchor" institutions, from primary and secondary schools to community colleges and universities, public libraries and museums to health care organizations.
The Internet2 community develops and deploys network technologies for the future of the Internet. These technologies include large-scale network performance measurement and management tools, secure identity and access management tools and capabilities such as scheduling high-bandwidth, high-performance circuits.
Internet2 members serve on several advisory councils, collaborate in a variety of working groups and special interest groups, gather at spring and fall member meetings, and are encouraged to participate in the strategic planning process.
History
As the Internet gained in public recognition and popularity, universities were among the first institutions to outgrow the Internet's bandwidth limitations because |
https://en.wikipedia.org/wiki/Hartley%20oscillator | The Hartley oscillator is an electronic oscillator circuit in which the oscillation frequency is determined by a tuned circuit consisting of capacitors and inductors, that is, an LC oscillator. The circuit was invented in 1915 by American engineer Ralph Hartley. The distinguishing feature of the Hartley oscillator is that the tuned circuit consists of a single capacitor in parallel with two inductors in series (or a single tapped inductor), and the feedback signal needed for oscillation is taken from the center connection of the two inductors.
History
The Hartley oscillator was invented by Hartley while he was working for the Research Laboratory of the Western Electric Company. Hartley invented and patented the design in 1915 while overseeing Bell System's transatlantic radiotelephone tests; it was awarded patent number 1,356,763 on October 26, 1920. Note that the basic schematic shown below labeled "Common-drain Hartley circuit" is essentially the same as in the patent drawing, except that the tube is replaced by a JFET, and that the battery for a negative grid bias is not needed.
In 1946 Hartley was awarded the IRE medal of honor "For his early work on oscillating circuits employing triode tubes and likewise for his early recognition and clear exposition of the fundamental relationship between the total amount of information which may be transmitted over a transmission system of limited band-width and the time required."(The second half of the citation refers to Hartley's work in information theory which largely paralleled Harry Nyquist.)
Operation
The Hartley oscillator is distinguished by a tank circuit consisting of two series-connected coils (or, often, a tapped coil) in parallel with a capacitor, with an amplifier between the relatively high impedance across the entire LC tank and the relatively low voltage/high current point between the coils. The original 1915 version used a triode as the amplifying device in common plate (cathode follower) config |
https://en.wikipedia.org/wiki/Regenerative%20circuit | A regenerative circuit is an amplifier circuit that employs positive feedback (also known as regeneration or reaction). Some of the output of the amplifying device is applied back to its input to add to the input signal, increasing the amplification. One example is the Schmitt trigger (which is also known as a regenerative comparator), but the most common use of the term is in RF amplifiers, and especially regenerative receivers, to greatly increase the gain of a single amplifier stage.
The regenerative receiver was invented in 1912 and patented in 1914 by American electrical engineer Edwin Armstrong when he was an undergraduate at Columbia University. It was widely used between 1915 and World War II. Advantages of regenerative receivers include increased sensitivity with modest hardware requirements, and increased selectivity because the Q of the tuned circuit will be increased when the amplifying vacuum tube or transistor has its feedback loop around the tuned circuit (via a "tickler" winding or a tapping on the coil) because it introduces some negative resistance.
Due partly to its tendency to radiate interference when oscillating, by the 1930s the regenerative receiver was largely superseded by other TRF receiver designs (for example "reflex" receivers) and especially by another Armstrong invention - superheterodyne receivers and is largely considered obsolete. Regeneration (now called positive feedback) is still widely used in other areas of electronics, such as in oscillators, active filters, and bootstrapped amplifiers.
A receiver circuit that used larger amounts of regeneration in a more complicated way to achieve even higher amplification, the superregenerative receiver, was also invented by Armstrong in 1922. It was never widely used in general commercial receivers, but due to its small parts count it was used in specialized applications. One widespread use during WWII was IFF transceivers, where single tuned circuit completed the entire electronics sy |
https://en.wikipedia.org/wiki/Toffoli%20gate | In logic circuits, the Toffoli gate (also CCNOT gate), invented by Tommaso Toffoli, is a universal reversible logic gate, which means that any classical reversible circuit can be constructed from Toffoli gates. It is also known as the "controlled-controlled-not" gate, which describes its action. It has 3-bit inputs and outputs; if the first two bits are both set to 1, it inverts the third bit, otherwise all bits stay the same.
Background
An input-consuming logic gate L is reversible if it meets the following conditions:
L(x) = y is a gate where for any output y, there is a unique input x.
The gate L is reversible if there is a gate L′(y) = x which maps y to x, for all y.
From common logic gates, NOT is reversible, as can be seen from its truth table below.
The common AND gate is not reversible, because the inputs 00, 01 and 10 are all mapped to the output 0.
Reversible gates have been studied since the 1960s. The original motivation was that reversible gates dissipate less heat (or, in principle, no heat).
More recent motivation comes from quantum computing. In quantum mechanics the quantum state can evolve in two ways, by Schrödinger's equation (unitary transformations), or by their collapse. Logic operations for quantum computers, of which the Toffoli gate is an example, are unitary transformations and therefore evolve reversibly.
Universality and Toffoli gate
Any reversible gate that consumes its inputs and allows all input computations must have no more input bits than output bits, by the pigeonhole principle. For one input bit, there are two possible reversible gates. One of them is NOT. The other is the identity gate, which maps its input to the output unchanged. For two input bits, the only non-trivial gate is the controlled NOT gate, which XORs the first bit to the second bit and leaves the first bit unchanged.
Unfortunately, there are reversible functions that cannot be computed using just those gates. In other words, the set consisting of NOT and |
https://en.wikipedia.org/wiki/60%20%28number%29 | 60 (sixty) () is the natural number following 59 and preceding 61. Being three times 20, it is called threescore in older literature (kopa in Slavic, Schock in Germanic).
In mathematics
60 is a highly composite number. Because it is the sum of its unitary divisors (excluding itself), it is a unitary perfect number, and it is an abundant number with an abundance of 48. Being ten times a perfect number, it is a semiperfect number.
60 is a Twin-prime sum of the fifth pair of twin-primes, 29 + 31.
It is the smallest number divisible by the numbers 1 to 6: there is no smaller number divisible by the numbers 1 to 5 since any number divisible by 2 and 3 must also be divisible by 6.
