Of course, since we are dealing with fermions, we have to have the operators satisfy canonical anti-commutation relations.

The functions J < sub > α </ sub >, Y < sub > α </ sub >, H < sub > α </ sub >< sup >( 1 )</ sup >, and H < sub > α </ sub >< sup >( 2 )</ sup > all satisfy the recurrence relations:

This is most helpful for those organizations that have data relationships that are not entirely clear or need to change these relations to satisfy the new business requirements.

The plan now is to show that for k sufficiently large, the above relations are impossible to satisfy because

A fundamental theorem states that if two distinct sets of matrices are given that both satisfy the Clifford relations, then they are connected to each other by a similarity transformation:

These new gammas will themselves satisfy the Clifford relations, because of the orthogonality of the Lorentz transformation.

The Fermat numbers satisfy the following recurrence relations:

( A " canonical coordinate system " consists of canonical position / momentum variables, that satisfy canonical Poisson-bracket relations.

Additionally, there is wide-ranging debate about defence, monetary policy, currency, international-trade and relations after independence and whether a renewed federalism would give political recognition to the Quebec nation ( along with the other ' founding ' peoples, including Canadian First Nations, the Inuit, and the British ) could satisfy the historic disparities between these cultural " nations " and create a more cohesive and egalitarian Canada.

A set of at least points in-dimensional Euclidean space is said to be in general linear position ( or just general position ) if no hyperplane contains more than points — i. e. the points do not satisfy any more linear relations than they must.

One can choose sign conventions such that the derivatives satisfy the anticommutation relations

In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.

In particular, there are three distinct complex structures, I, J, and K, which satisfy the quaternion relations

Although the quantity p < sub > kin </ sub > is the " physical momentum ", in that it is the quantity to be identified with momentum in laboratory experiments, it does not satisfy the canonical commutation relations ; only the canonical momentum does that.

The canonical coordinates satisfy the fundamental Poisson bracket relations:

Laguerre's polynomials satisfy the recurrence relations

These satisfy the relations

and that satisfy the commutation relations

The total angular momentum operators satisfy the required commutation relations

These satisfy the commutation relations:

These satisfy the commutation relations:

They satisfy anomalous commutation relations.

To satisfy a prurient taste the details of sexual relations are spread broadcast in the columns of the daily papers .... The intensity and complexity of life, attendant upon advancing civilization, have rendered necessary some retreat from the world, and man, under the refining influence of culture, has become more sensitive to publicity, so that solitude and privacy have become more essential to the individual ; but modern enterprise and invention have, through invasions upon his privacy, subjected him to mental pain and distress, far greater than could be inflicted by mere bodily injury.

Beside the PDEs, the operators also satisfy another relation, the commutation / anticommutation relations.

Students of the college who are candidates for the A.B. degree and can satisfy the academic requirements of the medical and business schools, may enter either of these associated schools at the beginning of senior year, thus completing the two-year postgraduate course in one year.

Chance, one would say, produced an innumerable multitude of individuals ; a small number found themselves constructed in such a manner that the parts of the animal were able to satisfy its needs ; in another infinitely greater number, there was neither fitness nor order: all of these latter have perished.

In all of these cases in nature, the same brilliant iridescence ( or play of colors ) can be attributed to the diffraction and constructive interference of visible lightwaves that satisfy Bragg ’ s law, in a matter analogous to the scattering of X-rays in crystalline solids.

Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.

The significant Late Neolithic and Early Bronze Age Cycladic culture is best known for its schematic flat idols carved out of the islands ' pure white marble centuries before the great Middle Bronze Age (" Minoan ") culture arose in Crete, to the south: these figures have been looted from burials to satisfy a thriving Cycladic antiquities market since the early 20th century.

A distributed system can satisfy any two of these guarantees at the same time, but not all three.

Many small projects don't satisfy either of these prerequisites, but they too can benefit from EVM, as described for simple implementations, above.

It can be shown, that, under these conditions, the electric and magnetic fields satisfy the electromagnetic wave equation:

Due to the sparse energy and raw material resources, Hungary is forced to import most of these materials to satisfy the demands of the industry.

with R < sub > AB </ sub > the five-dimensional Ricci curvature, may be re-expressed so that in four dimensions, these solutions satisfy Einstein's equations

AM, GM, and HM satisfy these inequalities:

Doctors Baikouzis and Magnasco state that " he odds that purely fictional references to these phenomena ( so hard to satisfy simultaneously ) would coincide by accident with the only eclipse of the century are minute.

A typical example of a file transfer that does not use the P2P model is the File Transfer Protocol ( FTP ) service in which the client and server programs are distinct: the clients initiate the transfer, and the servers satisfy these requests.

In particle physics, these operators turn out to be more convenient to work with, because they make it easier to formulate theories that satisfy the demands of relativity.

The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.

A set consists of three cards which satisfy all of these conditions:

Separate events must satisfy these conditions.

Sets of these cardinalities satisfy the first three characterizations above but not the fourth characterization.

Partially 3D and fully 2D games were still common in the industry early in the decade, but these have now become rare as developers look almost exclusively for fully 3D games to satisfy the increasing demand for them in the market.

The probability measure function must satisfy a simple requirement: the probability of a union of two ( or countably many ) disjoint events must be equal to the sum of probabilities of each of these events.

" I do not refer to real estate, or to personal property or to cold cash, but rather to that in life which tends to make these tangible substances count for most in the daily lives of people, namely, goodwill, fellowship, mutual sympathy and social intercourse among a group of individuals and families who make up a social unit … If he may come into contact with his neighbor, and they with other neighbors, there will be an accumulation of social capital, which may immediately satisfy his social needs and which may bear a social potentiality sufficient to the substantial improvement of living conditions in the whole community.

To satisfy these needs, " the Japanese portrayed and catalogued Taiwan's indigenous peoples in a welter of statistical tables, magazine and newspaper articles, photograph albums for popular consumption ".

If a collection B of subsets of X fails to satisfy either of these, then it is not a base for any topology on X.

Marketing satisfy these needs and wants through exchange processes and building long term relationships.