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If and constraints
If the media agency responsible for the authorized production allows material from fans, what is the limit before legal constraints from actors, music, and other considerations, come into play?
If the matrix is positive semidefinite matrix, then is a convex function: In this case the quadratic program has a global minimizer if there exists some feasible vector ( satisfying the constraints ) and if is bounded below on the feasible region.
If the constraints don't couple the variables too tightly, a relatively simple attack is to change the variables so that constraints are unconditionally satisfied.
If the person being questioned wouldn't necessarily consent to those constraints, the question is fallacious.
If there had been other constraints, triggers or cascades, every single change operation would have been checked in the same way as the above before the transaction was committed.
If grammars differ only by having different rankings of CON, then the set of possible human languages is determined by the constraints that exist.
If two or more constraints are active together, each constraint
If the dust disk is instead being generated from the outer debris disk, rather than from collisions in an asteroid belt, then no constraints on the planet's orbital eccentricity are needed to explain the dust distribution.
If there are no constraints, the solution is obviously a straight line between the points.
If we take basis vectors for V, those become non-commuting variables ( or indeterminants ) in T ( V ), subject to no constraints ( beyond associativity, the distributive law and K-linearity ).
If there are, say, m constraints then the zero in the north-west corner is an m × m block of zeroes, and there are m border rows at the top and m border columns at the left.
If vulcanoids are found not to exist, this would place different constraints on planet formation and suggest that other processes have been at work in the inner Solar System, such as planetary migration clearing out the area.
If there are n constraints holding n different expectation values constant, then the manifold is n-dimensional.
If the labels are all congruent rectangles, the corresponding 2-SAT instance can be shown to have only linearly many constraints, leading to near-linear time algorithms for finding a labeling.
If there is a unifying theme that runs through most of managerial economics, it is the attempt to optimize business decisions given the firm's objectives and given constraints imposed by scarcity, for example through the use of operations research, mathematical programming, game theory for strategic decisions, and other computational methods.
If we have more than n + 1 constraints ( n being the degree of the polynomial ), we can still run the polynomial curve through those constraints.
If humans escape these constraints, it is because in our case, listeners are primarily interested in mental states.
If the objective function is a ratio of a concave and a convex function ( in the maximization case ) and the constraints are convex, then the problem can be transformed to a convex optimization problem using fractional programming techniques.
If the person being questioned wouldn't necessarily consent to those constraints, the question is fallacious.
If no constraints are applied to the LSP then the routers simply send the
If a syntax error occurs or if any constraints are violated, the new row is not added to the table and an error returned instead.
If it is not possible to build a second antenna for the second transmitter due to space constraints, then the diplexer is used permanently.

If and linear
If the Af bond is linear then there are three reasonable positions for the hydrogen atoms: ( 1 ) The hydrogen atoms are centered and hence all lie on a sheet midway between the oxygen sheets ; ;
If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.
If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.
If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.
If there is a bounded linear operator from X onto Y, then Y is reflexive.
The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.
* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then
If these are linear with constant
If the resulting linear differential equations have constant coefficients one can take their Laplace transform to obtain a transfer function.
If we assume the controller C, the plant P, and the sensor F are linear and time-invariant ( i. e., elements of their transfer function C ( s ), P ( s ), and F ( s ) do not depend on time ), the systems above can be analysed using the Laplace transform on the variables.
If the function f is not linear ( i. e. its graph is not a straight line ), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.
If the matrix entries are real numbers, the matrix can be used to represent two linear mappings: one that maps the standard basis vectors to the rows of, and one that maps them to the columns of.
If λ < sub > 1 </ sub >, ..., λ < sub > ν </ sub > are the eigenvalues of J they will be resonant if one eigenvalue is an integer linear combination of two or more of the others.
If I told you my son's age, then there would no longer be two unknowns ( variables ), and the problem becomes a linear equation with just one variable, that can be solved as described above.
Likewise, a functor from G to the category of vector spaces, Vect < sub > K </ sub >, is a linear representation of G. In general, a functor G → C can be considered as an " action " of G on an object in the category C. If C is a group, then this action is a group homomorphism.
Tensor products: If C denotes the category of vector spaces over a fixed field, with linear maps as morphisms, then the tensor product defines a functor C × C → C which is covariant in both arguments.
If the object is a vector space we have a linear representation.
* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if is continuous and linear, then there exists an extension of φ which is also continuous and linear and which has the same norm as φ ( see Banach space for a discussion of the norm of a linear map ).
* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if z is an element of V not in the closure of U, then there exists a continuous linear map with ψ ( x ) = 0 for all x in U, ψ ( z ) = 1, and || ψ || = 1 / dist ( z, U ).
If the table size n is large enough, linear search will be faster than binary search, whose cost is O ( log n ).
If the list is stored as an ordered array, then binary search is almost always more efficient than linear search as with n > 8, say, unless there is some reason to suppose that most searches will be for the small elements near the start of the sorted list.

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