[en] A method is presented which constructs symmetrically a set of deorthogonalized ket-vectors from a set of given orthonormalized ket-vectors in atomic and molecular theory by means of variational minimization of the sum of squared distances between the sets. A new procedure of constraining the metric of deorthogonalization throughout the variational process is also described. (Auth.)

[en] Poynting's choice for the energy flow vector of the electromagnetic field has certain unattractive physical features. In order to eliminate such features Hines proposed an alternative choice. Here we show that Hine's choice does not lead to Larmor's result for the rate of radiation by an accelerated non-relativistic charge. (auth)

[en] A new method is presented for the variational calculation of a set of vectors under the condition that the metric of the vectors remains unchanged through the process of variation. Application of this method to typical measures (energy, overlap, distance, etc.) in quantum chemistry gives rise to new variational equations, for which the solution yields the Leowdin symmetric orthonormalization, the Kashiwagi--Sasaki generalization, the symmetric deothogonalization, and the Adams localization, etc

[en] In this article, we introduce orthogonal multiple vector-valued wavelets with three-scale, which are wavelets for vector fields, based on the notion of full rank subdivision operators. It is demonstrated that, like in the scalar and multiwavelet case, the existence of an orthogonal multiple vector-valued scaling function guarantees the existence of orthogonal multiple vector-valued wavelet functions. In this context, however, scaling functions as well as wavelet functions turn out to be multiple vector-valued functions. A method for constructing a class of orthogonal multiple vector-valued compactly supported wavelets is presented by means of matrix theory. The properties of the multiple vector-valued wavelet packets are characterized by virtue of operator theory and time-frequency analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Relation to some physical theories such as E-infinity Cantorian spacetime theory and fractal theory is also discussed.

[en] Analytic properties of Graham-Witten anomalies are considered. Weyl anomalies according to their analytic properties are of type A (coming from δ-singularities in correlators of several energy-momentum tensors) or of type B (originating in counterterms which depend logarithmically on a mass scale). It is argued that all Graham-Witten anomalies can be divided into two groups, internal and external, and that all external anomalies are of type B, whereas among internal anomalies there is one term of type A and all the rest are of type B. This argument is checked explicitly for the case of a free scalar field in a six-dimensional space with a two-dimensional submanifold

No abstract available

[en] We consider two classes of second-order parabolic matrix-vector systems (with solutions u element of M_mx1, m≥2) that can be reduced to a single second-order parabolic equation for a scalar function v=< p,u>, where p element of M_mx1 is a fixed stochastic constant vector. We consider the first boundary-value problem for a scalar second-order parabolic equation (with unbounded coefficients) in a domain unbounded with respect to x under the assumption of strong absorption at infinity. We obtain an a priori estimate for solutions of the first boundary-value problem in the generalized Tikhonov-Taecklind classes. (The problem under investigation has at most one solution in these classes.)

[en] Frequent key changes are very much desirable for the secret communications and are thus in high demand. A session-key distribution technique has been designed and implemented using the programming language C on which the communication between the end-users is encrypted is used for the duration of a logical connection. Each session-key is obtained from the key distribution center (KDC) over the same networking facilities used for end-user communication. The control vector is cryptographically coupled with the session-key at the time of key generation in the KDC. For this, the generated hash function, master key and the session-key are used for producing the encrypted session-key, which has to be transferred. All the operations have been performed using the C programming language. This process can be widely applicable to all sorts of electronic transactions online or offline; commercially and academically.(authors)

[en] Hertz potentials are used as an alternative to Fresnel's equation of wave normals to analyse harmonic plane wave propagation in uniaxially anisotropic media. Wave vector and amplitudes of ordinary and extraordinary waves are explicitly given. Refraction of a TM field at the plane face of a uniaxial medium is discussed and it is shown that in this particular situation, the refracted wave is identified with the extraordinary wave. Hertz potentials are also a powerful tool to tackle the same problems when harmonic plane waves are changed into Gaussian beams

[en] We examine the continuum limit of the piecewise flat locally finite gravity model introduced by 't Hooft. In the linear weak field limit, we find the energy-momentum tensor and metric perturbation of an arbitrary configuration of defects. The energy-momentum turns out to be restricted to satisfy certain conditions. The metric perturbation is mostly fixed by the energy-momentum except for its lightlike modes which reproduce linear gravitational waves, despite no such waves being present at the microscopic level.