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case and P
But if this is the case, then an arbitrary pencil of lines having a point, P, of **zg as vertex is transformed into a ruled surface of order Af having Af generators concurrent at P.
In the first case the fixed elements within each pencil are the multiple secant and the line joining the vertex, P, to the intersection of **zg and the plane of the pencil which does not lie on the multiple secant.
Thus, if what is at issue is whether `` All S is P '', it is indifferent whether `` Some S is not P '' or `` No S is P '', since in either case the judgment in question is false.
The best presentation of the case for Ambrose is by P. A. Ballerini in his complete edition of that father's works.
* If the balance factor of R is-1, a single left rotation ( with P as the root ) is needed ( Right-Right case ).
The second is a left rotation with P as the root ( Right-Left case ).
* If the balance factor of L is + 1, a single right rotation ( with P as the root ) is needed ( Left-Left case ).
The second is a right rotation with P as the root ( Left-Right case ).
In addition to the balancing described above for insertions, if the balance factor for the tree is 2 and that of the left subtree is 0, a right rotation must be performed on P. The mirror of this case is also necessary.
In the case of parallelization, Amdahl's law states that if P is the proportion of a program that can be made parallel ( i. e., benefit from parallelization ), and ( 1 − P ) is the proportion that cannot be parallelized ( remains serial ), then the maximum speedup that can be achieved by using N processors is
P is thought to be a strict subset in both cases ( and demonstrably cannot be strict in one case but not the other ).
In the nonrelativistic case, electron degeneracy pressure gives rise to an equation of state of the form, where P is the pressure, is the mass density, and is a constant.
catenary is suspended at given points P < sub > 1 </ sub > and P < sub > 2 </ sub > and with given length s. The equation can be determined in this case as follows:
According to Bertrand Russell's Theory of Descriptions, the negation operator in a singular sentence can take either wide or narrow scope: we distinguish between " some S is not P " ( where negation takes " narrow scope ") and " it is not the case that ' some S is P '" ( where negation takes " wide scope ").
Therefore whenever ( G ) appears before another representative lowercase letter ( subject ), the statement would read, " It is always Going to be the case ..." and whenever ( F ) appears before another subject, the statement would read, " At sometime in the Future it will be the case ...." Whenever ( H ) appears before another subject, the statement would read, " It Has always been the case ..." and whenever ( P ) appears before another subject, the statement would read, " At sometime in the Past it has been the case ...."
Geometric arrangement for Fresnel's calculation Consider the case of a point source located at a point P < sub > 0 </ sub >, vibrating at a frequency f. The disturbance may be described by a complex variable U < sub > 0 </ sub > known as the complex amplitude.

