MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.

Completeness of bounded model checking temporal logic of knowledge

In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge is introduced into the past tense operator, and then a new temporal epistemic logic LTLKP is obtained, so that LTLKP can naturally and precisely describe the system＇s reliability. Secondly, a set of prior algorithms are designed to calculate the maximal reachable depth and the length of the longest of loop free paths in the structure based on the graph structure theory. Finally, some theorems are proposed to show how to approximate the complete threshold with the diameter and recurrence diameter. The proposed work resolves the completeness threshold problem so that the completeness of bounded model checking can be guaranteed.

THE BASIC THEORY OF SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH BOUNDED DELAY IN THE SPACE OF INTEGRABLE FUNCTIONS

在可积函数空间中讨论有界滞量泛函微分方程，建立其解的基本理论，包括解的存在性，唯一性及延展性。

SOME PROPERTIES OF BOUNDED SETS IN INDUCTIVE LIMITS

Let (E,ξ）=indlim (En,ξn） be an inductive limit of a sequence of locally convex spaces,For brevity,denote by (DS) each set Bbounded in (E,ξ） is contained in some En； and (DST) each set B bounded in (E,ξ） is contained and bounded in some (En,ξn）. Theovem 1.(DS) holds provided that (i) for each n∈N,there is a neighborhood Un of o in (En,ξn） and m(n)∈ such that -↑Un^E包含于Em(n),and (ii) for any neighborhood V n of o in (En,ξn）,∞↑Un=1 Vn absorbs every bounded set in (E,ξ）. theorem 2 Let all (En,ξn） be metrizable and (DS) hold,then for each bounded set B IN (E,ξ）and each n ∈N thcrc is a neighborhood U k of o in (Ek,ξk）, 1≤k≤n ,and m(n)∈N such that ——↑(B+U1+U2+…+Un)^E包含于 Em(n). theorem 3. Let all (En,ξn） be Frechet spaces.Then (DST) holds if and only if (i) for each n ∈N,there is u neighborhood U n of in (En,ξn） and m(n)∈N such that 0↑Un^E包含于Em(n),and (ii) for each each closed ,absosed,absolutely conuex,bounded set B in (E,ξ）,∞↑Un=1(（εnB)∩Un）absorbs B,where U n is any neighborhood of o in (En,ξn） and εn is any positive number for every n ∈N。

GLOBALLY BOUNDED IN-TIME SOLUTIONS TO A PARABOLIC-ELLIPTIC SYSTEM MODELLING CHEMOTAXIS

In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained.

A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES

In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.

THE EQUIVALENT CHARACTERIZATION OF F(p,q,s)SPACE ON BOUNDED SYMMETRIC DOMAINS OF Cn

LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.

Wave packet solutions in a bounded equatorial ocean and its interannual and decadal variabilities

Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results are as follows. The wave packet is a superposition of eastward travelling Kelvin waves and westward travelling Rossby waves with the slowest speed, and satisfies the boundary conditions of eastern and western coasts, respectively.The decay coefficient of this solution to the north and south sides of the equator is inversely proportional only to the phase velocity of Kelvin waves in the upper water. The oscillation frequency of the wave packet, which is also the natural frequency of the ocean, is proportional to its mode number and the phase velocity of Kelvin waves and is inversely proportional to the length of the equatorial ocean in the east-west direction. The flow anomalies of the wave packet of Mode 1 most of the time appear as zonal flows with the same direction. They reach the maximum at the center of the equatorial ocean and decay rapidly away from the equator, manifested as equatorially trapped waves. The flow anomalies of the wave packet of Mode 2 appear as the zonal flows with the same direction most of the time in half of the ocean, and are always 0 at the center of the entire ocean which indicates stagnation, while decaying away from the equator with the same speed as that of Mode 1. The spatial structure and oscillation period of the wave packet solution of Mode 1 and Mode 2 are consistent with the changing periods of the surface spatial field and time coefficient of the first and second modes of complex empirical orthogonal function(EOF)analysis of flow anomalies in the actual equatorial ocean. This indicates that the solution does exist in the real ocean, and that El Ni?o-Southern Oscillation(ENSO) and Indian Ocean dipole(IOD) are both related to Mode 2.After considering the Indonesian throughflow, we can obtain the length of bounded equatorial ocean by taking the sum of that of the tropical Indian Ocean and the tropical Pacific Ocean, thus this wave packet can also explain the decadal variability(about 20 a) of the equatorial Pacific and Indian Oceans.

Energy-Optimal and Delay-Bounded Computation Offloading in Mobile Edge Computing with Heterogeneous Clouds

By Mobile Edge Computing(MEC), computation-intensive tasks are offloaded from mobile devices to cloud servers, and thus the energy consumption of mobile devices can be notably reduced. In this paper, we study task offloading in multi-user MEC systems with heterogeneous clouds, including edge clouds and remote clouds. Tasks are forwarded from mobile devices to edge clouds via wireless channels, and they can be further forwarded to remote clouds via the Internet. Our objective is to minimize the total energy consumption of multiple mobile devices, subject to bounded-delay requirements of tasks. Based on dynamic programming, we propose an algorithm that minimizes the energy consumption, by jointly allocating bandwidth and computational resources to mobile devices. The algorithm is of pseudo-polynomial complexity. To further reduce the complexity, we propose an approximation algorithm with energy discretization, and its total energy consumption is proved to be within a bounded gap from the optimum. Simulation results show that, nearly 82.7% energy of mobile devices can be saved by task offloading compared with mobile device execution.

