Level density of odd-A nuclei at saddle point

Based on the covariant density functional theory,by employing the core–quasiparticle coupling(CQC)model,the nuclear level density of odd-A nuclei at the saddle point is achieved.The total level density is calculated via the convolution of the intrinsic level density and the collective level density.The intrinsic level densities are obtained in the finite-temperature covariant density functional theory,which takes into account the nuclear deformation and pairing self-consistently.For saddle points on the free energy surface in the(β_(2),γ)plane,the entropy and the associated intrinsic level density are compared with those of the global minima.By introducing a quasiparticle to the two neighboring even–even core nuclei,whose properties are determined by the five-dimensional collective Hamiltonian model,the collective levels of the odd-A nuclei are obtained via the CQC model.The total level densities of the^(234-240)U agree well with the available experimental data and Hilaire’s result.Furthermore,the ratio of the total level densities at the saddle points to those at the global minima and the ratio of the total level densities to the intrinsic level densities are discussed separately.

HESSIAN MATRIX BASED SADDLE POINT DETECTION FOR GRANULES SEGMENTATION IN 2D IMAGE

Segmenting the touching objects in an image has been remaining as a hot subject due to the problematic complexities, and a vast number of algorithms designed to tackle this issue have come into being since a decade ago. In this paper, a new granule segmentation algorithm is developed using saddle point as the cutting point. The image is binarized and then sequentially eroded to form a gray-scale topographic counterpart, followed by using Hessian matrix computation to search for the saddle point. The segmentation is performed by cutting through the saddle point and along the maximal gradient path on the topographic surface. The results of the algorithm test on the given real images indicate certain superiorities in both the segmenting robustness and execution time to the referenced methods.

Distributed Resource Allocation via Accelerated Saddle Point Dynamics

In this paper,accelerated saddle point dynamics is proposed for distributed resource allocation over a multi-agent network,which enables a hyper-exponential convergence rate.Specifically,an inertial fast-slow dynamical system with vanishing damping is introduced,based on which the distributed saddle point algorithm is designed.The dual variables are updated in two time scales,i.e.,the fast manifold and the slow manifold.In the fast manifold,the consensus of the Lagrangian multipliers and the tracking of the constraints are pursued by the consensus protocol.In the slow manifold,the updating of the Lagrangian multipliers is accelerated by inertial terms.Hyper-exponential stability is defined to characterize a faster convergence of our proposed algorithm in comparison with conventional primal-dual algorithms for distributed resource allocation.The simulation of the application in the energy dispatch problem verifies the result,which demonstrates the fast convergence of the proposed saddle point dynamics.

Convergence analysis of the corrected Uzawa algorithm for symmetric saddle point problems

For the large sparse saddle point problems, Pan and Li recently proposed in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31（3）： 231-242] a corrected Uzawa algorithm based on a nonlinear Uzawa algorithm with two nonlinear approximate inverses, and gave the detailed convergence analysis. In this paper, we focus on the convergence analysis of this corrected Uzawa algorithm, some inaccuracies in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31（3）： 231-242] are pointed out, and a corrected convergence theorem is presented. A special case of this modified Uzawa algorithm is also discussed.

Coincidence Point Theorems,Intersection Theorems and Saddle Point Theorems on FC-spaces

In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.

Wide-range characteristics of beam perveance and saddle point potential of LIPS-200 ion thruster

Both the long-life and multi-mode versions of LIPS-200 ion thruster are under investigation in LIP(Lanzhou Institute of Physics).To confirm the feasible ranges of the beam current and accel(abbreviation for accelaration)grid potential to apply to the thruster,the wide-range beam perveance(the state of beam focus)and saddle point potential(the lowest potential along beamlet centerline)characteristics of LIPS-200 are studied with a test-verified PIC-MCC(Particle in Cell-Monte Carlo Collisions)model.These characteristics are investigated with both the initial and the eroded states of the accel grid aperture diameter.The results show that the feasible ranges of these parameters with respect to perveance/crossover(overfocused)limit extend as the operating time accumulates,while the feasible range of accel grid potential narrows due to a reduced EBSF(electron backstreaming failure)margin.The feasible ranges determined by the initial condition are:(i)the beam current up to 0.981 A,and(ii)the accel grid potential up to−85 V.A 23%enlargement of the aperture diameter would bring up to 48 V of EBSF margin loss.

MINIMAX THEOREM AND SADDLE POINT THEOREM WITHOUT LINEAR STRUCTURE

In this paper, a new kind of concavity of a function defined on a set without linear structure is introduced and a generalization of Fam Ky inequality is given. Minimax theorem in a general topological space is obtained. Moreover, a saddle point theorem on a topological space without any linear structure is established.

A New GMλ-KKM Theorem and Its Application to Saddle Points

In this paper,a new GMλ-KKM theorem is established for noncompact λ-hyperconvex metric spaces.As applications,the properties of the solution set of the variational inequality is shown and an existence theorem for saddle points is obtained.

Open Loop Saddle Point on Linear Quadratic Stochastic Differential Games

In this paper, we deal with one kind of two-player zero-sum linear quadratic stochastic differential game problem. We give the existence of an open loop saddle point if and only if the lower and upper values exist.