It is the smallest number with exactly 12 divisors. Having 12 as one of those divisors, 60 is also a refactorable number.
It is one of seven integers that have more divisors than any number less than twice itself , one of six that are also lowest common multiple of a consecutive set of integers from 1, and one of six that are divisors of every highly composite number higher than itself.
It is the smallest number that is the sum of two odd primes in six ways.
The smallest nonsolvable group (A5) has order 60.
There are four Archimedean solids with 60 vertices: the truncated icosahedron, the rhombicosidodecahedron, the snub dodecahedron, and the truncated dodecahedron. The skeletons of these polyhedra form 60-node vertex-transitive graphs. There are also two Archimedean solids with 60 edges: the snub cube and the icosidodecahedron. The skeleton of the icosidodecahedron forms a 60-edge symmetric graph.
There are 60 one-sided hexominoes, the polyominoes made from six squares.
In geometry, it is the number of seconds in a minute, and the number of minutes in a degree.
In normal space, the three interior angles of an equilateral triangle each measure 60 degrees, adding up to 180 degrees.
Because it is divisible by the sum of its digits in decimal, it is a Harshad number.
A number syst |
https://en.wikipedia.org/wiki/70%20%28number%29 | 70 (seventy) is the natural number following 69 and preceding 71.
In mathematics
70 is:
a sphenic number because its factors are 3 distinct primes.
a Pell number.
the seventh pentagonal number.
the fourth tridecagonal number.
the fifth pentatope number.
the number of ways to choose 4 objects out of 8 if order does not matter. This makes it a central binomial coefficient.
the smallest weird number, a natural number that is abundant but not semiperfect.
a palindromic number in bases 9 (779), 13 (5513) and 34 (2234).
a Harshad number in bases 6, 8, 9, 10, 11, 13, 14, 15 and 16.
an Erdős–Woods number, since it is possible to find sequences of 70 consecutive integers such that each inner member shares a factor with either the first or the last member.
The sum of the first 24 squares starting from 1 is 70 = 4900, i.e. a square pyramidal number. This is the only non trivial solution to the cannonball problem and relates 70 to the Leech lattice and thus string theory.
In science
70 is the atomic number of ytterbium, a lanthanide
Astronomy
Messier object M70, a magnitude 9.0 globular cluster in the constellation Sagittarius
The New General Catalogue object NGC 70, a magnitude 13.4 spiral galaxy in the constellation Andromeda
In religion
In Jewish tradition:
Seventy souls went down to Egypt to begin the Hebrews' Egyptian exile ().
There is a core of 70 nations and 70 world languages, paralleling the 70 names in the Table of Nations.
There were 70 men in the Great Sanhedrin, the Supreme Court of ancient Israel. (Sanhedrin 1:4.)
According to the Jewish Aggada, there are 70 perspectives ("faces") to the Torah (Numbers Rabbah 13:15).
Seventy elders were assembled by Moses on God's command in the desert ().
allots three score and ten (70 years) for a man's life, and the Mishnah attributes that age to "strength" (Avot 5:32), as one who survives that age is described by the verse as "the strong".
Ptolemy II Philadelphus ordered 72 Jewish elders to translate t |
https://en.wikipedia.org/wiki/80%20%28number%29 | 80 (eighty) is the natural number following 79 and preceding 81.
In mathematics
80 is:
the sum of Euler's totient function φ(x) over the first sixteen integers.
a semiperfect number, since adding up some subsets of its divisors (e.g., 1, 4, 5, 10, 20 and 40) gives 80.
a ménage number.
palindromic in bases 3 (22223), 6 (2126), 9 (889), 15 (5515), 19 (4419) and 39 (2239).
a repdigit in bases 3, 9, 15, 19 and 39.
the sum of the first 4 twin prime pairs ((3 + 5) + (5 + 7) + (11 + 13) + (17 + 19)).
The Pareto principle (also known as the 80-20 rule) states that, for many events, roughly 80% of the effects come from 20% of the causes.
Every solvable configuration of the 15 puzzle can be solved in no more than 80 single-tile moves.
In science
The atomic number of mercury
In religion
According to Exodus 7:7, Moses was 80 years old when he initially spoke to Pharaoh on behalf of his people. Today, 80 years of age is the upper age limit for cardinals to vote in papal elections.
In other fields
Eighty is also:
used in the classic book title Around the World in Eighty Days
the length of the Eighty Years' War or Dutch revolt (1568–1648)
the standard TCP/IP port number for HTTP connections
the 80A, 80B and 80C photographic filters correct for excessive redness under tungsten lighting
The year AD 80, 80 BC, or 1980
Eighty shilling ale
The older four-pin-base version of the 5Y3GT rectifier tube
A common limit for the characters per line, in computing, derived from the number of columns in IBM cards
American band Green Day has a song called "80"
A fictional alien superhero named Ultraman 80
On the Réaumur scale, 80 degrees is the boiling temperature of pure water at sea level
See also
List of highways numbered 80
References
External links
wiktionary:eighty for 80 in other languages.
Integers |
https://en.wikipedia.org/wiki/90%20%28number%29 | 90 (ninety) is the natural number following 89 and preceding 91.
In the English language, the numbers 90 and 19 are often confused, as they sound very similar. When carefully enunciated, they differ in which syllable is stressed: 19 /naɪnˈtiːn/ vs 90 /ˈnaɪnti/. However, in dates such as 1999, and when contrasting numbers in the teens and when counting, such as 17, 18, 19, the stress shifts to the first syllable: 19 /ˈnaɪntiːn/.
In mathematics
Ninety is a pronic number as it is the product of 9 and 10, and along with 12 and 56, one of only a few pronic numbers whose digits in decimal are also successive. In normal space, the interior angles of a rectangle measure 90 degrees each. In a right triangle, the angle opposing the hypotenuse measures 90 degrees, with the other two angles adding up to 90 for a total of degrees, which are the number of degrees that make up the interior angles of a triangle. Thus, an angle measuring 90 degrees is called a right angle. 90 is also and divisible by the sum of its base-ten digits, which makes it a Harshad number.
The twelfth triangular number, 78, is the only number to have an aliquot sum equal to 90, aside from 892 (which is centered octagonal). Only three numbers have a set of divisors that generate a sum equal to 90 (they are 40, 58 and 89).
