Related papers: Generalizations of Ceva's Theorem and Applications
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
We will give several reduction theorems for Noether's problem.
We introduce some general and special formulations of general position theorem for parametrized families of fractals and explain the techniques of its application to prove the existence of self-similar sets with prescribed special…
We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof…
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.
We consider a number of generalizations of the $\beta$-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements…
Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…
We find Feynman-Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.
We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series…
Several new applications of Katona's circle are given.
Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.
Analogues of Kolmogorov comparison theorems and some of their applications were established.
In this paper, we introduced the theory of the sieve function transformation. Using the principle of sieve function transformation, we improved sieve method, and obtained the difference range of similar sieve function values. For this, we…
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.
The theory of Selberg zeta functions is generalized to higher rank spaces. Applications towards analytic torsion numbers are given.
This paper evaluates some generalised Euler sums involving the digamma function.