Saddle Point Optimality Criteria of Interval Valued Non-Linear Programming Problem

The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.

A New Choice of the Preconditioner of PHSS Method for Saddle Point Problems

Bai, Golub and Pan presented a preconditioned Hermitian and skew-Hermitian splitting(PHSS) method [Numerische Mathematik, 2004, 32: 1-32] for non-Hermitian positive semidefinite linear systems. We improve the method to solve saddle point systems whose(1,1) block is a symmetric positive definite M-matrix with a new choice of the preconditioner and compare it with other preconditioners. The results show that the new preconditioner outperforms the previous ones.

A Note on Parameterized Preconditioned Method for Singular Saddle Point Problems

Recently, some authors (Li, Yang and Wu, 2014) studied the parameterized preconditioned HSS (PPHSS) method for solving saddle point problems. In this short note, we further discuss the PPHSS method for solving singular saddle point problems. We prove the semi-convergence of the PPHSS method under some conditions. Numerical experiments are given to illustrate the efficiency of the method with appropriate parameters.

NONMONOTONE LOCAL MINIMAX METHODS FOR FINDING MULTIPLE SADDLE POINTS

In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert spaces.Compared to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less computations.Firstly,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is constructed.Its feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative sequences.Secondly,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each iteration.Finally,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary conditions.Extensive numerical results indicate that our approach is very effective and speeds up the LMMs significantly.

Qualitative Properties of Equilibrium Point in a Discrete Predator-Prey Model

In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic Shengjin formula, we find the existence conditions for fixed points of the model. Then, by using the qualitative theory of ordinary differential equations and matrix theory we indicate which points are hyperbolic and which are non-hyperbolic and the associated conditions.

A RELAXED HSS PRECONDITIONER FOR SADDLE POINT PROBLEMS FROM MESHFREE DISCRETIZATION＊

In this paper, a relaxed Hermitian and skew-Hermitian splitting （RHSS） preconditioner is proposed for saddle point problems from the element-free Galerkin （EFG） discretization method. The EFG method is one of the most widely used meshfree methods for solving partial differential equations. The RHSS preconditioner is constructed much closer to the coefficient matrix than the well-known HSS preconditioner, resulting in a RHSS fixed-point iteration. Convergence of the RHSS iteration is analyzed and an optimal parameter, which minimizes the spectral radius of the iteration matrix is described. Using the RHSS pre- conditioner to accelerate the convergence of some Krylov subspace methods （like GMRES） is also studied. Theoretical analyses show that the eigenvalues of the RHSS precondi- tioned matrix are real and located in a positive interval. Eigenvector distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are obtained. A practical parameter is suggested in implementing the RHSS preconditioner. Finally, some numerical experiments are illustrated to show the effectiveness of the new preconditioner.

A New Fixed Point Theorem in Noncompact Hyperconvex Metric Spaces and Its Application to Saddle Point Problems

In this paper, a new fixed point theorem is established in noncompact hyperconvex metric spaces. As applications, a continuous selection and its fixed point theorem, an existence theorem for maximal elements, a Ky Fan minimax inequality and an existence theorem for saddle points are obtained.

Globally Proper Saddle Point in Ic-Cone-Convexlike Set-Valued Optimization Problems

The existence conditions of globally proper efficient points and a useful property of ic- cone-convexlike set-valued maps are obtained. Under the assumption of the ic-cone-convexlikeness, the optimality conditions for globally proper efficient solutions are established in terms of Lagrange multipliers. The new concept of globally proper saddle-point for an appropriate set-valued Lagrange map is introduced and used to characterize the globally proper efficient solutions. The results which are obtained in this paper are proven under the conditions that the ordering cone need not to have a nonempty interior.

A New Fixed Point Theorem in Noncompact L-Convex Metric Spaces with Applications to Minimax Inequalities and Saddle Points

In this paper,a new fixed point theorem is established in noncompact complete Lconvex metric spaces.As applications,a maximal element theorem,a minimax inequality and a saddle point theorem are obtained.

Thermal Fission Rate Calculated Numerically by Particles Multi-passing over SaddlePoint

Langevin simulation of the particles multi-passing over the saddle point is proposed to calculate thermal fission rate. Due to finite friction and the corresponding thermal fluctuation, a backstreaming exists in the process of the particle descent from the saddle to the scission. This leads to that the diffusion behind the saddle point has influence upon the stationary flow across the saddle point. A dynamical correction factor, as a ratio of the flows of multi- and first-overpassing the saddle point, is evaluated analytically. The results show that the fission rate calculated by the particles multi-passing over the saddle point is lower than the one calculated by the particle firstly passing over the saddle point, and the former approaches the results at the scission point.

PRECONDITIONED HSS-LIKE ITERATIVE METHOD FOR SADDLE POINT PROBLEMS

A new HSS-like iterative method is first proposed based on HSS-like splitting of non- Hermitian （1,1） block for solving saddle point problems. The convergence analysis for the new method is given. Meanwhile, we consider the solution of saddle point systems by preconditioned Krylov subspaee method and discuss some spectral properties of the preconditioned saddle point matrices. Numerical experiments are given to validate the performances of the preconditioners.