90 is the twentieth abundant and highly abundant numbers (with 20 the first primitive abundant number and 70 the second). It is also the eleventh nontotient (with 50 the fifth).
90 is the third unitary perfect number (like 60), since it is the sum of its unitary divisors excluding itself, and because it is equal to the sum of a subset of its divisors, it is also a semiperfect number.
The members of the first prime sextuplet (7, 11, 13, 17, 19, 23) generate a sum equal to 90, and the difference between respective members of the first and second prime sextuplets is also 90, where the second prime sextuplet is (97, 101, 103, 107, 109, 113). The last member of the second prime sextuple |
https://en.wikipedia.org/wiki/Simple%20theorems%20in%20the%20algebra%20of%20sets | The simple theorems in the algebra of sets are some of the elementary properties of the algebra of union (infix operator: ∪), intersection (infix operator: ∩), and set complement (postfix ') of sets.
These properties assume the existence of at least two sets: a given universal set, denoted U, and the empty set, denoted {}. The algebra of sets describes the properties of all possible subsets of U, called the power set of U and denoted P(U). P(U) is assumed closed under union, intersection, and set complement. The algebra of sets is an interpretation or model of Boolean algebra, with union, intersection, set complement, U, and {} interpreting Boolean sum, product, complement, 1, and 0, respectively.
The properties below are stated without proof, but can be derived from a small number of properties taken as axioms. A "*" follows the algebra of sets interpretation of Huntington's (1904) classic postulate set for Boolean algebra. These properties can be visualized with Venn diagrams. They also follow from the fact that P(U) is a Boolean lattice. The properties followed by "L" interpret the lattice axioms.
Elementary discrete mathematics courses sometimes leave students with the impression that the subject matter of set theory is no more than these properties. For more about elementary set theory, see set, set theory, algebra of sets, and naive set theory. For an introduction to set theory at a higher level, see also axiomatic set theory, cardinal number, ordinal number, Cantor–Bernstein–Schroeder theorem, Cantor's diagonal argument, Cantor's first uncountability proof, Cantor's theorem, well-ordering theorem, axiom of choice, and Zorn's lemma.
The properties below include a defined binary operation, relative complement, denoted by the infix operator "\". The "relative complement of A in B," denoted B \A, is defined as (A ∪) and as ∩B.
PROPOSITION 1. For any U and any subset A of U:
{} = U;
= {};
A \ {} = A;
{} \ A = {};
A ∩ {} = {};
A ∪ {} = A; *
A ∩ U = A; *
A |
https://en.wikipedia.org/wiki/Maternal%20effect | A maternal effect is a situation where the phenotype of an organism is determined not only by the environment it experiences and its genotype, but also by the environment and genotype of its mother. In genetics, maternal effects occur when an organism shows the phenotype expected from the genotype of the mother, irrespective of its own genotype, often due to the mother supplying messenger RNA or proteins to the egg. Maternal effects can also be caused by the maternal environment independent of genotype, sometimes controlling the size, sex, or behaviour of the offspring. These adaptive maternal effects lead to phenotypes of offspring that increase their fitness. Further, it introduces the concept of phenotypic plasticity, an important evolutionary concept. It has been proposed that maternal effects are important for the evolution of adaptive responses to environmental heterogeneity.
In genetics
In genetics, a maternal effect occurs when the phenotype of an organism is determined by the genotype of its mother. For example, if a mutation is maternal effect recessive, then a female homozygous for the mutation may appear phenotypically normal, however her offspring will show the mutant phenotype, even if they are heterozygous for the mutation.
Maternal effects often occur because the mother supplies a particular mRNA or protein to the oocyte, hence the maternal genome determines whether the molecule is functional. Maternal supply of mRNAs to the early embryo is important, as in many organisms the embryo is initially transcriptionally inactive. Because of the inheritance pattern of maternal effect mutations, special genetic screens are required to identify them. These typically involve examining the phenotype of the organisms one generation later than in a conventional (zygotic) screen, as their mothers will be potentially homozygous for maternal effect mutations that arise.
In Drosophila early embryogenesis
A Drosophila melanogaster oocyte develops in an egg chamber |
https://en.wikipedia.org/wiki/Wear%20leveling | Wear leveling (also written as wear levelling) is a technique for prolonging the service life of some kinds of erasable computer storage media, such as flash memory, which is used in solid-state drives (SSDs) and USB flash drives, and phase-change memory. There are several wear leveling mechanisms that provide varying levels of longevity enhancement in such memory systems.
The term preemptive wear leveling (PWL) has been used by Western Digital to describe their preservation technique used on hard disk drives (HDDs) designed for storing audio and video data. However, HDDs generally are not wear-leveled devices in the context of this article.
Rationale
EEPROM and flash memory media have individually erasable segments, each of which can be put through a limited number of erase cycles before becoming unreliable. This is usually around 3,000/5,000 cycles but many flash devices have one block with a specially extended life of 100,000+ cycles that can be used by the Flash memory controller to track wear and movement of data across segments. Erasable optical media such as CD-RW and DVD-RW are rated at up to 1,000 cycles (100,000 cycles for DVD-RAM media).
Wear leveling attempts to work around these limitations by arranging data so that erasures and re-writes are distributed evenly across the medium. In this way, no single erase block prematurely fails due to a high concentration of write cycles. In flash memory, a single block on the chip is designed for longer life than the others so that the memory controller can store operational data with less chance of its corruption.
Conventional file systems such as FAT, UFS, HFS/HFS+, EXT, and NTFS were originally designed for magnetic disks and as such rewrite many of their data structures (such as their directories) repeatedly to the same area. When these systems are used on flash memory media, this becomes a problem. The problem is aggravated by the fact that some file systems track last-access times, which can lead to file |
https://en.wikipedia.org/wiki/Set-theoretic%20limit | In mathematics, the limit of a sequence of sets (subsets of a common set ) is a set whose elements are determined by the sequence in either of two equivalent ways: (1) by upper and lower bounds on the sequence that converge monotonically to the same set (analogous to convergence of real-valued sequences) and (2) by convergence of a sequence of indicator functions which are themselves real-valued. As is the case with sequences of other objects, convergence is not necessary or even usual.
