Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Star-product approach to quantum field theory: The free scalar field
1990
The star-quantization of the free scalar field is developed by introducing an integral representation of the normal star-product. A formal connection between the Feynman path integral in the holomorphic representation and the star-exponential is established for the interacting scalar fields.
The mapping properties of the radiosity operator along an edge
2002
In this article we study the radiosity operator along an edge between two adjacent half-planes. First we show that the radiosity operator is invertible in a whole scale of anisotropic Sobolev spaces. In the absence of any shadows we are able to derive regularity properties of the solution, which depend only on the angle between the half-planes, the reflectivity coefficients and the right-hand side. This work can be considered as a supplement to the article of Rathsfeld (Mathematical Methods in the Applied Sciences 1999; 22: 217–241). Copyright © 2002 John Wiley & Sons, Ltd.
On the behavior of a three-dimensional fractional viscoelastic constitutive model
2016
In this paper a three-dimensional isotropic fractional viscoelastic model is examined. It is shown that if different time scales for the volumetric and deviatoric components are assumed, the Poisson ratio is time varying function; in particular viscoelastic Poisson ratio may be obtained both increasing and decreasing with time. Moreover, it is shown that, from a theoretical point of view, one-dimensional fractional constitutive laws for normal stress and strain components are not correct to fit uniaxial experimental test, unless the time scale of deviatoric and volumetric are equal. Finally, the model is proved to satisfy correspondence principles also for the viscoelastic Poisson’s ratio a…
A geometric street scattering channel model for car-to-car communication systems
2011
This paper presents a geometric street scattering channel model for car-to-car (C2C) communication systems under line-of-sight (LOS) and non-LOS (NLOS) propagation conditions. Starting from the geometric model, we develop a stochastic reference channel model, where the scatterers are uniformly distributed in rectangles in the form of stripes parallel to both sides of the street. We derive analytical expressions for the probability density functions (PDFs) of the angle-of-departure (AOD) and the angle-of-arrival (AOA). We also investigate the Doppler power spectral density (PSD) and the autocorrelation function (ACF) of the proposed model, assuming that the mobile transmitter (MT) and the mo…
The fixed angle scattering problem and wave equation inverse problems with two measurements
2019
We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the far field pattern generated by plane waves coming from exactly two opposite directions. This implies that a reflection symmetric potential is uniquely determined by its fixed angle scattering data. We also prove a Lipschitz stability estimate for an associated problem. Motivated by the point source inverse problem in geophysics, we show that a compactly supported potential is uniquely determined from boundary measurements of the waves generated by exactl…
Performance Analysis of M-DPSK Modulation over Fast-Hoyt Fading Channels under Non-Isotropic Scattering Conditions
2021
In this paper, we analyze the symbol error probability (SEP) performance of M-ary differential phase shift keying (M-DPSK) modulation schemes over frequency-flat fast-varying Hoyt multipath fading channels. Assuming general non-isotropic scattering conditions, we first derive a finite-range integral expression for the probability density function (PDF) of the phase difference between two non-isotropic Hoyt vectors perturbed by additive white Gaussian noise (AWGN). Based upon the theory of M-DPSK modulation and the obtained PDF formula, the SEP of M-DPSK and its corresponding asymptotic behavior in non-isotropic fast-Hoyt fading channels are derived. Specifically, a double semi-finite range …
“Anti-Bayesian” flat and hierarchical clustering using symmetric quantiloids
2017
A myriad of works has been published for achieving data clustering based on the Bayesian paradigm, where the clustering sometimes resorts to Naive-Bayes decisions. Within the domain of clustering, the Bayesian principle corresponds to assigning the unlabelled samples to the cluster whose mean (or centroid) is the closest. Recently, Oommen and his co-authors have proposed a novel, counter-intuitive and pioneering PR scheme that is radically opposed to the Bayesian principle. The rational for this paradigm, referred to as the “Anti-Bayesian” (AB) paradigm, involves classification based on the non-central quantiles of the distributions. The first-reported work to achieve clustering using the A…
Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem
2011
Abstract We determine the shape which minimizes, among domains with given measure, the first eigenvalue of a nonlocal operator consisting of a perturbation of the standard Dirichlet Laplacian by an integral of the unknown function. We show that this problem displays a saturation behaviour in that the corresponding value of the minimal eigenvalue increases with the weight affecting the average up to a (finite) critical value of this weight, and then remains constant. This critical point corresponds to a transition between optimal shapes, from one ball as in the Faber–Krahn inequality to two equal balls.
*-Representations of Partial *-Algebras
2002
This chapter is devoted to *-representations of partial *-algebras. We introduce in Section 7.1 the notions of closed, fully closed, self-adjoint and integrable *-representations. In Section 7.2, the intertwining spaces of two *-representations of a partial *-algebra are defined and investigated, and using them we define the induced extensions of a *-representation. Section 7.3 deals with vector representations for a *-representation of a partial *-algebra, which are the appropriate generalization to a *-representation of the notion of generalized vectors described in Chapter 5. Regular and singular vector representations are defined and characterized by the properties of the commutant, and…
Analysis of a parabolic cross-diffusion population model without self-diffusion
2006
Abstract The global existence of non-negative weak solutions to a strongly coupled parabolic system arising in population dynamics is shown. The cross-diffusion terms are allowed to be arbitrarily large, whereas the self-diffusion terms are assumed to disappear. The last assumption complicates the analysis since these terms usually provide H 1 estimates of the solutions. The existence proof is based on a positivity-preserving backward Euler–Galerkin approximation, discrete entropy estimates, and L 1 weak compactness arguments. Furthermore, employing the entropy–entropy production method, we show for special stationary solutions that the transient solution converges exponentially fast to its…