Some remarks about metric spaces

Some remarks about solenoids, 2

A class of solenoids is considered, including some aspects in n (topological) dimensions, where one basically gets some fractal versions of tori.

Some remarks about Cauchy integrals and fractal sets

Some aspects of Cauchy integrals on sets with dimension larger than 1 are briefly discussed.

Some remarks about Cauchy integrals

This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.

A few remarks about linear operators and disconnected open sets in the plane

Some aspects of analysis on disconnected open subsets of the plane with connected fractal boundary are discussed.

Some remarks about homeomorphisms, "energy", and so on

This paper briefly discusses some questions with analytical and topological aspects, with hopefully some useful references on both sides.

Remarks on Ultrametrics and Metric-Preserving Functions

Functions whose composition with every metric is a metric are said to be metric-preserving. In this article, we investigate a variation of the concept of metric-preserving functions where metrics are replaced by ultrametrics.

Some remarks about Clifford analysis and fractal sets

Although Clifford analysis is like complex analysis in many ways, there are obvious differences related to noncommutativity, and a few aspects of this are considered here.

Remarks about the existence of conformable derivatives and some consequences

The aim of the present paper is to make some notes to the newly introduced conformable derivative as a type local fractional derivative and to present a surprising result about the relation between the conformable derivatives and the usual integer order derivatives.

关于可变指数的Calderón-Hardy空间的注记

A remark about Calderón-Hardy spaces with variable exponents

本文改进了可变指数Calderón-Hardy空间中参数q的值，提升了相关理论的精确性。

Some remarks about Descartes' rule of signs

What can we deduce about the roots of a real polynomial in one variable by simply considering the signs of its coefficients? On one hand, we give a complete answer concerning the positive roots, by proposing a statement of Descartes' rule of signs which strengthens the available ones while remaining as elementary and concise as the original. On the other hand, we provide new kinds of restrictions on the combined numbers of positive and negative roots.

Some remarks about Cauchy integrals and totally real surfaces in C^m

There seems to be quite a bit of room for interesting things related to surfaces M in C^m with real dimension m which are totally real and aspects of several complex variables on C^m around M. A basic case occurs when m = 1, with Cauchy integral operators along curves, holomorphic functions on the complements of curves, and so on. In the present article we briefly indicate a few points concerning these matters.

A remark about critical sets in $R^3$

We give a necessary condition for a closed subset of $R^3$ to be the set of critical points of some smooth function. In particular we obtain that for example neither the Whitehead continuum nor the p-adic solenoid are such a critical sets.

Some remarks about q-Chebyshev polynomials and q-Catalan numbers and related results

The moments of the Lucas polynomials and of the Chebyshev polynomials of the first kind are (multiples of) central binomial coefficients and the moments of the Fibonacci polynomials and of the Chebyshev polynomials of the second kind are Catalan numbers. In this survey paper we present some generalizations of these results together with various q-analogues.

Some remarks about The Morse-Sard theorem and approximate differentiability

Let $n, m$ be positive integers, $n\geq m$. We make several remarks on the relationship between approximate differentiability of higher order and Morse-Sard properties. For instance, among other things we show that if a function $f:\mathbb{R}^n\to\mathbb{R}^m$ is locally Lipschitz and is approximately differentiable of order $i$ almost everywhere with respect to the Hausdorff measure $\mathcal{H}^{i+m-2}$, for every $i=2, \dots, n-m+1$, then $f$ has the Morse-Sard property (that is to say, the image of the critical set of $f$ is null with respect to the Lebesgue measure in $\mathbb{R}^m$).