More generally, again analogous to real-valued sequences, the less restrictive limit infimum and limit supremum of a set sequence always exist and can be used to determine convergence: the limit exists if the limit infimum and limit supremum are identical. (See below). Such set limits are essential in measure theory and probability.
It is a common misconception that the limits infimum and supremum described here involve sets of accumulation points, that is, sets of where each is in some This is only true if convergence is determined by the discrete metric (that is, if there is such that for all ). This article is restricted to that situation as it is the only one relevant for measure theory and probability. See the examples below. (On the other hand, there are more general topological notions of set convergence that do involve accumulation points under different metrics or topologies.)
Definitions
The two definitions
Suppose that is a sequence of sets. The two equivalent definitions are as follows.
Using union and intersection: define and If these two sets are equal, then the set-theoretic limit of the sequence exists and is equal to that common set. Either set as described above can be used to get the limit, and there may be other means to get the limit as well.
Using indicator functions: let equal if and otherwise. Define and where the expressions inside the brackets on the right are, respectively, the limit infimum and limit supremum of the real-valued seq |
https://en.wikipedia.org/wiki/Signal%20trace | In electronics, a signal trace or circuit trace on a printed circuit board (PCB) or integrated circuit (IC) is the equivalent of a wire for conducting signals. Each trace consists of a flat, narrow part of the copper foil that remains after etching. Signal traces are usually narrower than power or ground traces because the current carrying requirements are usually much less.
See also
Ground plane
Stripline
Microstrip
References
Electrical connectors
Printed circuit board manufacturing |
https://en.wikipedia.org/wiki/Electrical%20termination | In electronics, electrical termination is the practice of ending a transmission line with a device that matches the characteristic impedance of the line. Termination prevents signals from reflecting off the end of the transmission line. Reflections at the ends of unterminated transmission lines cause distortion, which can produce ambiguous digital signal levels and misoperation of digital systems. Reflections in analog signal systems cause such effects as video ghosting, or power loss in radio transmitter transmission lines.
Transmission lines
Signal termination often requires the installation of a terminator at the beginning and end of a wire or cable to prevent an RF signal from being reflected back from each end, causing interference, or power loss. The terminator is usually placed at the end of a transmission line or daisy chain bus (such as in SCSI), and is designed to match the AC impedance of the cable and hence minimize signal reflections, and power losses. Less commonly, a terminator is also placed at the driving end of the wire or cable, if not already part of the signal-generating equipment.
Radio frequency currents tend to reflect from discontinuities in the cable, such as connectors and joints, and travel back down the cable toward the source, causing interference as primary reflections. Secondary reflections can also occur at the cable starts, allowing interference to persist as repeated echoes of old data. These reflections also act as bottlenecks, preventing the signal power from reaching the destination.
Transmission line cables require impedance matching to carry electromagnetic signals with minimal reflections and power losses. The distinguishing feature of most transmission line cables is that they have uniform cross-sectional dimensions along their length, giving them a uniform electrical characteristic impedance. Signal terminators are designed to specifically match the characteristic impedances at both cable ends. For many systems, the ter |
https://en.wikipedia.org/wiki/Audio%20frequency | An audio frequency or audible frequency (AF) is a periodic vibration whose frequency is audible to the average human. The SI unit of frequency is the hertz (Hz). It is the property of sound that most determines pitch.
The generally accepted standard hearing range for humans is 20 to 20,000 Hz. In air at atmospheric pressure, these represent sound waves with wavelengths of to . Frequencies below 20 Hz are generally felt rather than heard, assuming the amplitude of the vibration is great enough. Sound frequencies above 20 kHz are called ultrasonic.
Sound propagates as mechanical vibration waves of pressure and displacement, in air or other substances. In general, frequency components of a sound determine its "color", its timbre. When speaking about the frequency (in singular) of a sound, it means the property that most determines its pitch. Higher pitches have higher frequency, and lower pitches are lower frequency.
The frequencies an ear can hear are limited to a specific range of frequencies. The audible frequency range for humans is typically given as being between about 20 Hz and 20,000 Hz (20 kHz), though the high frequency limit usually reduces with age. Other species have different hearing ranges. For example, some dog breeds can perceive vibrations up to 60,000 Hz.
In many media, such as air, the speed of sound is approximately independent of frequency, so the wavelength of the sound waves (distance between repetitions) is approximately inversely proportional to frequency.
Frequencies and descriptions
See also
Absolute threshold of hearing
Hypersonic effect, controversial claim for human perception above 20,000 Hz
Loudspeaker
Musical acoustics
Piano key frequencies
Scientific pitch notation
Whistle register
References
Acoustics
Sound
Sound measurements
Physical quantities
Audio engineering |
https://en.wikipedia.org/wiki/Living%20fossil | A living fossil is an extant taxon that cosmetically resembles related species known only from the fossil record. To be considered a living fossil, the fossil species must be old relative to the time of origin of the extant clade. Living fossils commonly are of species-poor lineages, but they need not be. While the body plan of a living fossil remains superficially similar, it is never the same species as the remote relatives it resembles, because genetic drift would inevitably change its chromosomal structure.
Living fossils exhibit stasis (also called "bradytely") over geologically long time scales. Popular literature may wrongly claim that a "living fossil" has undergone no significant evolution since fossil times, with practically no molecular evolution or morphological changes. Scientific investigations have repeatedly discredited such claims.
The minimal superficial changes to living fossils are mistakenly declared as an absence of evolution, but they are examples of stabilizing selection, which is an evolutionary process—and perhaps the dominant process of morphological evolution.
Characteristics
Living fossils have two main characteristics, although some have a third:
Living organisms that are members of a taxon that has remained recognisable in the fossil record over an unusually long time span.
They show little morphological divergence, whether from early members of the lineage, or among extant species.
They tend to have little taxonomic diversity.
The first two are required for recognition as a living fossil; some authors also require the third, others merely note it as a frequent trait.
Such criteria are neither well-defined nor clearly quantifiable, but modern methods for analyzing evolutionary dynamics can document the distinctive tempo of stasis. Lineages that exhibit stasis over very short time scales are not considered living fossils; what is poorly-defined is the time scale over which the morphology must persist for that lineage to be reco |
https://en.wikipedia.org/wiki/World%20Solar%20Challenge | The World Solar Challenge (WSC), since 2013 named Bridgestone World Solar Challenge, is an international event for solar powered cars driving 3000 kilometres through the Australian outback.
