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 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 obtain complete forgiveness ..." are from http :// aa-history. com / 12stephistory2. html

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 are not now afraid of atomic bombs in the same way that people once feared comets.

We talk about national character in the same way that Copernicus talked of the compulsions of celestial bodies to move in circles.

We were almost the same age, she was fifteen, I was twelve, and where I felt there was a life to look forward to Lilly felt she had had as much of it as was necessary.

We want the past forgiven, but at the same time we must be willing for God to direct the future.

We don't 'low nigras to walk on the same sidewalk with white men where I come from.

We can expect more of the same.

We all seek the same thing through different ways -- an end to this long night of two thousand years of darkness and unspeakable abuses which will continue to plague us until the Star of David flies over Zion ''.

We quickly ran into the same trouble that plagued Bill Ruger in his first experiments: Three or four bullets would be placed well in a six-inch bull at 100 yards and then, unaccountably, one could stray far out of the group.

We define these values as Af, and define g{t} in the same way for each T.

The same editorial continued that `` We expected to democratize Japan and Korea and to see a new China pattern itself easily on our institutions.

We assume that average total unit cost in the relevant region of operation is constant with respect to quantity produced ( the average cost curve is horizontal, and therefore is identical with the marginal cost curve ), and is the same for every firm ( and therefore for the industry ).

We have sought to be strictly neutral as between the parties, but at the same time we have been required frequently to rule on specific issues or situations as they arose.

We should say that we made our point with feeling the first time and little or no feeling the second time, but that it was the same point we were making.

We take leave of Pumblechook as he gloats over Pip's loss of fortune, extending his hand `` with a magnificently forgiving air '' and exhibiting `` the same fat five fingers '', one of which he identifies with `` the finger of Providence '' and shakes at Pip in a canting imputation of the latter's `` ingratitoode '' and his own generosity as Pip's `` earliest benefactor ''.

We know that the number of radio and television impulses, sound waves, ultra-violet rays, etc., that may occupy the very same space, each solitary upon its own frequency, is infinite.

We keep getting the same ones back again and again.

Said he: `` We will see whether whites and Negroes are treated the same around here ''.

`` We are directed to develop a sense of proportion, sir, which contributes the same effect ''.

Why, man, that's the same kind of music we've been playin ' since 1928 !... We didn't call it rock and roll back when we introduced it as our style back in 1928, and we don't call it rock and roll the way we play it now.

The Athanasian Creed, received in the Western Church as having the same status as the Nicene and Chalcedonian, says: " We worship one God in Trinity, and Trinity in Unity ; neither confounding the Persons nor dividing the Substance.

: We, then, following the holy Fathers, all with one consent, teach people to confess one and the same Son, our Lord Jesus Christ, the same perfect in Godhead and also perfect in manhood ;

We learn names by connecting an idea with a sound, so that speaker and hearer have the same idea when the same word is used.

We can continue this reasoning along the entire height of the slit to conclude that the condition for destructive interference for the entire slit is the same as the condition for destructive interference between two narrow slits a distance apart that is half the width of the slit.