We will call the first the furnace and the second the refrigerator .” Carnot then explains how we can obtain motive power, i. e. “ work ”, by carrying a certain quantity of heat from body A to body B.

We thus obtain a functor from the category of pointed topological spaces to the category of groups.

We can factor this expression to obtain

We thus obtain the inequality in terms of dimensions of kernel, which can then be converted to the inequality in terms of ranks by the rank-nullity theorem.

We obtain the same variation in probability amplitudes by allowing the time at which the photon left the source to be indeterminate, and the time of the path now tells us when the photon would have left the source, and thus what the angle of its " arrow " would be.

' We lose time, we destroy trees to obtain paper necessary to print this word.

We can, however, seek to obtain some form of consensus, with others, of what is real.

There is a special case of Lagrange inversion theorem that is used in combinatorics and applies when and Take to obtain We have

We thus obtain the recursion:

We obtain the sequence of Fibonacci numbers which begins:

We are deprived of a leader than whom the whole world would scarcely obtain a greater, whether in knowledge of true religion or in integrity and innocence of life, or in thirst for study of the most holy things, or in exhausting labour in advancing piety, or in authority and fulness of teaching, or in anything that is praiseworthy and renowned.

We obtain a Kleene algebra A with 0 being the empty set and 1 being the set that only contains the empty string.

We start with the standard assumption of independence of the two sides, enabling us to obtain the joint probabilities of pairs of outcomes by multiplying the separate probabilities, for any selected value of the " hidden variable " λ. λ is assumed to be drawn from a fixed distribution of possible states of the source, the probability of the source being in the state λ for any particular trial being given by the density function ρ ( λ ), the integral of which over the complete hidden variable space is 1.

We now use the Pythagorean theorem, the fact that the slope of the curve is equal to the tangent of its angle, and some trigonometric identities to obtain ds in terms of dx:

We perform our ' simran ' or meditation by Guru's Grace only and open tenth door of our body to obtain " band-khallaassi " or the ' moksha ' ( liberation from bondage of birth and death and attain ultimate oneness with the Lord.

We obtain:

We can " cut " the plane along the real axis, from − 1 to 1, and obtain a sheet on which g ( z ) is a single-valued function.

We can obtain a formula for r by substituting estimates of the covariances and variances based on a sample into the formula above.

We then obtain an equation of polynomials whose left-hand side is simply p ( x ) and whose right-hand side has coefficients which are linear expressions of the constants A < sub > ir </ sub >, B < sub > ir </ sub >, and C < sub > ir </ sub >.

We may integrate the expression for to obtain the Helmholtz energy:

We obtain that

: We had to create our own journals because it was impossible to obtain entry into the official journals of psychiatry and medicine.

If T is a statistic that is approximately normally distributed under the null hypothesis, the next step in performing a Z-test is to estimate the expected value θ of T under the null hypothesis, and then obtain an estimate s of the standard deviation of T. We then calculate the standard score Z = ( T − θ ) / s, from which one-tailed and two-tailed p-values can be calculated as Φ (−| Z |) and 2Φ (−| Z |), respectively, where Φ is the standard normal cumulative distribution function.

We can therefore derive a semi-discrete numerical scheme for the above problem with cell centres indexed as, and with cell edge fluxes indexed as, by differentiating ( 6 ) with respect to time to obtain:

We have complete facilities to accommodate 200 people ''.

The EPR paper says: " We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

A significantly different guitar-driven " We Don't Want To Die " mix appeared, with complete middle eight, on the limited edition 7-inch picture disc.

We believe therefore, that India must sever the British connection and attain Purna Swaraj or complete independence.

We know much more about early Latin comedy, because we have 20 complete plays by Plautus and 6 by Terence.

We do, however, have complete dominion over our behavior, and for Morita, that is a sacred responsibility.

We should have complete freedom in personnel policies and administration.

We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

We avoid this phrase, preferring to reserve the term ' stop ' for sounds in which there is a complete interruption of airflow.

We badly need a complete edition of Paine's writings on the model of Eric Foner's edition for the Library of America, but until that goal is achieved, Philip Foner's two-volume edition is a serviceable substitute.

* United We Stand, H. Ross Perot ; text of the book published by Perot in 1992 to mark the launch of his Presidential campaign, complete with charts.

We have complete texts extant by Aeschylus, Sophocles, and Euripides.

We want the complete political extinction of the Tory Party.

None has yet done it so sharply and so truly as In Which We Serve .... For the great thing which Mr. Coward has accomplished in this film is a full and complete expression of national fortitude ....

In 2007, Queen released a special edition of Queen Rock Montreal on Blu-ray and DVD formats containing their 1981 concert from The Forum in Montreal, Canada, and their complete Live Aid performance, along with Freddie Mercury and Brian May performing " Is This The World We Created ...?

We must wipe Amalek out of our hearts whenever — and wherever — he attacks so that we cannot serve God with complete joy.

We have revisited The Song Remains The Same and can now offer the complete set as played at Madison Square Garden.

We wish to show ( for small enough values of n ) that it is possible to color the edges of the graph in two colors ( say red and blue ) so that there is no complete subgraph on r vertices which is monochromatic ( every edge colored the same color ).

We hope to complete the album by the summer of 2012 and then embark on an extensive two month world tour in late 2012.

We can now give a complete description of w

We only wanted a Jew and a Muslim to make our Religious Museum complete " ( Life, i. 284 ).

For instance, in a publication entitled The Gift of Scripture, the Roman Catholic Church in England and Wales comments that " We should not expect to find in Scripture full scientific accuracy or complete historical precision ".

John Gordon, National Nuclear Security Administrator, stated " We have prepared a detailed bottom-up cost and schedule to complete the NIF project … The independent review supports our position that the NIF management team has made significant progress and resolved earlier problems ".