With the exception of a four-year gap between the 2019 and 2023 events, owing to the cancellation of the 2021 event, the World Solar Challenge is typically held every two years. The course is over through the Australian Outback, from Darwin, Northern Territory, to Adelaide, South Australia. The event was created to foster the development of solar-powered vehicles.
The WSC attracts teams from around the world, most of which are fielded by universities or corporations, although some are fielded by high schools. It has a 32-year history spanning fifteen events, with the inaugural event taking place in 1987. Initially held once every three years, the event became biennial from the turn of the century.
Since 2001 the WSC was won seven times out of ten efforts by the Nuna team and cars of the Delft University of Technology from the Netherlands. The Tokai Challenger, built by the Tokai University of Japan, was able to win 2009 and 2011. In the most recent edition (2019), the Belgian Agoria Solar Team from KU Leuven University won.
Starting in 2007, the WSC has multiple classes. After the German team of Bochum University of Applied Sciences competed with a four-wheeled, multi-seat car, the BoCruiser (in 2009), in 2013 a radically new "Cruiser Class" was introduced, stimulating the technological development of practically usable, and ideally road-legal, multi-seater solar vehicles. Since its inception, Solar Team Eindhoven's four- and five-seat Stella solar cars from Eindhoven University of Technology (Netherlands) won the Cruiser Class in all four events so far.
Remarkable technological progress has been achieved since the General Motors led, highly experimental, single-seat Sunraycer prototype first won the WSC with an average speed of . Once competing cars became steadily more c |
https://en.wikipedia.org/wiki/Multiplicative%20order | In number theory, given a positive integer n and an integer a coprime to n, the multiplicative order of a modulo n is the smallest positive integer k such that .
In other words, the multiplicative order of a modulo n is the order of a in the multiplicative group of the units in the ring of the integers modulo n.
The order of a modulo n is sometimes written as .
Example
The powers of 4 modulo 7 are as follows:
The smallest positive integer k such that 4k ≡ 1 (mod 7) is 3, so the order of 4 (mod 7) is 3.
Properties
Even without knowledge that we are working in the multiplicative group of integers modulo n, we can show that a actually has an order by noting that the powers of a can only take a finite number of different values modulo n, so according to the pigeonhole principle there must be two powers, say s and t and without loss of generality s > t, such that as ≡ at (mod n). Since a and n are coprime, a has an inverse element a−1 and we can multiply both sides of the congruence with a−t, yielding as−t ≡ 1 (mod n).
The concept of multiplicative order is a special case of the order of group elements. The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n. This is the group of units of the ring Zn; it has φ(n) elements, φ being Euler's totient function, and is denoted as U(n) or U(Zn).
As a consequence of Lagrange's theorem, the order of a (mod n) always divides φ(n). If the order of a is actually equal to φ(n), and therefore as large as possible, then a is called a primitive root modulo n. This means that the group U(n) is cyclic and the residue class of a generates it.
The order of a (mod n) also divides λ(n), a value of the Carmichael function, which is an even stronger statement than the divisibility of φ(n).
Programming languages
Maxima CAS : zn_order (a, n)
Rosetta Code - examples of mu |
https://en.wikipedia.org/wiki/Analog%20multiplier | In electronics, an analog multiplier is a device that takes two analog signals and produces an output which is their product. Such circuits can be used to implement related functions such as squares (apply same signal to both inputs), and square roots.
An electronic analog multiplier can be called by several names, depending on the function it is used to serve (see analog multiplier applications).
Voltage-controlled amplifier versus analog multiplier
If one input of an analog multiplier is held at a steady-state voltage, a signal at the second input will be scaled in proportion to the level on the fixed input. In this case, the analog multiplier may be considered to be a voltage controlled amplifier. Obvious applications would be for electronic volume control and automatic gain control (AGC). Although analog multipliers are often used for such applications, voltage-controlled amplifiers are not necessarily true analog multipliers. For example, an integrated circuit designed to be used as a volume control may have a signal input designed for 1 Vp-p, and a control input designed for 0-5 V dc; that is, the two inputs are not symmetrical and the control input will have a limited bandwidth.
By contrast, in what is generally considered to be a true analog multiplier, the two signal inputs have identical characteristics. Applications specific to a true analog multiplier are those where both inputs are signals, for example in a frequency mixer or an analog circuit to implement a discrete Fourier transform. Due to the precision required for the device to be accurate and linear over the input range a true analog multiplier is generally a much more expensive part than a voltage-controlled amplifier.
A four-quadrant multiplier is one where inputs and outputs may swing positive and negative. Many multipliers only work in 2 quadrants (one input may only have one polarity), or single quadrant (inputs and outputs have only one polarity, usually all positive).
Analog multiplie |
https://en.wikipedia.org/wiki/Rhino%20%28JavaScript%20engine%29 | Rhino is a JavaScript engine written fully in Java and managed by the Mozilla Foundation as open source software. It is separate from the SpiderMonkey engine, which is also developed by Mozilla, but written in C++ and used in Mozilla Firefox.
History
The Rhino project was started at Netscape in 1997. At the time, Netscape was planning to produce a version of Netscape Navigator written fully in Java and so it needed an implementation of JavaScript written in Java. When Netscape stopped work on Javagator, as it was called, the Rhino project was finished as a JavaScript engine. Since then, a couple of major companies (including Sun Microsystems) have licensed Rhino for use in their products and paid Netscape to do so, allowing work to continue on it.
Originally, Rhino compiled all JavaScript code to Java bytecode in generated Java class files. This produced the best performance, often beating the C++ implementation of JavaScript run with just-in-time compilation (JIT), but suffered from two faults. First, compiling time was long since generating bytecode and loading the generated classes was a resource-intensive process. Also, the implementation effectively leaked memory since most Java virtual machines (JVM) didn't collect unused classes or the strings that are interned as a result of loading a class file. (This has changed in later versions of Java.)
As a result, in the fall of 1998, Rhino added an interpretive mode. The classfile generation code was moved to an optional, dynamically loaded package. Compiling is faster and when scripts are no longer in use they can be collected like any other Java object.
