We study the properties of pulsed solutions to the scalar and vector wave equations composed of plane-waves with equal longitudinal spatial frequency. This condition guarantees that, at all times, the field profile is invariant in the longitudinal direction. Particular emphasis is placed on solutions with rotational symmetry. For these solutions, the wave concentrates strongly near the axis at ...

A variety of observational tests seem to suggest that the universe is anisotropic. This is incompatible with the standard dogma based on adiabatic, rotationally invariant perturbations. We point out that this is a consequence of the standard decomposition of the stress-energy tensor for the cosmological fluids, and that rotational invariance need not be assumed, if there is elastic rigidity in ...

The spin-orbit problem in celestial mechanics describes the motion of an oblate satellite moving on a Keplerian orbit around a primary body. We apply the conjugate points criterion for the nonexistence of rotational invariant tori. We treat both the conservative case and a case including a dissipative effect modeling a tidal torque generated by internal nonrigidity. As a by-product of the conju...

We propose a recurrent variational auto-encoder for texture synthesis. A novel loss function, FLTBNK, is used for training the texture synthesizer. It is rotational and partially color invariant loss function. Unlike L2 loss, FLTBNK explicitly models the correlation of color intensity between pixels. Our texture synthesizer 1 generates neighboring tiles to expand a sample texture and is evaluat...

This paper describes the parallel extension of the mask tuning scheme for texture feature extraction. Unlike other parallel systems in which specific parallel computer architectures are required, our parallel solution to increase processing speed is examined by introducing the concept of remote procedure call(RPC) in distributed systems for Iocal or remote interprocess communication. Based on o...

This note presents a method to reduce the discretization errors appearing when solving Quantum Field Theory in hypercubic lattice both position and momentum-space. The exploits artifacts that break rotational symmetry recover rotationally invariant results for two-point Green functions. We show combination of obtained momentum space can be useful signal presence making use their approximate Fou...

In this paper we give a construction, for any n, of an n-Venn diagram on the sphere that has antipodal symmetry; that is, the diagram is fixed by the map that takes a point on the sphere to the corresponding antipodal point. Thus, along with certain diagrams due to Anthony Edwards which can be drawn with rotational and reflective symmetry, for any isometry of the sphere that is an involution, t...

Non-invariant solutions of the Boyer-Finley equation determine exact solutions of the Einstein field equations with only one rotational Killing vector. For the case of Euclidean signature such a metric was constructed by Calderbank and Tod. Recently Martina, Sheftel and Winternitz applied the method of group foliation to the Boyer-Finley equation and reproduced the Calderbank-Tod solution toget...

In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This will be referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and...

Elementary information about convolutional codes over finite fields is introduced, and various motivations for extension to convolutional codes over finite rings are discussed. The recent primary motivation is found to be for use over phase modulation signals. Such ring codes enjoy the special property of phase weight equal to phase distance equal to the squared Euclidean distance between phase...