Any convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.

Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.

Any Lie group G can be decomposed into discrete, simple, and abelian groups in a canonical way as follows.

Any particular Boolean function can be represented by one and only one full disjunctive normal form, one of the two canonical forms.

Any two meromorphic 1-forms will yield linearly equivalent divisors, so the canonical divisor is uniquely determined up to linear equivalence ( hence " the " canonical divisor ).

Any ξ ∈ gives rise to a canonical vertical vector field X < sub > ξ </ sub > by taking the derivative of the right action of the 1-parameter subgroup of H associated to ξ.

Any sheaf has a canonical embedding into the flasque sheaf of all possibly discontinuous sections of the étalé space, and by repeating this we can find a canonical flasque resolution for any sheaf.

The canonical ring and therefore likewise the Kodaira dimension is a birational invariant: Any birational map between smooth compact complex manifolds induces an isomorphism between the respective canonical rings.

* Any base change of a finite morphism is finite, i. e. if is another ( arbitrary ) morphism, then the canonical morphism is finite.

Any conformal map on a portion of Euclidean space of dimension greater than 2 can be composed from three types of transformation: a homothetic transformation, an isometry, and a special conformal transformation.

Any such stress-energy pseudotensor can be made to vanish locally by a coordinate transformation.

* Any non-degenerate affine transformation takes a parallelogram to another parallelogram.

: Any linear transformation f: V → A from V to an algebra A over K can be uniquely extended to an algebra homomorphism from T ( V ) to A as indicated by the following commutative diagram:

Any transformation of the plane leaving this pattern invariant can be decomposed into a translation, ( x, y ) → ( n + x, y ), optionally followed by a reflection in either the horizontal axis, ( x, y ) → ( x ,− y ), or the vertical axis, ( x, y ) → (− x, y ), provided that this axis is chosen through or midway between two dots, or a rotation by 180 °, ( x, y ) → (− x ,− y ) ( ditto ).

Any waveform can be disassembled into its spectral components by Fourier analysis or Fourier transformation.

Any segments of the enterprise that are not service-oriented can also be documented in order to consider transformation requirements if a service needs to communicate with the business processes automated by such segments.

Any transformation semigroup can be turned into a semigroup action by the following construction.

Any two triplets obeying these relationships must be related by a linear transformation ; they represent utility indices differing only by scale and origin.

Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space.

* Any outside interference involving a person not involved in the match striking or holding a wrestler.

Any writer on Norman affairs attributed to venom any sudden death, except those involving violence.

Any change to the composition of the Cabinet involving more than one appointment is customarily referred to as a reshuffle ; a routine reshuffle normally occurs every summer.

Any process involving virtual particles admits a schematic representation known as a Feynman diagram, which facilitates the understanding of calculations.

Any statistical analysis involving multiple hypotheses is subject to inflation of the type I error rate if appropriate measures are not taken.

Any calculations involving the height of a building based on the height of a floor will take this into account.

Any complete group variety ( variety here meaning reduced and geometrically irreducible separated scheme of finite type over a field ) is automatically commutative, by an argument involving the action of conjugation on jet spaces of the identity.

Any dispute involving parties like licensor, licensee, service provider and consumers are resolved by TDSAT.

Over the next ten years, the term was used by other researchers to describe broader chemical interactions between organisms, and by 1996 the International Homeopathy Society defined allelopathy as " Any process involving secondary metabolites produced by plants, algae, bacteria and fungi that influences the growth and development of agriculture and biological systems.

* Any of the one-year offenses while operating a CMV for hazardous materials or second offense of any of the one-year or three-year offenses, or using a CMV to commit a felony involving manufacturing, distributing, or dispensing controlled substances: life suspension.

Any scenes involving drugs, you can rest assured I hated filming them.

* Any magic trick involving a rope

: Any offense involving the use of the mails … is a continuing offense and … may be … prosecuted in any district from, through, or into which such … mail matter … moves.

OR " Any transaction involving exchange of goods or service for something of equal value.

Any successful model of GRB emission must explain the physical process for generating gamma-ray emission that matches the observed diversity of light-curves, spectra, and other characteristics.

Any sort of saturated molecule can be the starting point for generating isolobal fragments.

Generation has been delicensed and captive generation freely permitted. i. e. Any generating company may establish, operate and maintain a generating station without obtaining a licence under this Act with only exception that it should comply with the technical standards relating to connectivity with the grid referred to in clause ( b ) of section 73.

Any function itself defines an equivalence relation on according to which if and only if.

Any cryptographic hash function, such as MD5 or SHA-1, may be used in the calculation of an HMAC ; the resulting MAC algorithm is termed HMAC-MD5 or HMAC-SHA1 accordingly.

Any compression algorithm can be viewed as a function that maps sequences of units ( normally octets ) into other sequences of the same units.

The blitter's block copying mode takes zero to three data sources in memory, called A, B and C, performs a programmable boolean function on the data sources and writes the result to a destination area, D. Any of these four areas can overlap.

Any real-valued differentiable function, H, on a symplectic manifold can serve as an energy function or Hamiltonian.

Any non-constant algebraic function of a single variable yields a transcendental value when applied to a transcendental argument.

Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.

Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and / or its surrounding.

Any poles on the imaginary axis have real strictly positive residues, and similarly at any zeros on the imaginary axis, the function has a real strictly positive derivative.

Any building requires a certain amount of internal infrastructure to function, which includes such elements like heating / cooling, power and telecommunications, water and wastewater etc.

Any such function is called a Urysohn function for A and B.

Any function can be restricted to a subset of its domain.

Any such K is referred to as a Lipschitz constant for the function ƒ.

Any impairment which limits the physical function of limbs or fine or gross motor ability is a physical disability.

* Any polynomial ( real or complex ) is an analytic function.

Any Taylor series for this function converges not only for x close enough to x < sub > 0 </ sub > ( as in the definition ) but for all values of x ( real or complex ).

* Any analytic function is smooth, that is, infinitely differentiable.

Any real analytic function on some open set on the real line can be extended to a complex analytic function on some open set of the complex plane.

" Any sequence of numbers that may be modeled by a mathematical function can be considered a pattern.

Any such satisficing problem can be formulated as an ( equivalent ) optimization problem using the Indicator function of the satisficing requirements as an objective function.