We can do this through the characteristic values and vectors of T in certain special cases, i.e., when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1.

Today many college bound students try to take a course in personal typing, as they feel a certain degree of mastery of this skill is almost essential for one who proposes to do academic work in college and a professional school.

It is not often realized to what degree certain trades are in many communities closed areas of employment, except for a lucky few.

Presumably, if the reverse is the case and the good effect is more certain than the evil result that may be forthcoming, not only must the good and the evil be prudentially weighed and found proportionate, but also calculation of the probabilities and of the degree of certainty or uncertainty in the good or evil effect must be taken into account.

A monastery must have been granted the status of an abbey by the Pope, and such monasteries are normally raised to this level after showing a degree of stability — a certain number of monks in vows, a certain number of years of establishment, a certain firmness to the foundation in economic, vocational and legal aspects.

Some researchers have speculated that this minority of Haplogroup C3 carriers among the Ainu may reflect a certain degree of unidirectional genetic influence from the Nivkhs, a traditionally nomadic people of northern Sakhalin and the adjacent mainland, with whom the Ainu have long-standing cultural interactions.

Although it was recognized that certain tributaries, represented for example, in the XVIIIth Dynasty tomb of Rekhmara at Egyptian Thebes as bearing vases of peculiar forms, were of some Mediterranean race, neither their precise habitat nor the degree of their civilization could be determined while so few actual prehistoric remains were known in the Mediterranean lands.

Chorbishops are not generally ordained bishops – they are not given the sacrament of Holy Orders in that degree – but function as assistants to the diocesan bishop with certain honorary privileges.

The connections of the bogie with the rail vehicle allow a certain degree of rotational movement around a vertical axis pivot ( bolster ), with side bearers preventing excessive movement.

This can be either a Masters or Doctoral level degree ; while in certain specialties a Ph. D. is notably more common than in others, it is hardly ever the majority ( except in academia ).

and Ph. D. programs will typically require applicants to have an undergraduate degree in BME, or another engineering discipline ( plus certain life science coursework ), or life science ( plus certain engineering coursework ).

Nathan states that certain commonalities allow college students to cohere: " What holds students together, really, is age, pop culture, a handful of ( recent ) historical events, and getting a degree " ( qtd.

Some, like Henry Sidgwick, argue that a certain degree of egoism promotes the general welfare of society for two reasons: because individuals know how to please themselves best, and because if everyone were an austere altruist then general welfare would inevitably decrease.

Mainstream CBT helps individuals replace " maladaptive ... coping skills, cognitions, emotions and behaviors with more adaptive ones ", by challenging an individual's way of thinking and the way that he / she reacts to certain habits or behaviors, but there is still controversy about the degree to which these traditional cognitive elements account for the effects seen with CBT over and above the earlier behavioral elements such as exposure and skills training.

Actors, musicians, models, directors, producers, comedians, television hosts and other entertainment-industry professionals are some of the highest-earning in America given that the entertainment industry based professional achieves a certain degree of success as a prerequisite.

The theory was based on how heat-treating metal works ( the temperatures are lowered to room temperature from a high degree causing certain strength increases in the molecular structure to occur ) and supposed that continuing the descent would allow for further strength increases.

All FARG computational models share certain key principles, among which are: that human thinking is carried out by thousands of independent small actions in parallel, biased by the concepts that are currently activated ; that activation spreads from activated concepts to less activated " neighbor concepts "; that there is a " mental temperature " that regulates the degree of randomness in the parallel activity ; that promising avenues tend to be explored more rapidly than unpromising ones.

) degree can refer to themselves as " doctor " only in certain provinces such as Alberta.

For Derrida the concept of neutrality is suspect and dogmatism is therefore involved in everything to a certain degree.

Boundary limits were agreed on by Durand and Abdur Rahman before the end of 1893, but there is some question about the degree to which Abdur Rahman willingly ceded certain regions.

It has been described as " a language lexically predominantly Romance, morphologically intensively agglutinative, and to a certain degree isolating in character ".

The work thus contains an understandable degree of bias, Einhard taking care to exculpate Charlemagne in some matters, not mention others, and to gloss over certain issues which would be of embarrassment to Charlemagne, such as the morality of his daughters ; by contrast, other issues are curiously not glossed over, like his concubines.

Often it is recognized that all the details of the pattern may not be essential to the outcome but, because the pattern was empirically determined and not developed through theoretical understanding, one is never quite certain which behavior elements are effective, and the whole pattern becomes ritualized.

With troops dispersed on fields of battle rather than on the parade ground, it may seem that a certain amount of monitoring is automatically enforced by the lines of communication.

However, his subject matter and basic themes have remained surprisingly consistent, and these, together with certain key poetic images, may be traced through all his work, including the new jazz experiments.

His may typify a certain kind of postwar New York experience, but his experience is certainly not typical of his `` generation's ''.

Or certain words or rituals that child and adult go through may do the trick.

While `` better late than never '' may have certain merits, the posthumous award of the Nobel Prize for Peace to the late Dag Hammarskjold strikes me as less than a satisfactory expression of appreciation.

The impression was unmistakable that, whatever one may choose to call it, natural law is a functioning generality with a certain objective existence.

It is difficult to tabulate exactly what was meant in each individual situation, but the conclusion may be drawn that 21 towns do not assess movable personal property, and of the remainder only certain types are valued for tax purposes.

Furthermore, a bad check may subject the maker to certain penalties.

You may find certain coverage costing much more than is economically feasible, thereby alerting you to desirable revisions.

It is possible that certain mutational forms may be produced such as antibiotic resistant strains.

There is some reason to think that thyroglobulin synthesis may proceed independently of iodination, for in certain transplantable tumours of the rat thyroid containing essentially no iodinated thyroglobulin, a protein that appears to be thyroglobulin has been observed in ultracentrifuge experiments ( Wolff, Robbins and Rall, 1959 ).

We pointed out that emotional excitement may lead to psychosomatic disorders and neurotic symptoms, particularly in certain types of personality, but it is also known that the reliving of a strong emotion ( `` abreaction '' ) may cure a battle neurosis.

At certain critical stages, and only for sound diagnostic reasons, it may be important to accompany family members in their use of these resources if their problem-solving behavior is to be constructive rather than defeating.

Finally, it may have certain very important, less obvious values.

-- Syllables are linguistic units centering in peaks which are usually vocalic but, as has been noted, are consonantal under certain circumstances, and which may or may not be combined with preceding and/or following consonants or combinations of consonants.

Morphophonemic rules may be thought of as joining certain points in the system.

There may be certain items which are quite similar to a net operating loss carryover or operating deficit and whose right to survive a reorganization should perhaps be subject to the conditions applicable to those items.

They may be related to mental immaturity or lack of aptitude for certain types of school work.

Because of these chewing troubles, a child may avoid certain foods he needs for adequate nutrition.

Small areas that aren't right for a certain crop may lie next to areas that are well suited to that crop.

You may have misgivings about certain aspects of our military establishment -- I certainly do -- but you know any comparison of over-all American strength with over-all Soviet strength finds the United States not only superior, but so superior both in present weapons and in the development of new ones that our advantage promises to be a permanent feature of U.S.-Soviet relations for the foreseeable future.

A certain vagueness may also be caused by tactical appreciation of the fact that the present council meeting is a semipublic affair, with no fewer than six Soviet correspondents accredited.