Related papers: Fillings method in number theory
A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for the evaluation of Feynman diagrams. The operational rules are described and the method is…
With an artificial (p', n')-system it has been proved that even numbers > (p(x))^2 are the sum of two p > p(x).
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
We develop Hilbert-Kunz theory in a combinatorial setting namely for binoids. We show that the Hilbert-Kunz multiplicity for commutative, finitely generated, semipositive, cancellative and reduced binoids exists and is a rational number.…
In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra and number theory.
Goldbach`s Conjecture, "every even number greater than 2 can be expressed as the sum of two primes" is renamed Goldbach`s Rule for it can not be otherwise. The conjecture is proven by showing that the existence of prime pairs adding to any…
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
In this paper, we used the principle of sieve function transformation to improve sieve method and the prime number theorem in the arithmetic sequence.For this, we proved General Riemann Hypothesis and Riemann Hypothesis to be true. further,…
The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is considered. Connections of this calculus to Bochner-Phillips functional calculus are indicated. In particular, the…
Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a quantum computational type logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness…
In [2] a new factorization for infinite Hessenberg banded matrices was introduced. In this note we prove that this kind of factorization can also be used for finite matrices. In addition, a new method for solving banded linear systems is…
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
The famous strongly binary Goldbach's conjecture asserts that every even number $2n \geq 8$ can always be expressible as the sum of two distinct odd prime numbers. We use a new approach to dealing with this conjecture. Specifically, we…
We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.
We describe a new method of finding interpolants for classical logic using certain refutation system as a starting point. Refutation can be thought of as an alternative approach to the analysis of formal systems: instead of focusing on…
Goldbach conjecture is one of the most famous open mathematical problems. It states that every even number, bigger than two, can be presented as a sum of 2 prime numbers. % In this work we present a deep learning based model that predicts…
An algebraic framework in which to study infinite sums is proposed, complementing and augmenting the usual topological tools. The framework subsumes numerous examples in the literature. It is developed using many varied examples, with a…