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Search Results: 1 - 10 of 149731 matches for " H. akalli "
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Slowly Oscillating Continuity
H. akalli
Abstract and Applied Analysis , 2008, DOI: 10.1155/2008/485706
Abstract: A function is continuous if and only if, for each point 0 in the domain, lim→∞()=(0), whenever lim→∞=0. This is equivalent to the statement that (()) is a convergent sequence whenever () is convergent. The concept of slowly oscillating continuity is defined in the sense that a function is slowly oscillating continuous if it transforms slowly oscillating sequences to slowly oscillating sequences, that is, (()) is slowly oscillating whenever () is slowly oscillating. A sequence () of points in is slowly oscillating if lim→1
A Study on -Quasi-Cauchy Sequences
Hüseyin ?akalli,Huseyin Kaplan
Abstract and Applied Analysis , 2013, DOI: 10.1155/2013/836970
On lacunary statistically quasi-Cauchy sequences
Hüseyin ?akalli,?i?dem Gündüz Aras,Ayse Sonmez
Mathematics , 2011,
Abstract: The main object of this paper is to investigate lacunary statistically ward continuity. We obtain some relations between this kind of continuity and some other kinds of continuities. It turns out that any lacunary statistically ward continuous real valued function on a lacunary statistically ward compact subset $E\subset{\textbf{R}}$ is uniformly continuous.
Euler-Lagrange Elasticity: Differential Equations for Elasticity without Stress or Strain  [PDF]
H. H. Hardy
Journal of Applied Mathematics and Physics (JAMP) , 2013, DOI: 10.4236/jamp.2013.17004

Differential equations to describe elasticity are derived without the use of stress or strain. The points within the body are the independent parameters instead of strain and surface forces replace stress tensors. These differential equations are a continuous analytical model that can then be solved using any of the standard techniques of differential equations. Although the equations do not require the definition stress or strain, these quantities can be calculated as dependent parameters. This approach to elasticity is simple, which avoids the need for multiple definitions of stress and strain, and provides a simple experimental procedure to find scalar representations of material properties in terms of the energy of deformation. The derived differential equations describe both infinitesimal and finite deformations.

Euler-Lagrange Elasticity with Dynamics  [PDF]
H. H. Hardy
Journal of Applied Mathematics and Physics (JAMP) , 2014, DOI: 10.4236/jamp.2014.213138
Abstract: The equations of Euler-Lagrange elasticity describe elastic deformations without reference to stress or strain. These equations as previously published are applicable only to quasi-static deformations. This paper extends these equations to include time dependent deformations. To accomplish this, an appropriate Lagrangian is defined and an extrema of the integral of this Lagrangian over the original material volume and time is found. The result is a set of Euler equations for the dynamics of elastic materials without stress or strain, which are appropriate for both finite and infinitesimal deformations of both isotropic and anisotropic materials. Finally, the resulting equations are shown to be no more than Newton's Laws applied to each infinitesimal volume of the material.
Linear Algebra Provides a Basis for Elasticity without Stress or Strain  [PDF]
H. H. Hardy
Soft (Soft) , 2015, DOI: 10.4236/soft.2015.43003
Abstract: Linear algebra provides insights into the description of elasticity without stress or strain. Classical descriptions of elasticity usually begin with defining stress and strain and the constitutive equations of the material that relate these to each other. Elasticity without stress or strain begins with the positions of the points and the energy of deformation. The energy of deformation as a function of the positions of the points within the material provides the material properties for the model. A discrete or continuous model of the deformation can be constructed by minimizing the total energy of deformation. As presented, this approach is limited to hyper-elastic materials, but is appropriate for infinitesimal and finite deformations, isotropic and anisotropic materials, as well as quasi-static and dynamic responses.
Spectral resolution in hyperbolic orbifolds, quantum chaos, and cosmology
H. Then
Physics , 2007,
Abstract: We present a few subjects from physics that have one in common: the spectral resolution of the Laplacian.
Arithmetic quantum chaos of Maass waveforms
H. Then
Mathematics , 2003,
Abstract: We compute numerically eigenvalues and eigenfunctions of the quantum Hamiltonian that describes the quantum mechanics of a point particle moving freely in a particular three-dimensional hyperbolic space of finite volume and investigate the distribution of the eigenvalues.
Maass cusp forms for large eigenvalues
H. Then
Mathematics , 2003,
Abstract: We investigate the numerical computation of Maass cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r=40000. These eigenvalues are the largest that have so far been found in the case of the modular group. They are larger than the 130millionth eigenvalue.
Static Electric-Spring and Nonlinear Oscillations  [PDF]
H. Sarafian
Journal of Electromagnetic Analysis and Applications (JEMAA) , 2010, DOI: 10.4236/jemaa.2010.22011
Abstract: The author designed a family of nonlinear static electric-springs. The nonlinear oscillations of a massively charged particle under the influence of one such spring are studied. The equation of motion of the spring-mass system is highly nonlinear. Utilizing Mathematica [1] the equation of motion is solved numerically. The kinematics of the particle namely, its position, velocity and acceleration as a function of time, are displayed in three separate phase diagrams. Energy of the oscillator is analyzed. The nonlinear motion of the charged particle is set into an actual three-dimensional setting and animated for a comprehensive understanding.
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