In any case, he had no intention of being caught asleep, so he carried his revolver in its holster on his hip and he took his Winchester with him and leaned it against the fence.

In any case but the last, such a course is sure to avenge itself upon the individual ; ;

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.

In any case I do not intend to let the present occasion pass without dealing more directly with the problem of implementing good intentions.

In any case, she told Thompson that she saw no reason why he might not see Katie again, `` now that this frank explanation has been made & no one can misunderstand ''.

But, here again, comparative benchmarks are lacking, and we do not know, in any case, what measure of profoundity and intensity to expect from healthy, young, secure and relatively inexperienced persons ; ;

In any case, who ever thought that New York is typical of anything??

`` Well, there's time, in any case.

And in any case, answers may clarify but they do not change anything.

unwarranted they were in any case for, as he stood facing the fille de chambre, his ears were assailed by new sounds from the interior of the shower room.

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 any assignment of an award, or any part thereof, which is made in writing and duly acknowledged and filed, after such award is certified to the Secretary of the Treasury, payment may, in the discretion of the Secretary of the Treasury, be made to the assignee, as his interest may appear.

Whenever the Secretary of the Treasury, or the Comptroller General of the United States, as the case may be, shall find that any person is entitled to any such payment, after such payment shall have been received by such person, it shall be an absolute bar to recovery by any other person against the United States, its officers, agents, or employees with respect to such payment.

In any case, our Peace Corps personnel should be offered as technician helpers in development projects of the U.N. and other international agencies.

In any case, there is no special milling or rabbeting required for the panels.

Continuing with the case in which **zg is a Af curve on a quadric Q, we first observe that the second regulus of Q consists precisely of the lines which join the two free intersections of **zg and the planes through any one of the multiple secants.

In any case, he refused to accept the implications of the analysis, that he needed to be made over.

In any case `` here in their judgment conditions require '' ( italics added ) they would `` form interim governmental authorities broadly representative of all democratic elements in the population and pledged to the earliest possible establishment through free elections of governments responsive to the will of the people ''.

That is, he did not claim in any of the four courts through which his case progressed that the jury charge had denied him any federal right.

In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

The term may be also used loosely or metaphorically to denote highly skilled people in any non -" art " activities, as well — law, medicine, mechanics, or mathematics, for example.

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.

In mathematics, depending on the context, a collection may refer to any of the following terms:

He did not want any of his sons to enter mathematics or science for " fear of lowering the family name ".

In mathematics, any number of cases supporting a conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample would immediately bring down the conjecture.

In mathematics, particularly theoretical computer science and mathematical logic, the computable numbers, also known as the recursive numbers or the computable reals, are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm.

Aside from these core elements, a civilization is often marked by any combination of a number of secondary elements, including a developed transportation system, writing, standardized measurement, currency, contractual and tort-based legal systems, characteristic art and architecture, mathematics, enhanced scientific understanding, metallurgy, political structures, and organized religion.

In mathematics, any vector space, V, has a corresponding dual vector space ( or just dual space for short ) consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors.

* Change of any variable quantity, in mathematics and the sciences ( More specifically, the difference operator.

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it.

This experimental fact is highly reproducible, and the mathematics of quantum mechanics ( see below ) allows us to predict the exact probability of an electron striking the screen at any particular point.

In mathematics and computational geometry, a Delaunay triangulation for a set P of points in a plane is a triangulation DT ( P ) such that no point in P is inside the circumcircle of any triangle in DT ( P ).

In mathematics, a directed set ( or a directed preorder or a filtered set ) is a nonempty set A together with a reflexive and transitive binary relation ≤ ( that is, a preorder ), with the additional property that every pair of elements has an upper bound: In other words, for any a and b in A there must exist a c in A with a ≤ c and b ≤ c.

Modern mathematics defines an " elliptic integral " as any function which can be expressed in the form

In mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.

In mathematics, more specifically algebraic topology, the fundamental group ( defined by Henri Poincaré in his article Analysis Situs, published in 1895 ) is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.

In mathematics, the Hausdorff dimension ( also known as the Hausdorff – Besicovitch dimension ) is an extended non-negative real number associated with any metric space.

Isomorphisms are studied in mathematics in order to extend insights from one phenomenon to others: if two objects are isomorphic, then any property that is preserved by an isomorphism and that is true of one of the objects, is also true of the other.

To acknowledge outstanding research contributions to mathematics, through the awarding of scientific prizes and to encourage and support other international mathematical activities, considered likely to contribute to the development of mathematical science in any of its aspects, whether pure, applied, or educational.

* Lambda indicates the wavelength of any wave, especially in physics, electronics engineering, and mathematics.

We may represent any given proposition with a letter which we call a propositional constant, analogous to representing a number by a letter in mathematics, for instance,.

Such an algorithm contradicts fundamental laws of mathematics because, if it existed, it could be applied repeatedly to losslessly reduce any file to length 0.