`` If you can firmly make the good knight sure to pleasure our Corporation '', Sturley wrote, `` besides that ordinary allowance for your diet you shall have 20 for recompence ''.

If you hold property for the production of rents or royalties you subtract, in computing Adjusted Gross Income, ordinary and necessary expenses and certain other deductions attributable to the property.

:: If patients fail to experience the healing power of Christian Science, and think they can be benefited by certain ordinary physical methods of medical treatment, then the Mind-physician should give up such cases, and leave invalids free to resort to whatever other systems they fancy will afford relief.

If light consisted strictly of ordinary or classical particles, and these particles were fired in a straight line through a slit and allowed to strike a screen on the other side, we would expect to see a pattern corresponding to the size and shape of the slit.

If a bishop, especially one acting as an ordinary – a head of a diocese or archdiocese – is to be ordained, three bishops must usually co-consecrate him with one bishop, usually an archbishop or the bishop of the place, being the chief consecrating prelate.

If no other jurisdiction has been established, recourse shall be to the ordinary courts.

If adults could effectively be baptised through a desire for the sacrament when prevented from actually receiving it, some speculated that perhaps sacramentally unbaptised infants too might be saved by some waterless equivalent of ordinary baptism when prevented.

If unskilled labourers had it in their power to compete with skilled, by merely taking the trouble of learning the trade, the difference of wages might not exceed what would compensate them for that trouble, at the ordinary rate at which labour is remunerated.

If anyone thus speaks, that the Roman Pontiff has only the office of inspection or direction, but not the full and supreme power of jurisdiction over the universal Church, not only in things which pertain to faith and morals, but also in those which pertain to the discipline and government of the Church spread over the whole world ; or, that he possesses only the more important parts, but not the whole plenitude of this supreme power ; or that this power of his is not ordinary and immediate, or over the churches altogether and individually, and over the pastors and the faithful altogether and individually: let him be anathema.

If the president then vetoed the new legislation, Congress could override the veto by its ordinary means, a two-thirds vote in both houses.

If requested to do so by a petition signed by a majority of the membership of the Seanad, and one-third of the membership of the Dáil, the President may, after consultation with the Council of State, decline to sign into law a bill ( other than a bill to amend the constitution ) he / she considers to be of great " national importance " until it has been approved by either the people in an ordinary referendum or the Dáil reassembling after a general election, held within eight months.

If the revolutionary government must be more active in its march and more free in his movements than an ordinary government, is it for that less fair and legitimate?

If the text is displayed correctly, there should be no visual difference from ordinary text.

If wormholes are possible, then ordinary subluminal methods of communication could be sent through them to achieve superluminal transmission speeds.

If the accused appeared, the accuser stated the case, and the investigation proceeded by the examination of witnesses as in an ordinary court of law.

If the issuer is liquidated, they carry the right to receive interest and / or a return of capital in priority to ordinary shareholders.

" If the firm " actually copied code from a GPL'd program, such a suit would be a perfectly ordinary assertion of copyright, which most private firms would defend if the shoe were on the other foot.

* Suppose & B is equivalent to & D. If we acquire new information A and then acquire further new information B, and update all probabilities each time, the updated probabilities will be the same as if we had first acquired new information C and then acquired further new information D. In view of the fact that multiplication of probabilities can be taken to be ordinary multiplication of real numbers, this becomes a functional equation

If ordinary double feasts ( referred to also as lesser doubles ) occurred with feasts of a higher rank, they could be simplified, except the octave days of some feasts and the feasts of the Doctors of the Church, which were transferred.

The latter example leads to a generalization of modules over rings: If C is a preadditive category, then Mod ( C ) := Add ( C, Ab ) is called the module category over C. When C is the one-object preadditive category corresponding to the ring R, this reduces to the ordinary category of ( left ) R-modules.

If such commercially-available items are not at hand, ordinary water bottles are sometimes used.

