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The Pattern and Uniform Integrals
In Chap. 5 we introduce the pattern and uniform integrals. Whereas the original applications of the pattern integrals were limited to summability...
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Elliptic integrals
While Lundberg and others found ways to parameterize the p-circle in the late 19th century, mathematicians have thought about using...
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Definite/Indefinite Integrals Involving Non-integral Powers for Certain Trigonometric Functions Times Special Functions
Treatment of definite integrals possessing non-integral power are mainly presented. Based on definite integrals with integral power(s), non-integral...
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Path Integrals
Integration of generalised 1-forms. The length of a path. Vector fields; conservative and symmetric vector fields.
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Economic preference for semiconductor trade deals using similarity measures defined by Choquet integrals
Many researchers have studied similarity measures theoretically and their application to effective decision-making techniques for problems involving...
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Sparse Domination and Weighted Inequalities for the \(\rho \)-Variation of Singular Integrals and Commutators
This paper gives pointwise sparse domination results for variation operators of singular integrals and commutators with kernels satisfying
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On the Commutators of Marcinkiewicz Integrals with Rough Kernels in Weighted Lebesgue Spaces
This paper is devoted to studying the boundedness and compactness of commutators for Marcinkiewicz integrals with rough kernels in weighted Lebesgue...
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Pattern Formation Inside Living Cells
While most of our tissues appear static, in fact, cell motion comprises an important facet of all life forms, whether in single or multicellular...
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Stable Determination of an Acoustic Medium Scatterer by a Single Far-Field Pattern
In this chapter, we are concerned with the stability analysis for inverse problems associated with time-harmonic acoustic scattering, where we follow...
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Investigating Integrals with Parameters
In this chapter we are interested in functions defined as integrals \(\displaystyle F(t) = \int \limits _a^bf(x,t) \,dx, \) where a and b...
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Weakly Canceling Operators and Singular Integrals
AbstractWe suggest an elementary harmonic analysis approach to canceling and weakly canceling differential operators, which allows us to extend...
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q-Rung Orthopair Fuzzy Points and Applications to q-Rung Orthopair Fuzzy Topological Spaces and Pattern Recognition
In this chapter, we introduce the concept of q-rung orthopair fuzzy point and propose a Dice similarity measure and a distance measure between q-rung...
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Pattern formation in a 2-population homogenized neuronal network model
We study pattern formation in a 2-population homogenized neural field model of the Hopfield type in one spatial dimension with periodic...
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Pattern Formation in a Reaction–Diffusion System with Time-Fractional Derivatives
AbstractIn this paper possible scenarios of pattern formation in nonlinear media with diffusion and differential operators of a noninteger order are...
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A radial integration displacement discontinuity method with discontinuous isoparametric elements for 3D fracture simulations
To improve the accuracy of displacement discontinuity method and enhance its adaptivity, a general-purpose 3D displacement discontinuity method with...
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Integrals of groups
An integral of a group G is a group H whose derived group (commutator subgroup) is isomorphic to G . This paper discusses integrals of groups, and in...
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Pattern Formation in a Three-Species Cyclic Competition Model
In nature, different species compete among themselves for common resources and favorable habitat. Therefore, it becomes really important to determine...
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Trajectory Optimality Conditions for Moving Object with Nonuniform Radiation Pattern
AbstractThe problem of optimal trajectory planning for a moving object with a nonuniform radiation pattern is considered and analytically solved as a...
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Applying Multidimensional Integrals to Geometry and Physics
This last chapter of the second part of this book series is devoted solely to the applications of the multidimensional integrals to practical...