If the heuristic can't find the correct setting, the variable is assigned randomly.

If one pursues this heuristic, one might expect the total number of ways to write a large even integer n as the sum of two odd primes to be roughly

If the antivirus software employs heuristic detection, success depends on achieving the right balance between false positives and false negatives.

If one accepts the validity of this sort of argumentation, then these arguments may serve alongside the Razor, and may perhaps be more conclusive, as a heuristic for selecting between competing, under-determined theories.

If the availability heuristic played a role in this, lying second would remain in jurors minds and they would most likely remember the witness lying over them telling the truth.

If the occurrence of a minimum in the absolute ( tangential ) velocity is used as a heuristic for segmentation, the pen-tip trajectory can be subdivided into segments corresponding to ballistic strokes.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).

If this limit exists, then it may be computed by taking the limit as h → 0 along the real axis or imaginary axis ; in either case it should give the same result.

If h is negative, then a + h is on the low part of the step, so the secant line from a to a + h is very steep, and as h tends to zero the slope tends to infinity.

If h is positive, then a + h is on the high part of the step, so the secant line from a to a + h has slope zero.

If K is a subset of ker ( f ) then there exists a unique homomorphism h: G / K → H such that f = h φ.

If G is a group and X is a set then a group action may be defined as a group homomorphism h from G to the symmetric group of X.

If the minibus exceeds 100 km / h, the beeping will turn into a sustained tone.

If a spatial extra dimension is of radius R, the invariant mass of such standing waves would be M < sub > n </ sub > = nh / Rc with n an integer, h being Planck's constant and c the speed of light.

If c, h, and e were all changed so that the values they have in metric ( or any other ) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our World.

If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

: If we are given h ( x )= g ( f < sub > 1 </ sub >( x ), ..., f < sub > m </ sub >( x ) )

⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.

If h has a fixed ( non-zero ) value instead of approaching zero, then the right-hand side of the above equation would be written

If ~ is a unary operation, then h (~ x ) = ~ h ( x ).

If * is a binary operation, then h ( x * y ) = h ( x ) * h ( y ).

If the norm of a Banach space satisfies this identity, the associated inner product which makes it into a Hilbert space is given by the polarization identity.

If is continuous in an open set Ω and the partial derivatives of ƒ with respect to x and y exist in Ω, and satisfies the Cauchy – Riemann equations throughout Ω, then ƒ is holomorphic ( and thus analytic ).

* If ƒ ( z ) is locally integrable in an open domain Ω ⊂ C, and satisfies the Cauchy – Riemann equations weakly, then ƒ agrees almost everywhere with an analytic function in Ω.

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: If A is a parent node of B then key ( A ) is ordered with respect to key ( B ) with the same ordering applying across the heap.

If the ranges of the morphisms of the inverse system of abelian groups ( A < sub > i </ sub >, f < sub > ij </ sub >) are stationary, that is, for every k there exists j ≥ k such that for all i ≥ j: one says that the system satisfies the Mittag-Leffler condition.

If a subspace satisfies a stronger condition that

If a model for a language moreover satisfies a particular sentence or theory ( set of sentences satisfying special conditions ), it is called a model of the sentence or theory.

If μ is not a positive measure, then N is μ-null if N is | μ |- null, where | μ | is the total variation of μ ; equivalently, if every measurable subset A of N satisfies μ ( A )

If the court satisfies itself that the defendant fully acknowledges the consequences of the plea agreement, and he / she was represented by the defense council, his / her will is expressed in full compliance with the legislative requirements without deception and coercion, also if there is enough body of doubtless evidence for the conviction and the agreement is reached on legitimate sentence-the court approves the plea agreement and renders guilty judgment.

If a function is harmonic ( that is, it satisfies Laplace's equation ) over a particular space, and is transformed via a conformal map to another space, the transformation is also harmonic.

If the string is stretched between two points where x = 0 and x = L and u denotes the amplitude of the displacement of the string, then u satisfies the one-dimensional wave equation in the region where 0 < x < L and t is unlimited.

If a delivery satisfies the criteria for both a No Ball and a Wide, the call and penalty of No Ball will take precedent.

If we now add another simultaneous equation to guarantee that we only perform this test when we are at a point that satisfies the

If the above integral is denoted by I ( b ), then the function I satisfies

In mathematics, and in particular linear algebra, a skew-symmetric ( or antisymmetric or antimetric ) matrix is a square matrix A whose transpose is also its negative ; that is, it satisfies the equation If the entry in the and is a < sub > ij </ sub >, i. e. then the skew symmetric condition is For example, the following matrix is skew-symmetric:

If is a basis, then the dual basis satisfies

If this trading strategy is followed, and any cash held is assumed to grow at the risk free rate r, then the total value V of this portfolio satisfies the SDE

* If H is a subgroup of G, the index of the normal core of H satisfies the following inequality:

If κ is measurable and p ∈ V < sub > κ </ sub > and M ( the ultrapower of V ) satisfies ψ ( κ, p ), then the set of α < κ such that V satisfies ψ ( α, p ) is stationary in κ ( actually a set of measure 1 ).

If the Ricci tensor satisfies the vacuum Einstein equation, then the manifold is an Einstein manifold, which have been extensively studied ( cf.

If we write in the form then the map satisfies

If a relief pitcher satisfies all of the criteria for a save, except he does not finish the game, he will often be credited with a hold ( which is not an officially recognized statistic by Major League Baseball ).

If is a fibration with fiber F, with the base B path-connected, and the fibration is orientable over a field K, then the Euler characteristic with coefficients in the field K satisfies the product property: