Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

Propagation of Airy beams from right-handed material to left-handed material

Based on the ABCD matrix formalism,the propagation property of an Airy beam from right-handed material（RHM） to left-handed material（LHM） is investigated.The result shows that when the Airy beam propagates in the LHM,the intensity self-bending due to its propagation in the RHM can be compensated.In particular,if the propagation distance in the RHM is equal to that in the LHM and the refractive index of the LHM is n L =-1,the transverse intensity distribution of the Airy beam can return to its original state.

Subwavelength rectangular cavity partially filled with left-handed materials

In this paper, we present the electromagnetic analysis of a rectangular cavity partially filled with a left-handed material slab. Our theoretical investigation shows that there exist novel resonant modes in the cavity, and such a cavity becomes a subwavelength cavity. The eigenvalue equation of the cavity is derived and the resonant frequencies of the novel modes are calculated by using numerical simulation. We also discuss the stability of the novel resonant modes and show the best condition under which a useful rectangular cavity of subwavelength dimensions with tolerable stability is obtained.

Design of Structural Left-handed Material based on Topology Optimization

An effective method to design structural Left-handed material（LHM） was proposed. A commercial finite element software HFSS and S-parameter retrieval method were used to determine the effective constitutive parameters of the metamaterials, and topology optimization technique was introduced to design the microstructure configurations of the materials with desired electromagnetic characteristics. The material considered was a periodic array of dielectric substrates attached with metal film pieces. By controlling the arrangements of the metal film pieces in the design domain, the potential microstructure with desired electromagnetic characteristics can be obtained finally. Two different LHMs were obtained with maximum bandwidth of negative refraction, and the experimental results show that negative refractive indices appear while the metamaterials have simultaneously negative permittivity and negative permeability. Topology optimization technique is found to be an effective tool for configuration design of LHMs.

Microwave left-handed composite material made of slim ferrite rods and metallic wires

This paper reports on experimental study of the microwave properties of a composite material consisting of ferrite and copper wires. It finds that the slim ferrite rods can modify the magnetic field distribution through their anisotropy, so that the ferrite＇s negative influence on the copper wires＇ plasma will be reduced. Left-handed properties are observed even in the specimen with close stuck ferrite rods and copper wires.

A power divider based on a new kind of composite right/left-handed transmission line (CRLH TL) unit

A new power divider, composed of a novel composite right/left-handed (CRLH) transmission line (TL) unit, is proposed. The properties of the power divider based on four CRLH TL unit cells are investigated theoretically. By adjusting the parameters of the capacitors and the inductors, the power divider shows perfectly symmetric power division at 5.13 GHz, return loss up to ?24 dB, with the transmitted power being close to ?3.1 dB. The phenomena are demonstrated by simulation results. Being compact in size and low-cost, the proposed power divider is very suitable for microwave and millimeter wave integrated circuits.

Novel resonator based on composite right/left-handed transmission lines

A new approach was introduced to analyze composite right/left-handed transmission lines （CRLH TLs）. The Bloch impedance and the dispersion relations are directly obtained from the S parameters of the unit cells. The LH and RH frequency bands are then identified by the real parts of the Bloch impedance and the phase delay of the unit cells. The new approach has some advantages over the LC parameters extraction method introduced by Caloz et a1.（2004）. Based on the new approach, a novel resonator is designed using CRLH TLs. The simulation and experimental results accorded well with the theoretical analysis. The novel resonator may have potential applications in filters with high harmonic suppression and compact structures,

A planar left-handed metamaterial based on electric resonators

A planar left-handed metamaterial（LHM） composed of electric resonator pairs is presented in this paper. Theoretical analysis, an equivalent circuit model and simulated results of a wedge sample show that this material exhibits a negative refraction pass-band around 9.6GHz under normal-incidence and is insensitive to a change in incidence angle. Furthermore, as the angle between the arm of the electric resonators and the strip connecting the arms increases, the frequency range of the pass-band shifts downwards. Consequently, this LHM guarantees a relatively stable torlerence of errors when it is practically fabricated. Moreover, it is a candidate for designing multi-band LHM through combining the resonator pairs with different angles.

