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.

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.

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.

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.

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.

Kinematic Geometry for the Saddle Line Fitting of Planar Discrete Positions

The position synthesis of planar linkages is to locate the center point of the moving joint on a rigid link, whose trajectory is a circle or a straight line. Utilizing the min-max optimization scheme, the fitting curve needs to minimize the maximum fitting error to acquire the dimension of a planar binary P-R link. Based on the saddle point programming, the fitting straight line is determined to the planar discrete point-path traced by the point of the rigid body in planar motion. The property and evolution of the defined saddle line error can be revealed from three given separate points. A quartic algebraic equation relating the fitting error and the coordinates is derived, which agrees with the classical theory. The effect of the fourth point is discussed in three cases through the constraint equations. The multi-position saddle line error is obtained by combination and comparison from the saddle point programming. Several examples are presented to illustrate the solution process for the saddle line error of the moving plane. The saddle line error surface and the contour map presented to show the variations of the fitting error in the fixed frame. The discrete kinematic geometry is then set up to disclose the relations of the separate positions of the rigid body, the location of the tracing point on the moving body, and the position and orientation of the saddle line to the point-path. This paper presents a new analytic geometry method for saddle line fitting and provides a theoretical foundation for position synthesis.

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 THEOREMS FOR SUBCONVEXLIKEFUNCTIONS WITH APPLICATIONS TO SADDLEPOINT PROBLEMS

In this paper some minimax theorems are presented for subconvexlike functions. These are then applied to obtain saddle point theorems.

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.

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.

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.

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.

奇异鞍点问题中广义位移分裂迭代方法的半收敛性分析

Recently,some authors(Shen and Shi,2016)studied the generalized shiftsplitting(GSS)iteration method for singular saddle point problem with nonsymmetric positive definite(1,1)-block and symmetric positive semidefinite(2,2)-block.In this paper,we further apply the GSS iteration method to solve singular saddle point problem with nonsymmetric positive semidefinite(1,1)-block and symmetric positive semidefinite(2,2)-block,prove the semi-convergence of the GSS iteration method and analyze the spectral properties of the corresponding preconditioned matrix.Numerical experiment is given to indicate that the GSS iteration method with appropriate iteration parameters is effective and competitive for practical use.

Probabilistic Error Estimate for Numerical Discretization of High-Index Saddle Dynamics with Inaccurate Models

We prove probabilistic error estimates for high-index saddle dynamics with or without constraints to account for the inaccurate values of the model,which could be encountered in various scenarios such as model uncertainties or surrogate model algorithms via machine learning methods. The main contribution lies in incorporating the probabilistic error bound of the model values with the conventional error estimate methods for high-index saddle dynamics. The derived results generalize the error analysis of deterministic saddle dynamics and characterize the affect of the inaccuracy of the model on the convergence rate.

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.