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In this paper, we investigate some boundary value problems for the Cauchy–Riemann equations in the lens domain M. We apply the parqueting-reflection method for the domain to achieve the points of the complex plane. Then the Schwarz representation formula is constructed by the C-auchy–Pompeiu formula and an explicit solution for the Schwarz boundary value problem for the inhomogeneous Cauchy–Riemann equation on the domain is presented. We also discuss about the condition of solvability and by using the Schwarz boundary value problem, the homogeneous Ne-umann and the inhomogeneous Dirichlet boundary value problems are investigated. [ABSTRACT FROM AUTHOR]

Leishmaniasis is caused by parasitic protozoa of the genus Leishmania. Cutaneous leishmaniasis (CL) is a complex disease with wide spectrum of clinical manifestations. In order to identify leishmania species causing CL in Isfahan by a definite molecular technique (PCR method), this study was undertaken over 2010- 2011. 124 Patients with suspicious lesion of Leishmaniasis and positive direct smear from lesion were selected. Samples were cultured in NNN and RPMI 1640 media Negative and positive control and clinical samples was applied for PCR in the same condition. In the next step, standard PCR was carried out using classic protocol. From 124 patients, 111 (89.51%) cases were infected as L. major and 12 (9.67%) cases were infected by L. tropica, However only in one patient simultaneous infectious with both L. major and L. tropica was identified by PCR techniques which could not be possible in microscopy. L.major was the most prevalent species in the studied patients (p-value

In this article, firstly we obtain Cauchy–Schwarz representation in a half lens in. Then, we consider the Schwarz boundary value problem for the inhomogeneous Cauchy–Riemann equation and explicit expression of solution is obtained. Secondly, the Schwarz problem is explicitly solved in two half lunes which are complements of the half lens with respect to two orthogonal half circles. [ABSTRACT FROM PUBLISHER]

In this paper, the direct algebra method is used to construct exact solutions of the Hamiltonian amplitude equation and the higher-order nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

In this paper we extend some properties analytic functions on several complex variables to solutions of overdetermined systems of complex partial differential equations. [ABSTRACT FROM AUTHOR]

By means of the two distinct methods, the direct algebraic method and the cosine method, we successfully performed an analytic study on the (2+1)-dimensional cubic nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce the homotopy perturbation method (HPM) and the reduced differential transform method (RDTM) for solving (1+1)-dimensional nonlinear Boussinesq equation. The analytical solution of the equation have been obtained in terms of convergent series with easily computable components. The obtained results show that the proposed methods are very powerful and convenient mathematical tool for nonlinear evolution equations in science and engineering. [ABSTRACT FROM AUTHOR]

In this paper, the first integral method is used to construct exact traveling wave solutions of (2 + 1)-dimensional dispersive long wave equation. The first integral method is an efficient method for obtaining exact solutions some of nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. [ABSTRACT FROM AUTHOR]

In this paper, the tanh-coth method and the extended (G'/G)-expansion method are used to construct exact solutions of the nonlinear Modified Improved Kadomtsev-Petviashvili (MIKP) equation. These methods transform nonlinear partial differential equation to ordinary differential equation and can be applied to nonintegrable equation as well as integrable ones. It has been shown that the two methods are direct, effective and can be used for many other nonlinear evolution equations in mathematical physics. [ABSTRACT FROM AUTHOR]

In this paper, we implemented modification of truncated expansion method for the exact solutions of the Konopelchenko-Dubrovsky equation the (n+1)-dimensional combined sinhcosh- Gordon equation and the Maccari system. Modification of truncated expansion method is a powerful solution method for obtaining exact solutions of nonlinear evolution equations. This method presents a wider applicability for handling nonlinear wave equations. [ABSTRACT FROM AUTHOR]

In this paper, the formal linearization method is used to construct the exact multisoliton solutions of the BBM equation and the Sine-Gordon equation. The formal linearization method is an efficient method for obtaining the exact multisoliton solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. [ABSTRACT FROM AUTHOR]