Volume integral
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A systematic and efficient method to compute multi-loop master integrals Open
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problem…
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Vector Space of Feynman Integrals and Multivariate Intersection Numbers Open
Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for the construction of multivariate intersection numbers relevant to Feynman inte…
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Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms Open
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a fourfold, rational (Feynman-)parametric representation …
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Iterative structure of finite loop integrals Open
In this paper we develop further and refine the method of differential equations for computing Feynman integrals. In particular, we show that an additional iterative structure emerges for finite loop integrals. As a concrete non-trivial ex…
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Helicity is the only integral invariant of volume-preserving transformations Open
Significance Helicity is a remarkable conserved quantity that is fundamental to all the natural phenomena described by a vector field whose evolution is given by volume-preserving transformations. This is the case of the vorticity of an in…
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Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers Open
The reduction of a large number of scalar multi-loop integrals to the smaller set of Master Integrals is an integral part of the computation of any multi-loop amplitudes. The reduction is usually achieved by employing the traditional Integ…
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Size and shape dependence of finite-volume Kirkwood-Buff integrals Open
Analytic relations are derived for finite-volume integrals over the pair correlation function of a fluid, the so-called Kirkwood-Buff integrals. Closed-form expressions are obtained for cubes and cuboids, the system shapes commonly employe…
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Evaluation of the general three-loop vacuum Feynman integral Open
We discuss the systematic evaluation of 3-loop vacuum integrals with arbitrary masses. Using integration by parts, the general integral of this type can be reduced algebraically to a few basis integrals. We define a set of modified finite …
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On some integral inequalities for (k,h)-Riemann-Liouville fractional integral Open
In this study, giving the de?nition of fractional integral, which are with the help of synchronous and monotonic function, some fractional integral inequalities have established.
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Existence of an integral operator and its consequences in fractional and conformable integrals Open
The study of integral operators has always been important in the subjects of mathematics, physics, and in diverse areas of applied sciences. It has been challenging to discover and formulate new types of integral operators. The aim of this…
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The General Fractional Integrals and Derivatives on a Finite Interval Open
The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for the functions on the real positive semi-axis. The main contribution of this paper is in introducing the general …
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A concise nodal-based derivation of the floating frame of reference formulation for displacement-based solid finite elements Open
The Floating Frame of Reference Formulation (FFRF) is one of the most widely used methods to analyze flexible multibody systems subjected to large rigid-body motion but small strains and deformations. The FFRF is conventionally derived via…
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A Fundamental Criteria to Establish General Formulas of Integrals Open
In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems…
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Numerical multi-loop calculations via finite integrals and one-mass EW-QCD Drell-Yan master integrals Open
We study a recently-proposed approach to the numerical evaluation of\nmulti-loop Feynman integrals using available sector decomposition programs. As\nour main example, we consider the two-loop integrals for the $\\alpha \\alpha_s$\ncorrect…
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On Some Integral Inequalities via Conformable Fractional Integrals Open
In the present note, we have given a new integral identity via Conformable fractional integrals and some further properties. We have proved some integral inequalities for different kinds of convexity via Conformable fractional integrals. W…
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Kirkwood–Buff integrals of finite systems: shape effects Open
The Kirkwood–Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a r…
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Boundary Element and Sensitivity Analysis of Anisotropic Thermoelastic Metal and Alloy Discs with Holes Open
The main aim of this paper was to develop an advanced processing method for analyzing of anisotropic thermoelastic metal and alloy discs with holes. In the boundary element method (BEM), the heat impact is expressed as an additional volume…
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New ideas for handling of loop and angular integrals in D-dimensions in QCD Open
A bstract We discuss new ideas for consideration of loop diagrams and angular integrals in D -dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basi…
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Existence of real time quantum path integrals Open
Many interesting physical theories have analytic classical actions. We show how Feynman's path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. We start by introducing a class of smo…
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The Path-Independent M Integral Implies the Creep Closure of Englacial and Subglacial Channels Open
Drainage channels are essential components of englacial and subglacial hydrologic systems. Here, we use the M integral, a path-independent integral of the equations of continuum mechanics for a class of media, to unify descriptions of cree…
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Integral equations and boundary-element solution for static potential in a general piece-wise homogeneous volume conductor Open
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment…
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Volume Integral Formulation for the Calculation of Material Independent Modes of Dielectric Scatterers Open
In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of …
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Coincidences of the Concave Integral and the Pan-Integral Open
In this note, we discuss when the concave integral coincides with the pan- integral with respect to the standard arithmetic operations + and ·. The subadditivity of the underlying monotone measure is one sufficient condition for this equal…
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Integral inequalities within the framework of generalized fractional integrals Open
In this work, a new generalized fractional integral is defined and studied, and different relationships (equalities and inequalities) are obtained, which have as particular cases several of those reported in the literature.Hermite-Hadamard…
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Regularized Integral Representations of the Reciprocal Gamma Function Open
This paper establishes a real integral representation of the reciprocal Gamma function in terms of a regularized hypersingular integral along the real line. A regularized complex representation along the Hankel path is derived. The equival…
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Aeroacoustic Scattering Using a Particle Accelerated Computational Fluid Dynamics/Boundary Element Technique Open
A particle accelerated computational fluid dynamics/boundary element method technique to predict the sound pressure field produced by low Mach number flow past a rigid body is presented. An incompressible computational fluid dynamics solve…
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All orders structure and efficient computation of linearly reducible elliptic Feynman integrals Open
A bstract We define linearly reducible elliptic Feynman integrals, and we show that they can be algorithmically solved up to arbitrary order of the dimensional regulator in terms of a 1-dimensional integral over a polylogarithmic integrand…
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Combinatorics in tensor-integral reduction Open
We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the $n$-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, on…
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Some Schemata for Applications of the Integral Transforms of Mathematical Physics Open
In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and gene…
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An extended J-integral for evaluating fluid-driven cracks in hydraulic fracturing Open
J-integral has served as a powerful tool in characterizing crack tip status. The main feature, i.e. path-independence, makes it one of the foremost fracture parameters. In order to remain the path-independence for fluid-driven cracks, J-in…