Impact of the relatively light fourth family neutrino on the Higgs boson search

The existence of a fourth fermion generation has mostly been considered as a source of enhanced Higgs signals with respect to the 3 family Standard Model predictions. However, a fourth Standard Model family neutrino could cause the opposite situation. It is shown that relatively light fourth family neutrino (2_mν4<_mH$2m_{{\nu }_4}<m_H$) could drastically change the interpretation of the search results for the Higgs boson, especially if _mH<170 GeV$m_H<170\text{GeV}$.     

Nonlinear optical rectification and the second and third harmonic generation in Pöschl–Teller quantum well under the intense laser field

In this work, the effect of a non-resonant intense laser field on the optical rectification and second and third harmonic generation in a Pöschl–Teller quantum well is theoretically investigated. In this regard, the coefficients of nonlinear optical rectification and second and third harmonic generation are obtained by using the compact-density matrix approach and an iterative method. Different values of the asymmetry parameters of the Pöschl–Teller potential as well as intense laser field strength have been considered. Numerical results presented for a typical GaAs quantum wells show that higher-order optical effects are considerably sensitive to intense laser field and can be adjusted by a correct choice of asymmetry parameters of the potential.     

Two distinct magnetic susceptibility peaks and magnetic reversal events in a cylindrical core/shell spin-1 Ising nanowire

The magnetization and susceptibility of a cylindrical core/shell spin-1 Ising nanowire are investigated within the effective-field theory with correlations for both ferromagnetic and antiferromagnetic exchange interactions between the shell and the core. We find that the nanowire system exhibits two distinct susceptibility peaks and two successive phase transitions; either both of them are second-order transitions or one is a second-order transition and the other is a first-order transition for a small exchange interaction. The susceptibility versus switching field and the hysteresis behavior are investigated for different temperatures. It is found that the magnetization reversal events appear as peaks in the susceptibility versus switching field curve, the positions of which define the coercive field points of the nanowire system; the distance between the two susceptibility peaks decreases with increasing temperature.     

The integer quantum Hall effect of a square lattice with an array of point defects

The electronic properties of a square lattice under an applied perpendicular magnetic field in the presence of impurities or vacancies are investigated by the tight-binding method including up to second nearest neighbor interactions. These imperfections result in new gaps and bands in the Hofstadter butterfly even when the second order interactions break the bipartite symmetry. In addition, the whole spectrum of the Hall conduction is obtained by the Kubo formula for the corresponding cases. The results are in accordance with the Thouless-Kohmoto-Nightingale-den Nijs integers when the Fermi energy lies in an energy gap. We find that the states due to the vacancies or impurities with small hopping constants are highly localized and do not contribute to the Hall conduction. However, the impurities with high hopping constants result in new Hall plateaus with constant conduction of σ(xy)?=±?e(2)/h, since high hopping constants increase the probability of an electron contributing to the conduction.     

The static stochastic knapsack problem with normally distributed item sizes

This paper develops exact and heuristic algorithms for a stochastic knapsack problem where items with random sizes may be assigned to a knapsack. An item’s value is given by the realization of the product of a random unit revenue and the random item size. When the realization of the sum of selected item sizes exceeds the knapsack capacity, a penalty cost is incurred for each unit of overflow, while our model allows for a salvage value for each unit of capacity that remains unused. We seek to maximize the expected net profit resulting from the assignment of items to the knapsack. Although the capacity is fixed in our core model, we show that problems with random capacity, as well as problems in which capacity is a decision variable subject to unit costs, fall within this class of problems as well. We focus on the case where item sizes are independent and normally distributed random variables, and provide an exact solution method for a continuous relaxation of the problem. We show that an optimal solution to this relaxation exists containing no more than two fractionally selected items, and develop a customized branch-and-bound algorithm for obtaining an optimal binary solution. In addition, we present an efficient heuristic solution method based on our algorithm for solving the relaxation and empirically show that it provides high-quality solutions.     

Ternary Kloosterman sums modulo 4

Garaschuk and Lisoněk (2008) in [3] characterised ternary Kloosterman sums modulo 4, leaving the cases $K(a)\equiv 1(\mathrm{mod}4)$ and $K(a)\equiv 3(\mathrm{mod}4)$ as open problems. In this paper we complete the characterisation using well-known theorems on Gauss sums and Kloosterman sums. We also give the number of elements satisfying these congruences.     

Galois theory for sets of operations closed under permutation,cylindrification, and composition

A set of operations on A is shown to be the set of linear term operations of some algebra on A if and only if it is closed under permutation of variables, addition of inessential variables, and composition, and if it contains all projections. A Galois framework is introduced to describe the sets of operations that are closed under the operations mentioned above, not necessarily containing all projections. The dual objects of this Galois connection are systems of pointed multisets, and the Galois closed sets of dual objects are described accordingly. Moreover, the closure systems associated with this Galois connection are shown to be uncountable (even if the closed sets of operations are assumed to contain all projections).     

A SASE free electron laser optimization based on new generation in-vacuum undulators

Optimization studies for an accelerator based light source, namely self-amplified spontaneous emission (SASE) free electron laser (FEL), based on new generation in-vacuum hybrid and superconducting undulator configurations, are compared and discussed. It is shown that the FEL wavelength should be down to soft X-rays ($～3\mathrm{nm}$) part of the spectrum while keeping the same linear accelerator (linac) energy about 1 GeV. On the other hand, numerical calculations and simulation results of the main performance parameters for SASE operation (1D gain length, saturation power and saturation length), are optimized. Finally, technological advantages and challenges for both cases, are briefly mentioned.