On affinity relating two positive measures and the connection coefficients between polynomials orthogonalized by these measures

We consider two positive, normalized measures dA(x) and dB(x) related by the relationship dA(x)=(C/(x+D))dB(x) or by dA(x) = (C/(x^2+E))dB(x) and dB(x) is symmetric. We show that then the polynomial sequences {a_{n}(x)}, {b_{n}(x)} orthogonal with respect to these measures are related by the relationship a_{n}(x)=b_{n}(x)+{\kappa}_{n}b_{n-1}(x) or by a_{n}(x) = b_{n}(x) + {\lambda}_{n}b_{n-2}(x) for some sequences {{\kappa}_{n}} and {{\lambda}_{n}}. We present several examples illustrating this fact and also present some attempts for extensions and generalizations. We also give some universal identities involving polynomials {b_{n}(x)} and the sequence {{\kappa}_{n}} that have a form of Fourier series expansion of the Radon--Nikodym derivative of one measure with respect to the other

On linearly related sequences of derivatives of orthogonal polynomials

We discuss an inverse problem in the theory of (standard) orthogonal polynomials involving two orthogonal polynomial families (Pn)n and (Qn)n whose derivatives of higher orders m and k (resp.) are connected by a linear algebraic structure relation such as for all n=0,1,2,..., where M and N are fixed nonnegative integer numbers, and ri,n and si,n are given complex parameters satisfying some natural conditions. Let u and v be the moment regular functionals associated with (Pn)n and (Qn)n (resp.). Assuming 0[less-than-or-equals, slant]m[less-than-or-equals, slant]k, we prove the existence of four polynomials [Phi]M+m+i and [Psi]N+k+i, of degrees M+m+i and N+k+i (resp.), such that the (k-m)th-derivative, as well as the left-product of a functional by a polynomial, being defined in the usual sense of the theory of distributions. If k=m, then u and v are connected by a rational modification. If k=m+1, then both u and v are semiclassical linear functionals, which are also connected by a rational modification. When k>m, the Stieltjes transform associated with u satisfies a non-homogeneous linear ordinary differential equation of order k-m with polynomial coefficients.http://www.sciencedirect.com/science/article/B6WK2-4SSNDCC-2/1/2844d686d4f273e5ddf7b4d7146c9ee

Local structural studies of Ba1−x_{1-x}Kx_xFe2_2As2_2 using atomic pair distribution function analysis

Systematic local structural studies of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ system are undertaken at room temperature using atomic pair distribution function (PDF) analysis. The local structure of the Ba$_{1-x}$K$_x$Fe$_2$As$_2$ is found to be well described by the long-range structure extracted from the diffraction experiments, but with anisotropic atomic vibrations of the constituent atoms ($U_{11}$ = $U_{22} \ne U_{33}$). The crystal unit cell parameters, the FeAs$_4$ tetrahedral angle and the pnictogen height above the Fe-plane are seen to show systematic evolution with K doping, underlining the importance of the structural changes, in addition to the charge doping, in determining the properties of Ba$_{1-x}$K$_x$Fe$_2$As$_2$

Adaptive responses to very low protein diets: The first comparison of ketoacids to essential amino acids

Adaptive responses to very low protein diets: The first comparison of ketoacids to essential amino acids. Eight patients with chronic renal failure (GFR 18.8 ± 2.7 ml/min) were randomized to a crossover comparison of a very low protein diet (VLPD) containing 0.28g protein and 35kcal per kg per day, plus an isomolar mixture of either ketoacids (KA) or essential amino acids (EAA). Subjects initiated the diets 14 days before hospital admission and following a four-day equilibration, a five-day nitrogen balance (BN) was performed. Whole-body protein turnover (WBPT) was measured during fasting and feeding using intravenous [1-13C]leucine and intragastric [5,5,5-2H3]leucine. Even though the VLPD/KA regimen contained 15% less nitrogen, BN was neutral and did not differ between the regimens. Nitrogen conservation with KA was due to a reduction in urea nitrogen appearance. Rates of WBPT measured during fasting and feeding did not differ between the KA or EAA regimens. During both regimens, feeding decreased protein degradation, whereas protein synthesis was unchanged. Although feeding stimulated leucine oxidation, rates were 50 to 100% lower than reported in CRF patients consuming 0.6 or 1.0g protein/kg/day. Thus, neutral BN with the VLPD regimen is achieved by a marked reduction in amino acid oxidation and a postprandial inhibition of protein degradation

Matrix interpretation of multiple orthogonality

In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials.We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector polynomials with matrix coefficients. We present a matrix interpretation of the type II multi-orthogonality conditions.We state a Favard type theorem and the expression for the resolvent function associated to the vector of linear functionals. Finally a reinterpretation of the type II Hermite- Padé approximation in matrix form is given

Western Diet in Adulthood, Timing of Menarche, and Economic Status Among Northeast Ohioans

I studied the age at first menstruation as a predictor of Western diet consumption among adults at The University of Akron and in Cleveland. I used stable carbon and nitrogen isotope compositions of human hair, as well as surveyed consumption of foods important to a Western diet (red meat, sugar, and dairy), to understand whether participants aligned with a Western dietary pattern. Age at survey and adult economic status were investigated as potential confounding variables. My data analysis and conclusions for this project has been completed and approved by my advisor and committee. To maintain collaborators\u27 ability to publish a comprehensive analysis of this dataset, I am not at liberty to publish my results here. Broader analyses of diet composition across lifetime, age at menarche, and economic status represent interesting avenues for future study

On Fourier integral transforms for qq-Fibonacci and qq-Lucas polynomials

We study in detail two families of $q$-Fibonacci polynomials and $q$-Lucas polynomials, which are defined by non-conventional three-term recurrences. They were recently introduced by Cigler and have been then employed by Cigler and Zeng to construct novel $q$-extensions of classical Hermite polynomials. We show that both of these $q$-polynomial families exhibit simple transformation properties with respect to the classical Fourier integral transform

Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure

This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure for x in [0,?), ? > ?1, a free parameter N and a shift c<0. We analyze the asymptotic behavior (both strong and relative to classical Laguerre polynomials) of these orthogonal polynomials as n tends to infinity