Basic Analytical Properties Research Articles

The Kaniadakis Distribution for the Analysis of Income and Wealth Data.

The paper reviews the "κ-generalized distribution", a statistical model for the analysis of income data. Basic analytical properties, interrelationships with other distributions, and standard measures of inequality such as the Gini index and the Lorenz curve are covered. An extension of the basic model that best fits wealth data is also discussed. The new and old empirical evidence presented in the article shows that the κ-generalized model of income/wealth is often in very good agreement with the observed data.

On a Class of Analytic Functions Related to Robertson’s Formula Involving Crescent Shaped Domain and Lemniscate of Bernoulli

In this paper, we introduce and study the class of analytic functions in the unit disc, which are derived from Robertson’s analytic formula for starlike functions with respect to a boundary point combined with a subordination involving lemniscate of Bernoulli and crescent shaped domains. Using their symmetry property, the basic geometrical and analytical properties of the introduced classes were proved. Early coefficients and the Fekete–Szegö functional were estimated. Results for both classes were also obtained by applying the theory of differential subordinations.

On the category of quotient Banach spaces after Wegner

We study Waelbroeck's category of Banach quotients after Wegner, focusing on its basic homological and functional analytic properties.

Koecher-Maass series associated to Hermitian modular forms of degree 2 and a characterization of cusp forms by the Hecke bound

We establish basic analytic properties of the Koecher-Maass series associated to Hermitian modular forms of degree 2, level N, twisted by Maass forms on 3-dimensional hyperbolic space. As one of its applications, we give a characterization of degree 2 Hermitian cusp forms by the growth of their Fourier coefficients.

Translated Logarithmic Lambert Function and its Applications to Three-Parameter Entropy

The translated logarithmic Lambert function is defined and basic analytic properties of the function are obtained including the derivative, integral, Taylor series expansion, real branches and asymptotic approximation of the function. Moreover, the probability distribution of the three-parameter entropy is derived which is expressed in terms of the translated logarithmic Lambert function.

Use of a Mixture of Polyols Based on Metasilicic Acid and Recycled PLA for Synthesis of Rigid Polyurethane Foams Susceptible to Biodegradation.

Two polyol raw materials were obtained in the conducted research, one based on metasilicic acid (MSA), the other based on poly(lactic acid) (PLA) waste. The obtained polyols were characterized in terms of their applicability for the production of rigid polyurethane foams (RPUFs). Their basic analytical properties (hydroxyl number, acid number, elemental analysis) and physicochemical properties (density, viscosity) were determined. The assumed chemical structure of the obtained new compounds was confirmed by performing FTIR and 1H NMR spectroscopic tests. Formulations for the synthesis of RPUFs were developed on the basis of the obtained research results. A mixture of polyols based on MSA and PLA in a weight ratio of 1:1 was used as the polyol component in the polyurethane formulation. The reference foam in these tests was a foam that was synthesized only on the basis of MSA-polyol. The obtained RPUFs were tested for basic functional properties (apparent density, compressive strength, water absorption, thermal conductivity coefficient etc.). Susceptibility to biodegradation in soil environment was also tested. It was found that the use of mixture of polyols based on MSA and PLA positively affected the properties of the obtained foam. The polyurethane foam based on this polyol mixture showed good thermal resistance and significantly reduced flammability in comparison with the foam based MSA-polyol. Moreover, it showed higher compressive strength, lower thermal conductivity and biodegradability in soil. The results of the conducted tests confirmed that the new foam was characterized by very good performance properties. In addition, this research provides information on new waste management opportunities and fits into the doctrine of sustainable resource management offered by the circular economy.

Online learning with stability guarantees: A memory-based warm starting for real-time MPC

We propose and analyze a real-time model predictive control (MPC) scheme that utilizes stored data to improve its performance by learning the value function online with stability guarantees. For linear and nonlinear systems, a learning method is presented that makes use of basic analytic properties of the cost function and is proven to learn the MPC control law and the value function on the limit set of the closed-loop state trajectory. The main idea is to generate a smart warm start based on historical data that improves future data points and thus future warm starts. We show that these warm starts are asymptotically exact and converge to the solution of the MPC optimization problem. Thereby, the suboptimality of the applied control input resulting from the real-time requirements vanishes over time. Numerical examples show that existing real-time MPC schemes can be improved by storing optimization data and using the proposed learning scheme.

