The Differential equation method: calculation of vertex-type diagrams with one non-zero mass Abstract The differential equation method is applied to evaluate analytically two-loop vertex Feynman diagrams. Three on-shell infrared divergent planar two-loop diagrams with zero thresholds contributing to the processes Z → bb (for zero b mass) and/or H → gg are calculated in order to demonstrate a ne...

abstract— in this paper, a new extended method of multi criteria decision making based on fuzzy-topsis theory is introduced. fuzzy mcdm algorithm for determining the best choice among all possible choices when the data are fuzzy is also presented. using a new index leads to procedure for choosing fuzzy ideal and negative ideal solutions directly from the fuzzy data observed alternatives.in this...

In this paper, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear system. Some numerical examples illustrate accuracy and reliability of our solutions. Also, effect of noise shows our solutions ...

In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients of the f...

Abstract Inspired by the squared eigenfunction symmetry constraint, we introduce a new τk-flow by “extending” a specific tn-flow of discrete KP hierarchy (DKPH). We construct extended discrete KPH (exDKPH), which consists of tnflow, τk-flow and tn evolution of eigenfunction and adjoint eigenfunctions, and its Lax representation. The exDKPH contains two types of discrete KP equation with self-co...

In this Letter, we present for the first time a calculation of complete next-to-leading order corrections to $gg \to ZH$ process. We use method small mass expansion tackle most challenging two-loop virtual amplitude, in which top quark dependence is retained throughout calculations. show that our provides reliable numeric results all kinematic regions, and phenomenological predictions total dif...

We present an analytical calculation of the next-to-next-to-leading order corrections to the partial decay width H → gg for a Higgs boson in the intermediate mass range. We apply an asymptotic expansion for MH ≪ 2Mt and compute three terms in the expansion. The leading term confirms the results present in the literature. It is argued that our result is equivalent to an exact calculation up to M...

Optical soliton solutions in a magneto-optical waveguide and other exact are investigated for the coupled system of nonlinear Biswas–Milovic equation with Kudryashov’s law using extended F-expansion method. Various types extracted, such as dark solutions, singular dark–singular combo soliton, Jacobi elliptic periodic hyperbolic rational exponential Weierstrass solutions. The obtained different ...

One-loop amplitudes are to a large extent determined by their unitarity cuts in four dimensions. We show that the remaining rational terms can be obtained from the ultraviolet behaviour of the amplitude, and determine universal form factors for these rational parts by applying reduction techniques to the Feynman diagrammatic representation of the amplitude. The method is valid for massless and ...