Finite dimensional spectral inverse problem for a bundle of hermitian quadratic forms

1995 ◽  
Vol 73 (3) ◽  
pp. 317-319
Author(s):  
M. I. Belishev ◽  
M. V. Putov
Keyword(s):  
Inverse Problem ◽  
Quadratic Forms ◽  
Finite Dimensional ◽  
Spectral Inverse Problem

scholarly journals Identifying the heat sink

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
J. D. Audu ◽  
A. Boumenir ◽  
K. M. Furati ◽  
I. O. Sarumi
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Temperature Profile ◽  
Spectral Methods ◽  
Heat Sink ◽  
Evolution Equations ◽  
Identification Problem ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Pseudo Spectral

<p style='text-indent:20px;'>In this paper we examine the identification problem of the heat sink for a one dimensional heat equation through observations of the solution at the boundary or through a desired temperature profile to be attained at a certain given time. We make use of pseudo-spectral methods to recast the direct as well as the inverse problem in terms of linear systems in matrix form. The resulting evolution equations in finite dimensional spaces leads to fast real time algorithms which are crucial to applied control theory.</p>

On the Integral Extensions of Quadratic Forms Over Local Fields

1970 ◽  
Vol 22 (2) ◽  
pp. 297-307 ◽  
Author(s):  
Melvin Band
Keyword(s):  
Prime Ideal ◽  
Local Field ◽  
Quadratic Forms ◽  
Sufficient Conditions ◽  
Local Fields ◽  
Ring Of Integers ◽  
Finite Dimensional ◽  
Integral Analogue ◽  
Necessary And Sufficient ◽  
Special Case

Let F be a local field with ring of integers and unique prime ideal (p). Suppose that V a finite-dimensional regular quadratic space over F, W and W′ are two isometric subspaces of V (i.e. τ: W → W′ is an isometry from W to W′). By the well-known Witt's Theorem, τ can always be extended to an isometry σ ∈ O(V).The integral analogue of this theorem has been solved over non-dyadic local fields by James and Rosenzweig [2], over the 2-adic fields by Trojan [4], and partially over the dyadics by Hsia [1], all for the special case that W is a line. In this paper we give necessary and sufficient conditions that two arbitrary dimensional subspaces W and W′ are integrally equivalent over non-dyadic local fields.

Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data

2020 ◽  
Vol 20 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Suzhen Jiang ◽  
Kaifang Liao ◽  
Ting Wei
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Fractional Diffusion ◽  
Initial Value ◽  
Diffusion Wave ◽  
One Dimensional ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Continuation Technique

AbstractIn this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation. By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique. The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation. We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.

scholarly journals An iterative method in a probabilistic approach to the spectral inverse problem

2010 ◽  
Vol 523 ◽  
pp. A44 ◽  
Author(s):  
F. F. Goryaev ◽  
S. Parenti ◽  
A. M. Urnov ◽  
S. N. Oparin ◽  
J.-F. Hochedez ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Iterative Method ◽  
Probabilistic Approach ◽  
Spectral Inverse Problem

scholarly journals Joining Forces for Reconstruction Inverse Problems

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1687
Author(s):  
Irene Sciriha
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Graph Matching ◽  
Isomorphism Problem ◽  
Reconstruction Problem ◽  
Graph Invariants ◽  
Minimal Set ◽  
Disconnected Graphs ◽  
Polynomial Reconstruction ◽  
Spectral Inverse Problem

A spectral inverse problem concerns the reconstruction of parameters of a parent graph from prescribed spectral data of subgraphs. Also referred to as the P–NP Isomorphism Problem, Reconstruction or Exact Graph Matching, the aim is to seek sets of parameters to determine a graph uniquely. Other related inverse problems, including the Polynomial Reconstruction Problem (PRP), involve the recovery of graph invariants. The PRP seeks to extract the spectrum of a graph from the deck of cards each showing the spectrum of a vertex-deleted subgraph. We show how various algebraic methods join forces to reconstruct a graph or its invariants from a minimal set of restricted eigenvalue-eigenvector information of the parent graph or its subgraphs. We show how functions of the entries of eigenvectors of the adjacency matrix A of a graph can be retrieved from the spectrum of eigenvalues of A. We establish that there are two subclasses of disconnected graphs with each card of the deck showing a common eigenvalue. These could occur as possible counter examples to the positive solution of the PRP.

A Witt Theorem for Non-Defective Lattices

1978 ◽  
Vol 30 (03) ◽  
pp. 499-511 ◽  
Author(s):  
Karl A. Morin-Strom
Keyword(s):  
Quadratic Form ◽  
Vector Space ◽  
Quadratic Forms ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional

In [10], Witt laid the foundation for the study of quadratic forms over fields. Suppose Q is a quadratic form defined on a finite dimensional vector space V over a field of characteristic not equal to 2. Witt showed that non-zero vectors x and y in V satisfying Q(x) = Q(y) can be mapped into each other via an isometry of the vector space V. More generally, if τ : W ⟶ W’ is an isometry between subspaces of V, then τ extends to an isometry ϕ of V.

FINITE DIMENSIONAL APPROXIMATIONS OF DIFFUSION PROCESSES ON BANACH SPACES

2001 ◽  
Vol 04 (04) ◽  
pp. 521-531
Author(s):  
T. S. ZHANG
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Quadratic Forms ◽  
Diffusion Processes ◽  
Existence Proof ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Dimensional Diffusion ◽  
Weak Limits

In this paper, we prove that the laws of diffusion processes on a Banach space X associated with quadratic forms (not necessarily symmetric) are the weak limits of laws of finite dimensional diffusions. A new existence proof for the infinite dimensional diffusion processes is obtained as a by-product.

SPECTRAL INVERSE PROBLEM IN SUPERSYMMETRIC QUANTUM MECHANICS

1993 ◽  
Vol 08 (23) ◽  
pp. 4123-4129 ◽  
Author(s):  
P.K. BERA ◽  
S. BHATTACHARYYA ◽  
B. TALUKDAR
Keyword(s):  
Inverse Problem ◽  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
State Energy ◽  
Bound State ◽  
Quantization Condition ◽  
Energy Spectra ◽  
Conventional Theory ◽  
Bound State Energy ◽  
Spectral Inverse Problem

The supersymmetric WKB quantization condition is used to study the so-called spectral inverse problem. Wavefunctions for the harmonic oscillator and hydrogen atom are obtained from the knowledge of their bound-state energy spectra. The analysis presented is based essentially on a repackaging of the conventional theory of integral equations.

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