Dual-band left-handed metamaterials fabricated by using tree-shaped fractal

A method of fabricating dual-band left-handed metematerials （LHMs） is investigated numerically and experimen- tally by single-sided tree-like fractals. The resulting structure features multiband magnetic resonances and two electric resonances. By appropriately adjusting the dimensions, two left-handed （LH） bands with simultaneous negative per- mittivity and permeability are engineered and are validated by full-wave eigenmode analysis and measurement as well in the microwave frequency range. To study the multi-resonant mechanism in depth, the LHM is analysed from three different perspectives of field distribution analysis, circuit model analysis, and geometrical parameters evaluation. The derived formulae are consistent with all simulated results and resulting electromagnetic phenomena, indicating the ef- fectiveness of the established theory. The method provides an alternative to the design of multi-band LHM and has the advantage of not requiring two individual resonant particles and electrically continuous wires, which in turn facilitates planar design and considerably simplifies the fabrication.

（3＋1）-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material

In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evolving-wave approximation, a generalized （3＋1）-dimensional wave equation first order in the propagation coordinate and suitable for both right-handed material （I^HM） and left-handed material （LHM） is derived. By the commonly used Drude dispersive model for LHM, a （3＋1）-dimensional nonlinear Schrodinger equation describing ultrashort pulsed beam propagation in LHM is obtained, and its difference from that for conventional RHM is discussed. Particularly, the self-steeping effect of ultrashort pulse is found to be anomalous in LHM.

Left-handed properties of a composite structure with metallic wires in a homogeneous Lorentz medium

The electromagnetic properties of a composite structure with metallic wires in a Lorentz medium were studied. The results show that the electromagnetic properties of the medium host influence the plasma resonance of metallic wires and the left-handed character of the composite. The plasma frequency of metallic wires reduces with the rise of permittivity or permeability of the medium host. Also, the negative permeability of the medium can destroy the wires’ plasma resonance and prevent the realization of left-handed properties. The high loss of medium permittivity or permeability also inhibits the metallic plasma resonance. The negative influence of the media host on the left-handed properties of the composite structure can be effectively reduced by proper structure design, such as introducing a nonmagnetic medium in the host or using an anisotropic medium.

Super energy flows in a waveguide filled with air and left-handed materials

The phenomena of super energy flows are studied theoretically and numerically in a parallel-plate waveguide which is filled with two layered equally-thick different media, i.e. air and specific left-handed materials （LHM） with εr1 = -1/（1 ＋δ） ＋iγ and μr1 = -（1 ＋ δ） ＋ iγ. In this special waveguide, two-directional super-energy flows are excited by a three-dimensional horizontal electric dipole at the same time, which has transmission patterns different from those of two-dimensional source and three-dimensional vertical electric dipole. We also show that the retardation and loss in LHM are sensitive to the amplitude of super power densities, and the dimensions of waveguide determine the propagating modes, which makes super energy flows more practical.

Characteristics of surface waves in anisotropic left-handed materials

We report the coexistence of TE and TM surface modes in certain same frequency domain at the interface between one isotropic regular medium and another biaxially anistotropic left-handed medium. The conditions for the existence of TE and TM polarized surface waves in biaxially anisotropic left-handed materials are identified, respectively. The Poynting vector and the energy density associated with surface modes are calculated. Depending on the system parameters, either TE or TM surface modes can have the time averaged Poynting vector directed to or opposite to the mode phase velocity. It is seen that the characteristics of surface waves in biaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.

From electromagnetic bandgap to left-handed metamaterials:modelling and applications

In this paper, numerical modelling of left-handed materials （LHMs） is presented using in-house and commercial software packages. Approaches used include the finite-difference time-domain （FDTD） method, finite element method （FEM） and method of moments （MoMs）. Numerical simulation includes verification of negative refraction and ＂perfect lenses＂ construction, investigation of evanescent wave behaviour in layered LHMs, reversed Shell＇s Law in electromagnetic band gap （EBG）-like structures and construction of LHMs using modified split ring resonators （SRRs）. Numerical results were verified to be in good agreement with theory, At the end of this paper, potential applications of LHMs in microwave engineering are discussed.

