A Finite-Time Convergent Analysis of Continuous Action Iterated Dilemma

Dear Editor,In this letter, a finite-time convergent analysis of continuous action iterated dilemma(CAID) is proposed. In traditional evolutionary game theory, the strategy of the player is binary(cooperation or defection), which limits the number of strategies a player can choose from.

A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION

This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.

THE EXTENSIVENESS AND SPECIFICITY OF EFFECT OF ELECTROACUPUNCTURE AT DIFFERENT ACUPOINTS ON NOCICEPTIVE RESPONSE OF CONVERGENT NEURONS IN TRIGEMINAL NUCLEUS CAUDALIS

Experiments were carried out on rats anaesthetized with uraethane. The sponta-neous discharges and nociceptive responses of convergent neurons in the right trigerninal nucleus cau-dalis(TNC) to noxious stimuli at receptive field (cheek) were recorded extracellularly with glass mi-cro-electrode. Electroacupuncture (EA ) was applied at bilateral " Xiaguan" (ST 7 on face ) or "Zusanli" (ST 36 on shank) acupoint with Iow (2V) and high (18V) intensity. The noclceptive re-sponse of convergent neurons in TNC could be inhihited by low intensity EA applied at "Xiaguan" butnot "Zusanlil", showing the specificity of acupoints. High intensity EA at either "Xiaguan" or "Zusan-li" also reduced the nociceptive responses, showing the analgesic extensiveness of acupoints. We sug-gest that "the gate of control" mechanism plays a main role in low intensity EA and "diffuse noxiousinhibitory controls" (DNIC) rnechanism does so in high intensity EA.The results suggest that we should pay attention to the location of acupoints,

Comparative transcriptomics highlights convergent evolution of energy metabolic pathways in group-living spiders

Although widely thought to be aggressive, solitary,and potentially cannibalistic, some spider species have evolved group-living behaviors. The distinct transition provides the framework to uncover groupliving evolution. Here, we conducted a comparative transcriptomic study and examined patterns of molecular evolution in two independently evolved group-living spiders and twelve solitary species. We report that positively selected genes among groupliving spider lineages are significantly enriched in nutrient metabolism and autophagy pathways. We also show that nutrient-related genes of group-living spiders convergently experience amino acid substitutions and accelerated relative evolutionary rates. These results indicate adaptive convergence of nutrient metabolism that may ensure energy supply in group-living spiders. The decelerated evolutionary rate of autophagy-related genes in group-living lineages is consistent with an increased constraint on energy homeostasis as would be required in a group-living environment. Together, the results show that energy metabolic pathways play an important role in the transition to group-living in spiders.

A Facile Convergent Approach to Octopus Polyestrone

Dendrimers have attracted attention in abroad area of chemistry. In this paper,octopus polyestrones were easily synthesized in a novel convergent

Using cylindrical implosions to investigate hydrodynamic instabilities in convergent geometry

Hydrodynamic instabilities such as the Rayleigh–Taylor(RT)and Richtmyer–Meshkov instabilities disrupt inertial confinement fusion(ICF)implosions through the growth of 3D perturbations.Growth of these 3D imperfections at the interfaces of an ICF capsule during implosion lead to mixing between materials that is detrimental to performance.These instabilities have been studied extensively in planar geometry,but such experiments lack the effects of convergence in spherical implosions.While several studies have been performed in spherical geometry,these often lack a direct means to measure perturbation growth.Experiments in cylindrical geometry include convergence effects while maintaining direct diagnostic access.Although cylinders have less compression than spheres,they do provide an excellent platform to validate modeling for convergent geometries.The problem with previous cylindrical implosion experiments was that the convergence ratios were limited to∼4.With the National Ignition Facility(NIF),larger cylindrical targets can be driven to convergences of 10–15 while maintaining a large enough final diameter to measure perturbation growth.This paper reviews the design process used to both benchmark radiation hydrodynamics codes and enable 1D post-processed simulations to explore design space to separate compression effects from acceleration/deceleration RT instability.Results from 1D simulations suggest that cylindrical implosions on the NIF can produce high-convergence experiments to validate RT instability growth for ICF implosions.

