Among other topics, quantitative behavioral finance studies behavioral effects together with the non-classical assumption of the finiteness of assets.

Without the finiteness restriction a posetal category with all products is automatically cocomplete, and dually, by a theorem about complete lattices.

His solution, establishing the finiteness of B < sub > 0 </ sub >( m, p ), used a relation with deep questions about identities in Lie algebras in finite characteristic.

tested the following hypothesis: “ If youth culture serves to help adolescents deal with problems of vulnerability and finiteness, then reminders of mortality should lead to increased allegiance to cultural practices and beliefs of the youth .” Their results supported their hypothesis and the results of previous studies, suggesting that youth culture is, in fact, a culture.

* Group schemes can be formed from smaller group schemes by taking restriction of scalars with respect to some morphism of base schemes, although one needs finiteness conditions to be satisfied to ensure representability of the resulting functor.

Paul Gottfried, a professor at Elizabethtown College in Pennsylvania, has said that " Modern Age represents humanistic learning, reverence for the eternal, and the sense of human finiteness, values that ( alas ) have less and less to do with the academic presentation of the liberal arts.

The essential distinction, similar to the concept of definable numbers, contrasts the finiteness of the domain of concepts that we can specify and discuss with the unbounded infinity of the set of numbers ; compare finitism.

Then the functions and can be related with each other via a Legendre transformation: more precisely, the functions and ( suitably extended to outside their domains of finiteness ) are a pair of conjugated convex functions, for

In the region, in fact, it is indeed one of the two along with land shortage, and land shortage itself ultimately is a consequence of continued population growth in the face of the finiteness of land resources.

In connecting with the evolving divine soul within, the sadhak moves away from ego, ignorance, finiteness, and the limitations of the outer being

* 1955 Jointly with Ostap Parasyuk proved the theorem on the finiteness and uniqueness ( for renormalizable theories ) of the scattering matrix in any order of perturbation theory ( Bogoliubov-Parasyuk theorem ) and developed a procedure ( R-operation ) for a practical subtraction of singularities in quantum field theory.

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.

The debate is interesting enough, however, that it is considered of note when a theorem in ZFC ( ZF plus AC ) is logically equivalent ( with just the ZF axioms ) to the axiom of choice, and mathematicians look for results that require the axiom of choice to be false, though this type of deduction is less common than the type which requires the axiom of choice to be true.

Assuming ZF is consistent, Paul Cohen employed the technique of forcing, developed for this purpose, to show that the axiom of choice itself is not a theorem of ZF by constructing a much more complex model which satisfies ZF ¬ C ( ZF with the negation of AC added as axiom ) and thus showing that ZF ¬ C is consistent.

He had introduced the adele ring in the late 1930s, following Claude Chevalley's lead with the ideles, and given a proof of the Riemann – Roch theorem with them ( a version appeared in his Basic Number Theory in 1967 ).

# Yoga of the Grothendieck – Riemann – Roch theorem ( K-theory, relation with intersection theory ).

For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.

* Metamath-a language for developing strictly formalized mathematical definitions and proofs accompanied by a proof checker for this language and a growing database of thousands of proved theorems ; while the Metamath language is not accompanied with an automated theorem prover, it can be regarded as important because the formal language behind it allows development of such a software ; as of March, 2012, there is no " widely " known such software, so it is not a subject of " automated theorem proving " ( it can become such a subject ), but it is a proof assistant.

* The case n = 1 can be illustrated by the claim that there always exist a pair of opposite points on the earth's equator with the same temperature, this can be shown to be true much more easily using the intermediate value theorem.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side can be cut into a square of side a, a square of side b, and two rectangles with sides a and b. With n = 3, the theorem states that a cube of side can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × b rectangular boxes.

Goldstone's theorem in quantum field theory states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone bosons.

A typical application is furnished by the Arzelà – Ascoli theorem and in particular the Peano existence theorem, in which one is able to conclude the existence of a function with some required properties as a limiting case of some more elementary construction.

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

* 1799: Doctoral dissertation on the Fundamental theorem of algebra, with the title: Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (" New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors ( i. e., polynomials ) of the first or second degree ")

The Sylow 2-subgroups are either cyclic, which is easy to handle using the transfer map, or generalized quaternion, which are handled with the Brauer – Suzuki theorem: in particular there are no simple groups of 2-rank 1.

This is because if a group has sectional 2-rank at least 5 then MacWilliams showed that its Sylow 2-subgroups are connected, and the balance theorem implies that any simple group with connected Sylow 2-subgroups is either of component type or characteristic 2 type.

He used the blanket for late morning naps when hosts of the night had gone off to jobs and proved reluctant to leave him in their small rooms with their few possessions.

There was a shattering, cracking sound as the concrete started to buckle, the air filled with dust and flying debris, and everyone in the room -- men and women hit the floor and used the desks as turtlebacks, as ordered.

when he went home at night, he took her with him in his mind, and she did the things the anonymous Woman used to do, and he did the thing afterwards each time as he used to do.

He said, lapsing into the profanity he often used when away from his parents and especially when he was with Charles.

When words can be used in a more fresh and primitive way so that they strike with the force of sights and sounds, when tones of sound and colors of paint and the carven shape all strike the sensibilities with an undeniable force of data in and of themselves, compelling the observer into an attitude of attention, all this imitates the way experience itself in its deepest character strikes upon the door of consciousness and clamors for entrance.

Then, with staring eyes and lips drawn thin, Miriam said to the young woman, `` You are ugly -- uglier than you used to be, and you were always very ugly.

I used to go with Watson to call on the eminent neurologist at his apartment, to sit among the doctor's excellent collection of statues, paintings, and books and drink Oriental coffee while Watson seemed to thaw out and become almost affable.

The President used to look at it with a ghost of a smile.

In 1687 the Turks, who had been in control of the city since the fifteenth century, with a truly shattering lack of prudence used the Parthenon as a powder magazine.

In the next few months of comparative silence, Pike waited patiently until conditions were perfect for a new attack, and then, displaying a remarkable grasp of the subtleties of political infighting, gained from his first bout with Woodruff, he used these changed conditions to excellent advantage.

On the other hand, the consensus of opinion is that, used with caution and in conjunction with other types of evidence, the native sources still provide a valid rough outline for the English settlement of southern Britain.

The narrator feels himself catching a glimpse of pre-history, learning of man's `` age-old familiarity with misfortune '', as well as his `` equally age-old ingenuity, his secret faith in endurance, however crammed with catastrophes, the same faith perhaps as the cave-men used to have in the face of famine ''.

The trouble with this machinery is that it is not used and the reason that it is not used is the absence of a conscious sense of community among the free nations.

This year's Senate measure would provide each state and the District of Columbia with $1,000,000 to be used in support of private, state, or municipal ETV efforts.

Gloria ( surname: Ziraldo ), circa 30, who was born in Italy and once did `` chorus work '' in Toronto, has been around longer than most of the others, wistfully remembers the old days when `` we used to get the seamen from the ships, you know, with big turtleneck sweaters and handkerchiefs and all.

This, of course, was the sort of thing that used to take place in Southern cities -- putting white houses of prostitution with colored girls in colored neighborhoods and carrying them on openly.

It was a word he was proud of, a word that meant much to him, and he used it with great pleasure, almost as if it were an exclusive possession, and more: he sensed himself to be very highly educated, four cuts above any of the folks back home.

Bern demands that the Lord's Supper be administered here as it used to be, with unleavened bread.

Hino talked very little about himself except for the infrequent times when he used a personal illustration in connection with another subject.

I used to play with the older one sometimes, when he'd let me.