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article

Outer Measures on a Commutative Ring Induced by Measures on Its Spectrum

Dariusz Dudzik, Marcin Skrzynski

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 63-70

On a commutative ring R we study outer measures induced by measures on Spec(R). The focus is on examples of such outer measures and on subsets of R that satisfy the Carathéodory condition.

article

Some Problems in the Calculus of Variations

Arrigo Cellina

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 5-55

We present some results and open problems in the Calculus of Variations.

article

A Generalization of m-Convexity and a Sandwich Theorem

Teodoro Lara, Janusz Matkowski, Nelson Merentes, Roy Quintero, more

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 107-126

Functional inequalities generalizing m-convexity are considered. A result of a sandwich type is proved. Some applications are indicated.

article

Multipliers of Uniform Topological Algebras

Mohammed El Azhari

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 71-81

Let E be a complete uniform topological algebra with Arens-Michael normed factors [...] within an algebra isomorphism ϕ. If each factor Eα is complete, then every multiplier of E is continuous and ϕ is a topological algebra isomorphism where M(E) is endowed with its seminorm topology.

article

Report of Meeting. The Seventeenth Katowice–Debrecen Winter Seminar Zakopane (Poland), February 1–4, 2017

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 187-204

article

Lie Derivations on Trivial Extension Algebras

Amir Hosein Mokhtari, Fahimeh Moafian, Hamid Reza Ebrahimi Vishki

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 141-153

In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be expressed as a sum of a derivation and a center valued map vanishing at commutators. We then apply our results for triangular algebras. Some illuminating examples are also included.

article

On Stability of the Cauchy Functional Equation in Groupoids

Imke Toborg, Peter Volkmann

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 155-164

We give some stability results for the functional equation a(xy) = a(x) + a(y), where a: G → E, G being a groupoid and E a Banach space.

article

Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces – Revisited

Mian Bahadur Zada, Muhammad Sarwar

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 173-185

In our previous work titled “Fixed Point Results Satisfying Rational type Contractive Conditions in Complex Valued Metric Spaces”[Ann. Math. Sil. 30 (2016), 89-110], some errors has been made in the main results (Theorem 3.1, Theorem 3.7 and Theorem 3.22), that may misguide the readers. This note provides corrections of these errors.

article

A Simple Proof of the Polar Decomposition Theorem

Paweł Wójcik

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 165-171

In this expository paper, we present a new and easier proof of the Polar Decomposition Theorem. Unlike in classical proofs, we do not use the square root of a positive matrix. The presented proof is accessible to a broad audience.

article

Numerical Solution of Time Fractional Schrödinger Equation by Using Quadratic B-Spline Finite Elements

Alaattin Esen, Orkun Tasbozan

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 83-98

In this article, quadratic B-spline Galerkin method has been employed to solve the time fractional order Schrödinger equation. Numerical solutions and error norms L2 and L∞ are presented in tables.

article

On Orthogonally Additive Functions With Big Graphs

Karol Baron

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 57-62

Let E be a separable real inner product space of dimension at least 2 and V be a metrizable and separable linear topological space. We show that the set of all orthogonally additive functions mapping E into V and having big graphs is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology.

article

Invariant Means on Banach Spaces

Radosław Łukasik

Annales Mathematicae Silesianae > 2017 > 31 > 1 > 127-140

In this paper we study some generalization of invariant means on Banach spaces. We give some sufficient condition for the existence of the invariant mean and some examples where we have not it.

article

A constructive approach for solving system of fractional differential equations

H.R. Marasi, Vishnu Narayan Mishra, M. Daneshbastam

Waves, Wavelets and Fractals > 2017 > 3 > 1 > 40-47

In this paper to solve a set of linear and nonlinear fractional differential equations, we modified the differential transform method. Adomian polynomials helped taking care of the non-linear terms. The main advantage of our algorithm over the numerical methods is being able to solve nonlinear systems without any discretization or restrictive assumption. We considered Caputo definition for fractional...

article

Enumeration and investigation of acute 0/1-simplices modulo the action of the hyperoctahedral group

Jan Brandts, Apo Cihangir

Special Matrices > 2017 > 5 > 1 > 158-201

The convex hull of n + 1 affinely independent vertices of the unit n-cube In is called a 0/1-simplex. It is nonobtuse if none its dihedral angles is obtuse, and acute if additionally none of them is right. In terms of linear algebra, acute 0/1-simplices in In can be described by nonsingular 0/1-matrices P of size n × n whose Gramians G = PTP have an inverse that is strictly diagonally dominant, with...

