Results 61 to 70 of about 84,466 (284)

Whittaker-Shintani functions for orthogonal groups

Tohoku Mathematical Journal, 2003
Paraphrasing from the authors' introduction: Let \(G=SO(m)\) be a split special orthogonal group of degree \(m=m'+r+1\), \(r\geq 0\), defined over a non-archimedean local field \(k\). Let \(Q\) be a parabolic subgroup of \(G\) whose Levi subgroup is isomorphic to \(SO(m'+1)\times GL(1)^r\), and let \(U\) be the unipotent radical of \(Q\).
Kato, Shin-ichi, Murase, Atsushi, Sugano, Takashi   +2 more
openaire   +2 more sources

The modulus of Whittaker functions [PDF]

Integral Transforms and Special Functions, 2020
The paper discusses some properties of the modulus $|W_{k,m}(z)|$ of the Whittaker function $W_{k,m}(z)$. In particular, completely monotone functions expressed in terms of $|W_{k,m}(z)|$ are found. The results follow from an integral representation for products of Whittaker functions due to Erdélyi (1938).
openaire   +2 more sources

Development of Raman Spectroscopy and Machine Learning Methods for Protein Aggregate Quantification: Application to BSA in Chromatographic Processes

Biotechnology and Bioengineering, EarlyView.
ABSTRACT Protein aggregation poses a significant risk to biopharmaceutical product quality, as even minor amounts of oligomeric species can compromise efficacy and safety. Rapid and reliable detection of protein aggregates thus remains a major challenge in biopharmaceutical manufacturing.
Jakob Heyer‐Müller, Robin Schiemer, Lars Robbel, Michael Schmitt, Jürgen Hubbuch   +4 more
wiley   +1 more source

A whittaker function of matrix argument

Linear Algebra and its Applications, 1998
Für positiv definite symmetrische \(p\times p\)-Matrizen und für \(\text{Re} (\beta-\alpha)> (p-3)/4\) wird die Whittaker-Funktion \(W_{\alpha,\beta} (A)\) durch folgende Gleichung definiert: \[ \begin{multlined} |A|^{-\beta- (p+1)/4} \Gamma_p(\beta- \alpha+(p+1)/4) e^{\text{tr } A/2} W_{\alpha,\beta}(A)=\\ \int|Z|^{\beta- \alpha-(p+1)/4} |I+Z|^{\alpha+
Mathai, A.M., Pederzoli, Giorgio
openaire   +1 more source

Mellin transforms of Whittaker functions [PDF]

Bulletin de la Société mathématique de France, 1993
The authors study in detail the Mellin transform of Jacquet's Whittaker function for \(\text{GL}(n,\mathbb{R})\) and give a new proof for its meromorphic continuation, see also [\textit{H. Jacquet} and \textit{J. Shalika}, Automorphic forms, Shimura varieties and \(L\)-functions, Proc. Conf. Ann Arbor 1988, Perspect. Math.
Friedberg, Solomon, Goldfeld, Dorian
openaire   +1 more source

Optimization of cut‐hole layout under high in situ stress based on numerical simulation and field tests

Deep Underground Science and Engineering, EarlyView.
This study investigates the blast‐induced rock damage patterns under different cut‐hole layouts and ground stress conditions through numerical simulations and field tests. The findings in this study provide valuable insights for similar underground engineering applications.
Junjie Zhao, Diyuan Li, P. G. Ranjith, Xinxin Lü, Yanliang Li, Xiaoli Su   +5 more
wiley   +1 more source

Angular invariant quantum mechanics in arbitrary dimension

Revista Brasileira de Ensino de Física
One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in a radially ...
Sergio Giardino
doaj   +1 more source

Umbral Vade Mecum

Frontiers in Physics, 2013
In recent years the umbral calculus has emerged from the shadows to provide an elegant correspondence framework that automatically gives systematic solutions of ubiquitous difference equations --- discretized versions of the differential cornerstones ...
Thomas L Curtright, Cosmas K Zachos
doaj   +1 more source

Developing a macroecology for human‐altered ecosystems

Ecography, EarlyView.
Although anthropogenically‐induced ecological disruptions are fundamentally important in defining ecosystem properties, they are largely overlooked by macroecological theory. Anthropogenic disruptions and their effects are generally not comparable to one another, nor to disturbances that are part of natural disturbance regimes.
Erica A. Newman, Mark Q. Wilber, Alexandre Génin, Oriana E. Chafe, Henry F. Houskeeper, Steven Lee, Eric L. Berlow, John Harte   +7 more
wiley   +1 more source

Deep refuges: the distribution of marine fish in warming subtropics

Ecography, EarlyView.
In light of global climate change, identifying critical marine habitats and conserving them is essential. Marine conservation planning recommends designating cooler habitats as marine protected areas. The ‘deep‐reef refugia' hypothesis suggests that deeper, suitable habitats may allow species to undergo the evolutionary changes necessary to adapt to ...
Anat Tsemel, Stephane Martinez, Shai Einbinder, Hagai Nativ, Avery Deveto, Ole J. Sorensen, Ido Izhaki, Dan Tchernov   +7 more
wiley   +1 more source