Related papers: A Note On Application Of Singular Rescaling

Although the results are correct, it was pointed out that the results follow from some previously known results. Accordingly, this version of the paper is withdrawn by the authors.

A simple method is shown to provide optimal variational bounds on $f$-divergences with possible constraints on relative information extremums. Known results are refined or proved to be optimal as particular cases.

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

We present a slightly simpler proof of the multilinear refined Strichartz estimate, and prove a slightly more general linear refined Strichartz estimate. Our arguments seek to clarify the connection between these estimates, refined…

In this note, we prove a quantization formula for singular reductions. The main result is obtained as a simple application of an extended quantization formula proved in [TZ2].

The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able…

Various uses of the renormalization group are examined.

Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…

Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show…

In this note, we provide with a simple example to show a defect in the definition of the geometric mixing scale, and then introduce an improved scale, called as the strong geometric mixing scale. The main theorem in this note is the…

In this paper, we give a new discovery of conversion of generalized singular values. New formulation is proposed.

Bifurcations are one of the most remarkable features of dynamical systems. Corral et al. [Sci. Rep. 8(11783), 2018] showed the existence of scaling laws describing the transient (finite-time) dynamics in discrete dynamical systems close to…

We will give a simple proof of the ambiguous class number formula.

We present some clues to the study of the renormalization group, at graduate level, as well as some bibliographical pointers to classical resources. Just the kind of things one had liked to hear when starting to study the subject.

We introduce the notions of mixed resolutions and simplicial sections, and prove a theorem relating them. This result is used (in another paper) to study deformation quantization in algebraic geometry.

Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.

We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…

With the dual variational principle and the saddle point reduction we use the abstract bifurcation theory recently developed by author in previous work to prove many new bifurcation results for solutions of four types of Hamiltonian…

The local zero structure of a smooth map may qualitatively change, when the map is subjected to small perturbations. The changes may include births and/or deaths of zeros. The qualitative properties are defined as the invariances of an…

A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…