Robust controller design for compound control missile with fixed bounded convergence time

A robust controller for bank to turn(BTT) missiles with aerodynamic fins and reaction jet control system(RCS) is developed based on nonlinear control dynamic models comprising couplings and aerodynamic uncertainties. The fixed time convergence theory is incorporated with the sliding mode control technique to ensure that the system tracks the desired command within uniform bounded time under different initial conditions. Unlike previous terminal sliding mode approaches, the bound of settling time is independent of the initial state, which means performance metrics like convergence rate can be predicted beforehand. To reduce the burden of control design in terms of robustness, extended state observer(ESO) is introduced for uncertainty estimation with the output substituted into the controller as feedforward compensation. Cascade control structure is employed with the proposed control law and therein the compound control signal is obtained.Afterwards, control inputs for two kinds of actuators are allocated on the basis of their inherent characteristics. Finally, a number of simulations are carried out and demonstrate the effectiveness of the designed controller.

INCOMPRESSIBLE LIMIT OF THE NON-ISENTROPIC MAGNETOHYDRODYNAMIC EQUATIONS IN BOUNDED DOMAINS

The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.

Bounded Real Lemma for Generalized Linear System with Finite Discrete Jumps

The strict bounded real lemma for linear system with finite discrete jumps was considered. Especially, the case where D matrices in the system are not assumed to be zero was dealt. Several versions of the bounded real lemma are presented in terms of solution to Riccati differential equations or inequalities with finite discrete jumps. Both the finite and infinite horizon cases are considered. These results generalize the existed bounded real lemma for linear systems.

Stochastic bounded consensus of second-order multi-agent systems in noisy environment

This paper investigates the stochastic bounded consensus of leader-following second-order multi-agent systems in a noisy environment. It is assumed that each agent received the information of its neighbors corrupted by noises and time delays. Based on the graph theory, stochastic tools, and the Lyapunov function method, we derive the sufficient conditions under which the systems would reach stochastic bounded consensus in mean square with the protocol we designed. Finally, a numerical simulation is illustrated to check the effectiveness of the proposed algorithms.

Stochastic resonance in the FitzHugh-Nagumo system driven by bounded noise

We investigate stochastic resonance （SR） in the FitzHugh-Nagumo system under combined bounded noise and weak harmonic excitation. Taking a spectral amplification factor as a signal-to-noise ratio, we show numerically that bounded noise can induce SR by adjusting either the intensity of bounded noise or its colour. Moreover, the increase of noise colour can enhance the SR and make the peak of the SR shift toward lower noise intensities, which is more feasible in practice. Since bounded noise is flexible to model random excitation, these findings may have some potential applications in engineering, neuroscience and biology.

Robust bounded control for uncertain flight dynamics using disturbance observer

The robust bounded flight control scheme is developed for the uncertain longitudinal flight dynamics of the fighter with control input saturation invoking the backstepping technique. To enhance the disturbance rejection ability of the robust flight control for fighters, the sliding mode disturbance observer is designed to estimate the compounded disturbance including the unknown external disturbance and the effect of the control input saturation. Based on the backstepping technique and the compounded disturbance estimated output, the robust bounded flight control scheme is proposed for the fighter with the unknown external disturbance and the control input saturation. The closed-loop system stability under the developed robust bounded flight control scheme is rigorously proved using the Lyapunov method and the uniformly asymptotical convergences of all closed-loop signals are guaranteed. Finally, simulation results are presented to show the effectiveness of the proposed robust bounded flight control scheme for the uncertain longitudinal flight dynamics of the fighter.

Continuous Dependence of Bounded Φ-variation Solutions on Parameter for a Class of Discontinuous Systems

The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.

INVERSE PROBLEMS FOR A GENERAL MULTI-CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS

This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum ft which is surrounded by simply connected bounded domains Ωi with smooth boundaries Ωi(i = 1,… ,m) where the Dirichlet, Neumann and Robin boundary conditions on Ωi(i = 1,…,m) are considered. Some geometrical properties of Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container Ω, although it can feel some geometrical properties of it.

COMPLETELY BOUNDED COHOMOLOGY OF NON-SELFADJOINT OPERATOR ALGEBRAS

The authors prove that all n-th completely bounded cohomology groups of a nest algebra T（N） acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T（N）-bimodule containing the nest algebra. They also prove that Hcb^n（A, M） ≌ Hcb^n（A, M） for all n ≥ 1 and a CSL algebra .A with an ultraweakly closed .A-bimodul.M containing A.

Box Dimension of Weyl Fractional Integral of Continuous Functions with Bounded Variation

We know that the Box dimension of f（x） ∈ C^1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.

Continuous Dependence of Bounded Φ-Variation Solutions on Parameters for Kurzweil Equations

The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.