Search results for "Applied Mathematics"

Note on sums containing small divisors

1976

Commutators of linear and bilinear Hilbert transforms

2003

Let α ∈ R \alpha \in \mathbb {R} , and let H α ( f , g ) ( x ) = 1 π p . v . ∫ f ( x − t ) g ( x − α t ) d t t H_\alpha (f,g)(x)=\frac {1}{\pi } p.v. \int f(x-t)g(x-\alpha t)\frac {dt}{t} and H f ( x ) = 1 π p . v . ∫ f ( x − t ) d t t Hf(x)= \frac {1}{\pi } p.v.\int f(x-t)\frac {dt}{t} denote the bilinear and linear Hilbert transforms, respectively. It is proved that, for 1 > p > ∞ 1>p>\infty and α 1 ≠ α 2 \alpha _1\ne \alpha _2 , H α 1 − H α 2 H_{\alpha _1}-H_{\alpha _2} maps L p × B M O L^p\times BMO into L p L^{p} and it maps B M O × L p BMO \times L^p into L p L^{p} if and only if sign ⁡ ( α 1 ) = sign ⁡ ( α 2 ) \operatorname {sign}(\alpha _1)=\operatorname {sign}(\alpha _2…

ON A PERMUTABILITY PROPERTY OF SUBGROUPS OF FINITE SOLUBLE GROUPS

2010

The structure and embedding of subgroups permuting with the system normalizers of a finite soluble group are studied in the paper. It is also proved that the class of all finite soluble groups in which every subnormal subgroup permutes with the Sylow subgroups is properly contained in the class of all soluble groups whose subnormal subgroups permute with the system normalizers while this latter is properly contained in the class of all supersoluble groups.

DAQs-based wattmeters for high accuracy measurements. Comparison with the Italian power primary standard

2013

Abstract This paper is focused on the use of data acquisition boards (DAQs) for the development of high accuracy PC-based instruments for the measurements of electrical power. The proposed systems are simple, portable and low cost because they are based on commercial data acquisition boards (DAQs) connected to a common personal computer. Data processing is carried out by a commercial software based on an interpolating windowed FFT. In the paper it is shown how the voltage can be sensed directly, thanks to the DAQ input range, thus avoiding expensive voltage dividers. The set up of the DAQs-based solutions is described and the evaluation of their metrological features is made by means of a c…

Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential

2016

Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations

Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting

2018

We show existence of a unique solution and a comparison theorem for a one-dimensional backward stochastic differential equation with jumps that emerge from a L\'evy process. The considered generators obey a time-dependent extended monotonicity condition in the y-variable and have linear time-dependent growth. Within this setting, the results generalize those of Royer (2006), Yin and Mao (2008) and, in the $L^2$-case with linear growth, those of Kruse and Popier (2016). Moreover, we introduce an approximation technique: Given a BSDE driven by Brownian motion and Poisson random measure, we consider BSDEs where the Poisson random measure admits only jumps of size larger than $1/n$. We show con…

Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality

2018

This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions …

Variational differential inclusions without ellipticity condition

2020

The paper sets forth a new type of variational problem without any ellipticity or monotonicity condition. A prototype is a differential inclusion whose driving operator is the competing weighted $(p,q)$-Laplacian $-\Delta_p u+\mu\Delta_q u$ with $\mu\in \mathbb{R}$. Local and nonlocal boundary value problems fitting into this nonstandard setting are examined.

“The First Mathematically Serious German School of Applied Mathematics”?

2021

This chapter is about the famous German-Austrian applied mathematician Richard von Mises (1883–1953) and his school in Berlin in the 1920s. The paper focuses on his interactions and controversies with mathematicians at the Technische Hochschule (Higher Technical College) in Berlin, in particular Georg Hamel and Rudolf Rothe, who claimed priority for their institution in the training of applied mathematicians. Von Mises emphasized the special place and characteristics of his Institute for Applied mathematics at the classical University of Berlin between pure mathematics, engineering, and industry. In the appendix of the paper the main stipulations of the “Mathematical practical course (Prakt…

Digital information receiver based on stochastic resonance

2003

International audience; An electronic receiver based on stochastic resonance is presented to rescue subthreshold modulated digital data. In real experiment, it is shown that a complete data restoration is achieved for both uniform and Gaussian white noise.