Why should Congress even consider allowing such a sum for that which can give no protection??

Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

The measured force, H, in cutting removal of coatings from their substrates consequently can be seen to be the sum of that force required to cut the coating, Af, that due to the bluntness of the knife, Af, and that due to the friction between the bottom of the knife and the substrate, Af, or Af.

These theoretical relationships are more clearly illustrated in Fig. 7 and their sum can be seen to correlate in form with practical measurements made with the Hesiometer as illustrated in the first portion of Fig. 5 for the cutting mechanism.

In its simplest form, the assumption of unit-treatment additivity states that the observed response from experimental unit when receiving treatment can be written as the sum of the unit's response and the treatment-effect, that is

The number of degrees of freedom DF can be partitioned in a similar way: one of these components ( that for error ) specifies a chi-squared distribution which describes the associated sum of squares, while the same is true for " treatments " if there is no treatment effect.

The algorithm can be extended to handle unequal sample weights, replacing the simple counter n with the sum of weights seen so far.

The sum, difference, product and quotient of two algebraic numbers is again algebraic ( this fact can be demonstrated using the resultant ), and the algebraic numbers therefore form a field, sometimes denoted by A ( which may also denote the adele ring ) or < span style =" text-decoration: overline ;"> Q </ span >.

Then we can express the variables as the sum of the ( time averaged ) mean field () that varies in space and a small fluctuating field () that varies in space and time.

Therefore no complete system, i. e. including the electromagnetic modes, can have negative temperatures, since there is no highest energy state, so that the sum of the probabilities of the states would diverge for negative temperatures.

The notations can be combined: and mean that the sum or product is over all prime divisors of n.

John R. Freuler, the studio President, explained, " We can afford to pay Mr Chaplin this large sum annually because the public wants Chaplin and will pay for him.

Thus, the sum of all applied forces and torques ( with respect to the origin of the coordinate system ) in the body can be given by

In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

Contrast that to a P2P network, where its aggregated bandwidth actually increases as nodes are added, since the P2P network's overall bandwidth can be roughly computed as the sum of the bandwidths of every node in that network.

It can also be considered that Cogito ergo sum is needed before any living being can go further in life ".

However, a rotating frame can be treated as if it were an inertial frame so that Newton's laws can be used if so-called fictitious forces ( also known as inertial or pseudo-forces ) are included in the sum of external forces on an object.

Thus the analysis using Newton's laws of motion can proceed as if the reference frame was inertial, provided the fictitious force terms are included in the sum of external forces.

Equivalently, the determinant can be expressed as a sum of products of entries of the matrix where each product has n terms and the coefficient of each product is − 1 or 1 or 0 according to a given rule: it is a polynomial expression of the matrix entries.

When waves are added together, their sum is determined by the relative phases as well as the amplitudes of the individual waves so that the summed amplitude of the waves can have any value between zero and the sum of the individual amplitudes.

The sum can then be used as a net present value figure.

This sum spent for foreign economic aid, the peace corps, food for peace, or any other program to solve the problems of the underdeveloped countries would be an investment that would pay off in world peace, increased world trade, and prosperity for every country on the globe.

( Each State's unadjusted allotment for any fiscal year, which exceeds its minimum allotment described in item 13 below by a percentage greater than one and one-half times the percentage by which the sum being allotted exceeds $23,000,000, must be reduced by the amount of the excess.

For example, the monthly bill of a residential consumer might be the sum of a $1 customer charge, a $5 charge for 250 kilowatt-hours of energy at

and the latter is the total sum of all the numbers in the square, by which all the other numbers are overshadowed and in which they may be said to be absorbed.

All consider the observations to be the sum of a model ( fit ) and a

( The reason for the term " colloquially ", is that the sum or product of a " sequence " of cardinals cannot be defined without some aspect of the axiom of choice.

Similarly their sum of bad deeds will be mirrored in their next life.

Baseballs cost three dollars apiece, a hefty sum at the time, which in 1900 would be equal to $ today ; club owners were therefore reluctant to spend much money on new balls if not necessary.

To quote Anthony and Brackett: Moreover, because the element of water does not move, the sum of all three forces must be zero.

