Results 61 to 70 of about 360 (180)
Hankel Determinants of q-Stirling Numbers
The Electronic Journal of CombinatoricsIn this paper, we consider the q-analogue of the Hankel determinants of the Bell numbers and give combinatorial proofs of these results. We show that the Hankel determinants of the q-Stirling numbers can be simplified to a determinant that is almost upper-triangular, and then construct sign-reversing involutions on certain sets of RG-words that
Yue Cai, Ting Yang
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Hankel determinants for some common lattice paths
Advances in Applied Mathematics, 2008 For a single value of $\ell$, let $f(n,\ell)$ denote the number of lattice paths that use the steps $(1,1)$, $(1,-1)$, and $(\ell,0)$, that run from $(0,0)$ to $(n,0)$, and that never run below the horizontal axis. Equivalently, $f(n,\ell)$ satisfies the quadratic functional equation $F(x) = \sum_{n\ge 0}f(n,\ell) x^n = 1+x^{\ell}F(x)+x^2F(x)^2.$ Let ...
Robert A. Sulanke, Guoce Xin
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Magnetic Resonance in Medicine, Volume 96, Issue 2, Page 542-547, August 2026.ABSTRACT Purpose This study investigates the effect of VAPOR water suppression and metabolite cycling on metabolite quantification and macromolecules in proton magnetic resonance spectroscopy. Methods Single‐voxel semi‐LASER spectra (TR/TE = 3000/28 ms) and metabolite‐nulled spectra (macromolecules) were acquired in five healthy subjects in the ...
Dinesh K. Deelchand +1 more
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Bounds of Hankel Determinant for a Class of Univalent Functions
International Journal of Mathematics and Mathematical Sciences, 2012 Summary: We study coefficient conditions for the class \(\mathfrak H_\alpha\) defined as the set of all analytic functions \(f\) with \(f(0) = 0\) and \(f'(0) = 1\) which satisfy \[ \mathrm{Re}\left\{(1 - \alpha)f'(z) + \alpha\left(1 +\frac{zf''(z)}{f'(z)}\right)\right\} > \alpha \] for all \(z\) in the open unit disk, where \(\alpha\) is a real number.
Sarika Verma +2 more
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Hankel Determinants, Padé Approximations, and Irrationality Exponents [PDF]
International Mathematics Research Notices, 2015 The irrationality exponent of an irrational number $ξ$, which measures the approximation rate of $ξ$ by rationals, is in general extremely difficult to compute explicitly, unless we know the continued fraction expansion of $ξ$. Results obtained so far are rather fragmentary, and often treated case by case.
Bugeaud, Yann +3 more
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Nanophotonics, Volume 15, Issue 13, 13 July 2026.Numerical modeling of mesoscopic material response models that capture the quantum dynamics of electrons does not have to come with discouraging computational bottlenecks. The main message is that through a shift in perspective in modeling toward integral equation methods and exploiting symmetry‐based arguments, it is possible to capture complicated ...
Christos Mystilidis +4 more
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Photonic Doping of Epsilon‐Near‐Zero Bragg Microcavities
Nanophotonics, Volume 15, Issue 13, 13 July 2026.Photonic doping of an epsilon‐near‐zero (ENZ) Bragg microcavity at optical frequencies induces strong magnetic responses from dielectric inclusions, enabling intense field localization, Purcell enhancement, and tunable hybrid Bragg–Mie modes. The platform supports perfect magnetic conductor and epsilon‐and‐mu‐near‐zero regimes, offering opportunities ...
Ali Panahpour +2 more
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In Situ pH Determination Using 1H‐MRS Acetate Chemical Shift for Noninvasive Postmortem Examinations
NMR in Biomedicine, Volume 39, Issue 7, July 2026.The chemical‐shift difference between acetate and myo‐inositol measured by MRS enables estimation of pH in the acidic range. Noninvasive pH assessment in forensic investigations is demonstrated in 58 cases and validated by measurements in extracted tissue.
Sabina Frese +4 more
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Residual Water Suppression in MRS Using HLSVD With Automatic Component Selection Strategy
NMR in Biomedicine, Volume 39, Issue 7, July 2026.Residual water signals in magnetic resonance spectroscopy distort baselines and hinder metabolite quantification. We propose an automatic residual water removal method using HLSVD with the metric, termed as residual water to metabolite variance ratio (RWVR), to guide component selection.
Yi‐Ru Lin +2 more
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Linear Algebra and its Applications, 2000 Recently a definition of Hankel determinants \(H^n_k\) with entries in a finite-dimensional real vector space was given in terms of designants and Clifford algebra. Sylvester's identity can still be used for computing these determinants recursively, but the aim of this paper is to present a more efficient method avoiding the use of the Clifford algebra
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