|
Flatness (other)
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 category theory See also * Flat (other) Flat or flats may refer to: Architecture * Flat (housing), an apartment in the United Kingdom, Ireland, Australia and other Commonwealth countries Arts and entertainment * Flat (music), a symbol () which denotes a lower pitch * Flat (soldier), a ... * Flattening {{disambig ... [...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-dimensional, 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 of the arts happened 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 reduction of ... [...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 out ... [...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. 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 or ground to achieve the required degree of flatness. High-definition metrology, such as digital holographic interferometry, of such a surface to confirm and ensure that the required degree of flatness has been achieved is a key step in such manufacturing processes. Flatness may be defined in terms of least squares fit to a plane ("statistical flatness"), worst-case or overall flatness (the distance between the two closest parallel planes within). Two parts that are flat to about 1 helium light band (HLB) can be "wrung" together, which means they will cling to each other when placed in contact. ... [...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 func ... [...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. 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 flat spectrum of a 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 "spiky". The spectral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flat (music)
In music, flat (Italian bemolle for "soft B") means "lower in pitch". Flat is the opposite of sharp, which is a raising of pitch. In musical notation, flat means "lower in pitch by one semitone (half step)", notated using the symbol which is derived from a stylised lowercase 'b'. For instance, the music below has a key signature with three flats (indicating either E major or C minor) and the note, D, has a flat accidental. : Under twelve-tone equal temperament, D for instance is enharmonically equivalent to C, and G is equivalent to F. In any other tuning system, such enharmonic equivalences in general do not exist. To allow extended just intonation, composer Ben Johnston uses a sharp as an accidental to indicate a note is raised 70.6 cents (ratio 25:24), and a flat to indicate a note is lowered 70.6 cents. In intonation, flat can also mean "slightly lower in pitch" (by some unspecified amount). If two simultaneous notes are slightly out-of-tune, the lower-pitche ... [...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, a flat module over a ring ''R'' is an ''R''- module ''M'' such that taking the 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''. See also flat morphism. Definition A module over a ring is ''flat'' if the following condition is satisfied: for every injective linear map \varphi: K \to L of -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 the inclusions of finitely generated ideals into . Equivalently, an -module is flat if the tensor product with is an exact functor; that is if, for every short exact sequence of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flat Morphism
In mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism ''f'' from a scheme ''X'' to a scheme ''Y'' is a morphism such that the induced map on every 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 ''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 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 the fiber product of schemes, applied to ''f'' and the inclu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flat (other)
Flat or flats may refer to: Architecture * Flat (housing), an apartment in the United Kingdom, Ireland, Australia 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 Bodies of water * Flat, a shallow wat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
