ON THE BOUNDEDNESS AND THE NORM OF A CLASS OF INTEGRAL OPERATORS

The boundedness and the norm of a class of integral operators Ta,b,c on Lλ^P spaces are studied in this paper. The author not only gives the sufficient and necessary condition for the boundedness of Ta,b,c on Lλ^P,but also obtains its accurate norm on Lλ^P for some range under the condition of c = n ＋ a ＋ b.

Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance

In this paper, a new approach is presented for finite-time control problems for linear systems subject to time-varying parametric uncertainties and exogenous disturbance. The disturbance is assumed to be time varying and bounded. Sufficient conditions are obtained for the existence of a linear parameter-dependent state feedback gain, which can ensure that the closed-loop system is finite-time bounded （FTB）. The conditions can be reduced to feasibility problems involving LMIs. Numerical examples show the validity of the proposed methodology.

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.

New Constructions of Nullnorms on Bounded Lattices

We propose two more general methods to construct nullnorms on bounded lattices. By some illustrative examples, we demonstrate that the new method differ from the existing approaches.

Bounded and Unbounded Solutions of the SD Oscillator at Resonance

In this paper we study the boundedness and unboundedness of the solutions of the smooth and discontinuous(SD)oscillatorbegin{equation*}x''+f(x)x'+x-frac{x}{sqrt{x^{2}+alpha^{2}}}=p(t).end{equation*}Since f(x)≠0,the system is non-Hamiltonian,so we have to introduce some reversibility assumptions to apply a suitable twist theorem,for reversible maps with small twist.Moreover,when the nonnegative parameterαdecreases to 0,the system becomes discontinuous.In this case,we need to introduce some suitable transformations to overcome the lack of regularity.We will prove that for any nonnegative parameterα,when p(t)is an odd periodic function satisfying∣∣∫2π0p(t)sintdift∣∣<4,all the solutions are bounded;when p(t)satisfies∣∣∫2π0p(t)sintdift∣∣>4,the SD oscillator has unbounded solutions,and when p(t)satisfies∣∣∫_(0)^(2π)p(t)sintdift∣∣≥4+|F|_(∞),all the solutions are unbounded.

NORM SUMMABILITY OF NRLUND LOGARITHMIC MEANS ON UNBOUNDED VILENKIN GROUPS

The （Noerlund） logarithmic means of the Fourier series is：tnf=1/ln ^n-1∑k=1 Skf/n-k, where ln=^n-1∑k=1 1/k In general, the Fej6r （C, 1） means have better properties than the logarithmic ones. We compare them and show that in the case of some unbounded Vilenkin systems the situation changes.

Probabilistic Norm of Operators and Continuity of Bounded Operators

In this paper,the equivalence for continuity and boundedness of the linear operators on a general PN space is proved by means of their probabilistic norm,and the corresponding result in [1] is improved.

Pacman Renormalization in Siegel Parameters of Bounded Type

A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.

The Covering Theorems for Normalized Holomorphic Mappings on Bounded Starlike Circular Domains in C^n

In this paper, we will investigate convex domains and starlike domains which contain the image set of normalized holomorphic mappings on bounded starlike circular domains in Cn.

Upper bound stability analysis of tiered geosynthetic-reinforced soil wall

The tiered geosynthetic-reinforced soil (GRS) walls have been increasingly applied in the high and steep retaining soil structures. However, very little is known about the design method for the tiered GRS wall in practice. This study is aimed at proposing an upper-bound stability analysis method of a tiered GRS wall. The proposed method was firstly validated by the existing results from the centrifuge test and the numerical method, and then a parametric study was performed to investigate the effects of the cohesionless backfill friction angle φ1 and the wall geometric parameters including the offset distance, the total wall height, the batter angle δ, the number of tiers n, and wall height ratio of adjacent tiers on the dimensionless equivalent earth pressure coefficient KT. The analysis results demonstrated that as the φ1 increases, the shear strength of backfill is enhanced and thus the KT or the total reinforcement tensile force decreases, and the KT decreases with the increase of the offset distance at the initial stage and then becomes stable when it reaches a certain critical value. For a fixed offset distance, the KT or the total reinforcement tensile force decreases with the increase of the δ. For the two-tiered GRS walls having the offset distance less than the critical value, the wall with the smaller wall height ratio has a larger KT. Further, the variation of the location of the critical failure surfaces of tiered GRS walls was presented in this study with the variation of the φ1 and the wall geometry.

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.

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.

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.

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.