105,445 research outputs found
Brief von H. Meixner an Kurt Rothschild
No full textBRIEF VON H. MEIXNER AN KURT ROTHSCHILD
Brief von H. Meixner an Kurt Rothschild ([1]
Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations
No full textWe investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations. It is shown that the coefficients in these recurrence relations can be expressed in terms of Wronskians of modified Bessel functions and confluent hypergeometric functions, respectively for the generalized Charlier and generalized Meixner polynomials. These Wronskians arise in the description of special function solutions of the third and fifth Painlevé equations
Josef Meixner: his life and his orthogonal polynomials
No full textThis paper starts with a biographical sketch of the life of Josef Meixner.
Then his motivations to work on orthogonal polynomials and special functions
are reviewed. Meixner's 1934 paper introducing the Meixner and
Meixner-Pollaczek polynomials is discussed in detail. Truksa's forgotten 1931
paper, which already contains the Meixner polynomials, is mentioned. The paper
ends with a survey of the reception of Meixner's 1934 paper.Comment: v5: 18 pages, expressions of weights for Meixner polynomials on p.6
and weight function for Meixner-Pollaczek polynomials on p.7 correcte
Hlder-type inequalities for norms of Wick products generated by a subclass of Meixner random variables
No full textThe class of Meixner random variables can be described in terms of a Lie Algebra structure generated by their quantum operators. This Lie Algebra structure is useful in computing first the kernels that give the second quantization operators, and then the Wick products generated by these random variables. We restrict our attention to three of the most important types of Meixner random variables: Gaussian, Poisson, and Gamma, and present some H Ì older inequalities for the norms of the Wick products generated by them. We show that these inequalities are related to sharp inequalities from classic Harmonic Analysis concerning the norms of some convolution-type productsNon UBCUnreviewedAuthor affiliation: Ohio State University at MarionFacult
MRM-FACTORS FOR THE PROBABILITY MEASURES IN THE MEIXNER CLASS
No full text It is known that the gamma distribution γκ is MRM-applicable for h(x) = ex and for some hypergeometric functions also. We are interested in the problem to determine all possible MRM-factors of probability measures which are MRM-applicable for ex. We may say that the measures are in Meixner class. Such typical measures are Gaussian, Poisson, gamma, negative binomial and Meixner distributions and others are obtained from their modifications by affine transforms. We will give the complete list of MRM-factors different from ex up to trivial deformation: (1) [Formula: see text] for gamma distribution γκ. (2) [Formula: see text] for gamma distribution γκ. (3) [Formula: see text] for standard Gaussian distribution. (4) [Formula: see text] for shifted negative binomial distribution. σβ NegBin (κ,p) with κ = 2, β = 1, for Meixner distribution Mκ,η with κ = 2 and for gamma distribution γκ with κ = 2, which is a special case of (2) with c = 1. </jats:p
Difference Equations for Generalized Meixner Polynomials
No full textAbstractIn this paper is introduced a system of polynomials orthogonal with respect to the classical discrete weight function for Meixner polynomials with an extra point mass added at x=0. A difference operator of infinite order is constructed for which these new polynomials are eigenfunctions and a second-order difference equation is given with polynomial coefficients, n-dependent and of at most degree 2, which these polynomials satisfy
J(Si,H) Coupling Constants of Activated Si-H Bonds
No full textWe outline in this combined experimental and theoretical NMR study that sign and magnitude of J(Si,H) coupling constants provide reliable indicators to evaluate the extent of the oxidative addition of Si-H bonds in hydrosilane complexes. In combination with experimental electron density studies and MO analyses a simple structure-property relationship emerges: positive J(Si,H) coupling constants are observed in cases where M → L π-back-donation (M = transition metal; L = hydrosilane ligand) dominates. The corresponding complexes are located close to the terminus of the respective oxidative addition trajectory. In contrast negative J(Si,H) values signal the predominance of significant covalent Si-H interactions and the according complexes reside at an earlier stage of the oxidative addition reaction pathway. Hence, in nonclassical hydrosilane complexes such as Cp2Ti(PMe3)(HSiMe3-nCln) (with n = 1-3) the sign of J(Si,H) changes from minus to plus with increasing number of chloro substituents n and maps the rising degree of oxidative addition. Accordingly, the sign and magnitude of J(Si,H) coupling constants can be employed to identify and characterize nonclassical hydrosilane species also in solution. These NMR studies might therefore help to reveal the salient control parameters of the Si-H bond activation process in transition-metal hydrosilane complexes which represent key intermediates for numerous metal-catalyzed Si-H bond activation processes. Furthermore, experimental high-resolution and high-pressure X-ray diffraction studies were undertaken to explore the close relationship between the topology of the electron density displayed by the η2(Si-H)M units and their respective J(Si,H) couplings. (Chemical Equation Presented)
Some new results for Charlier and Meixner polynomials
No full textAbstractIn Bavinck (1996), we proved the following general result for Laguerre polynomials. For all x,α ∈C∑k=jiksL(-α-i-1)i−k(−x)L(α+j)k−j (x)=σi, 2s+j(−x)s, i,j,s∈{0,1,2,…} provided that i ⩾ 2s + j. In this letter we derive the analogues of this formula for Charlier and Meixner polynomials
Zone 2 Intensity: A Critical Comparison of Individual Variability in Different Submaximal Exercise Intensity Boundaries
No full textIntroduction: Endurance athletes often utilize low-intensity training, commonly defined as Zone 2 (Z2) within a five-zone intensity model, for its potential to enhance aerobic adaptations and metabolic efficiency. This study aimed at evaluating intra- and interindividual variability of commonly used Z2 intensity markers to assess their precision in reflecting physiological responses during training. Methods: Fifty cyclists (30 males and 20 females) performed both an incremental ramp and a step test in a laboratory setting, during which the power output, heart rate, blood lactate, ventilation, and substrate utilization were measured. Results: Analysis revealed substantial variability in Z2 markers, with the coefficients of variation (CV) ranging from 6% to 29% across different parameters. Ventilatory Threshold 1 (VT1) and maximal fat oxidation (FatMax) showed strong alignment, whereas fixed percentages of HRmax and blood lactate thresholds exhibited wide individual differences. Discussion: Standardized markers for Z2, such as fixed percentages of HRmax, offer practical simplicity but may inaccurately reflect metabolic responses, potentially affecting training outcomes. Given the considerable individual variability, particularly in markers with high CVs, personalized Z2 prescriptions based on physiological measurements such as VT1 and FatMax may provide a more accurate approach for aligning training intensities with metabolic demands. This variability highlights the need for individualized low-intensity training prescriptions to optimize endurance adaptations in cyclists, accommodating differences in physiological profiles and improving training specificity.Validerad;2025;Nivå 1;2025-04-10 (u5);Full text license: CC BY 4.0;</p
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