Imaginary multiplicative chaos: Moments, regularity and connections to the Ising model

In this article we study imaginary Gaussian multiplicative chaos—namely a family of random generalized functions which can formally be written as $e^{iX(x)}$, where $X$ is a log-correlated real-valued Gaussian field on $\mathbf{R}^{d}$, that is, it has a logarithmic singularity on the diagonal of its covariance. We study basic analytic properties of these random generalized functions, such as what spaces of distributions these objects live in, along with their basic stochastic properties, such as moment and tail estimates. After this, we discuss connections between imaginary multiplicative chaos and the critical planar Ising model, namely that the scaling limit of the spin field of the critical planar XOR-Ising model can be expressed in terms of the cosine of the Gaussian free field, that is, the real part of an imaginary multiplicative chaos distribution. Moreover, if one adds a magnetic perturbation to the XOR-Ising model, then the scaling limit of the spin field can be expressed in terms of the cosine of the sine-Gordon field, which can also be viewed as the real part of an imaginary multiplicative chaos distribution. The first sections of the article have been written in the style of a review, and we hope that the text will also serve as an introduction to imaginary chaos for an uninitiated reader.

Abstract Coherent State Transforms Over Homogeneous Spaces of Compact Groups

This paper presents theoretical aspects of a unified generalization for the abstract theory of coherent state/voice transforms over homogeneous spaces of compact groups using operator theory. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and $$\mu $$ be the normalized G-invariant measure on G/H associated to the Weil’s formula with respect to the probability measures of G, H. Let $$(\pi ,\mathcal {H}_\pi )$$ be a continuous unitary representation of G with non-zero mean over H. In this article, we introduce the generalized notion of coherent state/voice transform associated to $$\pi $$ on the Hilbert function $$L^2(G/H,\mu )$$ . We then study basic analytic properties of these transforms.

κ-generalized models of income and wealth distributions: A survey

The paper provides a survey of results related to the "$\kappa$-generalized distribution", a statistical model for the size distribution of income and wealth. Topics include, among others, discussion of basic analytical properties, interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution field, such as the Gini index and the Lorenz curve. An extension of the basic model that is most able to accommodate the special features of wealth data is also reviewed. The survey of empirical applications given in this paper shows the $\kappa$-generalized models of income and wealth to be in excellent agreement with the observed data in many cases.

Twists and resonance of $L$-functions, I

We obtain the basic analytic properties, i.e. meromorphic continuation, polar structure and bounds for the order of growth, of all the nonlinear twists with exponents ≤ 1 / d of the L -functions of any degree d ≥ 1 in the extended Selberg class. In particular, this solves the resonance problem in all such cases.

Mappings of finite distortion between metric measure spaces

We establish the basic analytic properties of mappings of finite distortion between proper Ahlfors regular metric measure spaces that support a ( 1 , 1 ) (1,1) -Poincaré inequality. As applications, we prove that under certain integrability assumption for the distortion function, the branch set of a mapping of finite distortion between generalized n n -manifolds of type A A has zero Hausdorff n n -measure.

Discrete dynamics of one dimensional Collatz like integral value transformations

In Discrete dynamics and number theory, one of the most important challenging conjectures is Collatz conjecture. Some basic algebraic and analytical properties of Collatz like integral value transformations (IVTs) in the context of discrete dynamical system over \(\mathbb {N}_0\) are adumbrated. The dynamical maps associated to the dynamical systems are everywhere continuous but nowhere differentiable (smooth) in domain \(\mathbb {N}_0\). Under such Collatz like IVTs, for any initial point \(X_0\)\(\in \)\(\mathbb {N}_0\) the dynamical systems are convergent and converge eventually to a single point attractor, zero. In other words, the image sets associated to the Collatz like dynamical maps in each iteration converge to a single point image set consisting the point zero. The rate of convergence of the Collatz like dynamical system with respect to some property is also described. It is observed that the \(l_2\)-norm of the ith order derivative operator for all Collatz like map is a decreasing convergent sequence which converges to zero.

