Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlev\'e property. We then solve the LSRI equation using Painlev\'e truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions such as dromions, multidromions, instantons, multi-instantons and bounded solitary wave solutions.Comment: 13 pages, 6 figure

Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs

In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be scale-free with all physical variables varying as powers of cylindrical radius $r$ with compatible exponents. The unstable modes set in as neutral modes or stationary perturbation configurations with angular frequency $\omega=0$.Comment: 7 pages using AAS styl

A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions and its applications

A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained

The Shadows of a Cycle Cannot All Be Paths

A "shadow" of a subset $S$ of Euclidean space is an orthogonal projection of $S$ into one of the coordinate hyperplanes. In this paper we show that it is not possible for all three shadows of a cycle (i.e., a simple closed curve) in $\mathbb R^3$ to be paths (i.e., simple open curves). We also show two contrasting results: the three shadows of a path in $\mathbb R^3$ can all be cycles (although not all convex) and, for every $d\geq 1$, there exists a $d$-sphere embedded in $\mathbb R^{d+2}$ whose $d+2$ shadows have no holes (i.e., they deformation-retract onto a point).Comment: 6 pages, 10 figure

Boosting Stop Searches with a 100 TeV Proton Collider

A proton-proton collider with center of mass energy around 100 TeV is the energy frontier machine that is likely to succeed the LHC. One of the primary physics goals will be the continued exploration of weak scale naturalness. Here we focus on the pair-production of stops that decay to a top and a neutralino. Most of the heavy stop parameter space results in highly boosted tops, populating kinematic regimes inaccessible at the LHC. New strategies for boosted top-tagging are needed and a simple, detector-independent tagger can be constructed by requiring a muon inside a jet. Assuming 20% systematic uncertainties, this future collider can discover (exclude) stops with masses up to 6.5 (8) TeV with 3000 fb^-1 of integrated luminosity. Studying how the exclusion limits scale with luminosity motivates going beyond this benchmark in order to saturate the discovery potential of the machine.Comment: v2: 16 pages, 17 figures, results updated using NLL+NLO cross sections, journal versio

New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig

Redundancy relations and robust failure detection

All failure detection methods are based on the use of redundancy, that is on (possible dynamic) relations among the measured variables. Consequently the robustness of the failure detection process depends to a great degree on the reliability of the redundancy relations given the inevitable presence of model uncertainties. The problem of determining redundancy relations which are optimally robust in a sense which includes the major issues of importance in practical failure detection is addressed. A significant amount of intuition concerning the geometry of robust failure detection is provided

λϕ4\lambda\phi^4 model and Higgs mass in standard model calculated by Gaussian effective potential approach with a new regularization-renormalization method

Basing on new regularization-renormalization method, the $\lambda\phi^4$ model used in standard model is studied both perturbatively and nonperturbatively (by Gaussian effective potential). The invariant property of two mass scales is stressed and the existence of a (Landau) pole is emphasized. Then after coupling with the SU(2)$\times$U(1) gauge fields, the Higgs mass in standard model (SM) can be calculated as $m_H\approx$138GeV. The critical temperature ($T_c$) for restoration of symmetry of Higgs field, the critical energy scale ($\mu_c$, the maximum energy scale under which the lower excitation sector of the GEP is valid) and the maximum energy scale ($\mu_{max}$, at which the symmetry of the Higgs field is restored) in the standard model are $T_c\approx$476 GeV, $\mu_c\approx 0.547\times 10^{15}$GeV and $\mu_{\max}\approx 0.873 \times 10^{15}$ GeVv respectively.Comment: 12 pages, LaTex, no figur

Prevention and control of Zika fever as a mosquito-borne and sexually transmitted disease

The ongoing Zika virus (ZIKV) epidemic poses a major global public health emergency. It is known that ZIKV is spread by \textit{Aedes} mosquitoes, recent studies show that ZIKV can also be transmitted via sexual contact and cases of sexually transmitted ZIKV have been confirmed in the U.S., France, and Italy. How sexual transmission affects the spread and control of ZIKV infection is not well-understood. We presented a mathematical model to investigate the impact of mosquito-borne and sexual transmission on spread and control of ZIKV and used the model to fit the ZIKV data in Brazil, Colombia, and El Salvador. Based on the estimated parameter values, we calculated the median and confidence interval of the basic reproduction number R0=2.055 (95% CI: 0.523-6.300), in which the distribution of the percentage of contribution by sexual transmission is 3.044 (95% CI: 0.123-45.73). Our study indicates that R0 is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. In order to prevent and control the transmission of ZIKV, it must be treated as not only a mosquito-borne disease but also a sexually transmitted disease