A new regular infinite matrix defined by Jordan totient function and its matrix domain in ℓ p

2020 ◽  
Author(s):  
Merve İlkhan ◽  
Necip Şimşek ◽  
Emrah Evren Kara
Keyword(s):  
Infinite Matrix ◽  
Matrix Domain

scholarly journals Calculations on some sequence spaces

2004 ◽  
Vol 2004 (31) ◽  
pp. 1653-1670 ◽  
Author(s):  
Bruno de Malafosse
Keyword(s):  
Sequence Spaces ◽  
Infinite Matrix ◽  
Matrix Domain

We deal with space of sequences generalizing the well-known spacesw∞p(λ),c∞(λ,μ), replacing the operatorsC(λ)andΔ(μ)by their transposes. We get generalizations of results concerning the strong matrix domain of an infinite matrixA.

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

scholarly journals Infinite Matrix Products and the Representation of the Matrix Gamma Function

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
J.-C. Cortés ◽  
L. Jódar ◽  
Francisco J. Solís ◽  
Roberto Ku-Carrillo
Keyword(s):  
Gamma Function ◽  
Infinite Product ◽  
Infinite Matrix ◽  
Convergence Results ◽  
Matrix Products ◽  
The Matrix ◽  
Definition Of

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.

Solution of Levi Civita’s Problem by Infinite Matrix Inversion

1973 ◽  
Vol 40 (1) ◽  
pp. 31-36 ◽  
Author(s):  
M. Bentwich
Keyword(s):  
Flow Pattern ◽  
Flow Direction ◽  
Leading Edge ◽  
Arbitrary Cross Section ◽  
Matrix Inversion ◽  
Infinite Matrix ◽  
Algebraic Equations ◽  
Flow Past ◽  
Linear Algebraic Equations ◽  
Wet Surface

The author proposes a new method by which one can solve for the two-dimensional irrotational fully cavitating flow past a cylinder of arbitrary cross section. Unlike the available solutions, it is in the form of two expansions each valid in part of the complex potential plane w = Φ + iΨ. The a priori unknown coefficients in the two expansions are linked by infinitely many linear algebraic equations. By inverting the associated matrix and utilizing the boundary condition, that represent the geometry of the wet surface, the coefficients in the expansions are evaluated and the solution is completed. Cases in which the wet surface is circular, the pressure along the free streamlines is constant, and the entire flow pattern is symmetric with respect to flow direction at infinity are considered in detail. Also, the well-known solution for the flow past a flat plate is compared to that obtained by the method of matrix inversion. Judging from these results, the convergence of the series appears to be very rapid. The author finally discusses the applicability of the method to cases in which the obstacle has a sharp leading edge, the pressure in the cavity is not uniform, or the flow pattern is not symmetric.

Elastothermodynamic Damping of Fiber-Reinforced Metal-Matrix Composites

1995 ◽  
Vol 62 (2) ◽  
pp. 441-449 ◽  
Author(s):  
K. B. Milligan ◽  
V. K. Kinra
Keyword(s):  
Metal Matrix Composites ◽  
Metal Matrix ◽  
Axial Strain ◽  
Second Law Of Thermodynamics ◽  
Infinite Matrix ◽  
Matrix Composites ◽  
Fiber Reinforced ◽  
Continuous Fiber ◽  
Finite Matrix ◽  
Starting Point

Recently, taking the second law of thermodynamics as a starting point, a theoretical framework for an exact calculation of the elastothermodynamic damping in metal-matrix composites has been presented by the authors (Kinra and Milligan, 1994; Milligan and Kinra, 1993). Using this work as a foundation, we solve two canonical boundary value problems concerning elastothermodynamic damping in continuous-fiber-reinforced metal-matrix composites: (1) a fiber in an infinite matrix, and (2) using the general methodology given by Bishop and Kinra (1993), a fiber in a finite matrix. In both cases the solutions were obtained for the following loading conditions: (1) uniform radial stress and (2) uniform axial strain.

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