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.

Dynamic convergent shock compression initiated by return current in high-intensity laser-solid interactions

We investigate the dynamics of convergent shock compression in solid cylindrical targets irradiated by an ultrafast relativistic laser pulse.Our particle-in-cell simulations and coupled hydrodynamic simulations reveal that the compression process is initiated by both magnetic pressure and surface ablation associated with a strong transient surface return current with density of the order of 10^(17) A/m^(2) and lifetime of 100 fs.The results show that the dominant compression mechanism is governed by the plasma β,i.e.,the ratio of thermal pressure to magnetic pressure.For targets with small radius and low atomic number Z,the magnetic pressure is the dominant shock compression mechanism.According to a scaling law,as the target radius and Z increase,the surface ablation pressure becomes the main mechanism generating convergent shocks.Furthermore,an indirect experimental indication of shocked hydrogen compression is provided by optical shadowgraphy measurements of the evolution of the plasma expansion diameter.The results presented here provide a novel basis for the generation of extremely high pressures exceeding Gbar(100 TPa)to enable the investigation of high-pressure physics using femtosecond J-level laser pulses,offering an alternative to nanosecond kJ-laser pulse-driven and pulsed power Z-pinch compression methods.

Missile guidance law design based on free-time convergent error dynamics

To solve the finite-time error-tracking problem in mis-sile guidance,this paper presents a unified design approach through error dynamics and free-time convergence theory.The proposed approach is initiated by establishing a desired model for free-time convergent error dynamics,characterized by its independence from initial conditions and guidance parameters,and adjustable convergence time.This foundation facilitates the derivation of specific guidance laws that integrate constraints such as leading angle,impact angle,and impact time.The theoretical framework of this study elucidates the nuances and synergies between the proposed guidance laws and existing methodologies.Empirical evaluations through simulation comparisons underscore the enhanced accuracy and adaptability of the proposed laws.

Exponentially Convergent Multiscale Finite Element Method

We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation.The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions.Unlike most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity functions.In general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence.Indeed,there are online and offline parts in the function representation provided by the ExpMsFEM.The online part depends on the right-hand side locally and can be computed in parallel efficiently.The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.

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.

TAUBERIAN THEOREMS FOR WEAK ALMOST CONVERGENT FUNCTIONS

The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .

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,

Combinative Algorithms for the Multidisciplinary Collaborative Simulation of Complex Mechatronic Products Based on Major Step and Convergent Integration Step

Multidisciplinary collaborative simulation （MCS） is an important area of research in the domain of multidisciplinary design optimization （MDO）.Although previous research for MCS has to some extent addressed some issues like using of multiple tools,integration stability,control of step size,data synchronization,etc,further work is still necessary to study how to achieve improved precision.A theoretical model is formulated to describe and analyze the integration process of MCS.A basic algorithm with equal major steps is proposed based on the model,along with two methods of implementation for the model,namely the serial method and the parallel method.A further algorithm based on convergent integration step is proposed,which has a more flexible strategy for run-time integration.The influence of interpolation techniques on simulation performance is studied as well.Simulations of the performance of various algorithms with different interpolation techniques are performed for both a simple numerical example and a complex mechatronic product.The novel algorithm based on convergent integration step,when used with a high-order interpolation technique,has better performance in terms of precision and efficiency.The innovation of this paper is mainly on the validation of high precision of the proposed convergent integration step algorithm.

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.

Dragon Tails:Convergent Caudal Morphology in Winged Archosaurs

In the tails of dromaeosaurid dinosaurs and rhamphorhynchid pterosaurs, elongate osteological rods extend anteriorly from the chevrons and the prezygapophyses. These caudal rods are positioned in parallel and are stacked dorsoventrally. The fully articulated and three-dimensionally preserved caudal series of some dromaeosaurid specimens show that individually these caudal rods were flexible, not rigid as previously thought. However, examination of the arrangement of the caudal rods in cross-section indicates that the combined effect of multiple caudal rods did provide substantial rigidity in the dorsoventral, but not in the lateral, plane. The results of digital muscle reconstructions confirm that dromaeosaurids and rhamphorhynchids also shared greatly reduced caudofemoral muscles in the anterior tail region. The striking similarities between the tails of dromaeosaurids and rhamphorhynchids suggest that both evolved under similar behavioral and biomechanical pressures. Combined with recent discoveries of primitive deinonychosaurs that phylogenetically bracket the evolution of dromaeosaurid caudal rods between two arboreal gliding/flying forms, these results are evidence that the unique caudal morphologies of dromaeosaurids and rhamphorhynchids were both adaptations for an aerial lifestyle.

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.

Simulation of subcritical flow pattern in 180° uniform and convergent open-channel bends using SSIIM 3-D model

In meandering rivers, the flow pattern is highly complex, with specific characteristics at bends that are not observed along straight paths. A numerical model can be effectively used to predict such flow fields. Since river bends are not uniform-some are divergent and others convergent-in this study, after the SSIIM 3-D model was calibrated using the result of measurements along a uniform 180° bend with a width of 0.6 m, a similar but convergent 180v bend, 0.6 m to 0.45 m wide, was simulated using the SSI1M 3-D numerical model. Flow characteristics of the convergent 180° bend, including lengthwise and vertical velocity profiles, primary and secondary flows, lengthwise and widtbwise slopes of the water surface, and the helical flow strength, were compared with those of the uniform 180° bend. The verification results of the model show that the numerical model can effectively simulate the flow field in the uniform bend. In addition, this research indicates that, in a convergent channel, the maximum velocity path at a plane near the water surface crosses the channel＇s centerline at about a 30° to 40° cross-section, while in the uniform bend, this occurs at about the 50° cross-section. The varying range of the water surface elevation is wider in the convergent channel than in the uniform one, and the strength of the helical flow is generally greater in the uniform channel than in the convergent one. Also, unlike the uniform bend, the convergent bend exhibits no rotational cell against the main direction of secondary flow rotation at the 135° cross-section.

