PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE S_Q(T)(1≤Q≤∞)

Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the asymptotic equalities：λN,δ（W2^r（T）,μ,Sq（T））={（N^-1）^r＋p/2-1/q√1＋1/N·ln1/δ, 1≤q≤2, （N^-1）^r＋p/2-1/q（1＋N^-1/q√ln1/δ）,2〈q〈∞, （N^-1）^r＋p/2√lnN/δ, q=∞,and λN^（a）（W2^r（T）,μ,Sq（T））p={（N^-1）^r＋p/2-1/q, 1≤q〈∞, （N^-1）^r＋p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ （0, 1/2], ρ 〉 1, and Sq（T） is a subspace of L1（T）, in which the Fourier series is absolutely convergent in lq sense.

An analytical model for the vertical electric field distribution and optimization of high voltage REBULF LDMOS

In this paper, an analytical model for the vertical electric field distribution and optimization of a high voltage-reduced bulk field（REBULF） lateral double-diffused metal–oxide-semiconductor（LDMOS） transistor is presented. The dependences of the breakdown voltage on the buried n-layer depth, thickness, and doping concentration are discussed in detail.The REBULF criterion and the optimal vertical electric field distribution condition are derived on the basis of the optimization of the electric field distribution. The breakdown voltage of the REBULF LDMOS transistor is always higher than that of a single reduced surface field（RESURF） LDMOS transistor, and both analytical and numerical results show that it is better to make a thick n-layer buried deep into the p-substrate.

ω-Extension of Bicyclic Semigroup

In this paper, we discussed w-extension of bicyclic semigroups. Two types of this extension are proposed. In §2 we discussed strong semilattice extension and the structure of the extension is well presented. In §3 we discussed another order extension. We proved that congruence lattice of this extension semigroups is union set of two sublattice. One is the group congruence semilattice, the other is the pure idempotent congruence semilattice.

Results of Associated Implication Algebra on a Partial Ordered Set

Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.

A Crank-Nicolson Difference Scheme for Generalized Rosenau Equation

Much effort has been devoted to researching the common Rosenau equation, but the numerical method of it has not been studied. In this paper, a conservative Crank-Nicolson difference scheme for an initial-boundary value problem of the generalized Rosenau equation is proposed. Existence and uniqueness of numerical solutions are derived. By method of discrete energy, the second order convergence and stability are discussed. Numerical examples demonstrate the theoretical results.

Non-Linear Approximation of Functions with Mixed Smoothness by Sets of Finite Pseudo-Dimension

In this paper, the non-linear approximation on the class of multivariate functions with bounded mixed derivatives is investigated, and the asymptotic degree of the non-linear width on this class is determined.

A Liouville-Type Theorem for Higher-Order Parabolic Inequalities and Its Applications

In this paper, we establish a Liouville-type theorem for a system of higher-order parabolic inequalities by using the method of test functions and an integral estimate. As an application, we observe the Fujita blow-up phenomena for the corresponding parabolic system, which in particular fills up the gap in the recent result of Pang et. al. （Existence and nonexistence of global solutions for a higher-order semilinear parabolic system, Indiana Univ. Math. J., 55（2006）, 1113-1134）. Moreover, the importance of this observation is that we do not impose any regularity assumption on the initial data.

Multivariate irregular sampling theorem

In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.

A Dynamic ID-Based Authenticated Group Key Exchange Protocol without Pairings

So far, most of the proposed group key exchange （GKE） protocols do not consider the attack when the adversary reveals the parties＇ ephemeral private keys without their long-term private keys, so these GKE protocols are insecure on this attack. In this paper, for resisting above attack, we propose a dynamic authenticated group key exchange （AGKE） protocol in the ID-based setting. Different from previous ID-based protocols, our protocol does not utilize bilinear pairings, which makes it more efficient. At last, we analyze the security of the protocol in the cCK （enhanced Canetti-Krawczyk） security model.