Data Comparison between Elite and Amateur Soccer Players by 20 Hz GPS Data Collection

The athletic component in football is nowadays one of the most important factor to determinate the performance. This consideration is part of our study, which aims to evaluate and quantify the difference between the workload of an amateur footballer and an elite one. All this is allowed by match analysis made by GPS evaluation method for amateur and video tracking for elite. The examined teams were playing in 7th Italian league, and we used 10 GPS to track 6 games, 5 for each team. For every team and every game were analysed a forward, a central midfielder, a wide midfielder, a central defender and a full back （Age 25.3 ＋ 4.2, Weight 74.5 Kg a： 5.3, Height 1.76 cm ＋ 5.2）. In our study, we used a 20 Hz GPS （thanks to Advanced Research Group in Sport, School of Health and Sport Science with K-Sport Universal, Italy） to detect performance data, and then we compared the outcome with matches performance data from elite players gather from scientific literature. Data analysis shows that elite players reach higher values in almost all parameters taken into account. In particular, they obtained higher value in meters per minutes, High Speed Distance （〉 16 Km/h）, High Metabolic Power Distance （〉 20 W/Kg） and in high and very high and acceleration （2 m/s, 3 m/s, 〉 3 m/s） and deceleration （-2 m/s, -3 m/s, 〉 -3 m/s）. This study can be useful to select and catalogue player performance model, in order to better understand the real value of a player, and to help coaches and teams to identify talent, at least in physical values.

Correlation analysis of national elite Chinese male table tennis players’ shoulder proprioception and muscle strength

BACKGROUND Shoulder is the most injured part in table tennis players,and it takes multiple roles in transmitting power and striking the center of the ball during the stroke.Proprioception is strongly correlated with high level of athletic performance.It is customary to assume that there is a correlation between proprioception and muscle strength and therefore proprioceptive assessment and rehabilitation is often neglected.AIM To investigate the correlation between isokinetic muscle strength and proprioception in the internal and external rotation muscle groups of elite Chinese male table tennis players,to provide reference for physical training and rehabilitation of elite table tennis players.METHODS A total of 19 national elite table tennis players from the Chinese National Table Tennis Team were recruited in this research.All of them had more than 10 years training experience and had participated major competitions such as the National Games and World Youth Championships.IsoMed 2000 was used to test the peak torque of internal and external rotation isokinetic concentric contraction of the athletes'bilateral shoulder joints at low speed(60°/s)and high speed(180°/s)respectively;IsoMed 2000 was used to conduct the Joint Position Reproduction test to evaluate the athletes'proprioceptive ability capacity at low speed(60°/s)and high speed(180°/s)respectively.If the data satisfied the normal distribution,the correlation between the differences in peak torque s and angles in different directions was analyzed using a Pearson simple linear model;otherwise,Spearman correlation analysis was used.The comparison of proprioceptive ability between the table tennis racket-holding hand and non-racket-holding hands was performed using independent samples t-test if the data satisfied a normal distribution;otherwise,the Mann-Whitney U test was used.RESULTS There was no direct linear correlation between the strength and proprioceptive correlation analysis at slow speed(60°/s)and fast speed(180°/s)in the racket-holding hand;At the slow speed(60°/s)and fast speed(180°/s),there was no correlation between muscle strength and proprioception in the non-racket-holding hand except for the internal rotation variable error(VE)and external rotation relative peak torque,which showed a moderate positive correlation(r=0.477,P<0.05),(r=0.554,P<0.05).The internal rotation’s constant error(CE)and VE were 1.06±3.99 and 2.94±2.16,respectively,for the racket-holding hand,and-3.36±2.39 and 1.22±0.93,respectively,for the non-racket-holding hand;the internal rotation’s CE,VE of the racket-holding hand was lower than that of the non-racket-holding hand,and there was a highly significant difference(P<0.01).CONCLUSION There was no correlation between muscle strength and proprioceptive function in the internal and external rotation of the racket-holding hand’s shoulder in elite Chinese male table tennis players.These results may be useful for interventions for shoulder injuries and for the inclusion of proprioceptive training in rehabilitation programs.

Glycogen and amyloid-beta: key players in the shift from neuronal hyperactivity to hypoactivity observed in Alzheimer's disease?

Introduction：Alzheimer’s disease（AD）begins to develop decades prior to its clinical manifestation（Sperling et al.,2011）,and while it is the most common form of dementia,as of yet there is no cure.Two of the most researched pathological features contributing to disease development are the extracellular amyloid plaques composed of amyloid-beta proteins（Aβ）and neurofibrillary tangles of tau proteins.Another feature of AD is the progression of early neuronal excitability/hyperactivity to silencing/hypoactivity（Palop and Mucke,2010）,

A tunable dual-broad-band branch-line coupler utilizing composite right/left-handed transmission lines

A tunable dual-broad-band branch-line coupler (BLC) utilizing composite right/left-handed (CRLH) transmission lines is presented. Two λ/4 segments consisting of CRLH transmission lines are added to each port to broaden the dual bands of the branch-line coupler. Numerical simulation and optimal design of the novel coupler are presented. The dual bands of the novel coupler are tunable and broad. The 1-dB bandwidth of each pass band is more than 16% of the central frequency.

The Distribution of Benefits for Players in Agricultural Industrial Chain

Players of the agricultural industrial chain pursue their own profit maximization,which can lead to conflicts of interest and affect the stability of the industrial chain. Therefore,fair and reasonable profit allocation mechanism is the key to guaranteeing the development and strengthening the strategic alliance relationship between participate members. Shapley model is an effective method to solve the profit distribution in cooperative relations. But it does not consider the three factors: risks faced by players during the operation of the agricultural industrial chain,technology innovation ability,and the degree of participating in the cooperation. So,correction factors are introduced to modify the Shapley value model,in order to make the distribution of benefits more equitable and reasonable,and effectively guide practice.

The Prevalence and Characteristics of Thoracic Outlet Syndrome in High School Baseball Players

Thoracic outlet syndrome (TOS) is one of the common neurovascular disorders of the upper extremities, and the compression or traction of the brachial plexus is the main pathology. We hypothesized that baseball players are more likely to be affected by TOS compared with other overhead-throwing athletes because of strenuous use of their throwing arm. The purpose of this study was to investigate the prevalence and clinical characteristics of TOS in high school baseball players. One thousand two hundred eighty-eight high school baseball players were included in this study. The prevalence of symptomatic TOS and its association to disorders of the upper extremities were investigated. The prevalence of symptomatic TOS was 32.8%. Age- and position-adjusted logistic regression analysis revealed that subjects with symptomatic TOS were at significantly higher risk of shoulder and/or elbow pain (odds ratio [OR]: 1.96, 95% confidence interval [CI]: 1.50 - 2.58) and a higher recurrence rate of shoulder and/or elbow pain during the previous season (OR: 2.38, 95% CI: 1.87 - 3.04). As for physical findings, subjects with symptomatic TOS were also at significantly higher risk of MUCL tenderness (OR: 2.53, 95% CI: 1.83 - 3.50), positive milking maneuver, (OR: 2.63, 95% CI: 1.78 - 3.91), positive subacromial impingement sign (OR: 1.92, 95% CI: 1.20 - 3.07), and positive posterior impingement sign (OR: 2.34, 95% CI: 1.67 - 3.28) compared to the subjects without symptomatic TOS. It is necessary to recognize that TOS is not a rare pathology in overhead-throwing athletes, especially baseball players, and that players with symptomatic TOS are at significantly higher risk of shoulder/elbow pain.