: be broken down into component parts which are not in themselves meaningful within the framework of the musical language ... but are nevertheless basic elements ( not units ) of musical expression which, when altered, may be compared to the phonemes of speech in that they alter the museme ( morpheme ) of which they are part and may thereby also alter its meaning.

The easiest way to describe this release is to say that it reproduces an interesting and effective Steinberg performance with minimal alteration of its musical values.

The characteristic polynomial for A is Af and this is plainly also the minimal polynomial for A ( or for T ).

If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

The theorem which we prove is more general than what we have described, since it works with the primary decomposition of the minimal polynomial, whether or not the primes which enter are all of first degree.

( C ) if Af is the operator induced on Af by T, then the minimal polynomial for Af is Af.

It is clear that each vector in the range of Af is in Af for if **ya is in the range of Af, then Af and so Af because Af is divisible by the minimal polynomial P.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Hence the minimal polynomial for Af is Af.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

for since it is nilpotent, the minimal polynomial for this operator is of the form Af for some Af ; ;

but then since the operator is diagonalizable, the minimal polynomial cannot have a repeated root ; ;

hence Af and the minimal polynomial is simply x, which says the operator is 0.

In the primary decomposition theorem, it is not necessary that the vector space V be finite dimensional, nor is it necessary for parts ( A ) and ( B ) that P be the minimal polynomial for T.

Acceptance of radiopasteurization is likely to be delayed, however, for two reasons: ( 1 ) the storage life of fresh chicken under refrigeration is becoming a minimal problem because of constantly improved sanitation and distributing practices, and ( 2 ) treatment by antibiotics, a measure already approved by the Federal Food and Drug Administration, serves to extend the storage life of chicken at a low cost of about 0.5 cents per pound.

The unit of form is determined subjectively: `` the Heart, by the way of the Breath, to the Line ''.

For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.

The connective system, or network, is tailored to meet the requirements of the objective, and it is therefore not surprising that a military body acting as a single coordinated unit has a different communication network than a factory, a college, or a rural village.

The unit consists of a small motor that goes on as soon as it is plugged in.

According to Friends, the unit was organized by John Snook, a former World War 2, commando who is vice president and general manager of the telephone company.

A BTU is a unit of heat, and the BTU rating of a conditioner refers to how much heat your machine can pump out of your house in an hour.

The safest procedure is to let your builder estimate the size of the unit you need, rather than trying to do this yourself.

Still another approach to the changeable letter type of sign is a modular unit introduced by Merritt Products, Azusa, Calif..

`` Only one lumber dealer in ten is equipped to handle unit loads ; ;

only one producer in a hundred is equipped to package and ship unit loads ; ;

only one builder in a thousand is equipped to receive unit loads.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

A randomization of `` ups '' and `` downs '' is more likely than ordered `` ups '' and `` downs '' in position ( 3 ) since the hydrogen atoms are well separated and so the position of one could hardly affect the position of another, and also since ordered `` up '' and `` down '' implies a larger unit cell, for which no evidence exists.

It is assumed that the flux values increase by a factor of 2.512 per magnitude, in accordance with the opinion that the total mass flux in each unit range in magnitude is constant.

The international unit is equipotent with the USP unit adopted in 1952, which was defined as the amount of activity present in 20 mg of the USP reference substance.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

His view is that every religion pertains to a community, and, conversely, every community is in one aspect a religious unit.

Where boundary maintenance describes the boundaries or limits of the group, systemic linkage is defined `` as the process whereby one or more of the elements of at least two social systems is articulated in such a manner that the two systems in some ways and on some occasions may be viewed as a single unit.

The music director of the Pittsburgh Symphony Orchestra, William Steinberg, has molded his group into a prominent musical organization, which is his life.

`` Both children are musical and my wife is a music lover of unfailing instinct and judgement ''.

Jazz is the musical language of sex, the vocabulary of the orgasm ; ;

In the calm which follows the reading of a poem, for example, is the effect produced by the enforced quiet, by the musical quality of words and rhythm, by the sentiments or sense of the poem, by the associations with earlier readings, if it is familiar, by the boost to the self-esteem for the semi-literate, by the diversion of attention, by the sense of security in a legitimized withdrawal, by a kind license for some variety of fantasy life regarded as forbidden, or by half-conscious ideas about the magical power of words??

Lawrence Ferlenghetti and Bruce Lippincott have concentrated on writing a new poetry for reading with jazz that is very closely related to both the musical forms of jazz, and the vocabulary of the musician.

Although Patchen has given previous evidence of an interest in jazz, the musical group that he works with, the Chamber Jazz Sextet, is often ignored by jazz critics.

This is done at varying speeds, ranging from the slow and fast Shifte Telli ( a musical term meaning double strings ) to the fastest, ecstatic Karshilama ( meaning greetings or welcome ).

A low-power, `` carrier-current '' broadcasting station, KARL, heard only in the campus dormitories, is owned and operated by the students to provide an outlet for student dramatic, musical, literary, technical, and other talents, and to furnish information, music, and entertainment for campus listeners.

In these readings, the double bass is either kept discreetly in the background, or it is dressed in clown's attire -- the musical equivalent of a bull in a china shop.

Like the recent Scheherazade from London ( High Fidelity, Sept. 1961 ), it is successful because emphasis has been placed on good musical and engineering practices rather than on creating sensational effects.

It is this sort of experience that makes the concept of high fidelity of real musical significance for the home music listener.

With a large and circumspect 20th-Century technique, he wove the materials of national heroes and events, national folklore and children's fairy tales -- Slavic dances and love songs -- into a solid musical literature which served his people well, and is providing much enjoyment to the World at large.

I took a deep breath and an even deeper swallow of my drink, and said, `` I admit that going back to Ralph Waldo Emerson for humor is like going to a modern musical comedy for music and comedy ''.

Rangoni's first entrance is a musical shock, a sudden open fifth in a key totally unrelated to what has preceded it.

What Parker and his contemporaries -- Gillespie, Davis, Monk, Roach ( Tristano is an anomaly ), etc. -- did was to absorb the musical ornamentation of the older jazz into the basic structure, of which it then became an integral part, and with which it then developed.

Still, the network's willingness to experiment in this musical field is to be commended, and future essays happily anticipated.

One of the finest soft shoe tunes ever invented, `` Once In Love With Amy '' is also, of course, one of the most tantalizingly persistent of light love lyrics to come out of American musical comedy in our era.

The book is by Jerome Weidman and George Abbott, music by Jerry Bock, lyrics by Sheldon Harnick, choreography by Peter Gennaro, scenery, costumes and lighting by William and Jean Eckart, musical direction by Jack Elliott, and the production was directed by Mr. Abbott.

The company which performed the Pulitzer Prize musical here last night and will repeat it twice today is full of bounce, the politicians are in fine voice, the chorines evoke happy memories, and the Little Flower rides to break a lance again.

LaGuardia's multi-lingual rallies, when he is running for Congress, are well staged, and wind up in a wild Jewish folk-dance that is really great musical theater.

It has all been done in superb style, and the result is a show which deserves the support of every person hereabouts who enjoys good musical theater.