Limit circle invariance for two differential systems on time scales

In this paper we consider two linear differential systems on a time scale. Both systems depend linearly on a complex spectral parameter λ. We prove that if all solutions of these two systems are square integrable with respect to a given weight matrix for one value λ₀, then this property is preserved for all complex values λ. This result extends and improves the corresponding continuous time statement, which was derived by Walker (1975) for two non‐hermitian linear Hamiltonian systems, to appropriate differential systems on arbitrary time scales. The result is new even in the purely discrete case, or in the scalar time scale case, as well as when both time scale systems coincide. The latter case also generalizes a limit circle invariance criterion for symplectic systems on time scales, which was recently derived by the authors.     

New Lyapunov‐type inequalities for a class of even‐order linear differential equations

In this paper, we obtain some new Lyapunov‐type inequalities for a class of even‐order linear differential equations, the results are new and generalize and improve some early results in this field.     

Optimal reinsurance under risk and uncertainty

This paper deals with the optimal reinsurance problem if both insurer and reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also included. The insurer and reinsurer degrees of uncertainty do not have to be identical. The decision variable is not the retained (or ceded) risk, but its sensitivity with respect to the total claims. Thus, if one imposes strictly positive lower bounds for this variable, the reinsurer moral hazard is totally eliminated.Three main contributions seem to be reached. Firstly, necessary and sufficient optimality conditions are given in a very general setting. Secondly, the optimal contract is often a bang–bang solution, i.e., the sensitivity between the retained risk and the total claims saturates the imposed constraints. Thirdly, the optimal reinsurance problem is equivalent to other linear programming problem, despite the fact that risk, uncertainty, and many premium principles are not linear. This may be important because linear problems may be easily solved in practice, since there are very efficient algorithms.     

Efficient quantification of the importance of contacts for the dynamical stability of proteins

Understanding the stability of the native state and the dynamics of a protein is of great importance for all areas of biomolecular design. The efficient estimation of the influence of individual contacts between amino acids in a protein structure is a first step in the reengineering of a particular protein for technological or pharmacological purposes. At the same time, the functional annotation of molecular evolution can be facilitated by such insight. Here, we use a recently suggested, information theoretical measure in biomolecular design - the Kullback-Leibler-divergence - to quantify and therefore rank residue-residue contacts within proteins according to their overall contribution to the molecular mechanics. We implement this protocol on the basis of a reduced molecular model, which allows us to use a well-known lemma of linear algebra to speed up the computation. The increase in computational performance is around 10(1)- to 10(4)-fold. We applied the method to two proteins to illustrate the protocol and its results. We found that our method can reliably identify key residues in the molecular mechanics and the protein fold in comparison to well-known properties in the serine protease inhibitor. We found significant correlations to experimental results, e.g., dissociation constants and Φ values.     

3-羟基肉桂酸构筑的锌(Ⅱ)和镉(Ⅱ)配合物的合成、晶体结构和荧光性质

用水热法合成得到2个配合物,{[ML₂(bipy)(H₂O)₂]·2bipy}_n(M=Cd 1,Zn 2;HL=3-羟基肉桂酸,bipy=4,4′-联吡啶),并对它们进行了红外分析、元素分析,热重分析和单晶结构分析。配合物1和2为异质同晶,单斜晶系,P2/c空间群。中心金属M为六配位,相邻的M^Ⅱ通过4,4′-联吡啶桥联形成沿b轴延伸的一维链状结构,此外还存在未配位的4,4′-联吡啶作为客体分子位于链与链之间。通过对配合物1和2的固态荧光测试表明,它们在绿光区均显示发光效应。     

Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance

Finite-time boundedness and finite-time weighted L₂-gain for a class of switched delay systems with time-varying exogenous disturbances are studied. Based on the average dwell-time technique, sufficient conditions which guarantee the switched linear system with time-delay is finite-time bounded and has finite-time weighted L₂-gain are given. These conditions are delay-dependent and are given in terms of linear matrix inequalities. Detail proofs are given by using multiple Lyapunov-like functions. An example is employed to verify the efficiency of the proposed method.     

Design of controller for Lur’e systems guaranteeing dichotomy

In this paper, the problem of controller design for Lur’e systems guaranteeing dichotomy is investigated. On the basis of Kalman-Yakubovich-Popov (KYP) lemma and two frequency equalities, a new methodology for the dichotomy analysis of the Lur’e systems is proposed. A linear matrix inequality (LMI) based criterion is derived, which is equivalent to the Leonov’s frequency-domain one, while for the dichotomy analysis and synthesis which is more straightforward than the frequency-domain one. In virtue of this result, a dynamic output feedback controller ensuring the dichotomy property for Lur’e systems is designed. Finally a numerical example is included to demonstrate the validity and the applicability of the proposed approach.     

Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention 2n

The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed.     

Using the analytic center in the feasibility pump

The feasibility pump (FP) has proved to be a successful heuristic for finding feasible solutions of mixed integer linear problems. Briefly, FP alternates between two sequences of points: one of feasible solutions for the relaxed problem, and another of integer points. This short paper extends FP, such that the integer point is obtained by rounding a point on the (feasible) segment between the computed feasible point and the analytic center for the relaxed linear problem.     

Existence of optimal solutions for general stochastic linear complementarity problems

In this paper we show the solvability of the expected residual minimization (ERM) formulation for the general stochastic linear complementarity problem (SLCP) under mild assumptions. The properties of the ERM formulation are dependent on the choice of NCP functions. We focus on the ERM formulations defined by the “min” NCP function and the penalized FB function, both of which are nonconvex programs on the nonnegative orthant.