article

Laplace - Fibonacci transform by the solution of second order generalized difference equation

Sandra Pinelas, G. B. A. Xavier, S. U. Vasantha Kumar, M. Meganathan

Nonautonomous Dynamical Systems > 2017 > 4 > 1 > 22-30

The main objective of this paper is finding new types of discrete transforms with tuning factor t. This is not only analogy to the continuous Laplace transform but gives discrete Laplace-Fibonacci transform (LFt). This type of Laplace-Fibonacci transform is not available in the continuous case. The LFt generates uncountably many outcomes when the parameter t varies on (0,∞). This possibility is not...

article

Geometric singular approach to Poisson-Nernst-Planck models with excess chemical potentials: Ion size effects on individual fluxes

Mingji Zhang, Jianbao Zhang, Daniel Acheampong

Molecular Based Mathematical Biology > 2017 > 5 > 1 > 58-77

We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck model for ionic flows through membrane channels. Excess chemical potentials are included in this work to account for finite ion size effects. This is the main difference from the classical Poisson-Nernst-Planck models, which treat ion species as point charges and neglect ion-to-ion interactions. Due to the fact that most experiments...

article

Moisture Transport due to Baroclinic Waves: Linear Analysis of Precipitating Quasi-Geostrophic Dynamics

Alfredo N. Wetzel, Leslie M. Smith, Samuel N. Stechmann

Mathematics of Climate and Weather Forecasting > 2017 > 3 > 1 > 28-50

The effects of rainfall speed, VT, and meridional/vertical moisture gradients on the meridional moisture transport are examined in the context of mid-latitude baroclinic waves. These effects are investigated in an idealized model that can be solved analytically. The model is systematically derived in a precipitating quasi-geostrophic limit, starting from a moist atmospheric model with minimal representation...

article

About tests of the “simplifying” assumption for conditional copulas

Alexis Derumigny, Jean-David Fermanian

Dependence Modeling > 2017 > 5 > 1 > 154-197

We discuss the so-called “simplifying assumption” of conditional copulas in a general framework. We introduce several tests of the latter assumption for non- and semiparametric copula models. Some related test procedures based on conditioning subsets instead of point-wise events are proposed. The limiting distributions of such test statistics under the null are approximated by several bootstrap schemes,...

article

Exact distributions of order statistics from l_n,p-symmetric sample distributions

K. Müller, W.-D. Richter

Dependence Modeling > 2017 > 5 > 1 > 221-245

We derive the exact distributions of order statistics from a finite number of, in general, dependent random variables following a joint ln,p-symmetric distribution. To this end,we first review the special cases of order statistics fromspherical aswell as from p-generalized Gaussian sample distributions from the literature. To study the case of general ln,p-dependence, we use both single-out and cone...

article

Copula-Based Dependence Measures For Piecewise Monotonicity

Eckhard Liebscher

Dependence Modeling > 2017 > 5 > 1 > 198-220

The aim of the present paper is to develop and examine association coefficients which can be helpfully applied in the framework of regression analysis. The construction of the coeffiecients is connected with the well-known Spearman coeffiecient and extensions of it (see Liebscher [5]). The proposed coeffiecient measures the discrepancy between the data points and a function which is strictly increasing...

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Outer Measures on a Commutative Ring Induced by Measures on Its Spectrum

Some Problems in the Calculus of Variations

A Generalization of m-Convexity and a Sandwich Theorem

Multipliers of Uniform Topological Algebras

Report of Meeting. The Seventeenth Katowice–Debrecen Winter Seminar Zakopane (Poland), February 1–4, 2017

Lie Derivations on Trivial Extension Algebras

On Stability of the Cauchy Functional Equation in Groupoids

Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces – Revisited

A Simple Proof of the Polar Decomposition Theorem

Numerical Solution of Time Fractional Schrödinger Equation by Using Quadratic B-Spline Finite Elements

On Orthogonally Additive Functions With Big Graphs

Invariant Means on Banach Spaces

A constructive approach for solving system of fractional differential equations

Enumeration and investigation of acute 0/1-simplices modulo the action of the hyperoctahedral group

Laplace - Fibonacci transform by the solution of second order generalized difference equation

Geometric singular approach to Poisson-Nernst-Planck models with excess chemical potentials: Ion size effects on individual fluxes

Moisture Transport due to Baroclinic Waves: Linear Analysis of Precipitating Quasi-Geostrophic Dynamics

About tests of the “simplifying” assumption for conditional copulas

Exact distributions of order statistics from l_n,p-symmetric sample distributions

Copula-Based Dependence Measures For Piecewise Monotonicity

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