The author obtains the propagator for a charged particle in the presence of a constant magnetic field and any positive definite quadratic potential. The trace is then calculated and the eigenvalues of the Hamiltonian ...
The author obtains the propagator for a charged particle in the presence of a constant magnetic field and any positive definite quadratic potential. The trace is then calculated and the eigenvalues of the Hamiltonian concerned are obtained.
A formal derivation is presented of an efficient algorithm for comput.ng the "sums" of all segments, of a given length, of a sequence. Here, "sums" refers to the continued application of a binary o...
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A formal derivation is presented of an efficient algorithm for comput.ng the "sums" of all segments, of a given length, of a sequence. Here, "sums" refers to the continued application of a binary operator of which associativity is the only known property. Recurrence relations are used to separate two concerns, viz. characterisation of the values to be comput.d and choosing the order in which these values will be comput.d.
This article addresses the following problem. Given a set S of clauses and a set of constant and function symbols F that occur in the clauses of S, obtain a fully quantified (closed) formula S' from S by replacing...
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This article addresses the following problem. Given a set S of clauses and a set of constant and function symbols F that occur in the clauses of S, obtain a fully quantified (closed) formula S' from S by replacing expressions starting with symbols in F with existentially quantified variables. S' must be unsatisfiable if and only if S is unsatisfiable. A sound (but not complete) solution is given in the form of an outline of an algorithm.
A technique is proposed for aiding photointerpreters in detecting man-made features in aerial reconnaissance images. The technique, which uses a metric called fractal error, is based on the observed propensity of natu...
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A technique is proposed for aiding photointerpreters in detecting man-made features in aerial reconnaissance images. The technique, which uses a metric called fractal error, is based on the observed propensity of natural image features to fit a fractional Brownian motion model. Man-made features usually do not fit this model well, and consequently the fractal error metric may be used as a discriminant function for detecting man-made scene features.
The author obtains an expression for the stochastic Lagrangian as used in stochastic mechanics in a straightforward manner without obtaining the singular terms of Guerra et. at. (1983). He then presents a new derivati...
The author obtains an expression for the stochastic Lagrangian as used in stochastic mechanics in a straightforward manner without obtaining the singular terms of Guerra et. at. (1983). He then presents a new derivation of the Schrodinger equation.
One of the problems in linearized seismic inverse scattering, which has received little attention so far, is the existence of large gaps in the acquisition geometry due to the use of a limited number of sources and re...
One of the problems in linearized seismic inverse scattering, which has received little attention so far, is the existence of large gaps in the acquisition geometry due to the use of a limited number of sources and receivers. Frequently used Born inversion methods do not take this kind of sampling effect into account. Therefore, especially for three-dimensional problems, the results may suffer from serious artefacts. These problems are partially overcome by using iterative methods, based on the minimization of an error norm. For two-dimensional test problems, we have found that iterative methods give significantly more accurate results for sparsely sampled data. For large-scale seismic inverse problems, the rate of convergence of any iterative method is extremely important. We have found that fast convergence rates can be achieved with the aid of methods that are preconditioned with the Born inverse scattering operator. In particular, the rate of convergence of the preconditioned successive overrelaxation method and the preconditioned Krylov subspace method have been found to be much faster than the widely used conjugate gradient method. With these new methods, we have obtained acceptable results for problems containing as many as 90 000 unknowns, after only four iterations.
We prove the result that any perfect fluid solution of Einstein's field equations satisfying a barotropic equation of state p = p(mu) and the condition mu + p not-equal 0, which admits a proper conformal Killing v...
We prove the result that any perfect fluid solution of Einstein's field equations satisfying a barotropic equation of state p = p(mu) and the condition mu + p not-equal 0, which admits a proper conformal Killing vector (CKV) parallel to the fluid 4-velocity, is locally a Friedmann-Robertson-Walker model. Generalizations of this result to the case p not-equal p(mu) are then investigated. Finally, the consequences of the result are discussed and related to previous work on inheriting CKV, on asymptotic Friedmann-like CKV, on a conjecture that shear-free, perfect fluid models necessarily have either zero vorticity or zero expansion, and previous results from relativistic kinetic theory.
Molecular dynamic comput.r simulations of a two-dimensional Lennard-Jones liquid, along several isotherms, have been carried out to search for a distinct transition from a compressed liquid to an amorphous solid. The ...
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Molecular dynamic comput.r simulations of a two-dimensional Lennard-Jones liquid, along several isotherms, have been carried out to search for a distinct transition from a compressed liquid to an amorphous solid. The dynamics of the transition is examined in terms of tagged-particle van Hove correlation functions, for times up to 600 ps. The onset of localization and the transition to non-ergodicity occur simultaneously and abruptly within a very narrow range of density. Further analysis of the data on the intermediate scattering function indicate a good fit to a stretched exponential with an exponent beta equal to 0.62 and that this exponent is nearly independent of temperature. Thus, for the time scales investigated by this simulation, it is concluded that the transition observed is a glass transition.
The paper presents group-oriented (t, n) threshold digital signature schemes based on the difficulty of solving the discrete logarithm problem. By employing these schemes, any t out of n users in a group can represent...
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The paper presents group-oriented (t, n) threshold digital signature schemes based on the difficulty of solving the discrete logarithm problem. By employing these schemes, any t out of n users in a group can represent this group to sign the group signature. The size of the group signature and the verification time of the group signature are equivalent to that of an individual digital signature. In other words, the (t, n) threshold signature scheme has the following five properties: (i) any group signature is mutually generated by at least t group members;(ii) the size of the group signature is equivalent to the size of an individual signature;(iii) the signature verification process is simplified because there is only one group public key required;(iv) the group signature can be verified by any outsider;and (v) the group holds the responsibility to the signed message. In addition to the above properties, two of the schemes proposed do not require the assistance of a mutually trusted party. Each member selects its own secret key and the group public key is determined by all group members. Each group member signs a message separately and sends the individual signature to. a designated clerk. The clerk validates each individual signature and then combines all individual signatures into a group signature. The (n, n) threshold signature scheme can be easily extended to become a digital multi-signature scheme.
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