UNIFORMLY HIGHER ORDER ACCURATE EXTRAPOLATIONS TO SOLUTIONS OF UNIFORMLY CONVERGENT DISCRETIZATION METHODS FOR SINGULARLY PERTURBED PROBLEMS

We discuss the uniformly higher order accurate extrapolations,which are based on theuniform expansion for global error,to solutions of uniformly convergent discretizationmethods for singularly perturbed problems.By applying the approach to the Il’in-Allen-Southwell scheme for a non-self-adjoint problem,we obtain an extrapolation solution whichis uniformly convergent with order two.We confirm the result by numerical calculations.

A HIGH CONVERGENT PRECISION EXACT ANALYTIC METHOD FOR DIFFERENTIAL EQUATION WITH VARIABLE COEFFICIENTS

The exact analytic method was given by[1].It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision.In this paper,a new high precision algorithm is given based on[1],through a bending problem of variable cross-section beams.It can have the fourth convergent precision without increasing computation work.The present computation method is not only simple but also fast.The numerical examples are given at the end of this paper which indicate that the high convergent precision can be obtained using only a few elements.The correctness of the theory in this paper is confirmed.

A UNIFORMLY CONVERGENT SECOND ORDER DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED SELF-ADJOINT ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM

In this paper,based on the idea of El-Mistikawy and Werle[1]we construct a differencescheme for a singularly perturbed self-adjoint ordinary differential equation inconservation form.We prove that it is a uniformly convergent second order scheme.

Investigation of convergent Richtmyer–Meshkov instability at tin/xenon interface with pulsed magnetic driven imploding

The Richtmyer–Meshkov instability at the interface of solid state tin material and xenon gases under cylinder geometry is studied in this paper. The experiments were conducted at FP-1 facility in Institute of Fluid Physics, China Academy of Engineering Physics(CAEP). The FP-1 facility is a pulsed power driver which could generate high amplitude magnetic field to drive metal liner imploding. Convergent shock wave was generated by impacting a magnetic-driven aluminium liner onto a inner mounted tin liner. The convergent evolution of the disturbance pre-machined onto the tin liner's inner surface was diagnosed by x-radiography. The spike amplitudes were derived from x-ray frames and were compared with linear theory.An analytical model containing material strength effect was derived and matched well to the experimental results. This sensibility of the disturbance evolution to material strength property shines light to the application of Richtmyer–Meshkov instability to infer material strength.

DETERMINATION OF SPACE GROUP OF PrCo_(12)B_6 COMPOUND BY CONVERGENT BEAM ELECTRON DIFFRACTION

The space group of PrCo12B6,compound has been determined using the convergent beam elec-tron diffraction method.The space group is found to be R3m.

STUDIES ON MACROCYCLIC DITERPENOIDS（Ⅻ）──A Convergent and Stereoselective Synthesis of Sarcophytol－Q Precursor──（11S）－3，7，11，15－Tetramethyl－11－Hydroxy－14－Oxo－3E，7E，12E－Hexadecatrienal

ＳＴＵＤＩＥＳＯＮＭＡＣＲＯＣＹＣＬＩＣＤＩＴＥＲＰＥＮＯＩＤＳ（Ⅻ）──ＡＣｏｎｖｅｒｇｅｎｔａｎｄＳｔｅｒｅｏｓｅｌｅｃｔｉｖｅＳｙｎｔｈｅｓｉｓｏｆＳａｒｃｏｐｈｙｔｏｌ－ＱＰｒｅｃｕｒｓｏｒ──（１１Ｓ）－３，７，１１，１５－Ｔｅｔｒａｍｅｔ...

STUDIES ON MACROCYCLIC DITERPENOIDS（XI）──A Convergent and Stereoselective Synthesis of Cembrenene Precursor－4，10－Dimethyl－7－Isopropenyl－14－Oxo－3Z，5E，10E－Pentadecatrienal

ＳＴＵＤＩＥＳ ＯＮ ＭＡＣＲＯＣＹＣＬＩＣ ＤＩＴＥＲＰＥＮＯＩＤＳ（ＸＩ）──Ａ Ｃｏｎｖｅｒｇｅｎｔ ａｎｄ Ｓｔｅｒｅｏｓｅｌｅｃｔｉｖｅ Ｓｙｎｔｈｅｓｉｓ ｏｆ Ｃｅｍｂｒｅｎｅｎｅ Ｐｒｅｃｕｒｓｏｒ－４，１０－Ｄｉｍｅｔｈｙｌ－７－Ｉ...

