On the Quantum Kinetic Equation in Weak Turbulence

The quantum kinetic equation used in the study of weak turbulence is reconsidered in the context of a theory with a generic quartic interaction. The expectation value of the time derivative of the mode number operators is computed in a perturbation expansion which places the large diagonal component of the quartic term in the unperturbed Hamiltonian. Although one is not perturbing around a free field theory, the calculation is easily tractable owing to the fact that the unperturbed Hamiltonian can be written solely in terms of the mode number operators.Comment: 12 pages, LATEX, no figures, to appear in Phys. Rev.

A constructive approach to the soliton solutions of integrable quadrilateral lattice equations

Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Backlund transformation, and the method of solving a Riccati map by exploiting two kn own particular solutions. This leads to an expression for the N-soliton-type solutions of a generic equation within this class. As a particular instance we give an explicit N-soliton solution for the primary model, which is Adler's lattice equation (or Q4).Comment: 22 page

Sure success partial search

Partial search has been proposed recently for finding the target block containing a target element with fewer queries than the full Grover search algorithm which can locate the target precisely. Since such partial searches will likely be used as subroutines for larger algorithms their success rate is important. We propose a partial search algorithm which achieves success with unit probability

Fractional Generalization of Liouville Equations

In this paper fractional generalization of Liouville equation is considered. We derive fractional analog of normalization condition for distribution function. Fractional generalization of the Liouvile equation for dissipative and Hamiltonian systems was derived from the fractional normalization condition. This condition is considered considered as a normalization condition for systems in fractional phase space. The interpretation of the fractional space is discussed.Comment: 9 pages, LaTe

Artificial Neural Networks

Artificial Neural Network is a mathematical model, made in the form of software or hardware, built on the principle of biological neural networks of living cells. The neural network is a system of connected processors interacting with each other. If you compare them with the biological analogue, you will understand that the artificial network and the network of neurons are almost the same things. These processors are usually simple (compared to a CPU used in a PC). Each network processor either receives signals for processing or sent it to other processors. But if they are connected in a huge network with controlled interaction, these «simple» processors in large quantities can complete incredibly complicated tasks

Artificial Neural Networks

Artificial Neural Network is a mathematical model, made in the form of software or hardware, built on the principle of biological neural networks of living cells. The neural network is a system of connected processors interacting with each other. If you compare them with the biological analogue, you will understand that the artificial network and the network of neurons are almost the same things. These processors are usually simple (compared to a CPU used in a PC). Each network processor either receives signals for processing or sent it to other processors. But if they are connected in a huge network with controlled interaction, these «simple» processors in large quantities can complete incredibly complicated tasks