Related papers: A refinement of a theorem by Franks

In this paper, we establish a refined transversality theorem on linear perturbations from a new perspective of Hausdorff measures. Furthermore, we give its applications not only to singularity theory but also to multiobjective optimization.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

We introduce some generalized topological concepts to deal with union-closed families, and show that one can reduce the proof of Frankl's conjecture to some families of so-called supratopological spaces. We prove some results on the…

This review article brings forth some recent results in the theory of the Riemann zeta-function $qzeta(s)$.

In this paper, by studying the famous theorem of Pang and Zalcman, we find a normal family and obtain a result, which is an improvement of Pang and Zalcman's theorem in some sense. Meanwhile, several examples are provided to show that our…

In this short note we give counterexamples to several results related to extension theorems published recently.

Ordinary and transfinite recursion and induction and ZF set theory are used to construct from a fully interpreted object language and from an extra formula a new language. It is fully interpreted under a suitably defined interpretation.…

The theory of Weil-Stark elements is used to develop an axiomatic approach to the formulation of refined versions of Stark's Conjecture. This gives concrete new results concerning leading terms of Artin $L$-series and arithmetic properties…

We give a simple proof of the exponential de Finetti theorem due to Renner. Like Renner's proof, ours combines the post-selection de Finetti theorem, the Gentle Measurement lemma, and the Chernoff bound, but avoids virtually all…

We review sandwich theorems from the theory of convex functions.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

We present a new proof of a Finslerian version of Beltrami's theorem (1865) which works also in dimension 2.

Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.

We discuss two variations of Edwards' duality theorem. More precisely, we prove one version of the theorem for cones not necessarily containing all constant functions. In particular, we allow the functions in the cone to have a non-empty…

In this paper, we propose a generalization of a congruence due to Carlitz.

A special theorem related to the Fagnano's problem is proved and an example of the theorem is shown in a golden rectangle.

In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the…

This note gives results on the existence of semi-continuous solutions of a Fredholm integral equation of the second kind using Tarski's fixed point theorem.

We give some comments on W.M. Schmidt's theorem on Diophantine approximations with positive integers and our recent results on the topic.