Searching for perfection on hypergraphs

In this paper we study the family of oriented transitive 3-hypergraphs that arise from cyclic permutations and intervals in the circle, in order to search for the notion of perfection on hypergraphs.     

Impact of Modulation Index on Homodyne Crosstalk in Optically Switched Networks

The impact of imperfect modulation depth on crosstalk induced penalty in optical switched systems is theoretically and experimentally investigated. A nonlinear relationship with a clear "knee" is observed, indicating an optimum modulation index of 8 dB.     

Biomixing by Chemotaxis and Enhancement of Biological Reactions

Many phenomena in biology involve both reactions and chemotaxis. These processes can clearly influence each other, and chemotaxis can play an important role in sustaining and speeding up the reaction. However, to the best of our knowledge, the question of reaction enhancement by chemotaxis has not yet received extensive treatment either analytically or numerically. We consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction. The model is motivated, in particular, by studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We prove that in the framework of our model, chemotaxis plays a crucial role. There is a rigid limit to how much the fertilization efficiency can be enhanced if there is no chemotaxis but only advection and diffusion. On the other hand, when chemotaxis is present, the fertilization rate can be arbitrarily close to being complete provided that the chemotactic attraction is sufficiently strong. Moreover, an interesting feature of the estimates on fertilization rate and timescales in the chemotactic case is that they do not depend on the amplitude of the reaction term.     

Equation of state and stability of the helium-hydrogen mixture at cryogenic temperature

The equation of state and the stability of the helium-molecular hydrogen mixture at cryogenic temperature up to moderate pressure are studied by means of current molecular physics methods and statistical mechanics perturbation theory. The phase separation, segregation and hetero-coordination are investigated by calculating the Gibbs energy depending on the mixture composition, pressure and temperature. Low temperature quantum effects are incorporated via cumulant approximations of the Wigner-Kirkwood expansion. The interaction between He and H₂ is determined by Double Yukawa potentials. The equation of state is derived from the hard sphere system by using the scaled particle theory. The behavior of the mixture over a wide range of pressure is explored with the excess Gibbs energy of mixing and the concentration fluctuations in the long wavelength limit. The theory is compared to cryogenic data and Monte-Carlo calculation predictions. Contrary to previous similar works, the present theory retrieves the main features of the mixture below 50 K, such as the critical point and the condensation-freezing curve, and is found to be usable well below 50 K. However, the method does not distinguish the liquid from the solid phase. The binary mixture is found to be unstable against species separation at low temperature and low pressure corresponding to very cold interstellar medium conditions, essentially because H₂ alone condenses at very low pressure and temperature, contrary to helium.     

Light scalars as tetraquarks: Decays and mixing with quarkonia

The tetraquark assignment for light scalar states below 1 GeV is discussed on the light of strong decays. The next-to-leading order in the large-N expansion for the strong decays is considered. Mixing with quarkonia states above 1 GeV is investigated within a chiral approach and the inclusion of finite-width effects is taken into account.     

How often are two permutations comparable?

Two permutations of are comparable in the Bruhat order if one is closer, in a natural way, to the identity permutation, , than the other. We show that the number of comparable pairs is of order at most, and at least. For the related weak order, the corresponding bounds are and , where . In light of numerical experiments, we conjecture that for each order the upper bound is qualitatively close to the actual number of comparable pairs.

     

Novel permutation measures for image encryption algorithms

This paper proposes two measures for the evaluation of permutation techniques used in image encryption. First, a general mathematical framework for describing the permutation phase used in image encryption is presented. Using this framework, six different permutation techniques, based on chaotic and non-chaotic generators, are described. The two new measures are, then, introduced to evaluate the effectiveness of permutation techniques. These measures are (1) Percentage of Adjacent Pixels Count (PAPC) and (2) Distance Between Adjacent Pixels (DBAP). The proposed measures are used to evaluate and compare the six permutation techniques in different scenarios. The permutation techniques are applied on several standard images and the resulting scrambled images are analyzed. Moreover, the new measures are used to compare the permutation algorithms on different matrix sizes irrespective of the actual parameters used in each algorithm. The analysis results show that the proposed measures are good indicators of the effectiveness of the permutation technique.     

伪轨跟踪与完全正熵

本文主要给出了紧致度量空间上的连续满射f具有完全正熵的一个必要条件及当f具有伪轨跟踪性质时,f有完全正熵的一些等价条件．     

混合序列的强大数律

讨论了混合序列部分和的强收敛性,所得结果推广和改进了文献[1]、[2],并推广了Marcinkiewicz强大数律．     

Some aspects on thermodynamic properties, phase diagram and alloy formation in the ternary system BAs–GaAs—Part II: BGaAs alloy formation

We present a detailed analysis of the thermodynamics of the BGaAs alloy formation taking into account the question of boron solubility and Gibbs free energy change. We also predict a Gibbs free energy change for the gas phase formation of BAs to be compared to for GaAs. We show that the experimental boron solubility is actually an open question both theoretically and experimentally, while the maximum concentration obtained up to date is reaching 6–7%. It thus follows that despite the low boron solubility, the Gibbs free energy change for the alloy formation is dominated by the chemical term over the mixing energy change. We could deduce order of magnitude for the ratio of the boron partial pressure and that of gallium. P_B could be estimated as being always much lower than P_Ga; it is shown that the alloy content is probably controlled by the Ga equilibrium partial pressure.