A mixed ODE–PDE model for vehicular traffic

AbstractWe present a traffic flow model consisting of a gluing between the Lighthill–Whitham and Richards macroscopic model with a first‐order microscopic following the leader model. The basic analytical properties of this model are investigated. Existence and uniqueness are proved, as well as the basic estimates on the dependence of solutions from the initial data. Moreover, numerical integrations show some qualitative features of the model, in particular the transfer of information among regions where the different models are used. Copyright © 2014 John Wiley & Sons, Ltd.

A well-balanced numerical scheme for a one-dimensional quasilinear hyperbolic model of chemotaxis

We introduce a numerical scheme to approximate a quasi-linear hyperbolic system which models the movement of cells under the influence of chemotaxis. Since we expect to find solutions which contain vacuum parts, we propose an upwinding scheme which handles properly the presence of vacuum and, besides, which gives a good approximation of the time asymptotic states of the system. For this scheme we prove some basic analytical properties and study its stability near some of the steady states of the system. Finally, we present some numerical simulations which show the dependence of the asymptotic behavior of the solutions upon the parameters of the system.

Technological Features of Surface Functionalization of Nanosized Particles of Various Nature

The technological universality of the developed methods of surface functionalization was exemplified by carbon (160 nm) and ferrocarbon (4-6 nm) nanoparticles. Based on universal technological scheme, the study demonstrated the possibilities of methodical variants with due account for the intrinsic properties of the particles such as carbonic surface and magnetism. The basic analytic properties of the developed diagnostic systems were examined to assess their prospective use in detection of the stereospecific molecules and their interaction. The model systems have been developed, which demonstrated the analytic potencies of the reagents obtained.

Zeta functions of discrete self-similar sets

In this paper we study a class of countable and discrete subsets of a Euclidean space that are “self-similar” with respect to a finite set of (affine) similarities. Any such set can be interpreted as having a fractal structure. We introduce a zeta function for these sets, and derive basic analytic properties of this “fractal” zeta function. Motivating examples that come from combinatorial geometry and arithmetic are given particular attention.

Enhancing sensitivity and selectivity in the determination of aldehydes in olive oil by use of a Tenax TA trap coupled to a UV-ion mobility spectrometer

A Tenax TA trap was coupled to an ion mobility spectrometer in order to improve basic analytical properties such as sensitivity and selectivity. The analytical performance of this combination was assessed in the determination of volatile aldehydes between 3 and 6 carbon atoms present in olive oil. The aldehydes were extracted and adsorbed into the trap, from which they were thermally desorbed for analysis by UV-Ion Mobility Spectrometry (UV-IMS). Sensitivity was increased by the preconcentration step and selectivity by the combination of temperature programmed thermal desorption and the ability of the ion mobility spectrometer to monitor the desorbed analytes in real time. The limits of detection obtained were lower than 0.3 mg kg −1 and the relative standard deviation lower than 10%. A one-way analysis of variance (ANOVA) was used to identify significant differences between olive oil grades in terms of peak heights for the target aldehydes.

Modelling the dynamics of granular matter

This work presents a new model for the movement of granular matter. It is a synthesis of the Hadeler–Kuttler and of the Savage–Hutter models. The result is a 3 × 3 system of balance laws able to describe the deposition–erosion dynamics, as in the former model, while being compliant with energy dissipation, as in the latter one. First, the basic analytical properties of the new model are described. Then, several numerical integrations allow to compare the different models. The present model appears to provide better descriptions of granular matter behaviour, in particular as soon as the bed’s slope changes sign and deposition–erosion phenomena are relevant.

Coupling conditions for the $3\times 3$ Euler system

This paper is devoted to the extension to the full $3\times3$ Euler system of the basic analytical properties of the equations governing a fluid flowing in a duct with varying section. First, we consider the Cauchy problem for a pipeline consisting of 2 ducts joined at a junction. Then, this result is extended to more complex pipes. A key assumption in these theorems is the boundedness of the total variation of the pipe's section. We provide explicit examples to show that this bound is necessary.