|
Periodicity (other)
Periodicity or periodic may refer to: Mathematics * Bott periodicity theorem, addresses Bott periodicity: a modulo-8 recurrence relation in the homotopy groups of classical groups * Periodic function, a function whose output contains values that repeat periodically * Periodic mapping Physical sciences * Periodic table of chemical elements * Periodic trends, relative characteristics of chemical elements observed * Redshift periodicity, astronomical term for redshift quantization Other uses * Fokker periodicity blocks, which mathematically relate musical intervals * Periodic acid, a compound of iodine * Principle of periodicity, a concept in generally accepted accounting principles * Quasiperiodicity, property of a system that displays irregular periodicity See also * Aperiodic (other) * Cycle (other) * Frequency (other) * Period (other) * Periodical * Seasonality In time series data, seasonality is the presence of variations that occur a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bott Periodicity Theorem
In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by , which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres. Bott periodicity can be formulated in numerous ways, with the periodicity in question always appearing as a period-2 phenomenon, with respect to dimension, for the theory associated to the unitary group. See for example topological K-theory. There are corresponding period-8 phenomena for the matching theories, ( real) KO-theory and (quaternionic) KSp-theory, associated to the real orthogonal group and the quaternionic symplectic group, respectively. The J-homomorphism is a homomorphism from the homotopy groups of orthogonal groups to stable homotopy groups of spheres, which causes the period 8 Bott periodicity to be visible in the stable homotopy groups of spheres. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Function
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals of 2\pi radians, are periodic functions. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function that is not periodic is called aperiodic. Definition A function is said to be periodic if, for some nonzero constant , it is the case that :f(x+P) = f(x) for all values of in the domain. A nonzero constant for which this is the case is called a period of the function. If there exists a least positive constant with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental period. A function with period will repeat on intervals of length , and these intervals are sometimes also referred to as periods of the function. Geometrically, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Mapping
In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time. Iterated functions Given a mapping ''f'' from a set ''X'' into itself, :f: X \to X, a point ''x'' in ''X'' is called periodic point if there exists an ''n'' so that :\ f_n(x) = x where f_n is the ''n''th iterate of ''f''. The smallest positive integer ''n'' satisfying the above is called the ''prime period'' or ''least period'' of the point ''x''. If every point in ''X'' is a periodic point with the same period ''n'', then ''f'' is called ''periodic'' with period ''n'' (this is not to be confused with the notion of a periodic function). If there exist distinct ''n'' and ''m'' such that :f_n(x) = f_m(x) then ''x'' is called a preperiodic point. All periodic points are preperiodic. If ''f'' is a diffeomorphism of a differentiable manifold, so that the derivative f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Table
The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of chemistry. It is a graphic formulation of the periodic law, which states that the properties of the chemical elements exhibit an approximate periodic dependence on their atomic numbers. The table is divided into four roughly rectangular areas called blocks. The rows of the table are called periods, and the columns are called groups. Elements from the same group of the periodic table show similar chemical characteristics. Trends run through the periodic table, with nonmetallic character (keeping their own electrons) increasing from left to right across a period, and from down to up across a group, and metallic character (surrendering electrons to other atoms) increasing in the opposite direction. The underlying reason for these trends is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Trends
Periodic trends are specific patterns that are present in the periodic table that illustrate different aspects of a certain element. They were discovered by the Russian chemist Dmitri Mendeleev in the year 1863. Major periodic trends include atomic radius, ionization energy, electron affinity, electronegativity, valency and metallic character. These trends exist because of the similar electronic configuration of the elements within their respective groups or periods and because of the periodic nature of the elements. These give a qualitative assessment of the properties of each element. Summary Atomic radius The atomic radius is the distance from the atomic nucleus to the outermost electron orbital in an atom. In general, the atomic radius decreases as we move from left to right in a period, and it increases when we go down a group. This is because in periods, the valence electrons are in the same outermost shell. The atomic number increases within the same period wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Redshift Quantization
Redshift quantization, also referred to as redshift periodicity, redshift discretization, preferred redshifts and redshift-magnitude bands, is the hypothesis that the redshifts of cosmologically distant objects (in particular galaxies and quasars) tend to cluster around multiples of some particular value. In standard inflationary cosmological models, the redshift of cosmological bodies is ascribed to the expansion of the universe, with greater redshift indicating greater cosmic distance from the Earth (see Hubble's Law). This is referred to as cosmological redshift. Ruling out errors in measurement or analysis, quantized redshift of cosmological objects would either indicate that they are physically arranged in a quantized pattern around the Earth, or that there is an unknown mechanism for redshift unrelated to cosmic expansion, referred to as "intrinsic redshift" or "non-cosmological redshift". In 1973, astronomer William G. Tifft was the first to report evidence of this patter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fokker Periodicity Blocks
