Monomial Testing and Applications

In this paper, we devise two algorithms for the problem of testing $q$-monomials of degree $k$ in any multivariate polynomial represented by a circuit, regardless of the primality of $q$. One is an $O^*(2^k)$ time randomized algorithm. The other is an $O^*(12.8^k)$ time deterministic algorithm for the same $q$-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several applications of $q$-monomial testing are also given, including a deterministic $O^*(12.8^{mk})$ upper bound for the $m$-set $k$-packing problem.Comment: 17 pages, 4 figures, submitted FAW-AAIM 2013. arXiv admin note: substantial text overlap with arXiv:1302.5898; and text overlap with arXiv:1007.2675, arXiv:1007.2678, arXiv:1007.2673 by other author

On fast radial propagation of parametrically excited geodesic acoustic mode

The spatial and temporal evolution of parametrically excited geodesic acoustic mode (GAM) initial pulse is investigated both analytically and numerically. Our results show that the nonlinearly excited GAM propagates at a group velocity which is, typically, much larger than that due to finite ion Larmor radius as predicted by the linear theory. The nonlinear dispersion relation of GAM driven by a finite amplitude drift wave pump is also derived, showing a nonlinear frequency increment of GAM. Further implications of these findings for interpreting experimental observations are also discussed

Repeating head-on collisions in an optical trap and the evaluation of spin-dependent interactions among neutral particles

A dynamic process of repeating collisions of a pair of trapped neutral particles with weak spin-dependent interaction is designed and studied. Related theoretical derivation and numerical calculation have been performed to study the inherent coordinate-spin and momentum-spin correlation. Due to the repeating collisions the effect of the weak interaction can be accumulated and enlarged, and therefore can be eventually detected. Numerical results suggest that the Cr-Cr interaction, which has not yet been completely clear, could be thereby determined. The design can be in general used to determine various interactions among neutral atoms and molecules, in particular for the determination of very weak forces.Comment: 15 pages, 7 figure

Effect of C60_{60} giant resonance on the photoabsorption of encaged atoms

The absolute differential oscillator strengths (DOS's) for the photoabsorption of the Ne, Ar, and Xe atoms encapsulated in the C$_{60}$ have been evaluated using the time-dependent-density-functional-theory, which solves the quantum Liouvillian equation with the Lanczos chain method. The calculations are performed in the energy regions both inside and outside the C$_{60}$ giant resonance. The photoabsorption spectra of the atoms encaged in the C$_{60}$ demonstrate strong oscillations inside the energy range of the C$_{60}$ giant resonance. This type of oscillation cannot be explained by the confinement resonance, but is due to the energy transfer from the C$_{60}$ valence electrons to the photoelectron through the intershell coupling

More Toda-like (0,2) mirrors

In this paper, we extend our previous work to construct (0,2) Toda-like mirrors to A/2-twisted theories on more general spaces, as part of a program of understanding (0,2) mirror symmetry. Specifically, we propose (0,2) mirrors to GLSMs on toric del Pezzo surfaces and Hirzebruch surfaces with deformations of the tangent bundle. We check the results by comparing correlation functions, global symmetries, as well as geometric blowdowns with the corresponding (0,2) Toda-like mirrors. We also briefly discuss Grassmannian manifolds.Comment: 49 pages, LaTeX; v2: references adde

Assessing Ageing Condition of Mineral Oil-Paper Insulation by Polarization/Depolarization Current

Accurately assessing the ageing status of oil-paper insulation in transformer is essential and important. Polarization and Depolarization Current (PDC) technique is effective in assessing the condition of oil-paper insulation system. Though the PDC behaviour of mineral oil-paper insulation has been widely investigated, there is no report about how to make the quantitative analysis of mineral oil-paper insulation ageing condition by PDC. The PDC characteristics of mineral oil-paper insulation samples were investigated over the ageing period at 110°C. A new method for assessing the ageing condition of mineral oil-paper insulation by calculating the depolarization charge quantity was proposed. Results show that the depolarization charge quantity of mineral oil-paper insulation sample is very sensitive to its ageing condition. The stable depolarization charge quantity could be used to predict the ageing condition of mineral oil-paper insulation

Probing spin entanglement by gate-voltage-controlled interference of current correlation in quantum spin Hall insulators

We propose an entanglement detector composed of two quantum spin Hall insulators and a side gate deposited on one of the edge channels. For an ac gate voltage, the differential noise contributed from the entangled electron pairs exhibits the nontrivial step structures, from which the spin entanglement concurrence can be easily obtained. The possible spin dephasing effects in the quantum spin Hall insulators are also included.Comment: Physics Letters A in pres

A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem

We give a 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem.Comment: 6 figure