We investigate the role of partial stickiness among particles or with a surface for turbulent transport. For former case, we re-derive known results case compressible Kraichnan model by using method based on bi-orthogonality expansion propagator in terms left and right eigenvectors. In particular, show that enforcing constraints orthogonality normalization yields were previously obtained rigoro...

Abstract Orthogonality is a fundamental theme in representation theory and Fourier analysis. An orthogonality relation for characters of finite abelian groups (now recognized as an on $\mathrm {GL}(1)$ ) was used by Dirichlet to prove infinitely many primes arithmetic progressions. relations {GL}(2)$ {GL}(3)$ have been worked researchers with broad range applications number theory. We present h...

This paper examines experimental design procedures used to develop surrogates of computational models, exploring the interplay between experimental designs and approximation algorithms. We focus on two widely used approximation approaches, Gaussian process (GP) regression and nonintrusive polynomial approximation. First, we introduce algorithms for minimizing a posterior integrated variance (IV...

Abstract. This paper examines experimental design procedures used to develop surrogates of computational models, exploring the interplay between experimental designs and approximation algorithms. We focus on two widely used approximation approaches, Gaussian process (GP) regression and nonintrusive polynomial approximation. First, we introduce algorithms for minimizing a posterior integrated va...

In the manuscript, we discuss the blur kernel measurement giving the ground truth kernel and propose an effective kernel similarity (KS) metric. In this section, we provide examples and more results to justify the proposed kernel similarity metric in Section 3 of the manuscript. A good metric for kernel similarity should be shift and range (i.e., the size of kernel) invariant. Figure 1 shows th...

Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gauss-type quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a sign-variable measure, which arises in connection with Gauss-Kronrod quadrature, and power (or implicit) orthogonality enc...

ONE OF the principal merits of the singular-eigenfunction-expansion technique, introduced initially by CASE(‘) in regard to one-speed neutron transport theory, is the systematic and classical manner in which solutions to boundary-value problems in particle transport theory are constructed. In general, we first construct a sufficiently general set of solutions, denoted as normal modes, to the ho...

In this paper, the notion of rank−k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for > 0, the notion of Birkhoff-James approximate orthogonality sets for −higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed definitions yield a natural general...

abstract almond is an important nut tree which is cultivated in many mediterranean countries. this study was carried out to study some vegetative and reproductive traits as well as qualitative and quantitative characteristics and their correlation in some self-compatible and self-incompatible genotypes obtained from crossing between touno (male parent) and shahrood 12 (female parent). quantitat...

In this paper, we study the broadcasting performance of urban Vehicle-to-everything (V2X) communications at road intersections. such environments, dense buildings obstruct radio channel between vehicles in adjacent segments and Non-Line-Of-Sight (NLOS) signal propagation reduces received power level. Therefore, messages that originate from roads traveling a non-parallel direction usually have w...