The collects of the Breviary are largely drawn from the Gelasian and other Sacramentaries, and they are used to sum up the dominant idea of the festival in connection with which they happen to be used.

The inputs provide the numbers to be added, and the outputs will contain the final sum.

The great utility in creating CPUs that deal with vectors of data lies in optimizing tasks that tend to require the same operation ( for example, a sum or a dot product ) to be performed on a large set of data.

Consider the subset sum problem, an example of a problem that is easy to verify, but whose answer may be difficult to compute.

He said that he would invest a six-figure sum and other members of his consortium would invest a similar amount.

This was to be based on utilitarian principles ; he said: " Every man has a right to that, the exclusive possession of which being awarded to him, a greater sum of benefit or pleasure will result than could have arisen from its being otherwise appropriated.

He wrote a consort piece with the punning title " Semper Dowland, semper dolens " ( always Dowland, always doleful ), which may be said to sum up much of his work.

In their USA Today Magazine article titled " Saluting Pittsburgh's Finest " Richard E. Vatz and Lee S. Weinberg said Clemente was " arguably the best in the history of the game " and stated that " understanding the magnitude of Roberto Clemente requires an appreciation of the gestalt of his presence, which was greater than the sum of his statistics ".

The game is won by the player who has said three numbers whose sum is 15.

That is, Zeno is often said to have argued that the sum of an infinite number of terms must itself be infinite – with the result that not only the time, but also the distance to be travelled, become infinite.

The elusive character of Gossip Girl also pays tribute to the writer, asserting " Camus said that life is the sum of our choices.

for the Grand prix des sciences mathématiques was the theory of the decomposition of integer numbers into a sum of five squares ; and that the attention of competitors was directed to the results announced without demonstration by Eisenstein, whereas nothing was said about his papers dealing with the same subject in the Proceedings of the Royal Society.

If a number equals the sum of its proper divisors, it is said to be a perfect number.

Numbers less than the sum of their proper divisors are said to be abundant, while numbers greater than that sum are said to be deficient.

Rather, God is said to be the sum of all natural processes that allow man to become self-fulfilled.

In mathematics, an infinite series of numbers is said to converge absolutely ( or to be absolutely convergent ) if the sum of the absolute value of the summand is finite of convergence.

Vigilius is said to have agreed to the plans of the intriguing empress who promised him the Papal See and a large sum of money ( 700 pounds of gold ).

In Acts 7: 16, it is said that " Their ( Jacob and his family ) bodies were brought back to Shechem and placed in the tomb that Abraham had bought from the sons of Hamor at Shechem for a certain sum of money.

" In 2007 Heather Robinson and the hospital reached a settlement for an undisclosed sum, which Robinson said she would split with her biological grandmother, Patricia Sylvester.

As a result it was ordered that the election of subscribing the said sum of ten thousand dollars to the capital stock of the said railroad company be submitted to the qualified voters of the Dutchville Township and that an election be held in the said township at the proper voting place therein on the 8th day of October 1887.

Be it enacted by the General Assembly of Maryland that if any bank has established or shall, without authority from the State first had and obtained establish any branch, office of discount and deposit, or office of pay and receipt in any part of this State, it shall not be lawful for the said branch, office of discount and deposit, or office of pay and receipt to issue notes, in any manner, of any other denomination than five, ten, twenty, fifty, one hundred, five hundred and one thousand dollars, and no note shall be issued except upon stamped paper of the following denominations ; that is to say, every five dollar note shall be upon a stamp of ten cents ; every ten dollar note, upon a stamp of twenty cents ; every twenty dollar note, upon a stamp of thirty cents ; every fifty dollar note, upon a stamp of fifty cents ; every one hundred dollar note, upon a stamp of one dollar ; every five hundred dollar note, upon a stamp of ten dollars ; and every thousand dollar note, upon a stamp of twenty dollars ; which paper shall be furnished by the Treasurer of the Western Shore, under the direction of the Governor and Council, to be paid for upon delivery ; provided always that any institution of the above description may relieve itself from the operation of the provisions aforesaid by paying annually, in advance, to the Treasurer of the Western Shore, for the use of State, the sum of $ 15, 000.

And praying a Warrant for the said sum of £ 5, 580 — and also praying an Imprest of that sum to enable them to pay the Workmen.