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Flatness (other)
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Flatness may refer to: * Flatness (art) * Flatness (cosmology) * Flatness (liquids) * Flatness (manufacturing), a geometrical tolerance required in certain manufacturing situations * Flatness (systems theory), a property of nonlinear dynamic systems * Spectral flatness * Flat intonation * Flat module in abstract algebra * Flat morphism in algebraic geometry See also * Flat (other) * Flattening Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flatness (art)
In art criticism of the 1960s and 1970s, flatness described the smoothness and absence of curvature or surface detail of a two-dimensional work of art. Views Critic Clement Greenberg believed that flatness, or two-dimensionality, was an essential and desirable quality in painting, a criterion which implies rejection of painterliness and impasto. The valorization of flatness led to a number of art movements, including minimalism and post-painterly abstractionism. Modernism in the arts appeared during the second half of the 19th century and extended into most of the 20th. This period of art is identified by art forms consisting of an image on a flat two-dimensional surface. This art evolution began in the 1860s and culminated 50 years later. By this time almost all three-dimensional works had been eliminated. This new approach to painting was to create a visual appearance of realism. Looking at a surface with only two dimensions our perception of depth is an illusion. The reducti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flatness (cosmology)
In cosmology, flatness is a property of a space without curvature. Such a space is called a "flat space" or Euclidean space. Whether the universe is “flat″ could determine its ultimate fate; whether it will expand forever, or ultimately collapse back into itself. The geometry of spacetime has been measured by the Wilkinson Microwave Anisotropy Probe (WMAP) to be nearly flat. According to the WMAP 5-year results and analysis, “WMAP determined that the universe is flat, from which it follows that the mean energy density In physics, energy density is the quotient between the amount of energy stored in a given system or contained in a given region of space and the volume of the system or region considered. Often only the ''useful'' or extractable energy is measure ... in the universe is equal to the critical density (within a 1% margin of error). This is equivalent to a mass density of 9.9 × 10−30 g/cm3, which is equivalent to only 5.9 protons per cubic meter.” The WMAP da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flatness (liquids)
In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in the Earth's atmosphere (gas mixture). Unlike liquids, gases cannot form a free surface on their own. Fluidized/ liquified solids, including slurries, granular materials, and powders may form a free surface. A liquid in a gravitational field will form a free surface if unconfined from above. Under mechanical equilibrium this free surface must be perpendicular to the forces acting on the liquid; if not there would be a force along the surface, and the liquid would flow in that direction. Thus, on the surface of the Earth, all free surfaces of liquids are horizontal unless disturbed (except near solids dipping into them, where surface tension distorts the surface in a region called the meniscus). In a free liquid that is not affected by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flatness (manufacturing)
In manufacturing and mechanical engineering, flatness is an important geometric condition for workpieces and tools. Flatness is the condition of a surface or derived median plane having all elements in one plane. Geometric dimensioning and tolerancing has provided geometrically defined, quantitative ways of defining flatness operationally. Flatness deviation may be defined in terms of least squares fit to a plane ("statistical flatness") or worst-case (the distance between the two closest parallel planes within). It can be specified for a given area and/or over an entire surface. In the manufacture of precision parts and assemblies, especially where parts will be required to be connected across a surface area in an air-tight or liquid-tight manner, flatness is a critical quality of the manufactured surfaces. Such surfaces are usually machined Machining is a manufacturing process where a desired shape or part is created using the controlled removal of material, most often m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flatness (systems Theory)
Flatness in systems theory is a system property that extends the notion of controllability from linear systems to nonlinear dynamical systems. A system that has the flatness property is called a ''flat system''. Flat systems have a (fictitious) ''flat output'', which can be used to explicitly express all states and inputs in terms of the flat output and a finite number of its derivatives. Definition A nonlinear system \dot(t) = \mathbf(\mathbf(t),\mathbf(t)), \quad \mathbf(0) = \mathbf_0, \quad \mathbf(t) \in R^m, \quad \mathbf(t) \in R^n, \text \frac = m is flat, if there exists an output \mathbf(t) = (y_1(t),...,y_m(t)) that satisfies the following conditions: * The signals y_i,i=1,...,m are representable as functions of the states x_i,i=1,...,n and inputs u_i,i=1,...,m and a finite number of derivatives with respect to time u_i^, k=1,...,\alpha_i: \mathbf = \Phi(\mathbf,\mathbf,\dot,...,\mathbf^). * The states x_i,i=1,...,n and inputs u_i,i=1,...,m are representable as fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Flatness