Rhino was released to Mozilla Foundation in April 1998. Originally Rhino classfile generation had been held back from release. However the licensors of Rhino have now agreed to release all of Rhino as open source, including class file generation. Since its release to open source, Rhino has found a variety of uses and an increasing number of people have contribu |
https://en.wikipedia.org/wiki/Glen%20Canyon%20Dam | Glen Canyon Dam is a concrete arch-gravity dam in the southwestern United States, located on the Colorado River in northern Arizona, near the town of Page. The dam was built by the Bureau of Reclamation (USBR) from 1956 to 1966 and forms Lake Powell, one of the largest man-made reservoirs in the U.S. with a capacity of more than . The dam is named for Glen Canyon, a series of deep sandstone gorges now flooded by the reservoir; Lake Powell is named for John Wesley Powell, who in 1869 led the first expedition to traverse the Colorado River's Grand Canyon by boat.
A dam in Glen Canyon was studied as early as 1924, but these plans were initially dropped in favor of the Hoover Dam (completed in 1936) which was located in the Black Canyon. By the 1950s, due to rapid population growth in the seven U.S. and two Mexican states comprising the Colorado River Basin, the Bureau of Reclamation deemed the construction of additional reservoirs necessary. The Glen Canyon Dam remains a central issue for modern environmentalist movements. Beginning in the late 1990s, the Sierra Club and other organizations renewed the call to dismantle the dam and drain Lake Powell in Lower Glen Canyon. Glen Canyon and Lake Powell are managed by the Department of the Interior within Glen Canyon National Recreation Area.
Since first filling to capacity in 1980, Lake Powell water levels have fluctuated greatly depending on water demand and annual runoff. The operation of Glen Canyon Dam helps ensure an equitable distribution of water between the states of the Upper Colorado River Basin (Colorado, Wyoming, and most of New Mexico and Utah) and the Lower Basin (California, Nevada and most of Arizona). During years of drought, Glen Canyon guarantees a water delivery to the Lower Basin states, without the need for rationing in the Upper Basin. In wet years, it captures extra runoff for future use. The dam is also a major source of hydroelectricity, averaging over 4 billion kilowatt hours per year. The lon |
https://en.wikipedia.org/wiki/New%20media | New media are communication technologies that enable or enhance interaction between users as well as interaction between users and content. In the middle of the 1990s, the phrase "new media" became widely used as part of a sales pitch for the influx of interactive CD-ROMs for entertainment and education. The new media technologies, sometimes known as Web 2.0, include a wide range of web-related communication tools such as blogs, wikis, online social networking, virtual worlds, and other social media platforms.
The phrase "new media" refers to computational media that share material online and through computers. New media inspire new ways of thinking about older media. Media do not replace one another in a clear, linear succession, instead evolving in a more complicated network of interconnected feedback loops . What is different about new media is how they specifically refashion traditional media and how older media refashion themselves to meet the challenges of new media.
Unless they contain technologies that enable digital generative or interactive processes, broadcast television programs, feature films, magazines, and books are not considered to be new media.
History
In the 1950s, connections between computing and radical art began to grow stronger. It was not until the 1980s that Alan Kay and his co-workers at Xerox PARC began to give the computability of a personal computer to the individual, rather than have a big organization be in charge of this. In the late 1980s and early 1990s, however, we seem to witness a different kind of parallel relationship between social changes and computer design. Although causally unrelated, conceptually, it makes sense that the Cold War and the design of the Web took place at exactly the same time.
Writers and philosophers such as Marshall McLuhan were instrumental in the development of media theory during this period which is now famous declaration in Understanding Media: The Extensions of Man, that "the medium is the mess |
https://en.wikipedia.org/wiki/B%C3%BCchi%20automaton | In computer science and automata theory, a deterministic Büchi automaton is a theoretical machine which either accepts or rejects infinite inputs. Such a machine has a set of states and a transition function, which determines which state the machine should move to from its current state when it reads the next input character. Some states are accepting states and one state is the start state. The machine accepts an input if and only if it will pass through an accepting state infinitely many times as it reads the input.
A non-deterministic Büchi automaton, later referred to just as a Büchi automaton, has a transition function which may have multiple outputs, leading to many possible paths for the same input; it accepts an infinite input if and only if some possible path is accepting. Deterministic and non-deterministic Büchi automata generalize deterministic finite automata and nondeterministic finite automata to infinite inputs. Each are types of ω-automata. Büchi automata recognize the ω-regular languages, the infinite word version of regular languages. They are named after the Swiss mathematician Julius Richard Büchi, who invented them in 1962.
Büchi automata are often used in model checking as an automata-theoretic version of a formula in linear temporal logic.
Formal definition
Formally, a deterministic Büchi automaton is a tuple A = (Q,Σ,δ,q0,F) that consists of the following components:
Q is a finite set. The elements of Q are called the states of A.
Σ is a finite set called the alphabet of A.
δ: Q × Σ → Q is a function, called the transition function of A.
q0 is an element of Q, called the initial state of A.
F⊆Q is the acceptance condition. A accepts exactly those runs in which at least one of the infinitely often occurring states is in F.
In a (non-deterministic) Büchi automaton, the transition function δ is replaced with a transition relation Δ that returns a set of states, and the single initial state q0 is replaced by a set I of initial states. |
https://en.wikipedia.org/wiki/Asymmetry | Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property of both physical and abstract systems and it may be displayed in precise terms or in more aesthetic terms. The absence of or violation of symmetry that are either expected or desired can have important consequences for a system.
In organisms
Due to how cells divide in organisms, asymmetry in organisms is fairly usual in at least one dimension, with biological symmetry also being common in at least one dimension.
Louis Pasteur proposed that biological molecules are asymmetric because the cosmic [i.e. physical] forces that preside over their formation are themselves asymmetric. While at his time, and even now, the symmetry of physical processes are highlighted, it is known that there are fundamental physical asymmetries, starting with time.
Asymmetry in biology
Asymmetry is an important and widespread trait, having evolved numerous times in many organisms and at many levels of organisation (ranging from individual cells, through organs, to entire body-shapes). Benefits of asymmetry sometimes have to do with improved spatial arrangements, such as the left human lung being smaller, and having one fewer lobes than the right lung to make room for the asymmetrical heart. In other examples, division of function between the right and left half may have been beneficial and has driven the asymmetry to become stronger. Such an explanation is usually given for mammal hand or paw preference (handedness), an asymmetry in skill development in mammals. Training the neural pathways in a skill with one hand (or paw) may take less effort than doing the same with both hands.
