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 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 may carry this sequence one step further and say that at seventy he was a poet at the height of his powers, wanting only the impetus of two tragedies, one personal, the other national, to loose those powers in poetry.

We leap from event to event -- including the formation of the posse -- even though the events, in `` reality '' are taking place not in sequence but simultaneously, and not near each other but at a considerable distance.

Thus the DTFT of the s sequence is also the Fourier transform of the modulated Dirac comb function .< ref group =" note "> We may also note that:

We want the size of the union of disjoint sets to be the sum of their individual sizes, even for an infinite sequence of disjoint sets.

We are observing this sequence until a predefined number r of failures has occurred.

We might write such a sequence as a numbered list:

We bumped into some trouble with some opinions-Eddie Manix, the studio manager, thought the Halloween sequence was wrong, but it was left in.

Producer Gary Weis said " We were sitting around in Eric's kitchen one day, planning a sequence that really ripped into the mythology and George looked up and said, ' We were the Beatles, you know!

We prove that if an increasing sequence is bounded above, then it is convergent and the limit is.

Label sequence starts at 99004 to 99008, with the final recording We Shall Overcome ( for label number 99008 ) that was recorded in the Greystone Ballroom was withdrawn and transferred to GORDY 7023B of I Have A Dream speech by Rev.

We then have a short exact sequence of Lie groups:

According to Malcolm McDowell on Camera 2 in the summer of 2002: " We did a sequence in Aylesbury.

Given the observation space, the state space, a sequence of observations, transition matrix of size such that stores the transition probability of transiting from state to state, emission matrix of size such that stores the probability of observing from state, an array of initial probabilities of size such that stores the probability that. We say a path is a sequence of states that generate the observations.

We can define a pseudogene operationally as a fragment of nucleotide sequence that resembles a known protein domain's but with stop codons or frameshifts mid-domain.

We can embed the rational numbers into the reals by identifying the rational number r with the equivalence class of the sequence ( r, r, r, …).

As depicted in every opening sequence of every episode, a TV anchorman announces, " We interrupt this program to bring you ...

We re-analyzed published mitochondrial gene sequence data ( 12S, 16S, cyt b, ND4-tRNALeu ) by employing partition-specific modeling in a combined DNA analysis to clarify existing gaps in the phylogeny of Chinese Phrynocephalus.

Writing in 1960, he begins: " Consider a very long sequence of symbols ... We shall consider such a sequence of symbols to be ' simple ' and have a high a priori probability, if there exists a very brief description of this sequence-using, of course, some sort of stipulated description method.

We apply G to this sequence, chop off the last term, and compute homology to get L < sub > i </ sub > G ( X ).

We would like to construct a curve whose shape is described by a sequence of p points, which plays the role of a control polygon.

We end up with a sequence of numbers which denote the height of each throw to be made.