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Multiplication Sign
The multiplication sign, also known as the times sign or the dimension sign, is the symbol , used in mathematics to denote the multiplication operation and its resulting product. While similar to a lowercase X (), the form is properly a four-fold rotationally symmetric saltire. History The earliest known use of the symbol to represent multiplication appears in an anonymous appendix to the 1618 edition of John Napier's . This appendix has been attributed to William Oughtred, who used the same symbol in his 1631 algebra text, , stating:"Multiplication of species .e. unknownsconnects both proposed magnitudes with the symbol 'in' or : or ordinarily without the symbol if the magnitudes be denoted with one letter." Two earlier uses of a notation have been identified, but do not stand critical examination. Uses In mathematics, the symbol × has a number of uses, including * Multiplication of two numbers, where it is read as "times" or "multiplied by" * Cross product of two vect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary information encoded in genes, which can be transmitted to future generations. Another major theme is evolution, which explains the unity and diversity of life. Energy processing is also important to life as it allows organisms to move, grow, and reproduce. Finally, all organisms are able to regulate their own internal environments. Biologists are able to study life at multiple levels of organization, from the molecular biology of a cell to the anatomy and physiology of plants and animals, and evolution of populations.Based on definition from: Hence, there are multiple subdisciplines within biology, each defined by the nature of their research questions and the tools that they use. Like other scientists, biologists use the sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Full Stop
The full stop (Commonwealth English), period (North American English), or full point , is a punctuation mark. It is used for several purposes, most often to mark the end of a declarative sentence (as distinguished from a question or exclamation). This sentence-ending use, alone, defines the strictest sense of ''full stop''. Although ''full stop'' technically applies only when the mark is used to end a sentence, the distinction – drawn since at least 1897 – is not maintained by all modern style guides and dictionaries. The mark is also used, singly, to indicate omitted characters or, in a series, as an ellipsis (), to indicate omitted words. It may be placed after an initial letter used to stand for a name or after each individual letter in an initialism or acronym (e.g., "U.S.A."). However, the use of full stops after letters in an initialism or acronym is declining, and many of these without punctuation have become accepted norms (e.g., "UK" and "NATO"). This trend has pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dot Operator
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a ''product''. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''. Both numbers can be referred to as ''factors''. :a\times b = \underbrace_ For example, 4 multiplied by 3, often written as 3 \times 4 and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: :3 \times 4 = 4 + 4 + 4 = 12 Here, 3 (the ''multiplier'') and 4 (the ''multiplicand'') are the ''factors'', and 12 is the ''product''. One of the main properties of multiplication is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated between the Baltic and North seas to the north, and the Alps to the south; it covers an area of , with a population of almost 84 million within its 16 constituent states. Germany borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, and France, Luxembourg, Belgium, and the Netherlands to the west. The nation's capital and most populous city is Berlin and its financial centre is Frankfurt; the largest urban area is the Ruhr. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity. A region named Germania was documented before AD 100. In 962, the Kingdom of Germany formed the bulk of the Holy Roman Empire. During the 16th ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''algebra'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sign Function
In mathematics, the sign function or signum function (from '' signum'', Latin for "sign") is an odd mathematical function that extracts the sign of a real number. In mathematical expressions the sign function is often represented as . To avoid confusion with the sine function, this function is usually called the signum function. Definition The signum function of a real number is a piecewise function which is defined as follows: \sgn x :=\begin -1 & \text x 0. \end Properties Any real number can be expressed as the product of its absolute value and its sign function: x = , x, \sgn x. It follows that whenever is not equal to 0 we have \sgn x = \frac = \frac\,. Similarly, for ''any'' real number , , x, = x\sgn x. We can also ascertain that: \sgn x^n=(\sgn x)^n. The signum function is the derivative of the absolute value function, up to (but not including) the indeterminacy at zero. More formally, in integration theory it is a weak derivative, and in convex function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