Spectral flatness or tonality coefficient, also known as Wiener entropy, is a measure used in digital signal processing to characterize an audio spectrum. Spectral flatness is typically measured in decibels, and provides a way to quantify how much a sound resembles a pure tone, as opposed to being noise-like. Interpretation The meaning of ''tonal'' in this context is in the sense of the amount of peaks or resonant structure in a power spectrum, as opposed to the flat spectrum of white noise. A high spectral flatness (approaching 1.0 for white noise) indicates that the spectrum has a similar amount of power in all spectral bands — this would sound similar to white noise, and the graph of the spectrum would appear relatively flat and smooth. A low spectral flatness (approaching 0.0 for a pure tone) indicates that the spectral power is concentrated in a relatively small number of bands — this would typically sound like a mixture of sine waves, and the spectrum would appear "spik ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flat (music)
In music, flat means lower in pitch. It may either be used in a general sense to mean any lowering of pitch, or to specifically refer to lowering pitch by a semitone. A flat is the opposite of a sharp () which indicates a raised pitch in the same way. The flat symbol () appears in key signatures to indicate which notes are flat throughout a section of music, and also in front of individual notes as an accidental, indicating that the note is flat until the next bar line. Pitch change The symbol is a stylised lowercase ''b'', derived from Italian ''be molle'' for "soft B" and German ''blatt'' for "planar, dull". It indicates that the note to which it is applied is played one semitone lower. In the standard modern tuning system, 12 tone equal temperament, this corresponds to 100 cents. In older tuning systems (from the 16th and 17th century), and in modern microtonal tunings, the difference in pitch indicated by a sharp or flat is normally smaller than the stan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intonation (music)
In music, intonation is the pitch accuracy of a musician or musical instrument. Intonation may be flat, sharp, or both, successively or simultaneously. In vocal music, intonation also signifies the singing of an opening phrase. Interval, melody, and harmony The lower or upper pitch of an interval may be sharp or flat, or both pitches of an interval. If the lower pitch is sharp or the upper pitch is flat, the interval may be said to be flat given that as a whole it is too narrow; while if the lower pitch is flat or the upper pitch is sharp, the interval may be said to be sharp given that as a whole it is too wide. Intervals are conventionally measured from the bottom, as such in an interval that is too wide the upper pitch is thus sharp. Intonation exists within the context of musical temperament, of which there are several types. However, the interval itself may be in tune, in relation to itself (i.e. both notes of the interval are in tune in relation to each other), but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flat Module
In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module (mathematics), module ''M'' over a ring (mathematics), ring ''R'' is ''flat'' if taking the tensor product of modules, tensor product over ''R'' with ''M'' preserves exact sequences. A module is faithfully flat if taking the tensor product with a sequence produces an exact sequence if and only if the original sequence is exact. Flatness was introduced by in his paper ''Géometrie Algébrique et Géométrie Analytique''. Definition A left module over a ring is ''flat'' if the following condition is satisfied: for every injective module homomorphism, linear map \varphi: K \to L of right -modules, the map : \varphi \otimes_R M: K \otimes_R M \to L \otimes_R M is also injective, where \varphi \otimes_R M is the map induced by k \otimes m \mapsto \varphi(k) \otimes m. For this definition, it is enough to restrict the injections \varphi to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flat Morphism
In mathematics, in particular in algebraic geometry, a flat morphism ''f'' from a scheme (mathematics), scheme ''X'' to a scheme ''Y'' is a morphism such that the induced map on every Stalk (sheaf), stalk is a flat map of rings, i.e., :f_P\colon \mathcal_ \to \mathcal_ is a flat map for all ''P'' in ''X''. A map of rings A\to B is called flat if it is a homomorphism that makes ''B'' a flat module, flat ''A''-module. A morphism of schemes is called faithfully flat if it is both surjective and flat. Two basic intuitions regarding flat morphisms are: *flatness is a generic property; and *the failure of flatness occurs on the jumping set of the morphism. The first of these comes from commutative algebra: subject to some finiteness condition on a morphism of schemes, finiteness conditions on ''f'', it can be shown that there is a non-empty open subscheme Y' of ''Y'', such that ''f'' restricted to Y' is a flat morphism (generic flatness). Here 'restriction' is interpreted by means of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flat (other)
Flat or flats may refer to: Architecture * Apartment, known as a flat in the United Kingdom, Ireland, and other Commonwealth countries Arts and entertainment * Flat (music), a symbol () which denotes a lower pitch * Flat (soldier), a two-dimensional toy soldier made of tin or plastic * Flat (theatre), a flat piece of theatrical scenery * Flat, a leading type of wordplay, as identified by the National Puzzlers' League * '' Flat!'' (2010), an Indian film * Flats (band), an English band * Flats (comics), the first stage in the comic coloring process Footwear * Flats, footwear which is not high-heeled * Ballet flats, derived from ballet shoes, for casual wear as well as dancing * Ballet shoes (also known as ballet slippers), often referred to as "flats" or "flat shoes" * Racing flats, lightweight shoes used primarily for running a race Geography Landforms * Flat (landform), a relatively level area within a region of greater relief * Mudflat, intertidal wetland with a substr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