Fokker periodicity blocks are a concept in tuning theory used to mathematically relate musical intervals in just intonation to those in equal tuning. They are named after Adriaan Daniël Fokker. These are included as the primary subset of what Erv Wilson refers to as constant structures, where "each interval occurs always subtended by the same number of steps". The basic idea of Fokker's periodicity blocks is to represent just ratios as points on a lattice, and to find vectors in the lattice which represent very small intervals, known as commas. Treating pitches separated by a comma as equivalent "folds" the lattice, effectively reducing its dimension by one; mathematically, this corresponds to finding the quotient group of the original lattice by the sublattice generated by the commas. For an ''n''-dimensional lattice, identifying ''n'' linearly independent commas reduces the dimension of the lattice to zero, meaning that the number of pitches in the lattice is finite; m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Acid
Periodic acid ( ) is the highest oxoacid of iodine, in which the iodine exists in oxidation state +7. Like all periodates it can exist in two forms: orthoperiodic acid, with the chemical formula , and metaperiodic acid, which has the formula . Periodic acid was discovered by Heinrich Gustav Magnus and C. F. Ammermüller in 1833. Synthesis Modern industrial scale production involves the oxidation of a solution of sodium iodate under alkaline conditions, either electrochemically on a anode, or by treatment with chlorine: : (counter ions omitted for clarity) ''E''° = -1.6 V : Orthoperiodic acid can be dehydrated to give metaperiodic acid by heating to 100 °C under reduced pressure. : Further heating to around 150 °C gives iodine pentoxide () rather than the expected anhydride ''diiodine heptoxide'' (). Metaperiodic acid can also be prepared from various orthoperiodates by treatment with dilute nitric acid. Properties Orthoperiodic acid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generally Accepted Accounting Principles
Publicly traded companies typically are subject to rigorous standards. Small and midsized businesses often follow more simplified standards, plus any specific disclosures required by their specific lenders and shareholders. Some firms operate on the cash method of accounting which can often be simple and straight forward. Larger firms most often operate on an accrual basis. Accrual basis is one of the fundamental accounting assumptions and if it is followed by the company while preparing the Financial statements then no further disclosure is required. Accounting standards prescribe in considerable detail what accruals must be made, how the financial statements are to be presented, and what additional disclosures are required. Some important elements that accounting standards cover include: identifying the exact entity which is reporting, discussing any "going concern" questions, specifying monetary units, and reporting time frames. Limitations The notable limitations of accounting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasiperiodicity
Quasiperiodicity is the property of a system that displays irregular periodicity. Periodic behavior is defined as recurring at regular intervals, such as "every 24 hours". Quasiperiodic behavior is a pattern of recurrence with a component of unpredictability that does not lend itself to precise measurement. It is different from the mathematical concept of an almost periodic function, which has increasing regularity over multiple periods. The mathematical definition of quasiperiodic function is a completely different concept; the two should not be confused. Climatology Climate oscillations that appear to follow a regular pattern but which do not have a fixed period are called ''quasiperiodic''. Within a dynamical system such as the ocean-atmosphere oscillations may occur regularly, when they are forced by a regular external forcing: for example, the familiar winter-summer cycle is forced by variations in sunlight from the (very close to perfectly) periodic motion of the earth aro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aperiodic (other)
Aperiodic means non-periodic. Typically it refers to aperiodic function. Aperiodic may also refer to: * Aperiodic finite state automaton * Aperiodic frequency * Aperiodic graph * Aperiodic semigroup In mathematics, an aperiodic semigroup is a semigroup ''S'' such that every element ''x'' ∈ ''S'' is aperiodic, that is, for each ''x'' there exists a positive integer ''n'' such that ''x'n'' = ''x'n'' + 1. An aperiodic monoid is an aperi ... * Aperiodic set of prototiles * Aperiodic tiling See also * Periodic (other) * Strange attractor, a region reached asymptotically by a dynamic system showing no periodic repeating pattern {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cycle (other)
Cycle, cycles, or cyclic may refer to: Anthropology and social sciences * Cyclic history, a theory of history * Cyclical theory, a theory of American political history associated with Arthur Schlesinger, Sr. * Social cycle, various cycles in social sciences ** Business cycle, the downward and upward movement of gross domestic product (GDP) around its ostensible, long-term growth trend Arts, entertainment, and media Films * ''Cycle'' (2008 film), a Malayalam film * ''Cycle'' (2017 film), a Marathi film Literature * ''Cycle'' (magazine), an American motorcycling enthusiast magazine * Literary cycle, a group of stories focused on common figures Music Musical terminology * Cycle (music), a set of musical pieces that belong together ** Cyclic form, a technique of construction involving multiple sections or movements ** Interval cycle, a collection of pitch classes generated from a sequence of the same interval class **Song cycle, individually complete songs designed to be perf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