APL (programming Language)
APL (named after the book ''A Programming Language'') is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the Array data type#Multi-dimensional arrays, multidimensional array. It uses a large range of APL syntax and symbols, special graphic symbols to represent most functions and operators, leading to very concise code. It has been an important influence on the development of concept modeling, spreadsheets, functional programming, and computer math packages. It has also inspired several other programming languages. History Mathematical notation A mathematical notation for manipulating arrays was developed by Kenneth E. Iverson, starting in 1957 at Harvard University. In 1960, he began work for IBM where he developed this notation with Adin Falkoff and published it in his book ''A Programming Language'' in 1962. The preface states its premise: This notation was used inside IBM for short research reports on computer systems, such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monad (functional Programming)
In functional programming, a monad is a software design pattern with a structure that combines program fragments (Function (computer programming), functions) and wraps their return values in a Type system, type with additional computation. In addition to defining a wrapping monadic type, monads define two Operator (computer programming), operators: one to wrap a value in the monad type, and another to compose together functions that output values of the monad type (these are known as monadic functions). General-purpose languages use monads to reduce boilerplate code needed for common operations (such as dealing with undefined values or fallible functions, or encapsulating bookkeeping code). Functional languages use monads to turn complicated sequences of functions into succinct pipelines that abstract away control flow, and side-effect (computer science), side-effects. Both the concept of a monad and the term originally come from category theory, where a monad is defined as a Func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calendar Date
A calendar date is a reference to a particular day represented within a calendar system. The calendar date allows the specific day to be identified. The number of days between two dates may be calculated. For example, "25 " is ten days after "15 ". The date of a particular event depends on the observed time zone. For example, the air attack on Pearl Harbor that began at 7:48 a.m. Hawaiian time on 7 December 1941 took place at 3:18 a.m. Japan Standard Time, 8 December in Japan. A particular day may be assigned a different nominal date according to the calendar used, so an identifying suffix may be needed where ambiguity may arise. The Gregorian calendar is the world's most widely used civil calendar, and is designated (in English) as AD or CE. Many cultures use religious or regnal calendars such as the Gregorian ( Western Christendom, AD), Hebrew calendar (Judaism, AM), the Hijri calendars ( Islam, AH), Julian calendar ( Eastern Christendom, AD) or any other o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Historian
A historian is a person who studies and writes about the past and is regarded as an authority on it. Historians are concerned with the continuous, methodical narrative and research of past events as relating to the human race; as well as the study of all history in time. Some historians are recognized by publications or training and experience.Herman, A. M. (1998). Occupational outlook handbook: 1998–99 edition. Indianapolis: JIST Works. Page 525. "Historian" became a professional occupation in the late nineteenth century as research universities were emerging in Germany and elsewhere. Objectivity During the ''Irving v Penguin Books and Lipstadt'' trial, people became aware that the court needed to identify what was an "objective historian" in the same vein as the reasonable person, and reminiscent of the standard traditionally used in English law of "the man on the Clapham omnibus". This was necessary so that there would be a legal benchmark to compare and contrast the scholar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crocosmia × Crocosmiiflora
''Crocosmia'' × ''crocosmiiflora'', montbretia, is a garden hybrid of '' C. aurea'' and '' C. pottsii'', first bred in 1880 in France by Victor Lemoine.Parnell, J. and Curtis, T. 2012. ''Webb's An Irish Flora.'' Cork University Press. The name "montbretia" is often found in horticultural literature.Everett, T.H., ed. ''Montbreitia'', In: ''New Illustrated Encyclopedia of Gardening'', Greystone Press, New York, 1960. pp. 1181-1182. Description ''Crocosmia'' × ''crocosmiiflora'' grows to 90 cm high with long sword-shaped leaves, shorter than the flowering stem and arising from the plant base, ribbed and up to 20mm wide. The base is a corm, a swollen underground stem lasting one year. The flowers are up to 5 cm long and coloured deep orange. Cultivation In the United States, ''Crocosmia'' × ''crocosmiiflora'' is considered suitable for planting in hardiness zones 5–9, but in more northerly locations it can be planted in the spring and the corms dug out in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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