𝑞-Tricomi functions and quantum algebra representations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mumtaz Riyasat ◽  
Tabinda Nahid ◽  
Subuhi Khan
Keyword(s):  
Irreducible Representation ◽  
Series Expansion ◽  
Quantum Groups ◽  
Bessel Functions ◽  
Special Functions ◽  
Quantum Algebra ◽  
Two Dimensional ◽  
Quantum Algebras ◽  
Mathematical Software ◽  
First Time

AbstractThe quantum groups nowadays attract a considerable interest of mathematicians and physicists. The theory of 𝑞-special functions has received a group-theoretic interpretation using the techniques of quantum groups and quantum algebras. This paper focuses on introducing the 𝑞-Tricomi functions and 2D 𝑞-Tricomi functions through the generating function and series expansion and for the first time establishing a connecting relation between the 𝑞-Tricomi and 𝑞-Bessel functions. The behavior of these functions is described through shapes, and the contrast between them is observed using mathematical software. Further, the problem of framing the 𝑞-Tricomi and 2D 𝑞-Tricomi functions in the context of the irreducible representation (\omega) of the two-dimensional quantum algebra \mathcal{E}_{q}(2) is addressed, and certain relations involving these functions are obtained. 2-Variable 1-parameter 𝑞-Tricomi functions and their relationship with the 2-variable 1-parameter 𝑞-Bessel functions are also explored.

APPLICATIONS OF COMPUTER ALGEBRA IN QUANTUM GROUPS

1994 ◽  
Vol 05 (04) ◽  
pp. 701-706
Author(s):  
W.-H. STEEB
Keyword(s):  
Quantum Groups ◽  
Computer Algebra ◽  
Kronecker Product ◽  
Quantum Algebra ◽  
Theoretical Physics ◽  
Baxter Equation ◽  
Quantum Algebras ◽  
Helpful Tool

Quantum groups and quantum algebras play a central role in theoretical physics. We show that computer algebra is a helpful tool in the investigations of quantum groups. We give an implementation of the Kronecker product together with the Yang-Baxter equation. Furthermore the quantum algebra obtained from the Yang-Baxter equation is implemented. We apply the computer algebra package REDUCE.

scholarly journals Influence of a Standing Wave Flow-Field on the Dynamics of a Spray Diffusion Flame

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 27
Author(s):  
J. Barry Greenberg ◽  
David Katoshevski
Keyword(s):  
Liquid Phase ◽  
Flow Field ◽  
Standing Wave ◽  
Diffusion Flame ◽  
Stokes Number ◽  
Flame Height ◽  
Wave Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
First Time

A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid phase, the use of a small Stokes number as the perturbation parameater enables a solution of the governing equations to be developed. Influence of the standing wave flow-field on droplet grouping is described by a specially constructed modification of the vaporization Damkohler number. Instantaneous flame front shapes are found via a solution for the usual Schwab–Zeldovitch parameter. Numerical results obtained from the analytical solution uncover the strong bearing that droplet grouping, induced by the standing wave flow-field, can have on flame height, shape, and type (over- or under-ventilated) and on the existence of multiple flame fronts.

scholarly journals Tetrazine molecules as efficient electronic diversion channel in 2D organic-inorganic perovskites

2021 ◽  
Author(s):  
Ferdinand Lédée ◽  
Pierre Audebert ◽  
Gaëlle Trippé-Allard ◽  
Laurent Galmiche ◽  
Damien Garrot ◽  
...  
Keyword(s):  
Organic Component ◽  
Two Dimensional ◽  
Diversion Channel ◽  
Halide Perovskites ◽  
First Time

We present the synthesis of two novel two-dimensional (2D) hybrid organic-inorganic halide perovskites incorporating for the first time 100% of a photoactive tetrazine derivative as the organic component. With this...

scholarly journals Exfoliation in a low boiling point solvent and electrochemical applications of MoO3

2020 ◽  
Vol 11 ◽  
pp. 662-670
Author(s):  
Matangi Sricharan ◽  
Bikesh Gupta ◽  
Sreejesh Moolayadukkam ◽  
H S S Ramakrishna Matte
Keyword(s):  
Energy Storage ◽  
Electrode Material ◽  
Electronic Devices ◽  
High Specific Capacitance ◽  
Two Dimensional ◽  
Energy Storage Devices ◽  
Intrinsic Nature ◽  
Storage Devices ◽  
Scan Rate ◽  
First Time

MoO3 is a versatile two-dimensional transition metal oxide having applications in areas such as energy storage devices, electronic devices and catalysis. To efficiently utilize the properties of MoO3 arising from its two-dimensional nature exfoliation is necessary. In this work, the exfoliation of MoO3 is carried out in 2-butanone for the first time. The achieved concentration of the dispersion is about 0.57 mg·mL−1 with a yield of 5.7%, which are the highest values reported to date. These high values of concentration and yield can be attributed to a favorable matching of energies involved in exfoliation and stabilization of MoO3 nanosheets in 2-butanone. Interestingly, the MoO3 dispersion in 2-butanone retains its intrinsic nature even after exposure to sunlight for 24 h. The composites of MoO3 nanosheets were used as an electrode material for supercapacitors and showed a high specific capacitance of 201 F·g−1 in a three-electrode configuration at a scan rate of 50 mV·s−1.

