On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions

Mathematics Subject Classification: 33D60, 33D90, 26A33Fractional q-integral operators of generalized Weyl type, involving generalized basic hypergeometric functions and a basic analogue of Fox’s H-function have been investigated. A number of integrals involving various q-functions have been evaluated as applications of the main results

Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.The object of this article is to present the computational solution of one-dimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function. It provides an elegant extension of a result given earlier by Debnath, and by Saxena et al. The main result is obtained in the form of Theorem 1. Three special cases of this theorem are given as corollaries. Computational representation of the fundamental solution of the proposed equation is also investigated

On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function

2000 Mathematics Subject Classification: 33D60, 26A33, 33C60The present paper envisages the applications of Riemann-Liouville fractional q-integral operator to a basic analogue of Fox H-function. Results involving the basic hypergeometric functions like Gq(.), Jv(x; q), Yv(x; q),Kv(x; q), Hv(x; q) and various other q-elementary functions associated with the Riemann-Liouville fractional q-integral operator have been deduced as special cases of the main result

On the numerical evaluation of algebro-geometric solutions to integrable equations

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey-Stewartson and the multi-component nonlinear Schr\"odinger equations.Comment: 29 pages, 20 figure

A rare case of arteriovenous malformation following hysterectomy in a case of choriocarcinoma

A uterine arteriovenous malformation (AVM) is a rare cause of uterine bleeding. It may have varied presentations ranging from being completely asymptomatic; to features of congestive heart failure, to vaginal bleeding which may at times life be threatening. Clinical findings in such cases are often un-reliable; requiring a high index of suspicion to make the diagnosis. We report a case of a 46-year-old lady who presented with heavy vaginal bleeding. She has undergone hysterectomy with a histopathology of choriocarcinoma one and half months back. She has received chemotherapy and 8 fractions of radiotherapy for the same. AVM was diagnosed following a CT angiogram and was managed by embolization. We also discuss in brief about this uncommon but serious condition which the radiologist/gynaecologist may encounter in their practice. AV Malformation is a rare but potentially life-threatening cause of vaginal bleeding which must be kept in the differential diagnosis of sudden and massive vaginal bleeding. It requires a high index of clinical suspicion. Despite its rarity, early recognition of an AVM is imperative to enable timely diagnosis and intervention

Multiple system atrophy in a man misdiagnosed with parkinsonism

Multiple system atrophy (MSA) is a rare sporadic, progressive, neurodegenerative disorder with autonomic deficits, with a yearly incidence of 0.000006%. MSA is often misdiagnosed as idiopathic Parkinson’s Disease (PD). It may present with a combination of parkinsonian, autonomic, and cerebellar signs. From a prognostic point of view, accurate diagnosis is essential. Our patient was misdiagnosed as having PD, but after thorough workup was diagnosed as having MSA type Parkinson’s. Because of this, the patient was put on supportive treatment for MSA. The authors strive to differentiate between the types of multiple system atrophy and its diagnostic criteria as well as differences between MSA and Parkinson’s.

Certain Expansion Formulae Involving a Basic Analogue of Fox’s H-Function

Certain expansion formulae for a basic analogue of the Fox’s H-function have been derived by the applications of the q-Leibniz rule for the Weyl type q-derivatives of a product of two functions. Expansion formulae involving a basic analogue of Meijer’s G-function and MacRobert’s E-function have been derived as special cases of the main results