In other words, nationalism worked well enough when it had limited application, both as to geography and as to population ; ;

But because it is the function of the mind to turn the one into the other by means of the capacities with which words endow it, we do not unwisely examine the type of distinction, in the sphere of politics, on which decisions hang.

by this term he means to ridicule their professions of acting in the interest of the Church despite their own education and manner of life -- a gibe, in other words, at the `` Presbyterianism '' in Harley's family and at Bolingbroke's reputed impiety.

Once more, in other words, Steele is said to be indebted to Swift for his `` wit '' ; ;

In other words, as students go through college, those who are most successful academically tend to become more committed to a `` Bill of Rights '' orientation.

in other words its existence belongs to the period of Roman Britain.

The problem, in other words, is strictly a chronological one.

In other words, atrocities by savages wearing the uniform of the central government might be condoned, had the victims been serving the cause of dissident Katanga.

In other words, the Secretary General is to be a nonpartisan, international servant, not a political, national one.

In other words, the whole storage and pipeline system does not belong to the homeowners nor to the town but rather to Tri-State.

Poster Products Inc., Chicago, Ill.: a changeable copy and display sign which consists of an extruded impact styrene background in choice of colors, onto which are mounted snap-in letters, figures, or words screened on acetate or other types of sheet stock.

In other words, if an ideal gas is compressed and kept at constant temperature, the work done in compressing it is completely converted into heat and transferred to the surrounding heat sink.

In other words, the anastomoses between the bronchial artery and pulmonary artery should be considered as functional or demand shunts.

In other words, if F satisfies the differential equation Af, then F is uniquely expressible in the form Af where Af satisfies the differential equation Af.

In other words, these curves have only fixed intersections common to them all.

But if no two lines of the regulus of multiple secants of **zg can intersect, then the regulus must be quadratic, or in other words, **zg must be either a Af or a Af curve on a nonsingular quadric surface.

In the urban area, in other words, they, unlike some urban ethnic groups, do not concentrate in ghetto colonies.

In other words, the Soviet Union was determined to create a Poland so strong as to be a powerful bulwark against Germany and so closely tied to Russia that there would never be any question of her serving as a cordon sanitaire against the Soviets or posing as an independent, balancing power in between Russia and Germany.

In other words the burden of pleading clearly rested upon the pleader by state law.

It will not, however, be used for symbolic assignment until all other index words or electronic switches have been assigned for the first time.

In other words, like automation machines designed to work in tandem, they shared the same programming, a mutual understanding not only of English words, but of the four stresses, pitches, and junctures that can change their meaning from black to white.

Even less regard for mom and mom's apple pie goes with: Af In other words, the way the speaker relates to mother is clearly indicated.

In other words, the promulgators of the murder plan made clear that physically exterminating the Jews was but an extension of the anti-Semitic measures already operating in every phase of German life, and that the new conspiracy counted on the general anti-Semitism that had made those measures effective, as a readiness for murder.

Although it was at the Battle of The Little Horn, about which more words have been written than any other battle in American history, that the 7th Cavalry first made its mark in history, the regiment was ten years old by then.

Section 7 is designed to arrest in its incipiency not only the substantial lessening of competition from the acquisition by one corporation of the whole or any part of the stock of a competing corporation, but also to arrest in their incipiency restraints or monopolies in a relevant market which, as a reasonable probability, appear at the time of suit likely to result from the acquisition by one corporation of all or any part of the stock of any other corporation.

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.

Classically, it is forbidden to escape, but according to the ( then ) newly-discovered principles of quantum mechanics, it has a tiny ( but non-zero ) probability of " tunneling " through the barrier and appearing on the other side to escape the nucleus.

In other words, there is an algorithm for a quantum computer ( a quantum algorithm ) that solves the decision problem with high probability and is guaranteed to run in polynomial time.

For example, Hacking writes " And neither the Dutch book argument, nor any other in the personalist arsenal of proofs of the probability axioms, entails the dynamic assumption.

In part, the growth was spurred by new connections and applications to other fields, ranging from algebra to probability, from functional analysis to number theory, etc.

This is totally spurious, since no matter who measured first the other will measure the opposite spin despite the fact that ( in theory ) the other has a 50 % ' probability ' ( 50: 50 chance ) of measuring the same spin, unless data about the first spin measurement has somehow passed faster than light ( of course TI gets around the light speed limit by having information travel backwards in time instead ).

As with other branches of statistics, experimental design is pursued using both frequentist and Bayesian approaches: In evaluating statistical procedures like experimental designs, frequentist statistics studies the sampling distribution while Bayesian statistics updates a probability distribution on the parameter space.

In other words, increasing the sample size increases the probability of the estimator being close to the population parameter.

) This conflicts with the standard claim that the frequency interpretation is somehow more " objective " than other theories of probability.

Fourier analysis has many scientific applications – in physics, partial differential equations, number theory, combinatorics, signal processing, imaging, probability theory, statistics, option pricing, cryptography, numerical analysis, acoustics, oceanography, sonar, optics, diffraction, geometry, protein structure analysis and other areas.

In other words, the previous losses in no way contribute to the odds of the remaining attempts, but there are fewer remaining attempts to gain a win, which results in a lower probability of obtaining it.

Copying the numbers that won the previous lottery draw gives an equal probability, although a rational gambler might attempt to predict other players ' choices and then deliberately avoid these numbers.

In other words, if a typical set of m records is hashed to n table slots, the probability of a bucket receiving many more than m / n records should be vanishingly small.

In other words, this is a measure of how much, on the average, the probability distribution on X will change if we are given the value of Y.

In other words, the probability associated with each event is evenly distributed across N!

The probability of obtaining two particles in the state is 0. 25 ; the probability of obtaining two particles in the state is 0. 25 ; and the probability of obtaining one particle in the state and the other in the state is 0. 5.

When we perform the experiment, the probability of obtaining two particles in the state is now 0. 33 ; the probability of obtaining two particles in the state is 0. 33 ; and the probability of obtaining one particle in the state and the other in the state is 0. 33.

The reason for stricter dietary observance on these eleven days is that the probability of the finalisation of the next birth is much more on these days compared to the other days.

In other words the more people who are using a product the greater the probability of any individual starting to use the product.