Results 61 to 70 of about 3,786,908 (243)

Nevanlinna Theory of the Wilson Divided-difference Operator

, 2017
Sitting at the top level of the Askey-scheme, Wilson polynomials are regarded as the most general hypergeometric orthogonal polynomials. Instead of a differential equation, they satisfy a second order Sturm-Liouville type difference equation in terms of ...
Cheng, Kam Hang, Chiang, Yik-Man
core   +2 more sources

Torus Knot Polynomials and Susy Wilson Loops [PDF]

Letters in Mathematical Physics, 2014
We give, using an explicit expression obtained in [V. Jones, Ann. of Math. 126, 335 (1987)], a basic hypergeometric representation of the HOMFLY polynomial of $(n,m)$ torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result the $(m,n)\leftrightarrow (n,m)$ symmetry and the leading polynomial
Giasemidis, Georgios, Tierz, Miguel
openaire   +3 more sources

Optimization of F¯ Removal From Wastewater Utilizing Alternating Current Electrocoagulation Coupled With Sonication Using a Statistical Design Approach

Asia-Pacific Journal of Chemical Engineering, EarlyView.
ABSTRACT Combining electrochemical and advanced oxidation processes (AOPs) has greatly mitigated the limitations of electrocoagulation (EC) in water treatment. This study examined the effectiveness of sonolysis (US)‐assisted alternating current (AC)–EC in reducing fluoride (F¯) from landfill leachate wastewater (LLW), with measurements of electrical ...
Perumal Asaithambi, Madhappan Santhamoorthy, Arun Thirumurugan, Suresh Pratap, Bheem Pratap, Ravikumar Jayabal, Vishal Kumar Parida, Subramaniapillai Niju   +7 more
wiley   +1 more source

Series Solution to a Fuchsian-Type Differential Equation in Terms of Orthogonal Polynomials

Journal of Mathematics
In this paper, we study a thirteen-parameter Fuchsian-type second-order linear differential equation that involves five regular singularities. By employing a tridiagonal representation technique, we formulate four cases under which the series solutions ...
Saiful Rahman Mondal, Pratap Narayan Pathak   +1 more
doaj   +1 more source

Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations

Symmetry, Integrability and Geometry: Methods and Applications, 2009
Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors.
Ryu Sasaki, Wen-Li Yang, Yao-Zhong Zhang
doaj   +1 more source

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

IEEE Access, 2023
Discrete Racah polynomials (DRPs) are highly efficient orthogonal polynomials and used in various scientific fields for signal representation. They find applications in disciplines like image processing and computer vision.
Basheera M. Mahmmod, Sadiq H. Abdulhussain, Tomas Suk, Muntadher Alsabah, Abir Hussain   +4 more
doaj   +1 more source

Wilson function transforms related to Racah coefficients

, 2005
The irreducible $*$-representations of the Lie algebra $su(1,1)$ consist of discrete series representations, principal unitary series and complementary series.
A.N. Kirillov, D.P. Gupta, E. Buffenoir, E. Koelink, E.G. Kalnins, G. Gasper, G. Racah, G.A. Kerimov, G.A. Kerimov, H. Rosengren, H.T. Koelink, H.T. Koelink, H.T. Koelink, H.T. Koelink, I.M. Burban, J.A. Wilson, J.P. Elliott, J.V. Stokman, J.V. Stokman, K. Schmüdgen, L.C. Biedenharn, L.C. Biedenharn, L.L. Vaksman, M. Noumi, N.J. Vilenkin, R. Askey, R. Askey, R. Koekoek, S. Lievens, T.H. Koornwinder, T.H. Koornwinder, T.H. Koornwinder, V. Bargmann, W. Groenevelt, W. Groenevelt, W. Groenevelt, Wolter Groenevelt, Y.F. Smirnov   +37 more
core   +2 more sources

Emergent Spin Hall Quantization and High‐Order van Hove singularities in Square‐Octagonal MA2Z4

Advanced Physics Research, EarlyView.
Square‐octagonal MA2Z4 (M = Mo/W, A = Si/Ge, Z = pnictogen) monolayers are predicted to realize quantum spin Hall insulators with nearly quantized spin Hall conductivity enabled by an emergent spin U(1) quasi‐symmetry. Materials with Z = As and Sb host quasi‐flat bands with high‐order van Hove singularities near the Fermi level, making them promising ...
Rahul Verma, Yash Vardhan, Hsin Lin, Bahadur Singh   +3 more
wiley   +1 more source

Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts [PDF]

, 2017
In our previous papers, the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials and the Casoratian identities for the Askey-Wilson polynomial and its reduced form polynomials were presented.
Odake, Satoru
core   +3 more sources

Adaptive Machine Learning Framework for Optimizing the Affinity Purification of Adeno‐Associated Viral Vectors

Biotechnology and Bioengineering, EarlyView.
ABSTRACT Adeno‐associated viral (AAV) vectors for gene therapy are becoming integral to modern medicine, providing therapeutic options for diseases once deemed incurable. Currently, viral vector purification is a critical bottleneck in the gene therapy industry, impacting product efficacy and safety as well as accessibility and cost to patients ...
Kelvin P. Idanwekhai, Shriarjun Shastry, Morgan R. Hurst, Arianna Minzoni, Eduardo Barbieri, Luke Remmler, Eugene N. Muratov, Michael A. Daniele, Stefano Menegatti, Alexander Tropsha   +9 more
wiley   +1 more source