It is well known that the system of eigenfunctions of a formally self-adjointdifferential operator with arbitrary self-adjoint boundary conditions providing a point spectrum isan orthonormal basis in the space L2. The...
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It is well known that the system of eigenfunctions of a formally self-adjointdifferential operator with arbitrary self-adjoint boundary conditions providing a point spectrum isan orthonormal basis in the space L2. The problem as to whether the basis property is preservedunder a weak, in a sense, perturbation of the original self-adjoint operator with discrete spectrumwas considered in numerous papers (e.g., see [1, 2]).
We are concerned with proving the existence of one or more than one positive solution of an n-point right-focal boundaryvalue problem for the nonlinear dynamic equation (-1)(n-1)x(Delta n)(t) =lambda r( t) f(t, x(sig...
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We are concerned with proving the existence of one or more than one positive solution of an n-point right-focal boundaryvalue problem for the nonlinear dynamic equation (-1)(n-1)x(Delta n)(t) =lambda r( t) f(t, x(sigma) (t)). We will also obtain criteria which lead to nonexistence of positive solutions. Here the independent variable t is in a time scale. We will use fixed point theorems for operators on a Banach space. Copyright (c) 2006 Ilkay Yaslan Karaca.
In order to enlarge the set of boundaryvalueproblems on time scales, for which we can use the lower and upper solutions technique to get existence of solutions, we extend this method to the case when the pair lacks ...
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In order to enlarge the set of boundaryvalueproblems on time scales, for which we can use the lower and upper solutions technique to get existence of solutions, we extend this method to the case when the pair lacks ordering. We use the degree theory and a priori estimates to obtain the existence of solutions for the second-order Dirichlet boundaryvalueproblems. To illustrate a wider application of this result, we conclude with an example which shows that a combination of well- and nonwell- ordered pairs can yield the existence of multiple solutions. Copyright (c) 2006 Petr Stehlik.
Karabulut and Sibert [J. Math. Phys. 38, 4815 (1997)] have constructed an orthogonal set of functions from linear combinations of equally spaced Gaussians. In this paper we show that they are actually eigenfunctions o...
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Karabulut and Sibert [J. Math. Phys. 38, 4815 (1997)] have constructed an orthogonal set of functions from linear combinations of equally spaced Gaussians. In this paper we show that they are actually eigenfunctions of a q-oscillator in coordinate representation. We also reinterpret the coordinate representation example of q-oscillator given by Macfarlane as the functions orthogonal with respect to an unusual inner product definition. It is shown that the eigenfunctions in both q-oscillator examples are infinitely degenerate. (c) 2006 American Institute of Physics.
We will expand the scope of application of a fixed point theorem due to Krasnosel'skii and Zabreiko to the family of second-order dynamic equations described by u(Delta Delta)(t) = f(u(sigma)(t)), t is an element ...
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We will expand the scope of application of a fixed point theorem due to Krasnosel'skii and Zabreiko to the family of second-order dynamic equations described by u(Delta Delta)(t) = f(u(sigma)(t)), t is an element of [0,1] boolean AND T, with multipoint boundary conditions u(0) = 0, u(sigma(2)(1)) = Sigma(n)(i=1) alpha(i)u(eta(i)), and Sigma(n)(i=1) alpha(i) <= 1 for the purpose of establishing existence results. We will determine sufficient conditions on our function f such that the assumptions of the fixed point theorem are satisfied, which in return gives us the existence of solutions. Copyright (c) 2006 B. Karna and B. A. Lawrence. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The article comments on the articles 'Dyadic Eigenfunctions and Natural Modes for Hybrid Waves in Planar Media,' and the 'Dyadic Green's Function for Planar Media: A Dyadic Eigenfunction Approach.'...
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The article comments on the articles 'Dyadic Eigenfunctions and Natural Modes for Hybrid Waves in Planar Media,' and the 'Dyadic Green's Function for Planar Media: A Dyadic Eigenfunction Approach.' The author stated that the notation, k = k(x), of both articles was confusing and justifies clarification.
A method based in the pseudo-harmonics method was developed to solve the fixed source problem. The pseudo-harmonics method is based on the eigenfunctions associated with the leakage and removal matrix operator of the ...
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A method based in the pseudo-harmonics method was developed to solve the fixed source problem. The pseudo-harmonics method is based on the eigenfunctions associated with the leakage and removal matrix operator of the neutron diffusion equation, which will be treated here in three dimensions and two groups of energy. This matrix is built in this work through the nodal discretization supplied by coarse mesh finite differences method (CMFDM). CMFDM has as input data the average currents and the average fluxes in the faces of the node, and the average flux in the node, previously obtained by the nodal expansion method. The results obtained with the pseudo-harmonics procedure show good accuracy when compared to the reference results of the source problem tested. Moreover, it is a method which can be easily implemented to solve this type of problems. (c) 2005 Elsevier Ltd. All rights reserved.
作者：
de Castro, ASUNESP
Dept Fis & Quim BR-12516410 Guaratingueta SP Brazil
The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boun...
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The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the eigenfunctions which ensure that the effective Hamiltonian is Hermitian for all the points of the space. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist. (c) 2005 Elsevier B.V. All rights reserved.
Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the bounda...
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Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called "***, "for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.
The new coupled solver SOAR (SIMPLE Optimized and Automated Relaxation factors) proposed by the author has been reformulated on a collocated grid and compared with the SIMPLE method for computing performance as the gr...
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The new coupled solver SOAR (SIMPLE Optimized and Automated Relaxation factors) proposed by the author has been reformulated on a collocated grid and compared with the SIMPLE method for computing performance as the grid is refined. The functional relation between calculational time T and total grid points N has been studied through 22 calculations for a rectangular tank and can be expressed as T approximate to k x N-m. Here, the value of the exponent in has been found to range from 1.2 to 1.5 for the SOAR solver and from 2.4 to 3.0 for the SIMPLE solver, and it is clear that the SOAR method has better computing performance than the SIMPLE method as the grid is refined. For large numbers of grid points, which are increasingly required for assessment of confidence in computational fluid dynamics, this translates into significant and predictable reductions in run times and faster project turnaround.
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