A quantum algebra approach to basic multivariable special functions

1994 ◽  
Vol 27 (20) ◽  
pp. 6781-6797 ◽  
Author(s):  
R Floreanini ◽  
L Lapointe ◽  
L Vinet
Keyword(s):  
Special Functions ◽  
Quantum Algebra ◽  
Algebra Approach

On the generalized fractional Laplacian

2021 ◽  
Vol 24 (6) ◽  
pp. 1797-1830
Author(s):  
Chenkuan Li
Keyword(s):  
Fractional Laplacian ◽  
Special Functions ◽  
Computational Techniques ◽  
Residue Theorem ◽  
End Points ◽  
Proper Subspace ◽  
Classical Sense ◽  
First Time ◽  
Cauchy’S Residue Theorem ◽  
Integral Identities

Abstract The objective of this paper is, for the first time, to extend the fractional Laplacian (−△) s u(x) over the space Ck (Rn ) (which contains S(Rn ) as a proper subspace) for all s > 0 and s ≠ 1, 2, …, based on the normalization in distribution theory, Pizzetti’s formula and surface integrals in Rn . We further present two theorems showing that our extended fractional Laplacian is continuous at the end points 1, 2, … . Two illustrative examples are provided to demonstrate computational techniques for obtaining the fractional Laplacian using special functions, Cauchy’s residue theorem and integral identities. An application to defining the Riesz derivative in the classical sense at odd numbers is also considered at the end.

scholarly journals Salmonella Typhi and Salmonella Paratyphi A elaborate distinct systemic metabolite signatures during enteric fever

eLife ◽  
2014 ◽  
Vol 3 ◽  
Author(s):  
Elin Näsström ◽  
Nga Tran Vu Thieu ◽  
Sabina Dongol ◽  
Abhilasha Karkey ◽  
Phat Voong Vinh ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Gas Chromatography ◽  
Bacterial Infections ◽  
Enteric Fever ◽  
Salmonella Typhi ◽  
Two Dimensional ◽  
Flight Mass Spectrometry ◽  
Metabolite Profiles ◽  
Diagnostic Approaches ◽  
First Time

The host–pathogen interactions induced by Salmonella Typhi and Salmonella Paratyphi A during enteric fever are poorly understood. This knowledge gap, and the human restricted nature of these bacteria, limit our understanding of the disease and impede the development of new diagnostic approaches. To investigate metabolite signals associated with enteric fever we performed two dimensional gas chromatography with time-of-flight mass spectrometry (GCxGC/TOFMS) on plasma from patients with S. Typhi and S. Paratyphi A infections and asymptomatic controls, identifying 695 individual metabolite peaks. Applying supervised pattern recognition, we found highly significant and reproducible metabolite profiles separating S. Typhi cases, S. Paratyphi A cases, and controls, calculating that a combination of six metabolites could accurately define the etiological agent. For the first time we show that reproducible and serovar specific systemic biomarkers can be detected during enteric fever. Our work defines several biologically plausible metabolites that can be used to detect enteric fever, and unlocks the potential of this method in diagnosing other systemic bacterial infections.

scholarly journals TWO-DIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMS

2016 ◽  
Vol 56 (3) ◽  
pp. 245
Author(s):  
Marzena Szajewska ◽  
Agnieszka Tereszkiewicz
Keyword(s):  
Boundary Value Problems ◽  
Special Functions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Dirichlet Condition ◽  
Two Dimensional ◽  
Neumann Type ◽  
Neumann Boundary Value Problems ◽  
Real Euclidean Space

Boundary value problems are considered on a simplex <em>F</em> in the real Euclidean space R<sup>2</sup>. The recent discovery of new families of special functions, orthogonal on <em>F</em>, makes it possible to consider not only the Dirichlet or Neumann boundary value problems on <em>F</em>, but also the mixed boundary value problem which is a mixture of Dirichlet and Neumann type, ie. on some parts of the boundary of <em>F</em> a Dirichlet condition is fulfilled and on the other Neumann’s works.

scholarly journals Structural Transitions at Microtubule Ends Correlate with Their Dynamic Properties in Xenopus Egg Extracts

2000 ◽  
Vol 149 (4) ◽  
pp. 767-774 ◽  
Author(s):  
Isabelle Arnal ◽  
Eric Karsenti ◽  
Anthony A. Hyman
Keyword(s):  
Dynamic Instability ◽  
Dynamic Properties ◽  
Microtubule Assembly ◽  
Two Dimensional ◽  
Egg Extracts ◽  
Xenopus Egg ◽  
Xenopus Egg Extracts ◽  
First Time ◽  
The Relationship ◽  
Dynamic Populations

Microtubules are dynamically unstable polymers that interconvert stochastically between growing and shrinking states by the addition and loss of subunits from their ends. However, there is little experimental data on the relationship between microtubule end structure and the regulation of dynamic instability. To investigate this relationship, we have modulated dynamic instability in Xenopus egg extracts by adding a catastrophe-promoting factor, Op18/stathmin. Using electron cryomicroscopy, we find that microtubules in cytoplasmic extracts grow by the extension of a two- dimensional sheet of protofilaments, which later closes into a tube. Increasing the catastrophe frequency by the addition of Op18/stathmin decreases both the length and frequency of the occurrence of sheets and increases the number of frayed ends. Interestingly, we also find that more dynamic populations contain more blunt ends, suggesting that these are a metastable intermediate between shrinking and growing microtubules. Our results demonstrate for the first time that microtubule assembly in physiological conditions is a two-dimensional process, and they suggest that the two-dimensional sheets stabilize microtubules against catastrophes. We present a model in which the frequency of catastrophes is directly correlated with the structural state of microtubule ends.

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