Related papers: On two extensions of Poncelet theorem
We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.
In the present note a generalization of Borel-Cantelli Lemma is proposed.
In this note, we give a criteria whether given two Eisenstein polynomials over a padic field define the same extension (Proposition 1.6). In particular, we completely identify Eisenstein polynomials of degree p (Theorem 1.16). This note is…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
We propose two distinct interpretations of extended probabilities which are realistic for the physical world.
Working from definitions and an elementarily obtained integral formula for the Euler-Mascheroni constant, we give an alternative proof of the classical Puiseux representation of the exponential integral.
We give a simple proof of the Emch closing theorem by introducing a new invariant measure on the circle. Special cases of that measures are well-known and have been used in the literature to prove Poncelet's and Zigzag theorems. Some…
We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.
The main purpose of this paper is to propose some interesting number theory problems related to the Legendre's symbol and the two-term exponential sums.
We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.
These notes contain a presentation of the noncommutative generalization of the classical moment problem introduced in [10] and [12]. They also contain a short summary of the classical moment problem in infinite dimension.
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…
We compare a traditional and non-traditional view on the subject of P-partitions, leading to formulas counting linear extensions of certain posets.
In this note a far extension of the Banach fixed point theorem is proved.
In this paper we extend the classical Korovkin theorems to the framework of comonotone additive, sublinear and monotone operators. Based on the theory of Choquet capacities, several concrete examples illustrating our results are also…
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
There has been considerable recent literature connecting Poncelet's theorem to ellipses, Blaschke products and numerical ranges, summarized, for example, in the recent book [11]. We show how those results can be understood using ideas from…