By contrast, the energetic reaction of the leader to the full demands his decision imposes upon him strengthens the moral intuition and gives us the measure of the man.

By contrast, even experienced linguists commonly know no more of the range of possibilities in tone systems than the over-simple distinction between register and contour languages.

By contrast, a good deal of nuclear pacifism begins with the contingencies and the probabilities, and not with the moral nature of the action to be done ; ;

By contrast, the National Union Party was united and energized as Lincoln made emancipation the central issue, and state Republican parties stressed the perfidy of the Copperheads.

By contrast, the cursive developed out of the Nabataean alphabet in the same period soon became the standard for writing Arabic, evolving into the Arabic alphabet as it stood by the time of the early spread of Islam.

has no zero in F. By contrast, the fundamental theorem of algebra states that the field of complex numbers is algebraically closed.

By contrast, the Rijndael specification per se is specified with block and key sizes that may be any multiple of 32 bits, both with a minimum of 128 and a maximum of 256 bits.

The largest species are red alder ( A. rubra ) on the west coast of North America, and black alder ( A. glutinosa ), native to most of Europe and widely introduced elsewhere, both reaching over 30 m. By contrast, the widespread Alnus viridis ( green alder ) is rarely more than a 5 m tall shrub.

By the standards of 19th century tycoons, Carnegie was not a particularly ruthless man but a humanitarian with enough acquisitiveness to go in the ruthless pursuit of money ; on the other hand, the contrast between his life and the lives of many of his own workers and of the poor, in general, was stark.

By contrast, Kabbalism assumed an " eternal Torah " which was not identical to the Torah written in Hebrew.

By contrast, while defendants in most civil law systems can be compelled to give a statement, this statement is not subject to cross-examination by the prosecutor and not given under oath.

By contrast, in an inquisitiorial system, the fact that the defendant has confessed is merely one more fact that is entered into evidence, and a confession by the defendant does not remove the requirement that the prosecution present a full case.

By contrast, Tom Wolfe's Bonfire of the Vanities ( 1987 ) portrays a wealthy, white protagonist, Sherman McCoy, getting lost off the Major Deegan Expressway in the South Bronx and having an altercation with locals.

By contrast, in mainstream Analytical philosophy the topic is more confined to abstract investigation, in the work of such influential theorists as W. V. O. Quine, to name one of many.

By contrast, substance theory explains the compresence of properties by asserting that the properties are found together because it is the substance that has those properties.

By contrast, evidence based on the textual differences between the Septuagint and the Masoretic Text has been used to argue that the context of the MT truly does depict a historical Jeremiah.

By contrast most of the party's seats were won either due to the absence of a candidate from one of the other parties or in rural areas on the " Celtic fringe ", where local evidence suggests that economic ideas were at best peripheral to the electorate's concerns.

By contrast, the normal vaginal discharge will vary in consistency and amount throughout the menstrual cycle and is at its clearest at ovulation-about 2 weeks before the period starts.

By contrast, the British press were jubilant ; many newspapers sought to portray the battle as a victory for Britain over anarchy, and the success was used to attack the supposedly pro-republican Whig politicians Charles James Fox and Richard Brinsley Sheridan.

By contrast, in civil law jurisdictions ( the legal tradition that prevails in, or is combined with common law in, Europe and most non-Islamic, non-common law countries ), courts lack authority to act where there is no statute, and judicial precedent is given less interpretive weight ( which means that a judge deciding a given case has more freedom to interpret the text of a statute independently, and less predictably ), and scholarly literature is given more.

By contrast to statutory codification of common law, some statutes displace common law, for example to create a new cause of action that did not exist in the common law, or to legislatively overrule the common law.

By contrast, a hard conversion or an adaptive conversion may not be exactly equivalent.

" By contrast, the composition from the Byzantine point of view portrays Constantine Palaeologus as a brave leader who gave his life for the cause.

By contrast, in ceremonial monarchies, the monarch holds little actual power or direct political influence.

By contrast, Liechtenstein and Monaco are considered democratic states, yet the ruling monarchs in these countries wield significant executive power.

By 1949, Weyl was thoroughly disillusioned with the ultimate value of intuitionism, and wrote: " Mathematics with Brouwer gains its highest intuitive clarity.

By 1617, the VOC required all their ships to take the Brouwer route.

By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint that is closest to Brouwer.

By Anne-Marie de Brouwer, Sandra Ka Hon Chu and Samer Muscati.

By adding a second fixed-point unit, a second floating point unit, and other performance enhancements to the design, the POWER2 had leadership performance when it was announced in November 1993.

By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.

By the completeness theorem of first-order logic, a statement is universally valid if and only if it can be deduced from the axioms, so the can also be viewed as asking for an algorithm to decide whether a given statement is provable from the axioms using the rules of logic.

By setting K = ker ( f ) we immediately get the first isomorphism theorem.

* By the convolution theorem, Fourier transforms turn the complicated convolution operation into simple multiplication, which means that they provide an efficient way to compute convolution-based operations such as polynomial multiplication and multiplying large numbers.

By " satisfactory " one would mean at least the equivalent of Plancherel theorem.

By the fundamental theorem of arithmetic, every positive integer has a unique prime factorization.

By the Glivenko – Cantelli theorem, if the sample comes from distribution F ( x ), then D < sub > n </ sub > converges to 0 almost surely.

By this theorem, once a star's chemical composition and its position on the main sequence is known, so too is the star's mass and radius.

By Gödel's incompleteness theorem, Peano arithmetic is incomplete and its consistency is not internally provable.

By Rice's theorem, the 1-halting problem is undecidable.

By the corollary to the recursion theorem, there is an index such that returns.

By Liouville's theorem, Hamiltonian flows preserve the volume form on the phase space.

By the fundamental theorem, we may replace the new set by the old set subject to a unitary transformation.

By the first isomorphism theorem, the image of A under ƒ is a substructure of B isomorphic to the quotient of A by this congruence.

By the central limit theorem, this distribution approaches the normal distribution as n increases.

By analogy to the prior and posterior probability terms in Bayes ' theorem, Bayes ' rule can be seen as Bayes ' theorem in odds form.

By the extreme value theorem, a continuous function on a closed interval must attain its minimum and maximum values at least once.

By the rank-nullity theorem, a system of n vectors in k dimensions ( where all dimensions are necessary ) satisfies a ( p = n − k )- dimensional space of relations.

By Tychonoff's theorem we have that is compact since is, so the closure of in is a compactification of.

By Stone's representation theorem every Boolean ring is isomorphic to a field of sets ( treated as a ring with these operations ).

By induction, Hilbert's basis theorem establishes that, the ring of all polynomials in n variables with coefficients in, is a Noetherian ring.

By Euler's rotation theorem, we may replace the vector with where is a 3x3 rotation matrix and is the position of the particle at some fixed point in time, say t = 0.

By the divergence theorem Gauss's law can alternatively be written in the differential form: