The Robin Problem for Singular Perturbed Integral Differential Equations of Volterra Type

In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,under the appropriate assumptions,by constructing the special function of upper and lower solutions,we demonstrate the existence of the solution for singularly preturbed integral differential equation of Volterra type,and give the uniformly valid approximate estimation.

“性致”问题妙方可解

在婚姻生活中，“七年之痒”常常悄然而至。在婚姻之“痒”的背后，夫妻之间的激情，早已随着时间和生活琐事的打磨，慢慢陷入平淡，甚至步入倦怠。

Improved Consensus Speed for Discrete-Time Multi-agent Systems

The consensus problem of a linear discrete-time multi- agent system with directed communication topologies was investigated. A protocol was designed to solve consensus with an improved convergence speed achieved by designing protocol gains. The clo6ed-loop multi.agent system converged to an expected type of consensus function, which was divided into four types： zero, non- zero constant vector, bounded trajectories, and ramp trajectories. An algorithm was further provided to construct the protocol gains, which were determined in terms of a classical pole placement algorithm and a modified algebraic Riccati equation. Finally, an example to illustrate the effectiveness of theoretical results was presented.

Finite Time Consensus Problem for Multiple Non-Holonomic Agents with Communication Delay

In this paper, finite time consensus problem is discussed for multiple non-holonomic mobile agents with constant communication delay. The objective is to design non-smooth distributed control laws such that multiple non-holonomic mobile agents can be all in agreement within any given finite time larger than communication delay. The authors propose a novel switching control strategy with the help of Lyapunov-based method and graph theory.

Output Consensus for Heterogeneous Nonlinear Multi-Agent Systems Based on T-S Fuzzy Model

In this paper, the output consensus problem of general heterogeneous nonlinear multi-agent systems subject to different disturbances is considered. A kind of Takagi-Sukeno fuzzy modeling method is used to describe the nonlinear agents' dynamics. Based on the model, a distributed fuzzy observer and controller are designed based on parallel distributed compensation scheme and internal reference models such that the heterogeneous nonlinear multi-agent systems can achieve output consensus. Then a necessary and sufficient condition is presented for the output consensus problem. And it is shown that the consensus trajectory of the global fuzzy model is determined by the network topology and the initial states of the internal reference models. Finally, some simulations are given to illustrate and verify the effectiveness of the proposed scheme.

Characteristic model-based consensus of networked heterogeneous robotic manipulators with dynamic uncertainties

In this paper, we address the characteristic model-based discrete-time consensus problem of networked robotic manipulators with dynamic uncertainties. The research objective is to achieve joint-position consensus of multiple robotic agents interconnected on directed graphs containing a spanning tree. A novel characteristic model-based distributed adaptive control scenario is proposed with a state-relied projection estimation law and a characteristic model-based distributed controller. The performance analysis is also unfolded where the uniform ultimate boundedness(UUB) of consensus errors is derived by resorting to the discrete-time-domain stability analysis tool and the graph theory. Finally, numerical simulations illustrate the effectiveness of the proposed theoretical strategy.

CONSENSUS CONTROL DESIGN FOR MULTI-AGENT SYSTEMS USING RELATIVE OUTPUT FEEDBACK

This paper studies the consensus problem of multi-agent systems in which all agents are modeled by a general linear system. The authors consider the case where only the relative output feedback between the neighboring agents can be measured. To solve the consensus problem, the authors first construct a static relative output feedback control under some mild constraints on the system model. Then the authors use an observer based approach to design a dynamic relative output feedback control. If the adjacent graph of the system is undirected and connected or directed with a spanning tree, with the proposed control laws, the consensus can be achieved. The authors note that with the observer based approach, some information exchange between the agents is needed unless the associated adjacent graph is completely connected.

Geometric and topological rigidity for compact submanifolds of odd dimension

We investigate rigidity problems for odd-dimensional compact submanifolds.We show that if Mn（n 5） is an odd-dimensional compact submanifold with parallel mean curvature in Sn＋p,and if RicM ＆gt;（n- 2-1n）（1 ＋ H2） and H ＆lt; δn,where δn is an explicit positive constant depending only on n,then M is a totally umbilical sphere.Here H is the mean curvature of M.Moreover,we prove that if Mn（n 5） is an odd-dimensional compact submanifold in the space form Fn＋p（c） with c 0,and if RicM ＆gt;（n-2-εn）（c＋H2）,where εn is an explicit positive constant depending only on n,then M is homeomorphic to a sphere.

