On the basis that all citizens of the state are entitled to benefit equally in the development of its resources, plans for the provision of essential services ( such as water ) will be based on need regardless of arbitrary political boundaries, within the framework of the state plan.

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.

On being criticized for his arbitrary behavior -- he answered: `` I have to make decisions.

Scholars made numbered sets of as many things as possible in Nature, or assigned arbitrary numbers to individual things, in a fashion that seems to the modern scientific mind as downright nonsensical, and philosophical ideas based upon all this tended to stifle speculative thought in China for many centuries.

But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

: Precise instructions ( in language understood by " the computer ") for a fast, efficient, " good " process that specifies the " moves " of " the computer " ( machine or human, equipped with the necessary internally contained information and capabilities ) to find, decode, and then process arbitrary input integers / symbols m and n, symbols + and =

The axiom of choice can be seen as asserting the generalization of this property, already evident for finite collections, to arbitrary collections.

Caracalla left for the frontier, where for the rest of his short reign he was known for his unpredictable and arbitrary operations launched by surprise after a pretext of peace negotiations.

It provided basic services for requesting responses to arbitrary commands and performing out-of-band status queries.

Model theory generalizes the notion of algebraic extension to arbitrary theories: an embedding of M into N is called an algebraic extension if for every x in N there is a formula p with parameters in M, such that p ( x ) is true and the set

He fundamentally defined his arbitrary orientation for the cell as being that in which the internal current would run parallel to and in the same direction as a hypothetical magnetizing current loop around the local line of latitude which would induce a magnetic dipole field oriented like the Earth's.

In the wake of the 11 July dismissal of Jacques Necker, the people of Paris, fearful that they and their representatives would be attacked by the royal military, and seeking to gain ammunition and gunpowder for the general populace, stormed the Bastille, a fortress-prison in Paris which had often held people jailed on the basis of lettres de cachet, arbitrary royal indictments that could not be appealed.

In what follows, c < sub > 1 </ sub > and c < sub > 2 </ sub > denote arbitrary complex numbers, c * denotes the complex conjugate of c, A and B denote arbitrary linear operators, and these properties are to hold for any choice of bras and kets.

BDB stores arbitrary key / data pairs as byte arrays, and supports multiple data items for a single key.

Despite several army mutinies and increasing civic concern both at his erratic style and arbitrary, corrupt method of governing he was re-elected for another 6-year term in September 1999.

Explicitly, this means that for every arbitrary collection

Explicitly, this means that for every arbitrary collection

In general, for an arbitrary metal M, the reaction is as follows:

`` The commercials have just been for money, there hasn't been any real incentive for me to do them, but in Underwater Western Eye I'd have a chance to act.

I am not making a clinical judgment here, for such personal tragedies are real and are commonplace in the analyst's consulting room, but literature makes a different claim upon our sympathies than tragedy in life.

`` I've served as a counsel for the U.N. for some years, specializing particularly in real estate matters or other problems that the regular U.N. legal staff might not be equipped to handle.

Thus, many a creativity-oriented aspirant for a career in architecture, drama, or journalism, resigns himself to a real estate business ; ;

they merely do their best to make it real for others ''.

After a dinner party for which she had come down to New York, Mrs. Lewis and Casanova arrived to see them off, and Elinor Wylie made tart observations that indicated that Lewis had been less discreet than he had promised to be about the real nature of their separation.

The only real problem is to devise a plan whereby the owners of the above-water land can develop their property without the public losing its underwater land and the right to its development for public use and enjoyment.

`` A better position for negotiations is the real point of this speech.

When he was in the war, he was in Law or Supplies or something like that, and an old buddy of his told me he would come down on Sundays to the Pentagon and read the citations for medals -- just like the one we sent in for Trig -- and go away with a real glow.

The bank which held the mortgage on the old church declared that the interest was considerably in arrears, and the real estate people said flatly that the land across the river was being held for an eventual development for white working people who were coming in, and that none would be sold to colored folk.

Only afterwards did an act like that become meaningless, so that he would puzzle over it for days, whereas at the time it had seemed quite real.

