Complete chaotic synchronization mechanism of polarization mode of VCSEL with anisotropic optical feedback

We numerically investigate the complete chaotic synchronization mechanism of polarization mode of VCSEL with anisotropic optical feedback. Firstly, the synchronization quality of the x-linear polarization (LP) mode and the y-LP mode are both periodically changed with the angle θ between the polarizer and the light axes. Secondly, in a enough large scale region of the feedback coefficient and the injection current, where each LP mode can obtained good synchronization quality when the angle θ exists in the former half period region and the injection current is fixed at a certain value, which is over the threshold current. Under this condition, their synchronization quality is independent of the polarization states. By contrast, in the latter half period region of the angle θ where each LP mode can be obtained very instable and inferior synchronized quality. At last, the robustness of the synchronization scheme is sensitive to the internal and external parameter mismatch between the transmitter-VCSEL and the receiver-VCSEL.     

Structural studies of cyclic ureas: 3. Enthalpy of formation of barbital

A thermochemical and thermophysical study has been carried out for crystalline barbital [5,5′-diethylbarbituric acid]. The thermochemical study was made by static bomb combustion calorimetry, from which the standard () molar enthalpy of formation of the crystalline barbital, at T = 298.15 K, was derived as −(753.0 ± 1.8) kJ · mol⁻¹. The thermophysical study was made by differential scanning calorimetry over the temperature interval (265 to 470) K. A solid–solid phase transition was found at T = 413.3 K. The vapour pressures of the crystalline barbital were measured at several temperatures between T = (355 and 377) K, by the Knudsen mass-loss effusion technique, from which the standard molar enthalpy of sublimation, at T = 298.15 K was derived as (117.3 ± 0.6) kJ · mol⁻¹. The combination of the experimental results yielded the standard molar enthalpy of formation of barbital in the gaseous phase, at T = 298.15 K, as −(635.8 ± 1.9) kJ · mol⁻¹. This value is compared and discussed with our theoretical calculations by several methods (Gaussian-n theories G2 and G3, complete basis set CBS-QB3, density functional B3P86 and B3LYP) by means of atomization and isodesmic reaction schemes.     

Separating invariants and finite reflection groups

A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating algebra. This allows us to prove that only groups generated by reflections may have polynomial separating algebras, and only groups generated by bireflections may have complete intersection separating algebras.     

A note on a paper of I.D. Arand?elovi? on asymptotic contractions

W.A. Kirk [W.A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl. 277 (2003) 645-650] defined the notion of an asymptotic contraction on a metric space and using ultrapower techniques he gave a nonconstructive proof of an asymptotic version of the Boyd-Wong fixed point theorem. Subsequently, I.D. Arand?elovi? [I.D. Arand?elovi?, On a fixed point theorem of Kirk, J. Math. Anal. Appl. 301 (2005) 384-385] established somewhat more general version of Kirk's result and he gave an elementary proof of it. However, our purpose is to show that there is an error in this proof and, moreover, Arand?elovi?'s theorem is false. We also explain how to correct this result.     

Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs

We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n+1 rungs. Such an assignment yields an index one current graph with current group Z_12n+7 that generates an orientable face 2-colorable triangular embedding of the complete graph K_12n+7 or, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+7. We use our characterization to construct Skolem sequences that give rise to such current assignments. These produce many nonisomorphic orientable biembeddings of cyclic Steiner triple systems of order 12n+7.     

Complete symmetry group and nonlocal symmetries for some two-dimensional evolution equations

The complete symmetry group of an 1+1 evolution equation of maximal symmetry has been demonstrated to be represented by the six-dimensional Lie algebra of point symmetries sl(2,R)s_⊕W, where W is the three-dimensional Heisenberg-Weyl algebra. We construct a complete symmetry group of a 1+2 evolution equation ut=(Fy(u)ux) for some functions F using the point symmetries admitted by the equation. The 1+2 equation is not completely specifiable by point symmetries alone for some specific functions F. We make use of Ansätze already reported by Myeni and Leach [S.M. Myeni, P.G.L. Leach, Nonlocal symmetries and complete symmetry groups of evolution equations, J. Nonlinear Math. Phys. 13 (2006) 377-392] which provide a route to the determination of the required generic nonlocal symmetries necessary to supplement the point symmetries for the complete specification of these 1+2 evolution equations. Further we find that taking some suitable linear combination of Lie point symmetries helps to optimise the procedure of specifying the equation. A general result concerning the number of symmetries required to form a complete symmetry group of evolution is presented in the Conclusion.     

Establishing the broadcast efficiency of the Subset Difference Revocation Scheme

When an organisation chooses a system to make regular broadcasts to a changing user base, there is an inevitable trade off between the number of keys a user must store and the number of keys used in the broadcast. The Complete Subtree and Subset Difference Revocation Schemes were proposed as efficient solutions to this problem. However, all measurements of the broadcast size have been in terms of upper bounds on the worst-case. Also, the bound on the latter scheme is only relevant for small numbers of revoked users, despite the fact that both schemes allow any number of such users. Since the broadcast size can be critical for limited memory devices, we aid comparative analysis of these important techniques by establishing the worst-case broadcast size for both revocation schemes.      

完全相容稳定模糊谓词转换器

谓词转换器语义是用程序验证技术来定义程序语言的一种方式.为描述程序的语义,在稳定模糊谓词的基础上建立完全相容稳定模糊谓词转换器,讨论完全相容稳定模糊谓词转换器的拓扑语义. 同时给出它与状态转换器之间的一个保序关系,说明完全相容稳定模糊谓词转换器一定是状态转换器.     

Optimally chosen Nakajima–Zwanzig master equation for mean field approximation

We define an ensemble of projection operators, each of which has an exact associated Nakajima–Zwanzig master equation for quantum open system evolution. A mean field approximation for the memory kernels is introduced that yields a completely determined inhomogeneous master equation for every projection operator. A specific projection operator is then chosen so that the master equation optimally matches an abstract mathematical form which preserves positivity, complete positivity, and correctly equilibrates. We study a nitrogen vacancy center in diamond interacting with ¹³C impurities to illustrate the method.     

范畴Ω-Cat的完备性

Ω-范畴具有范畴论和序理论的双重意义,可为计算机程序语言的语义提供量化的模型,本文研究了范畴Ω-Cat中的等值子和乘积,给出了范畴Ω-Cat中乘积的有点式和无点式刻画,证明了范畴Ω-Cat是完备范畴。