相关论文: Old and new applications of Katona's circle

It gives some new forms of General Neron Desingularization and new applications.

We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.

We announce numerous new results in the theory of orthogonal polynomials on the unit circle.

In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.

We prove some new results related to Tanaka's formula.

It is shown that the squared operation of the Dirac equation which is widely applied may create new solutions and moreover may change the inner nature of original equation. Some illustrating examples are considered as well.

A construction similar to Hagge's construction for circles through the orthocentre is shown to apply for any point.

Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various…

Analogues of Kolmogorov comparison theorems and some of their applications were established.

Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.

Based on Lyndon words, a new Sudoku-like puzzle is presented and some relative theoretical questions are proposed.

We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.

I present a few new and recent ideas of the multiloop calculations.

Various uses of the renormalization group are examined.

This short note deals with some applications of the Beta function

New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…

This survey contains the introduction to the subject. Many new results are also included.

The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.