gave a slight generalization, defining the product and involution on B = A ⊕ A for A an algebra with involution ( with ( xy )< sup >*</ sup >

A slight generalization of those representations are the G-modules: a G-module is an abelian group M together with a group action of G on M, with every element of G acting as an automorphism of M. In the sequel we will write G multiplicatively and M additively.

A slight generalization applying to dyons also exists.

There exists a slight generalization of Kummer theory which deals with abelian extensions with Galois group of exponent n, and an analogous statement is true in this context.

To make a slight generalization of the above example, let and represent the allele frequencies of A in and respectively ( and and likewise represent a ).

Whereas in the CN-case, the resulting maximal subgroups M are still Frobenius groups, the maximal subgroups that occur in the proof of the odd-order theorem need no longer have this structure, and the analysis of their structure and interplay produces 5 possible types of maximal subgroups, called types I, II, III, IV, V. Type I subgroups are of " Frobenius type ", a slight generalization of Frobenius group, and in fact later on in the proof are shown to be Frobenius groups.

Emmy Noether showed that a slight but profound generalization of Lie's notion of symmetry can result in an even more powerful method of attack.

( In a slight generalization, one sometimes requires B ( t < sub > 1 </ sub >)

This method can also be used to prove Euler's theorem, with a slight alteration in that 1 to ( p-1 ) is substituted for the numbers less than and relatively prime to some base m ( instead of p ).

In mathematics, this term is ( by a slight abuse ) also sometimes used for examples illustrating the necessity of the full hypothesis of a theorem, by considering a case where a part of the hypothesis is not verified, and where one can show that the conclusion does not hold.

In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be ( by a slight deformation ) approximated by ones that are piecewise of the simplest kind.

Studied a slight variant of Thabit ibn Qurra's theorem on amicable numbers.

The slight flutter that had disturbed the motion of her heart when she entered the forest was gone now, and even the dim groves of trees through which she occasionally passed did not reawaken her fear.

Graceful as his fencing and dancing lessons had taught him to be in addition to the natural grace of his slight, wiry frame, he cut enough of a figure to have evoked a nickname in the college, to which he himself referred in Prolusion 6::

The extent of such interference -- which may be so slight as to be undetectable at any point where either of the stations renders a usable signal, or may be so great as to virtually destroy the service areas of both stations -- depends on many factors, among the principal ones being the distance between the stations, their respective radiated power, and, of particular significance here, the time of day.

New car sales in Dallas County during March showed slight signs of recovering from the doldrums which have characterized sales this year.

He contends this idea doesn't conflict with experiments on which the principle of conservation of matter and energy is based because some slight error must be assumed in such experiments.

His mother, who had seen little of him for four years, appeared worried about his sailing off by himself for an Orient which, she herself having slight knowledge of it, had to be distrusted.

The site is located in Section 64, on a slight rise, which gives it a view of the Pentagon.

: The Original Version, Restored and Revised ( Second Printing 2007 ), which restored the book to its original content, with slight revisions, and added comprehensive end notes, an index, and an appendix.

" After a string quartet ," Martin explains, " I do not think there is a satisfactory sound for strings until one has at least three players on each line ... as a rule two stringed instruments together create a slight " beat " which does not give a smooth sound.

At this apparent slight, R. Ḥiyya manifested chagrin, and R. Abbahu hastened to comfort him by comparing himself to the pedler of glittering fineries that always attracted the eyes of the masses, while his rival was a trader in precious stones, the virtues and values of which were appreciated only by the connoisseur.

` Abdu ' l-Bahá was at this point noted for having black hair which flowed to his shoulders, large blue eyes, alabaster coloured skin and a slight Roman nose.

Natural beryllium, save for slight contamination by cosmogenic radioisotopes, is essentially beryllium-9, which has a spin of-3 / 2.

His centre was secured by Ramillies itself, lying on a slight eminence which gave distant views to the north and east.

A slight success over Octavian's tired soldiers encouraged him to make a general attack, in which he was decisively beaten.

Cosmological perturbation theory, which describes the evolution of slight inhomogeneities in the early universe, has allowed cosmologists to precisely calculate the angular power spectrum of the radiation, and it has been measured by the recent satellite experiments ( COBE and WMAP ) and many ground and balloon-based experiments ( such as Degree Angular Scale Interferometer, Cosmic Background Imager, and Boomerang ).

This allows for homeostatic regulation of the distribution of neuroendocrine factors, to which slight changes can cause problems or damage to the nervous system.

More subtle is the slight over-representation of string operations, which is largely language-related: both Ada and Pascal have strings as normal variables in the language, whereas C does not, so what was simple variable assignment in reference benchmarks became buffer copy operations in the C library.

In 2003 GDP was estimated to have grown by 2 percent, a slight improvement over 2002, the last year for which firm figures are available, when GDP expanded by 1. 8 percent in real terms to about US $ 600 million.

Differences in praxis ( practice ) tend to be slight ; they involve such things as the order in which a particular set of hymns are sung or what time a particular service is celebrated.

The Gregorian calendar reforms made slight changes to the system for determining which years were leap years and thus contained a 29-day February.

She wrote of the Americans, " The boy learns to make advances and rely upon the girl to repulse them whenever they are inappropriate to the state of feeling between the pair ", as contrasted to the British, where " the girl is reared to depend upon a slight barrier of chilliness ... which the boys learn to respect, and for the rest to rely upon the men to approach or advance, as warranted by the situation.

Among these are " jumbo " frets, which have much thicker gauge, allowing for use of a slight vibrato technique from pushing the string down harder and softer.

Nayler and his followers refused to remove their hats while Fox prayed, which Fox took as both a personal slight and a bad example.

Jordanes, a Goth writing in Italy in 551, a century after the collapse of the Hunnic Empire, describes the Huns as a " savage race, which dwelt at first in the swamps, a stunted, foul and puny tribe, scarcely human, and having no language save one which bore but slight resemblance to human speech.

During the first few days of wearing the appliance and immediately following each adjustment, Susan may have a slight discomfort or soreness, but after a short time this will disappear.

This perceived slight, known as the Telegram Crisis, greatly outraged Hitler and he immediately recalled his ambassador from Copenhagen and expelled the Danish ambassador from Germany.

The latter goal is achieved by splitting the stators into eight concentric rings, each fed with a slight time delay compared to the ring immediately inwards, thereby attempting to simulate a point source.

She makes a slight but definite gesture to the right, which the young man follows immediately and without hesitation.

Frank Loving, who had only a slight scratch on the hand, was immediately taken to jail.

The reason for the fearsome reputation of the cape is not immediately obvious from maps, where it appears as the southwestern point of a slight hump in the coastline, bounded at its other end by Cabo Falso Bojador, ten nautical miles to the northeast.

In this manner, the loyal knights will have a slight head start and will be less likely to be defeated immediately.

* Reduced side effects-After testing RISUG on more than 250 volunteers, neither Guha nor other researchers in the field report side effects other than a slight scrotal swelling in some men immediately following the injection, which goes away after a few weeks, though there are also unconfirmed reports of kidney problems ( see Controversy section below for further details ).