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case and when
At last, when I put it to him directly, the clerk was forced to admit that the delay in my case was unusual.
In any case, Miss Millay's sweet-throated bitterness, her variations on the theme that the world was not only well lost for love but even well lost for lost love, her constant and wonderfully tragic posture, so unlike that of Fitzgerald since it required no scenery or props, drew from the me that I was when I fell upon her verses an overwhelming yea.
American history should clinch the case when Congress is asked to approve.
But in the case of moving targets, and targets which have limited mobility, what will their location be when it is time to destroy them??
The reader will find it helpful to think of the special case when the primes are of degree 1, and even more particularly, to think of the proof of Theorem 10, a special case of this theorem.
This circumstance in the patient's case plus the fact that his tactual capacity remained basically in sound working order constitutes its exceptional value for the problem at hand since the evidence presented by the authors is overwhelming that, when the patient closed his eyes, he had absolutely no spatial ( that is, third-dimensional ) awareness whatsoever.
In the specific case of time diffusion, we must emphasize the significance of the earlier development of mistrust when it is combined with the inevitable time crisis experienced by most ( if not all ) adolescents in our society, and with the failure of the adolescent period to provide opportunities for developing trust.
You may think we didn't need Nancy and Jean, but you always get what you can when you can, and we had no guarantee that a fingerprint record on them couldn't be useful before we were through with this case.
A mistrial was declared in the case against the other seven when the jury was unable to agree on a verdict.
Then, when the case went to the jury, the judge excused one of the jurors, saying the juror had told him he had been accosted by masked men at his motel the night before the trial opened.
But one wishes, when the appetite is whetted, as it was in the case of the all-too-brief excerpt from the Blomdahl opera, that further opportunity would be provided both for hearing the works in their entirety and for a closer analytical look at the sense and nature of the compositions.
Pete came to meet us when we stepped out of the elevator on Seven -- he'd had a case of post-operative shock, but it was all taken care of now.
After an appeal is heard, the " mandate " is a formal notice of a decision by a court of appeal ; this notice is transmitted to the trial court and, when filed by the clerk of the trial court, constitutes the final judgment on the case, unless the appeal court has directed further proceedings in the trial court.
In their observations of medical ethics committees, Jonsen and Toulmin note that a consensus on particularly problematic moral cases often emerges when participants focus on the facts of the case, rather than on ideology or theory.
Chan's method for estimating the mean is numerically unstable when and both are large, because the numerical error in is not scaled down in the way that it is in the case.
This is the case when electron correlation is large.
At extremely rare intervals the thermometer has fallen below zero (- 18 ° C ), as was the case in the remarkable cold wave of the 12th-13 February 1899, when an absolute minimum of-17 ° F (- 29 ° C ) was registered at Valley Head.
The case was legally resolved on October 19, 1973 when U. S. District Judge Earl R. Larson held the ENIAC patent invalid, ruling that the ENIAC derived many basic ideas from the Atanasoff – Berry Computer.
This can have important consequences when dealing with issues such as consensual sadomasochistic sexual activity, the most notable case being the Operation Spanner case.
In any case, it existed by 635, when Gunzo appointed John of Grab bishop.
While these positions were well suited for most of his local constituency, this was not the case when he stepped outside that region politically.
Arbor Day reached its height of popularity on its 125th anniversary in 1997, when David J. Wright, noticed that a Nebraska nonprofit organization called the National Arbor Day Foundation had taken the name of the holiday and commercialized it for their own use as a trademark for their publication " Arbor Day ," so he countered their efforts, launched a website, and trademarked it for " public use celebrations " and defended the matter in a federal district court in the United States to ensure it was judged as property of the public domain, the case was settled in October 1999.
In February 2011, the Bombay High Court reaffirmed astrology's standing in India when it dismissed a case which had challenged its status as a science.

case and endomorphism
To see this consider the case of a supersingular elliptic curve over a finite field of characteristic p. The endomorphism ring of this is an order in a quaternion algebra over the rationals, and should act on the first cohomology group, which should be a 2 dimensional vector space over the coefficient field by analogy with the case of a complex elliptic curve.
When the field is not algebraically closed, the case where the endomorphism ring is as small as possible is of particular interest: A simple module over k-algebra is said to be absolutely simple if its endomorphism ring is isomorphic to k. This is in general stronger than being irreducible over the field k, and implies the module is irreducible even over the algebraic closure of k.
If p is congruent to 1 modulo 4, then the right hand side equals ω, so in this case the Frobenius endomorphism of Z /( p ) is the identity.

case and ring
If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.
Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.
For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies
* The reinforce: This portion of the piece is frequently divided into a first reinforce and a second reinforce, but in any case is marked as separate from the chase by the presence of a narrow circular reinforce ring or band at its foremost end.
Some authors also require the domain of the Euclidean function be the entire ring R ; this can always be accommodated by adding 1 to the values at all nonzero elements, and defining the function to be 0 at the zero element of R, but the result is somewhat awkward in the case of K. The definition is sometimes generalized by allowing the Euclidean function to take its values in any well-ordered set ; this weakening does not affect the most important implications of the Euclidean property.
In general, the surrounding graph must be systematically recolored to turn the ring's coloring into a good one, as was done in the case above where there were 4 neighbors ; for a general configuration with a larger ring, this requires more complex techniques.
If R is a Euclidean domain in which euclidean division is given algorithmically ( as is the case for instance when R = F where F is a field, or when R is the ring of Gaussian integers ), then greatest common divisors can be computed using a form of the Euclidean algorithm based on the division procedure.
Jewellery can also be symbolic of group membership, as in the case of the Christian crucifix or Jewish Star of David, or of status, as in the case of chains of office, or the Western practice of married people wearing a wedding ring.
* 1942 – The Federal Bureau of Investigation ( FBI ) convicts 33 members of a German spy ring headed by Fritz Joubert Duquesne in the largest espionage case in United States history — the Duquesne Spy Ring.
This meaning survived into the early nineteenth century: during a case heard in London in 1824 regarding the legal validity of a marriage ceremony consisting of nothing more than the groom placing a ring on the bride's finger before witnesses, a court official commented that the ceremony " amounted to nothing more than a broomstick marriage, which the parties had it in their power to dissolve at will.
Rather than excluding the special case n = 0, it is more useful to include ( which, as mentioned before, is isomorphic to the ring of integers ), for example when discussing the characteristic of a ring.
In the case of the latter, the ring is termed a heterocycle.
For a second ring, the label will be 2 ( naphthalene: c1cccc2c1cccc2 ( note the lower case for aromatic compounds )), and so on.
This ring seems to allow a closed time loop with stable wormholes when analyzed using semiclassical gravity, although without a full theory of quantum gravity it is uncertain whether the semiclassical approach is reliable in this case.
See, for example, the case of Meyer v. Mitnick, 625 N. W. 2d 136 ( Michigan, 2001 ), whose ruling found the following reasoning persuasive: " the so-called ' modern trend ' holds that because an engagement ring is an inherently conditional gift, once the engagement has been broken, the ring should be returned to the donor.

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