Top Yukawa coupling measurement with indefinite CP Higgs in e+e−→ttˉΦe^+e^-\to t\bar{t}\Phi

We consider the issue of the top quark Yukawa coupling measurement in a model in dependent and general case with the inclusion of CP-violation in the coupling. Arguably the best process to study this coupling is the associa ted production of Higgs boson along with a $t\bar t$ pair in a machine like the International Linear Collider (ILC). While detailed analyses of the sensitivity of the measurement assuming a Standard Model (SM) - like coupling are available in the context of ILC, conclude that th e coupling could be pinned down at about 10\% level with modest luminosity, our investigations show that the scenario could be different in case of a more general coupling. The modified Lorentz structure resulting in a changed functional dependence of the cross section on the couplin g, along with the difference in the cross section itself leads to considerable deviation in the sensitivity. Our studies with an ILC of center of mass energies of 500 GeV, 800 GeV and 1000 GeV show that moderate CP-mixing in the Higgs sector could change the sensitivity to about 20\ %, while it could be worsened to 75\% in cases which could accommodate more dramatic changes in the coupling. While detailed considerations of the decay distributions point to a need for a relook at the analysis strategy followed for the case of SM such as for a model independent analysis of the top quark Yukawa coupling measurement. This study strongly suggests that, a joint analysis of the CP properties and the Yukawa coupling measurement would be the way forward at the ILC and that caution must be excercised in the measurem ent of the Yukawa couplings and the conclusions drawn from it.Comment: 18 pages, 7 figures, uses revte

A Single Server Retrial Queue with Impatient Customers

In the present paper, a single server retrial queue with impatient customers is studied. The primary arrivals and repeating calls follow the Poisson distribution. The service time is exponentially distributed. Explicit time-dependent probabilities of an exact number of arrivals and departures from the orbit are obtained by solving the differential-difference equations recursively. Steady state solution of the number of busy servers is obtained. The numerical results are graphically displayed to illustrate the effect of arrival rate, retrial rate and service rate on different probabilities against time. Some special cases of interest are also deduced

Efficient algorithms for tensor scaling, quantum marginals and moment polytopes

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our algorithm provides an efficient weak membership oracle for the associated moment polytopes, an important family of implicitly-defined convex polytopes with exponentially many facets and a wide range of applications. These include the entanglement polytopes from quantum information theory (in particular, we obtain an efficient solution to the notorious one-body quantum marginal problem) and the Kronecker polytopes from representation theory (which capture the asymptotic support of Kronecker coefficients). Our algorithm can be applied to succinct descriptions of the input tensor whenever the marginals can be efficiently computed, as in the important case of matrix product states or tensor-train decompositions, widely used in computational physics and numerical mathematics. We strengthen and generalize the alternating minimization approach of previous papers by introducing the theory of highest weight vectors from representation theory into the numerical optimization framework. We show that highest weight vectors are natural potential functions for scaling algorithms and prove new bounds on their evaluations to obtain polynomial-time convergence. Our techniques are general and we believe that they will be instrumental to obtain efficient algorithms for moment polytopes beyond the ones consider here, and more broadly, for other optimization problems possessing natural symmetries

Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach

Certain spin Hamiltonians that give rise to tunnel splittings that are viewed in terms of interfering instanton trajectories, are restudied using a discrete WKB method, that is more elementary, and also yields wavefunctions and preexponential factors for the splittings. A novel turning point inside the classically forbidden region is analysed, and a general formula is obtained for the splittings. The result is appled to the \Fe8 system. A previous result for the oscillation of the ground state splitting with external magnetic field is extended to higher levels.Comment: RevTex, one ps figur

Planar Embeddings with Small and Uniform Faces

Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MINMAXFACE and UNIFORMFACES of embedding a given biconnected multi-graph such that the largest face is as small as possible and such that all faces have the same size, respectively. We prove a complexity dichotomy for MINMAXFACE and show that deciding whether the maximum is at most $k$ is polynomial-time solvable for $k \leq 4$ and NP-complete for $k \geq 5$. Further, we give a 6-approximation for minimizing the maximum face in a planar embedding. For UNIFORMFACES, we show that the problem is NP-complete for odd $k \geq 7$ and even $k \geq 10$. Moreover, we characterize the biconnected planar multi-graphs admitting 3- and 4-uniform embeddings (in a $k$-uniform embedding all faces have size $k$) and give an efficient algorithm for testing the existence of a 6-uniform embedding.Comment: 23 pages, 5 figures, extended version of 'Planar Embeddings with Small and Uniform Faces' (The 25th International Symposium on Algorithms and Computation, 2014

Study of Future Wireless Technology: Li-Fi

Since the day earth exists, human is going develop day by day. New technologies are generated as human beings are developing. Now, internet is a compulsory part of our life. We are using Wi-Fi for internet access. But it has some limitations, so there is a new wireless technology i.e. Li-Fi (Light Fidelity), which overcomes some of the shortcomings of Wi-Fi. This paper consists a study of Li-Fi basics like advantages, limitations, applications and future scope

Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) Instantons

Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the Fe8 molecular solid. It is shown that such paths are essential to a proper understanding of the phenomenon of quenched spin tunneling in these molecules. In the Fe8 problem, such paths are shown to arise as soon as a fourth order anisotropy term in the energy is turned on, making this term a singular perturbation from the semiclassical point of view. The instanton approximation is shown to quantitatively explain the magnetic field dependence of the tunnel splitting, as well as agree with general rules for the number of quenching points allowed for a given value of spin. An accurate approximate formula for the spacing between quenching points is derived