Nature also provides several examples of handedness in traits that are usually symmetric. The following are examples of animals with obvious left-right asymmetries:
Most snails, because of torsion during development, show remarkable as |
https://en.wikipedia.org/wiki/Chemosynthesis | In biochemistry, chemosynthesis is the biological conversion of one or more carbon-containing molecules (usually carbon dioxide or methane) and nutrients into organic matter using the oxidation of inorganic compounds (e.g., hydrogen gas, hydrogen sulfide) or ferrous ions as a source of energy, rather than sunlight, as in photosynthesis. Chemoautotrophs, organisms that obtain carbon from carbon dioxide through chemosynthesis, are phylogenetically diverse. Groups that include conspicuous or biogeochemically important taxa include the sulfur-oxidizing Gammaproteobacteria, the Campylobacterota, the Aquificota, the methanogenic archaea, and the neutrophilic iron-oxidizing bacteria.
Many microorganisms in dark regions of the oceans use chemosynthesis to produce biomass from single-carbon molecules. Two categories can be distinguished. In the rare sites where hydrogen molecules (H2) are available, the energy available from the reaction between CO2 and H2 (leading to production of methane, CH4) can be large enough to drive the production of biomass. Alternatively, in most oceanic environments, energy for chemosynthesis derives from reactions in which substances such as hydrogen sulfide or ammonia are oxidized. This may occur with or without the presence of oxygen.
Many chemosynthetic microorganisms are consumed by other organisms in the ocean, and symbiotic associations between chemosynthesizers and respiring heterotrophs are quite common. Large populations of animals can be supported by chemosynthetic secondary production at hydrothermal vents, methane clathrates, cold seeps, whale falls, and isolated cave water.
It has been hypothesized that anaerobic chemosynthesis may support life below the surface of Mars, Jupiter's moon Europa, and other planets. Chemosynthesis may have also been the first type of metabolism that evolved on Earth, leading the way for cellular respiration and photosynthesis to develop later.
Hydrogen sulfide chemosynthesis process
Giant tube worms |
https://en.wikipedia.org/wiki/Intuitionistic%20type%20theory | Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics.
Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematician and philosopher, who first published it in 1972. There are multiple versions of the type theory: Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, shown to be inconsistent by Girard's paradox, gave way to predicative versions. However, all versions keep the core design of constructive logic using dependent types.
Design
Martin-Löf designed the type theory on the principles of mathematical constructivism. Constructivism requires any existence proof to contain a "witness". So, any proof of "there exists a prime greater than 1000" must identify a specific number that is both prime and greater than 1000. Intuitionistic type theory accomplished this design goal by internalizing the BHK interpretation. An interesting consequence is that proofs become mathematical objects that can be examined, compared, and manipulated.
Intuitionistic type theory's type constructors were built to follow a one-to-one correspondence with logical connectives. For example, the logical connective called implication () corresponds to the type of a function (). This correspondence is called the Curry–Howard isomorphism. Previous type theories had also followed this isomorphism, but Martin-Löf's was the first to extend it to predicate logic by introducing dependent types.
Type theory
Intuitionistic type theory has 3 finite types, which are then composed using 5 different type constructors. Unlike set theories, type theories are not built on top of a logic like Frege's. So, each feature of the type theory does double duty as a feature of both math and logic.
If you are unfamiliar with type theory and know set theory, a quick summary is: Types contain terms just like sets contain elements. |
https://en.wikipedia.org/wiki/Jonathan%20Schaeffer | Jonathan Herbert Schaeffer (born 1957) is a Canadian researcher and professor at the University of Alberta and the former Canada Research Chair in Artificial Intelligence.
He led the team that wrote Chinook, the world's strongest American checkers player, after some relatively good results in writing computer chess programs. He is involved in the University of Alberta GAMES group developing computer poker systems. Schaeffer is also a member of the research group that created Polaris, a program designed to play the Texas Hold'em variant of poker. He is a Founder of Onlea, which produces online learning experiences.
Early life
Born in Toronto, Ontario, he received a Bachelor of Science degree in 1979 from the University of Toronto. He received a Master of Mathematics degree in 1980 and a Ph.D. in 1986 from the University of Waterloo. Schaeffer reached national master strength in chess while in his early 20s, but has played little competitive chess since that time.
Draughts: Chinook
Chinook is the first computer program to win the world champion title in a competition against humans. In 1990 it won the right to play in the human World Championship by being second to Marion Tinsley in the US Nationals. At first the American Checkers Federation and English Draughts Association were against the participation of a computer in a human championship. When Tinsley resigned his title in protest, the ACF and EDA created the new title Man vs. Machine World Championship, and competition proceeded. Tinsley won with four wins to Chinook's two.
In a rematch, Chinook was declared the Man-Machine World Champion in checkers in 1994 in a match against Marion Tinsley after six drawn games, and Tinsley's withdrawal due to pancreatic cancer. While Chinook became the world champion, it had never defeated the best checkers player of all time, Tinsley, who was significantly superior to even his closest peer.
The championship continued with Chinook defending its title against Don Laffert |
https://en.wikipedia.org/wiki/System%207 | System 7, codenamed "Big Bang", and later (as of version 7.6) also known as Mac OS 7, is a graphical user interface-based operating system for Macintosh computers and is part of the classic Mac OS series of operating systems. It was introduced on May 13, 1991, by Apple Computer It succeeded System 6, and was the main Macintosh operating system until it was succeeded by Mac OS 8 in 1997. Current for more than six years, System 7 was the longest-lived major version series of the classic Macintosh operating system (to date, only Mac OS X had a longer lifespan). Features added with the System 7 release included virtual memory, personal file sharing, QuickTime, QuickDraw 3D, and an improved user interface.
With the release of version 7.6 in 1997, Apple officially renamed the operating system "Mac OS", a name that had first appeared on System 7.5.1's boot screen. System 7 was developed for Macs that used the Motorola 680x0 line of processors, but was ported to the PowerPC after Apple adopted the new processor in 1994 with the introduction of the Power Macintosh.
