Error Probability for <Emphasis Type="Italic">L</Emphasis>-branch Coherent BPSK Equal Gain Combiners over Generalized Rayleigh Fading Channels

In this paper, a closed-form expression for the probability of error in a coherent BPSK system over Generalized Rayleigh fading channels is derived. An L-branch equal gain combining diversity scheme is used. Theoretical results for the probability of error are plotted for various values of the number of degrees of freedom (n) and diversity order (L). A simulation is performed and the simulated results are found to match very well with the theoretical results.

Random Motions at Finite Speed in Higher Dimensions

We present a general method of studying the transport process , t≥0, in the Euclidean space ℝ ^m , m≥2, based on the analysis of the integral transforms of its distributions. We show that the joint characteristic functions of are connected with each other by a convolution-type recurrent relation. This enables us to prove that the characteristic function (Fourier transform) of in any dimension m≥2 satisfies a convolution-type Volterra integral equation of second kind. We give its solution and obtain the characteristic function of in terms of the multiple convolutions of the kernel of the equation with itself. An explicit form of the Laplace transform of the characteristic function in any dimension is given. The complete solution of the problem of finding the initial conditions for the governing partial differential equations, is given. We also show that, under the standard Kac condition on the speed of the motion and on the intensity of the switching Poisson process, the transition density of the isotropic transport process converges to the transition density of the m-dimensional homogeneous Brownian motion with zero drift and diffusion coefficient depending on the dimension m. We give the conditional characteristic functions of the isotropic transport process in terms of the inverse Laplace transform of the powers of the Gauss hypergeometric function. Some important models of the isotropic transport processes in lower dimensions are considered and some known results are derived as the particular cases of our general model by means of the method developed.     

竖直恒温面自然对流边界层不稳定性研究

在无扰动、随机式扰动以及正弦式扰动下,通过对竖直恒温面处状态Ra为1.328×10^9、Pr为6.24的自然对流进行模拟,探索了热边界层的不稳定性和共振强化自然对流换热。结果表明:(1)竖直自然对流边界层上游位置的随机式扰动对热边界层的影响主要体现在稳定阶段;(2)该状态下的竖直自然对流边界层的特征频率为15 067,且相比于无扰动状态,频率为15 067的正弦式扰动能在竖直恒温面处提高5.15%的换热量;(3)在竖直自然对流边界层上游位置加入特征频率的正弦式扰动,竖直恒温面处的局部努塞尔数Nu均出现明显波动,且波动随着边界层高度的增加而增大。     

Degradation pattern of contact resistance and characteristic trap energy in blue organic light-emitting diodes

Thin and lightweight organic light-emitting diodes (OLEDs) are promising candidates for next-generation rollable displays; they offer numerous advantages, such as scalable manufacturing, high color contrast ratio, flexibility, and wide viewing angle. Despite the numerous merits of OLEDs, the insufficient lifetime and stability of blue OLEDs remain unresolved, thereby necessitating a feedback strategy for lifetime extension. Herein, we propose a simple yet effective methodology to determine the contact resistance (R_CT) and characteristic trap energy (E_T) of OLEDs simultaneously in the trapped-charge-limited-conduction regime, where electroluminescence occurs primarily. To validate our approach, the extracted R_CT and E_T values are directly compared with each other by connecting a commercial resistor (R_C) to a blue OLED in series. The percent errors discovered in R_C and E_T are less than 7% and 4%, demonstrating the high feasibility and accuracy of our approach. We further employ this method to study the degradation mechanism of a blue OLED by presenting the electrical stress time- and cycle-dependent R_CT, E_T, ideality factor, and turn-on voltage, revealing different degradation patterns of the metal-to-transport layer interface and emission layer, respectively. Our results provide better insights into the electrical parameter extraction method and electrical current degradation mechanism in blue OLEDs.     

Hermitian adjacency matrix of the second kind for mixed graphs

This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind (N-matrix for short) introduced by Mohar [25]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u to v is equal to the sixth root of unity $\omega =\frac{1+\mathbf{i}\sqrt{3}}{2}$ (and its symmetric entry is $\overline{\omega }=\frac{1?\mathbf{i}\sqrt{3}}{2}$); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. The main results of this paper include the following: equivalent conditions for a mixed graph that shares the same spectrum of its N-matrix with its underlying graph are given. A sharp upper bound on the spectral radius is established and the corresponding extremal mixed graphs are identified. Operations which are called two-way and three-way switchings are discussed–they give rise to some cospectral mixed graphs. We extract all the mixed graphs whose rank of its N-matrix is 2 (resp. 3). Furthermore, we show that if $M_G$ is a connected mixed graph with rank 2, then $M_G$ is switching equivalent to each connected mixed graph to which it is cospectral. However, this does not hold for some connected mixed graphs with rank 3. We identify all mixed graphs whose eigenvalues of its N-matrix lie in the range $(?\alpha ,\alpha )$ for $\alpha \in \{\sqrt{2},\sqrt{3},2\}$.     

Hyperbolic measures, moments and coefficients. Algebra on hyperbolic functions

With convolutions, we determine the Fourier transform of when n is a positive integer. Studying the expansion and taking the Fourier transform of when n and d are strictly positive integers, we obtain some polynomials and new probability densities related to them.     

Integrals of equivariant forms and a Gauss-Bonnet theorem for constructible sheaves

The Berline-Vergne integral localization formula for equivariantly closed forms ([N. Berline, M. Vergne, Classes caractéristiques équivariantes. Formules de localisation en cohomologie équivariante, C. R. Acad. Sci. Paris 295 (1982) 539-541], Theorem 7.11 in [N. Berline, E. Getzler, M. Vergne, Heat Kernels and Dirac Operators, Springer-Verlag, 1992]) is well-known and requires the acting Lie group to be compact. In this article, we extend this result to real reductive Lie groups G_R.As an application of this generalization, we prove an analogue of the Gauss-Bonnet theorem for constructible sheaves. If F is a G_R-equivariant sheaf on a complex projective manifold M, then the Euler characteristic of M with respect to F

     

Stability criteria for certain high even order delay differential equations

In this paper we study the asymptotic stability of the zero solution of even order linear delay differential equations of the form

     

Characteristic Functions for Multicontractions and Automorphisms of the Unit Ball

A multicontraction on a Hilbert space is an n-tuple of operators T = (T₁,..., T_n) acting on , such that . We obtain some results related to the characteristic function of a commuting multicontraction, most notably discussing its behaviour with respect to the action of the analytic automorphisms of the unit ball.