Is this for real??

The O'Dwyers were real religious people except for Kate.

Under this program, property sales specialists in the Small Business Administration regional offices help small business concerns to locate Federal property for sale and insure that small firms have the opportunity to bid competitively for surplus personal and real property and certain natural resources, including timber from the national forests.

It is this sort of experience that makes the concept of high fidelity of real musical significance for the home music listener.

He appeared in the hopples about November 14, was treated for worms on the 18th, the latter date being the first time he struck a real pace.

`` That House & Home Round Table was the real starting point for today's revolution in materials handling '', says Clarence Thompson, long chairman of the Lumber Dealers' Research Council.

We devote a chapter to the binomial distribution not only because it is a mathematical model for an enormous variety of real life phenomena, but also because it has important properties that recur in many other probability models.

Another use of roleplaying for evaluation illustrates how this procedure can be used in real life situations without special equipment or special assistants during the daily course of work.

I see no real prospects for an all-Negro school population.

Because the responsibility for resolving the issue lay with the President, rather than with his doctors, nothing raises more surely for us the difficulties simple goodness faces in dealing with complex moral problems under political pressure.

Is the Oedipus complex, the clinical syndrome, material for a tragedy??

I am suggesting that a case-history approach to the Oedipus complex is a blind alley for a storyteller.

Our data indicate that these students of today do basically accept the existing institutions of the society, and, in the face of the realities of complex and large-scale economic and political problems, make a wary and ambivalent delegation of trust to those who occupy positions of legitimized responsibility for coping with such collective concerns.

Moreover, on complex projects, design work must be completed and orders for machinery and equipment placed months or even years before construction can commence.

More importantly, several of the more advanced of the less developed countries have found through experience that they must plan their own complex investment programs for at least 5 years forward and tentatively for considerably more than that if they are to be sure that the various interdependent activities involved are all to take place in the proper sequence.

But there is still the sometimes complex problem of helping campers choose the best equipment for their individual needs.

In considering roleplaying for analysis we enter a more complex area, since we are now no longer dealing with a simple over-all decision but rather with the examination and evaluation of many elements seen in dynamic functioning.

This behavior is more `` veridical '' -- or true -- than other testing behavior for some types of evaluation, and so can give quick and accurate estimates of complex functioning.

Such mannerisms would be less worthy of remark, were it not that in Great Expectations, as in no other of Dickens' novels, hands serve as a leitmotif of plot and theme -- a kind of unifying symbol or natural metaphor for the book's complex of human interrelationships and the values and attitudes that motivate them.

After all, the average American as he lies and waits for the enemy in Korea or as she scans the newspaper in some vain hope of personal contact with the front is unconcerned that his or her plight is the result of a complex of personal, economic and governmental actions far beyond the normal citizen's comprehension and control.

The vast industrial interests caught up in the Selden suit, as well as the complex character of the automotive art, encouraged both sides to exploit `` every possible chance '' for or against the patent, said Parker.

C & O president Walter J. Tuohy was summoned back for cross-examination by New York Central attorneys before examiner John Bradford who is hearing the complex case.

The President had set for himself the task, which he believed vital, of awakening the U. S. and its allies to the hard and complex effort necessary to shift that balance.

( 2 ) Realtors realize, of course, that they are involved in an increasingly complex legal and political system that is opening up opportunities for leverage on their relation to clients as well as opportunities for evasion of their responsibility for racial discrimination in housing.

ANOVA is difficult to teach, particularly for complex experiments, with split-plot designs being notorious.

for summarizing complex high-dimensional inferences ..."

More complex assistive technology devices have been developed over time, and as a result, sports for people with disabilities " have changed from being a clinical therapeutic tool to an increasingly competition-oriented activity ".

It is the belief of Old Babylonian scholars such as Carruccio that Old Babylonians " may have used the abacus for the operations of addition and subtraction ; however, this primitive device proved difficult to use for more complex calculations ".

Natural language expressions of algorithms tend to be verbose and ambiguous, and are rarely used for complex or technical algorithms.