Development
The development of the Macintosh system software up to System 6 followed a fairly smooth progression with the addition of new features and relatively small changes and upgrades over time. Major additions were fairly limited. Some perspective on the scope of the changes can be seen by examining the official system documentation, Inside Macintosh. This initially shipped in three volumes, adding another to describe the changes introduced with the Mac Plus, and another for the Mac II and Mac SE.
These limited changes meant that the original Macintosh system remained largely as it was when initially introduced. That is, the machine was geared towards a single user and task running on a floppy disk based machine of extremely limited RAM. However, many of the assumptions of this model were no longer appropriate. Most notable among these was the single-tasking model, the replacement of which had first been |
https://en.wikipedia.org/wiki/List%20of%20differential%20geometry%20topics | This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics.
Differential geometry of curves and surfaces
Differential geometry of curves
List of curves topics
Frenet–Serret formulas
Curves in differential geometry
Line element
Curvature
Radius of curvature
Osculating circle
Curve
Fenchel's theorem
Differential geometry of surfaces
Theorema egregium
Gauss–Bonnet theorem
First fundamental form
Second fundamental form
Gauss–Codazzi–Mainardi equations
Dupin indicatrix
Asymptotic curve
Curvature
Principal curvatures
Mean curvature
Gauss curvature
Elliptic point
Types of surfaces
Minimal surface
Ruled surface
Conical surface
Developable surface
Nadirashvili surface
Foundations
Calculus on manifolds
See also multivariable calculus, list of multivariable calculus topics
Manifold
Differentiable manifold
Smooth manifold
Banach manifold
Fréchet manifold
Tensor analysis
Tangent vector
Tangent space
Tangent bundle
Cotangent space
Cotangent bundle
Tensor
Tensor bundle
Vector field
Tensor field
Differential form
Exterior derivative
Lie derivative
pullback (differential geometry)
pushforward (differential)
jet (mathematics)
Contact (mathematics)
jet bundle
Frobenius theorem (differential topology)
Integral curve
Differential topology
Diffeomorphism
Large diffeomorphism
Orientability
characteristic class
Chern class
Pontrjagin class
spin structure
differentiable map
submersion
immersion
Embedding
Whitney embedding theorem
Critical value
Sard's theorem
Saddle point
Morse theory
Lie derivative
Hairy ball theorem
Poincaré–Hopf theorem
Stokes' theorem
De Rham cohomology
Sphere eversion
Frobenius theorem (differential topology)
Distribution (differential geometry)
integral curve
foliation
integrability conditions for differential systems
Fiber bundles
Fiber bundle
Principal bundle
Frame bundle
Hopf bundle
Associated bundle
Vector bundle
Tangent bundle
Cotangent bundle
Line bundle
Jet bundle
Fundamental st |
https://en.wikipedia.org/wiki/Texas%20Instruments%20SN76489 | The SN76489 Digital Complex Sound Generator (DCSG) is a TTL-compatible programmable sound generator chip from Texas Instruments. Its main application was the generation of music and sound effects in game consoles, arcade games and home computers (such as the TI-99/4A, BBC Micro, ColecoVision, IBM PCjr, Tomy Tutor, and Tandy 1000), competing with the similar General Instrument AY-3-8910.
It contains:
3 square wave tone generators
A wide range of frequencies
16 different volume levels
1 noise generator
2 types (white noise and periodic)
3 different frequencies
16 different volume levels
Overview
The SN76489 was originally designed to be used in the TI-99/4 computer, where it was first called the TMS9919 and later SN94624, and had a 500 kHz max clock input rate. Later, when it was sold outside of TI, it was renamed the SN76489, and a divide-by-8 was added to its clock input, increasing the max clock input rate to , to facilitate sharing a crystal for both NTSC colorburst and clocking the sound chip. A version of the chip without the divide-by-8 input was also sold outside of TI as the SN76494, which has a max clock input rate.
Tone Generators
The frequency of the square waves produced by the tone generators on each channel is derived from two factors:
The speed of the external clock
A 10-bit value provided in a control register for that channel (called N)
Each channel's frequency is arrived at by dividing the external clock by 4 (or 32 depending on the chip variant), and then dividing the result by N. Thus the overall divider range is from 4 to 4096 (or 32 to 32768). At maximum clock input rate, this gives a frequency range of 122 Hz to 125 kHz. Or typically 108 Hz to 111.6 kHz, with an NTSC colorburst (~3.58 MHz) clock input – a range from roughly A2 (two octaves below middle A) to 5–6 times the generally accepted limits of human audio perception.
Noise Generator
The pseudorandom noise feedback is generated from an XNOR of bits 12 and 13 for feedback, |
https://en.wikipedia.org/wiki/Envelope%20detector | An envelope detector (sometimes called a peak detector) is an electronic circuit that takes a (relatively) high-frequency amplitude modulated signal as input and provides an output, which is the demodulated envelope of the original signal.
Circuit operation
The capacitor in the circuit above stores charge on the rising edge and releases it slowly through the resistor when the input signal amplitude falls. The diode in series rectifies the incoming signal, allowing current flow only when the positive input terminal is at a higher potential than the negative input terminal.
General considerations
Most practical envelope detectors use either half-wave or full-wave rectification of the signal to convert the AC audio input into a pulsed DC signal. Filtering is then used to smooth the final result. This filtering is rarely perfect and some "ripple" is likely to remain on the envelope follower output, particularly for low frequency inputs such as notes from a bass instrument. Reducing the filter cutoff frequency gives a smoother output, but decreases the high frequency response. Therefore, practical designs must reach a compromise.
Definition of the envelope
Any AM or FM signal can be written in the following form
In the case of AM, φ(t) (the phase component of the signal) is constant and can be ignored. In AM, the carrier frequency is also constant. Thus, all the information in the AM signal is in R(t). R(t) is called the envelope of the signal. Hence an AM signal is given by the function
with m(t) representing the original audio frequency message, C the carrier amplitude and R(t) equal to C + m(t). So, if the envelope of the AM signal can be extracted, the original message can be recovered.
In the case of FM, the transmitted has a constant envelope R(t) = R and can be ignored.
However, many FM receivers measure the envelope anyway for received signal strength indication.
Diode detector
The simplest form of envelope detector is the diode detector which is |
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