Quasideterminant Darboux solutions of Noncommutative Equations of Langmuir Oscillations

This article encloses some results on nonncommutative analogue of nonabelian equations of Langmuir oscillations. One of the main contributions of this work is to construct the Darbboux transformation for the solution of that equation in noncommutative framework incorporating associated discrete Lax system. Further the standard Darboux transformation on arbitrary eigenfunctions of the Lax system are presented in quasideterminants for few index values. Moreover, these computations include the derivation of noncommutative version of nonabelian discrete nonlinear Schr$\ddot{o}$dinger which coincides with its classical model under commutative limit. The end portion of this article reveals the identity of noncommutative formalism incorporating a derivation of an equation of motion which coincides with its existing commutative form in background zero value of spectral parameter

Lax pair representation and Darboux transformation of noncommutative Painlevé second equation

The extension of Painlevé equations to noncommutative spaces has been considering extensively in the theory of integrable systems and it is also interesting to explore some remarkable aspects of these equations such as Painlevé property, Lax representation, Dar- boux transformation and their connection to well know integrable equations. This paper is devoted to the Lax formulation, Darboux transformation and Quasideterminant solution of noncommutative Painlevé second equation which is recently introduced by V. Retakh and V. Rubtsov

Non-trivial Darboux solutions of Classical Painlev\'e second equation

In this article an other equivalent linear representation of classical Painlev\'e second equation is derived by introducing a gauge transformation to old Lax pair. The new linear system of that equation carries similar structure as other integrable systems possess in AKNS scheme. That system yields non-trivial Darboux solutions of classical Painlev\'e second equation which are further generalized to the $N$-th form in terms of Wranskian. Finally we present the exact solutions of that equation through its associated Riccati system

Investigating the Technology Diffusion Problems in a Multi Culture Environment: A Case of Telecom Sector

Technology diffusion is an important aspect that is considered as economically important, while offering particularly large benefits to the organizations (Erik.

Quantum Painlev\'e II Lax Pair and Quantum (Matrix) Analogues of Classical Painlev\'e II equation

In this article, we present a new quantum Painlev\'e II Lax pair which explicitly involves the Planck constant $\hbar$ and an arbitrary field variable $v$ so these two objects make this new pair different from Flaschka-Newell Painlev\'e II Lax pair and that pair appears as particular case of our's pair which consolidates the Painlev\'e II equation from quantum mechanical point of view. It is shown that the compatibility of quantum Painlev\'e II Lax pair simultaneously yields a quantum Painlev\'e II equation and a quantum commutation relation between field variable $v$ and independent variable $z$. We manifest that with the different choices of arbitrary field variable system reduces to its classical version, matrix Painlev\'e II equation and derivative matrix Painlev\'e II equation. Further, we construct the gauge equivalence of quantum Painlev\'e II Lax pair whose compatibility condition gives rise to quantum p34 equation that involves $\hbar$ with power $+1$ which makes our system more quantized as compared to the existed one that carries $\hbar$ with power $+2$

Determinant Attributes of Customer Choice of Banks, Supplying Mortgage Products

The present study focuses on finding out the main attributes that determine the customer’s choice of bank for supplying the mortgage products. The data has been gathered through questionnaires from 400 customers using mortgage products of different banks. Reviewing the literature four variable are taken for study to determine the dependent variable customer choice of banks using mortgage products and they include cost of bank, quality of services, confidence of customer in bank and convenience of customer using mortgage product. Results were analyzed using ordinary least square (OLS) regression and correlation techniques and findings of the data have been tested which appeared as significant statistically. The results indicated that choice of customers for the mortgage product depends on all the independent variables like quality of services, cost of mortgage product, confidence level of customers build by the bank and convenience of the customers. Further analysis can be done on exploring more independent variables, which are important for customers in choosing a bank providing mortgage products

Sarcoidosis presented as retroperitoneal and lung mass

Sarcoidosis is a multisystem granulomatous disorder of unknown aetiology characterised pathologically by the presence of non-caseating granulomas in involved organs. Sarcoidosis most frequently involves the lungs followed by eye and skin. Presentation as retroperitoneal and lung mass is rare in sarcoidosis. We describe an unusual case of sarcoidosis where the patient presented with large retroperitoneal and lung masses, and was treated as tuberculosi