Results 51 to 60 of about 8,523 (167)

Confluence of hypergeometric functions and integrable hydrodynamic type systems

, 2016
It is known that a large class of integrable hydrodynamic type systems can be constructed through the Lauricella function, a generalization of the classical Gauss hypergeometric function. In this paper, we construct novel class of integrable hydrodynamic
Kodama, Y., Konopelchenko, B.
core   +1 more source

Extension of Nikiforov-Uvarov Method for the Solution of Heun Equation

, 2015
We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method.
D. Demirhan, F. Büyükkılıç, Flügge S., H. Karayer, Ince E. L., Pahlavani M. R., Ronveaux A.   +6 more
core   +1 more source

Properties and Applications of Extended Hypergeometric Functions

Ingeniería y Ciencia, 2014
In this article, we study several properties of extended Gauss hypergeometric and extended confluent hypergeometric functions. We derive several integrals, inequalities and establish relationship between these and other special functions.
Daya Krishna Nagar, Raúl Alejandro Morán-Vásquez, Arjun K Gupta   +2 more
doaj   +1 more source

A Class of Extended Mittag–Leffler Functions and Their Properties Related to Integral Transforms and Fractional Calculus

Mathematics, 2015
In a joint paper with Srivastava and Chopra, we introduced far-reaching generalizations of the extended Gammafunction, extended Beta function and the extended Gauss hypergeometric function.
Rakesh K. Parmar
doaj   +1 more source

Supersymmetry, shape invariance and the hypergeometric equation

, 2014
It has been shown earlier that the solubility of the Legendre and the associated Legendre equations can be understood as a consequence of an underlying supersymmetry and shape invariance. We have extended this result to the hypergeometric equation. Since
Das, Ashok K., Kalauni, Pushpa
core   +1 more source

Non-Integrability of Some Higher-Order Painlev\'e Equations in the Sense of Liouville [PDF]

, 2015
In this paper we study the equation $$ w^{(4)} = 5 w" (w^2 - w') + 5 w (w')^2 - w^5 + (\lambda z + \alpha)w + \gamma, $$ which is one of the higher-order Painlev\'e equations (i.e., equations in the polynomial class having the Painlev\'e property).
Christov, Ognyan, Georgiev, Georgi
core   +2 more sources

A 3D Astrocyte Microenvironment Model Enables Rapid Ca2+‐Resolved Analysis and Therapeutic Modulation of Oxidative Neuroinflammation

Advanced Healthcare Materials, EarlyView.
This work presents ARC‐3D, a soft 3D model that recreates how brain support cells, called astrocytes, react to oxidative stress. The system visualizes rapid calcium changes and inflammatory signals, and shows how the drug KDS12025 can protect cells from damage. ARC‐3D offers a simple, reliable way to study early drivers of brain inflammation.
Ju‐Kang Kim, Ye‐Ji Kim, Seyoung Ryu, Daeui Park, Kyoung‐Sik Moon, Yu Bin Lee, Dong Ho Woo   +6 more
wiley   +1 more source

Integral representations for products of two parabolic cylinder functions with different arguments and orders

, 2015
This paper derives new integral representations for products of two parabolic cylinder functions. In particular, expressions are obtained for D_{nu}(x)D_{mu}(y), with x>0 and y>0, that allow for different orders and arguments in the two parabolic ...
Veestraeten, Dirk
core   +1 more source

Low‐Temperature Fabrication of Thymosin β4‐Loaded Soluble Microneedles to Promote Wound Healing by Specific Binding to Downregulated Immune Regulators Vsig4 and IL22rɑ2

Advanced Healthcare Materials, EarlyView.
Schematic diagram depicting the fabrication and application of thymosin β4 (Tβ4)‐loaded microneedle patches for wound treatment. The Tβ4 was loaded into chitosan (CS) and sucrose MNs under mild conditions (4°C, 65% relative humidity). The Tβ4 MN patch specifically binds to the downregulated immune regulators Vsig4 and IL22rα2, thereby accelerating ...
Shilong He, Mei Yuan, Changkang Feng, Yixuan Zhang, Jinjing Che   +4 more
wiley   +1 more source

Transformations of Heun's equation and its integral relations

, 2011
We find transformations of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation.
Arscott F M, Bartolomeu D B Figueiredo, Decarreau A, Erdélyi A, Erdélyi A, Figueiredo B D B, Ince E L, Ince E L, Kantowski R, Léa Jaccoud El-Jaick, McLachlan N W, Olver F W J, Ronveaux A, Slavyanov S Yu   +13 more
core   +1 more source