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Showing 1 to 14 of 14 for “"adjoint operator"”.
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Strong Ordering in the Self Adjoint Operator Space
Made available in DSpace on 2014-12-05T21:50:00Z (GMT). No. of bitstreams: 1 0006916.pdf: 2740465 bytes, checksum: cb28ddcdfb5785816f88611e4ef10912 (MD5) Previous issue date: 1953
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The sixth-order Krall differential expression and self-adjoint operators.
… how this theory was applied to find a self-adjoint operator in L2 \mu(-1, 1) generated by the sixth-order Lagrangian symmetric Krall differential equation, as done by S. M. Loveland. We later construct the self-adjoint operator generated by the Krall differential equation in the extended …
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Particle Spreading in a Simple Majda Flow and Eigenvalue Estimation Through a Cayley Transform
The spectrum of the integral operator whose kernel is the covariance function of a random variable plays an important role in finding the distribution of the random variable. We consider methods for producing estimates of the eigenvalues of such operators. If such an operator can be written in the …
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Asymptotic behavior of the solutions to a family of PDE's arising from the chemotaxis equations of Keller and Segal
… Av is considered where A is a non-negative, self-adjoint operator which commutes with the Laplacian. The operator is considered to have eigenvalues lambda n = nrholambda1, and the system is considered on [0,1] x [0,T] with homogeneous Neumann boundary conditions. The operators which lead to global …
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Design and Computation of Warped Time-Frequency Transforms
… warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted …
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On multigroup transport theory with a degenerate transfer kernel
The multigroup transport operator is studied in plane geometry assuming that the transfer kernel can be represented in a degenerate form. The eigenvalue spectrum is analyzed constructing the pertinent dispersion matrix in a block matrix form. The associated eigensolutions are obtained in terms of …
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Domain partitioning to bound moments of differential equations using semidefinite optimization
… to ensure numerical stability. Using the adjoint operator, linear constraints involving the boundary conditions and moments of the solution are developed for each partition. Semidefinite constraints are imposed on the moments, and an optimization problem is solved to obtain the bounds. We …
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Glazman-Krein-Naimark theory, left-definite theory, and the square of the Legendre polynomials differential operator.
… associated with the classical Legendre self-adjoint second-order differential operator A in L² (−1, 1) which has the Legendre polynomials {Pn} ∞ n=0 as eigenfunctions. As a consequence, they explicitly determined the domain D(A2) of the self-adjoint operator A2 . However, this domain, in …
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Applied left-definite theory : the Jacobi polynomials, their Sobolev orthogonality, and self-adjoint operators.
… of the Jacobi polynomials and construct a self-adjoint operator in a certain Hilbert-Sobolev space having the entire sequence of Jacobi polynomials as eigenfunctions. The key to this construction is the left-definite theory associated with the Jacobi differential equation, and the left-definite …
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Self-adjoint extensions to the Dirac Coulomb Hamiltonian
… eigenvalue equation H# = E* for a Hamiltonian operator H and energy eigenvalue E through separation of variables. The energy eigenvalues obtained by solving this equation must be real- one of the axioms of quantum mechanics is that physical observables, in this case energy, correspond to …
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System Optimization and Iterative Image Reconstruction in Photoacoustic Computed Tomography for Breast Imaging
… that employs an approximated but much faster adjoint operator during iterations, which can reduce the computation time by a factor of six without significantly compromising image quality. Finally, some clinical results are presented to demonstrate that the PACT breast imaging can resolve most …
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Efficient seismic imaging with the double plane wave data
… shot profile RTM. Two of the methods utilize the adjoint state method, and they are known as the time domain DPW-based RTM and the frequency domain DPW-based RTM. A third migration method using the DPW data is derived under the Born approximation. This method employs the frequency domain plane …
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Continued fractions and representations of graphs
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-08-25 without embargo terms
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Set Operators
<p>My research is centered on set operators. These are universally applicable regardless of the internal structure (numeric or non-numeric) of each individual observed datum. In our research, we have developed the theory of set operators to fill holes and gaps in observed data and eliminate paper …