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We study the spectral properties of a class of Sturm-Liouville type operators on the real line where the derivatives are replaced by a q-difference operator which has been introduced in the context of orthogonal polynomials. Using the relation of this operator to a direct integral of doubly-infinite Jacobi matrices, we construct examples for isolated pure point, dense pure point, purely absolutely
The Stieltjes-Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted L2-spaces. Under some additional assumptions these measures are exactly the solutions to the q-Pearson equation
We consider Jacobi matrices whose essential spectrum is a finite union of closed intervals. We focus on Szego{double acute}'s theorem, Jost solutions, and Szego{double acute} asymptotics for this situation. This announcement describes talks the authors gave at OPSFA 2007.
Classical graphical modeling of random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some coordinate processes of the multivariate stochastic process are unobserved, the local independence graph of the observed coordinate processes is a directed mixed graph (DMG). Tw
Let e ⊂ ℝ be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szego{double acute} condition is equivalent to (this includes prior results of Widom and Peherstorfer-Yuditskii). Using Remling's extension of the Denisov-Rakhmanov theorem and an analysis of Jost functions, we provide a
This is the first of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 1 contains most of the material on orthogonal polynomials, from the classical orthogonal polynomials of Hermite, Laguerre and Jacobi to the Askey–Wilson polynomials, which are the most general basic hypergeometric orthogonal polynomials. Separate chapter
Co- and post-translational modifications can significantly impact the structure, dynamics, and function of proteins. In this study, we investigate how N-terminal acetylation affects misfolding and self-assembly of the enzyme superoxide dismutase 1 (SOD1), implicated in amyotrophic lateral sclerosis (ALS). Studies of protein inclusions in patient samples and animal models have shown that wild-type
Background: Available fluid biomarkers, neuroimaging techniques, and clinical assessments may enhance prediction of conversion to secondary progressive multiple sclerosis (SPMS). Objectives: : To identify robust real-world predictors of MS progression in the literature. Methods: : A systematic review was conducted in EMBASE. A total of 20,338 MS patients from 64 eligible studies were included. A p
The glioblastoma (GBM) microenvironment undergoes adaptations to support tumor progression, including a dysregulated extracellular matrix, with altered heparan sulfate (HS) proteoglycans. We investigated N-deacetylase/N-sulfotransferase-1 (NDST1) because NDSTs are initial modifying enzymes of HS biosynthesis and have key roles in designing the HS sulfation pattern. This, in turn governs interactio
Let e ⊂ ℝ be a finite union of disjoint closed intervals. In the study of orthogonal polynomials on the real line with measures whose essential support is e, a fundamental role is played by the isospectral torus. In this paper, we use a covering map formalism to define and study this isospectral torus. Our goal is to make a coherent presentation of properties and bounds for this special class as a
The effect of the phase constitution of BCC/B2, FCC, Cr7C3 and their microstructural attributes are conspicuous on the hardness properties of AlCoCrFeNi HEAs [1]. The correlation of unsolicited C and O contaminant with process parameters (milling duration/rpm) and process control agent (PCA) categorically established that contamination increases with duration of mechanical alloying (MA) [2] . It i
With the rapid evolution of semiconductor technology and the growing demand for high-performance, low-power System-on-Chip solutions, the design of efficient and scalable on-chip interconnect architectures has become a critical challenge in modern ASIC development. This thesis focuses on design space exploration of replacing multiple ARM CoreLink NIC-400 crossbar-based interconnects with a unified
Power amplifiers play a crucial role in wireless communication systems. However, they can achieve high efficiency only when operating in the nonlinear region. To maintain linear output while operating in this region, several techniques have been developed, among which digital pre-distortion (DPD) is one of the most widely used. In this thesis, we designed and analyzed a digital predistortion (DPD)