If an ordinary switch is used to control the winding current, this can cause sparks at the terminals of the switch.

If hypothetical mirror matter exists, Zurab Silagadze proposes that demons can be envisaged, " which can act like perpetuum mobiles of the second kind: extract heat energy from only one reservoir, use it to do work and be isolated from the rest of ordinary world.

If the torus carries the ordinary Riemannian metric from its embedding in R < sup > 3 </ sup >, then the inside has negative Gaussian curvature, the outside has positive Gaussian curvature, and the total curvature is indeed 0.

If the market discount is less than the de minimis amount, the discount on the bond is generally treated as a capital gain upon disposition or redemption rather than as ordinary income.

If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

If we are discussing differentiable complex-valued functions, then Af and V are complex vector spaces, and Af may be any complex numbers.

If X and Y are Banach spaces over the same ground field K, the set of all continuous K-linear maps T: X → Y is denoted by B ( X, Y ).

If a system is composed of two subsystems described in V and W respectively, then the Hilbert space of the entire system is the tensor product of the two spaces.

* 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 f: X → Y morphism of pointed spaces, then every loop in X with base point x < sub > 0 </ sub > can be composed with f to yield a loop in Y with base point y < sub > 0 </ sub >.

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 first-countability axiom were imposed on the topological spaces in question, the two above conditions would be equivalent.

If M is an open subset of R < sup > n </ sup >, then M is a C < sup >∞</ sup > manifold in a natural manner ( take the charts to be the identity maps ), and the tangent spaces are all naturally identified with R < sup > n </ sup >.

If there are multiple page or segment tables, there are multiple virtual address spaces and concurrent applications with separate page tables redirect to different real addresses.

If X and Y are topological vector spaces, the space L ( X, Y ) of continuous linear operators f: X → Y may carry a variety of different possible topologies.

* If ( X, Σ ) and ( Y, Τ ) are Borel spaces, a measurable function f: ( X, Σ ) → ( Y, Τ ) is also called a Borel function.

Let V and W be vector spaces ( or more generally modules ) and let T be a linear map from V to W. If 0 < sub > W </ sub > is the zero vector of W, then the kernel of T is the preimage of the zero subspace

Punchcutting: If the glyph design includes enclosed spaces ( counters ) then a counterpunch is made.

If ƒ: A → B is a homomorphism between two algebraic structures ( such as homomorphism of groups, or a linear map between vector spaces ), then the relation ≡ defined by

If the topology of the topological vector space is induced by a metric which is homogenous, as in the case of a metric induced by the norm of normed vector spaces, then the two definitions coincide.

If the player answers the question correctly, their turn continues ; if the player's piece was on one of the category headquarters spaces, they collect a wedge of the same color, which fits into their playing piece.

* Suppose that is a sequence of Lipschitz continuous mappings between two metric spaces, and that all have Lipschitz constant bounded by some K. If ƒ < sub > n </ sub > converges to a mapping ƒ uniformly, then ƒ is also Lipschitz, with Lipschitz constant bounded by the same K. In particular, this implies that the set of real-valued functions on a compact metric space with a particular bound for the Lipschitz constant is a closed and convex subset of the Banach space of continuous functions.

If we further consider both spaces with the sup norm the extension map becomes an isometry.

If V and W are vector spaces, the null space ( or kernel ) of a linear transformation T: V → W is the set of all vectors in V that map to zero:

# If the filename contains characters not allowed in an 8. 3 name ( including space which was disallowed by convention though not by the APIs ) or either part is too long, the name is stripped of invalid characters such as spaces and extra periods.

If the string inserted is too short, then it is padded out, usually with spaces or null characters.

If, for example, the 43 letters long ( ignoring the spaces ) description " not divisible by any integer other than 1 and itself " were assigned to the number 43, then this would be true.

If virtual memory is used, processes execute the same physical page of RAM, mapped into the different address spaces of each process.