Convergent robust stabilization conditions for fuzzy chaotic systems based on the edgewise subdivision approach

This paper concerns the problem of stabilizing fuzzy chaotic systems via the viewpoint of the edgewise subdivision approach.Firstly,a new edgewise subdivision algorithm is proposed to implement the simplex edgewise subdivision which divides the overall fuzzy chaotic systems into a lot of sub-systems by a kind of algebraic description.These sub-systems have the same volume and shape characteristics.Secondly,a novel kind of control scheme which switches by the transfer of different operating sub-systems is proposed to achieve convergent stabilization conditions for the underlying controlled fuzzy chaotic systems.Finally,a numerical example is given to demonstrate the validity of the proposed methods.

TYPES OF CONVERGENT NEURONS OF DORSAL HORN IN THE SPINAL CORD FROM SOMATIC AND VISCERAL INPUTS IN SPINAL RATS

ＴＹＰＥＳＯＦＣＯＮＶＥＲＧＥＮＴＮＥＵＲＯＮＳＯＦＤＯＲＳＡＬＨＯＲＮＩＮＴＨＥＳＰＩＮＡＬＣＯＲＤＦＲＯＭＳＯＭＡＴＩＣＡＮＤＶＩＳＣＥＲＡＬＩＮＰＵＴＳＩＮＳＰＩＮＡＬＲＡＴＳ￥ＺｈｕＺｈｏｎｇｌｉａｎｇ（李忠良）；ＪｉａｎｇＳａｉｎａｎ（江赛...

COMPARISONS OF ABSOLUTELY CONVERGENT TRIGONOMETRIC SERIES

In this paper, we first discuss the methods of comparing two special absolutely convergentsine series, sinnx and sinnx. We state the theorem in.one dimensional case as follows; Theorem. Let be convergent series with nonnegative terms. SupposeThen for all x∈[0,π]If, in addition,

A QP-FREE AND SUPERLINEARLY CONVERGENT ALGORITHM FOR INEQUALITY CONSTRAINED OPTIMIZATIONS

In this paper, a new mixed quasi-Newton method for inequality constrained optimization problems is proposed. The feature of the method is that only the systems of linear equations are solved in each iteration, other than the quadratic programming, which decrease the amount of computations and is also efficient for large scale problem. Under some mild assumptions without the strict complementary condition, the method is globally and superlinearly convergent.

The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics

The interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field is numerically investigated within the framework of ideal magnetohydrodynamics.Three fluids of differing densities are initially separated by the two perturbed cylindrical interfaces.The initial incident converging shock is generated from a Riemann problem upstream of the first interface.The effect of the magnetic field on the instabilities is studied through varying the field strength.It shows that the Richtmyer-Meshkov and Rayleigh-Taylor instabilities are mitigated by the field,however,the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations.The degree of asymmetry of the interfacial growth rate is increased when the seed field strength is increased.

An Efficient Second-Order Convergent Scheme for One-Side Space Fractional Diffusion Equations with Variable Coefficients

In this paper,a second-order fnite-diference scheme is investigated for time-dependent space fractional difusion equations with variable coefcients.In the presented scheme,the Crank-Nicolson temporal discretization and a second-order weighted-and-shifted Grünwald-Letnikov spatial discretization are employed.Theoretically,the unconditional stability and the second-order convergence in time and space of the proposed scheme are established under some conditions on the variable coefcients.Moreover,a Toeplitz preconditioner is proposed for linear systems arising from the proposed scheme.The condition number of the preconditioned matrix is proven to be bounded by a constant independent of the discretization step-sizes,so that the Krylov subspace solver for the preconditioned linear systems converges linearly.Numerical results are reported to show the convergence rate and the efciency of the proposed scheme.