case and is
This is the only case in modern history of a people of Britannic origin submitting without continued struggle to what they view as foreign domination.
he is very close to being a mental case.
What was only a vague suspicion in the case of Sherlock Holmes now appears as a direct accusation: the private eye is in danger of turning into his opposite.
In the case of social decay, form is displaced simply by the process of dissolution with no form at the terminus of the process.
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
This text from Dr. Huxley is sometimes used by enthusiasts to indicate that they have the permission of the scientists to press the case for a wonderful unfoldment of psychic powers in human beings.
There may be a case of this sort, but it is not one we wish to argue, here.
In any case but the last, such a course is sure to avenge itself upon the individual ; ;
The first thing to do is get her some money by a temporary but definite adjustment pending a final disposition of the case.
Such, he implies, is the case with his friend, who is not really a new convert himself but merely a favorer of new converts.
Although because of the important achievements of nineteenth century scholars in the field of textual criticism the advance is not so striking as it was in the case of archaeology and place-names, the editorial principles laid down by Stevenson in his great edition of Asser and in his Crawford Charters were a distinct improvement upon those of his predecessors and remain unimproved upon today.
That fact is very clearly illustrated in the case of the many present-day intellectuals who were Communists or near-Communists in their youth and are now so extremely conservative ( or reactionary, as many would say ) that they can define no important political conviction that does not seem so far from even a centrist position as to make the distinction between Mr. Nixon and Mr. Khrushchev for them hardly worth noting.
In any case, who ever thought that New York is typical of anything??
American history should clinch the case when Congress is asked to approve.
Senator Mundt's gross distortion of President Eisenhower's conversation into a denunciation of President Kennedy as too left wing, a statement Mr. Eisenhower declared to be entirely false, is another case in point.
The Connally amendment says that the United States, rather than the court, shall determine whether a matter is essentially within the domestic jurisdiction of the United States in a case before the World Court to which the United States is a party.
If the case is thus determined by us to be domestic, the court has no jurisdiction.
Besides the lack of an adequate ethical dimension to the Governor's case, one can ask seriously whether our lead over the Russians in quality and quantity of nuclear weapons is so slight as to make the tests absolutely necessary.
In my own case, I submit that such reasonable and fair exercise is woefully lacking.
In connection with any claim decided by the Commission pursuant to this Title in which an award is made, the Commission may, upon the written request of the claimant or any attorney heretofore or hereafter employed by such claimant, determine and apportion the just and reasonable attorney's fees for services rendered with respect to such claim, but the total amount of the fees so determined in any case shall not exceed 10 per centum of the total amount paid pursuant to the award.
in the case of a partnership or corporation, the existence of which has been terminated and on behalf of which an award is made, payment shall be made, except as provided in paragraphs ( 3 ) and ( 4 ), to the person or persons found by the Comptroller General of the United States to be entitled thereto ; ;

case and convolution
* In the case when the integral kernel depends only on the difference between its arguments, it becomes a convolution kernel, as in
An important special case is the circular convolution of and defined by where is a periodic summation:
In this case, a significant reduction in computational complexity can be obtained if the filter can be separated as the convolution of one 1D filter in the horizontal direction and one 1D filter in the vertical direction.
Therefore, for N even the convolution is cyclic, but in this case N is composite and one would normally use a more efficient FFT algorithm such as Cooley – Tukey.
In this case, the impulse response of the system is desired to be a close replica ( picture ) of that feature which is being searched for in the input plane field, so that a convolution of the impulse response ( an image of the desired feature ) against the input plane field will produce a bright spot at the feature location in the output plane.
The alert reader will note that the integral above tacitly assumes that the impulse response is NOT a function of the position ( x ', y ') of the impulse of light in the input plane ( if this were not the case, this type of convolution would not be possible ).
By the convolution theorem, the FT of an arbitrary transparency function-multiplied ( or truncated ) by an aperture function-is equal to the FT of the non-truncated transparency function convolved against the FT of the aperture function, which in this case becomes a type of " Greens function " or " impulse response function " in the spectral domain.
In the case where A = L < sup > 1 </ sup >( R < sub >+</ sub >), the L < sup > 1 </ sup >- convolution algebra of the real half-line, then Φ < sub > A </ sub > is homeomorphic to
The Hilbert transform was originally defined for periodic functions, or equivalently for functions on the circle, in which case it is given by convolution with the Hilbert kernel.
A distinction needs to be made between a random variable whose distribution function or density is the sum of a set of components ( i. e. a mixture distribution ) and a random variable whose value is the sum of the values of two or more underlying random variables, in which case the distribution is given by the convolution operator.
Averaging is a special case of discrete convolution.
In this case, due to symmetry, the time-reversed complex conjugate of is in fact, allowing us to call the impulse response of our matched filter convolution system.
The existence of a fundamental solution for any operator with constant coefficients the most important case, directly linked to the possibility of using convolution to solve an arbitrary right hand side was shown by Malgrange and Leon Ehrenpreis.
In that case, it can be readily verified that the convolution I * F with F ( x )=| x |/ 2 is a solution, i. e., has second derivative equal to I.
In the case of windowed sinc filters, the frequency response of the reconstruction filter can be understood in terms of the frequency response of the window, as the frequency response of a windowed filter is the convolution of the original response ( for sinc, a brick-wall ) with the frequency response of the window.
In the case of monochromatic neutron sources the convolution

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