Some Remarks on Korn Inequalities

A recent joint paper with Doina Cioranescu and Julia Orlik was concerned with the homogenization of a linearized elasticity problem with inclusions and cracks(see[Cioranescu, D., Damlamian, A. and Orlik, J., Homogenization via unfolding in periodic elasticity with contact on closed and open cracks, Asymptotic Analysis, 82, 2013, 201–232]). It required uniform estimates with respect to the homogenization parameter. A Korn inequality was used which involves unilateral terms on the boundaries where a nopenetration condition is imposed. In this paper, the author presents a general method to obtain many diverse Korn inequalities including the unilateral inequalities used in [Cioranescu, D., Damlamian, A. and Orlik, J., Homogenization via unfolding in periodic elasticity with contact on closed and open cracks, Asymptotic Analysis, 82, 2013, 201–232]. A preliminary version was presented in [Damlamian, A., Some unilateral Korn inequalities with application to a contact problem with inclusions, C. R. Acad. Sci. Paris, Ser. I,350, 2012, 861–865].

Robust Semi-Global Leaderless Consensus and Containment Control of Identical Linear Systems with Imperfect Actuators

This paper investigates both the robust semi-global leaderless consensus problem and the robust semi-global containment control problem for a group of identical linear systems with imperfect actuators. The imperfect actuators are characterized by nonlinearities such as saturation and dead zone and there input output relationships are not precisely known. The dynamics of follower agents are also affected by the input additive disturbances. Low-and-high gain feedback consensus protocols are constructed to solve these problems. More specifically, it is shown that robust semi-global leaderless consensus can be achieved over a connected undirected graph and robust semi-global containment control can be achieved when each follower agent has access to the information of at least one leader agent. Numerical simulation illustrates the theoretical results.

Properties of quark matter in a new quasiparticle model with QCD running coupling

The running of the QCD coupling in the effective mass causes thermodynamic inconsistency problem in the conventional quasiparticle model. We provide a novel treatment which removes the inconsistency by an effective bag constant. The chemical potential dependence of the renormalization subtraction point is constrained by the Cauchy condition in the chemical potential space. The stability and microscopic properties of strange quark matter are then studied within the completely self-consistent quasiparticle model, and the obtained equation of state of quark matter is applied to the investigation of strange stars. It is found that our improved model can describe well compact stars with mass about two times the solar mass, which indicates that such massive compact stars could be strange stars.

Pattern of rubber bullet injuries in the lower limbs： A report from Kashmir

Purpose： Rubber bullets are considered a non-lethal method of crowd control and are being used over the world. However the literature regarding the pattern and management of these injuries is scarce for the forensic pathologist as well as for the traumatologist. The objective of this report was to add our experience to the existing literature. Methods： From June 2008 to August 2010 the Government Hospital for Bone and Joint Surgery Barzulla and the Department of Orthopaedics, SKIMS Medical College/Hospital Bemina Srinagar received 28 patients for management of their orthopaedic injuries caused by rubber bullets. We documented all injuries and also recorded the management issues and complications that we encountered. Results： All patients were males with an age range of 11-32 years and were civilians who had been hit by rubber bullets fired by the police and the paramilitary forces. Among them, 19 patients had injuries of the lower limbs and 9 patients had injuries of the upper limbs. All patients were received within 6 h of being shot. Conclusion： Our findings suggest that these weapons are capable of causing significant injuries including fractures and it is important for the surgeon to be well versed with the management of such injuries especially in areas of unrest, The report is also supportive of the opinion that these weapons are lethal and should hence be reclassified_

Model Selection Consistency of Lasso for Empirical Data

Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is fixed while dimensionality grows with n. The authors consider the model selection problem of lasso for this kind of data. The authors investigate both theoretical guarantees and simulations, and show that the lasso is robust for various kinds of data.

Finite-time consensus for a stochastic multi-species system

This paper considers the finite-time consensus problem for a stochastic multi-species system. First, we give out a nonlinear consensus protocol for the multi-species system with Brownian motion, and propose the definition of finite-time consensus in probability. Second, we prove that the multi-species system can achieve finite-time consensus in probability with different proper protocols by use of graph theory, stochastic Lyapunov function method and probability theory. Finally, some simulations are provided to illustrate the effectiveness of the theoretical results.

Characterization of Essential Stability in Lower Pseudocontinuous Optimization Problems

Characterization of essential stability of minimum solutions for a class of optimization problems with boundedness and lower pseudocontinuity on a compact metric space is given. It shows that any optimization problem considered here has one essential component(resp. one essential minimum solution) if and only if its minimum solution set is connected(resp. singleton) and that those optimization problems which have a unique minimum solution form a residual set(however, which need not to be dense).