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 the uniform expansion for global error, to solutions of uniformly convergent discretization methods for singularly perturbed problems. By applying the approach to the in-Allen-Southwell scheme for a non-self-adjoint problem, we obtain an extrapolation solution which is uniformly convergent with order two. We confirm the result by numerical calculations.

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.

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

A precursor of sarcophytol-Q, (11 S) -3, 7, 11, 15-tetramethyl-11-hydroxy-14-oxo-3E, 7E, 12E-hexadecatrienal, was synthesized by a convergent and stereoselective manner from geraniol via nine steps employing asymmetric Sharpless epoxidation and be (n-BuLi)-induce dehydrohalogenation rearrangement of chiral epoxy chloride (4) and the phase transfer catalytic coupling reaction of allylic phenyl sulfone (9) with chiral allylic chloride (6) as key steps.

Experimental Study and 3D CFD Analysis on the Optimization of Throttle Angle for a Convergent Vortex Tube

Seven adjustments of convergent-type Vortex Tube （VT） with different throttle angles were applied. The adjustments were made to analyze the influences of such angles on cold and hot temperature drops as well as flow structures inside the VTs. An experimental setup was designed, and tests were performed on different convergent VT configurations at injection pressures ranging from 0.45 to 0.65 MPa. The angles of the throttle valve were arranged between 30° to 90°, and the numbers of injection nozzles ranged between 2 and 6. Laboratory results indicated that the maximum hot and cold temperature drops ranged from 23.24 to 35 K and from 22.87 to 32.88 K, respectively, at four injection nozzles. Results also showed that temperature drop is a function of hot throttle valve angle with the maximum hot and cold temperature drops depending on the angle applied. We used graphs to demonstrate the changes in the cold and hot temperature drops with respect to hot throttle angle values. These values were interpreted and evaluated to determine the optimum angle, which was 60°. The CFD outputs agreed very well with the laboratory results. The proposed CFD results can help future researchers gain good insights into the complicated separation process taking place inside the VTs.

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

A cembrenene precursor,4,10-dimethyl-7-isopropenyl-14-oxo-3Z,5E,10Epentadecatrienal,was prepared in a convergent and stereoselective manner starting from geranylacetone via six steps employing allylic chlorination,Wittig reaction(SCOOPY),alkylation of the allylic chloride 11, and the reductive elimination of the vicinal acetoxyl sulfone adduct to introduce stereoselectively the trans double bond of the target molecule as keysteps.

The development of an evidence-informed Convergent Care Theory:Working together to achieve optimal health outcomes

Background Healthcare is a complex and divergent system with uncertainty,unpredictability,and multi-layered stakeholders.The relationships among the stakeholders are multifaceted and dynamic,requiring continual interpersonal connections,networks,and co-evolution.It is pivotal to have an evidence-informed theory to explain the phenomenon,uniting the multifaceted stakeholders’efforts.Purpose To describe the development of an evidence-informed theory,the Convergent Care Theory,assembling healthcare stakeholders to work together and achieve optimal health outcomes.Methods The Convergent Care Theory was developed using a theory synthesis approach based on empirical research and literature reviews published by the theory-proposing author.The empirical evidence was categorized into:patients and families,healthcare providers,healthcare organizations,and patients’and healthcare providers’self-care.Results The Convergent Care Theory includes four concepts:all-inclusive organizational care,healthcare professional collaborative care,person-centered precision care,and patients’and healthcare providers’self-care.Achieving convergent care is a process requiring all stakeholders to work together.Six major facilitators emerged from the research evidence:competence,compassion,accountability,trusting,sharing,and engaging.Conclusion This article introduced the development process of the evidence-informed Convergent Care Theory.Healthcare systems are complex,with multiple stakeholders’needs to meet.The Convergent Care Theory strives to unite healthcare stakeholders,bond resources,and join forces to achieve optimal healthcare outcomes.The underpinning of the theory is a caring culture,which is an underlying code for organizational and team behaviors and the foundation of optimal health outcomes.

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.

Weakly Nonlinear Rayleigh–Taylor Instability in Cylindrically Convergent Geometry

The Rayleigh–Taylor instability（RTI） in cylindrical geometry is investigated analytically through a second-order weakly nonlinear（WN） theory considering the Bell–Plesset（BP） effect. The governing equations for the combined perturbation growth are derived. The WN solutions for an exponentially convergent cylinder are obtained. It is found that the BP and RTI growths are strongly coupled, which results in the bubble-spike asymmetric structure in the WN stage. The large Atwood number leads to the large deformation of the convergent interface. The amplitude of the spike grows faster than that of the bubble especially for large mode number m and large Atwood number A. The averaged interface radius is small for large mode number perturbation due to the mode-coupling effect.