Evolutionary prisoner’s dilemma game on weighted scale-free networks

This paper investigates the evolutionary prisoner’s dilemma on weighted scale-free networks. The weighted networks are generated by adopting Barabási-Albert scale-free network and assigning link weight with w_ij=(k_i×k_j)^β. Simulation results show that the cooperation frequency has a strong dependence on β. The value of β which is associated with the maximal cooperation frequency has been sought out. Moreover, Gini coefficient and Pareto exponent of the system’s wealth distribution are investigated. The inequality of wealth distribution is minimized at β≈−1.     

Density functional study of $$\hbox {AgScO}_2$$: Electronic and optical properties

Dielectric relaxation studies of binary (jk) polar mixtures of tetrahydrofuran with N-methyl acetamide, N,N-dimethyl acetamide, N-methyl formamide and N,N-dimethyl formamide dissolved in benzene(i) for different weight fractions (w _{j k} ’s) of the polar solutes and mole fractions (x _j ’s) of tetrahydrofuran at 25 ^°C are attempted by measuring the conductivity of the solution under 9.90 GHz electric field using Debye theory. The estimated relaxation time (τ _{j k} ’s) and dipole moment (μ _{j k} ’s) agree well with the reported values signifying the validity of the proposed methods. Structural and associational aspects are predicted from the plot of τ _{j k} and μ _{j k} against x _j of tetrahydrofuran to arrive at solute–solute (dimer) molecular association upto x _j =0.3 of tetrahydrofuran and thereafter solute–solvent (monomer) molecular association upto x _j =1.0 for all systems except tetrahydrofuran + N,N-dimethyl acetamide.     

Promotion of cooperation induced by nonuniform payoff allocation in spatial public goods game

A nonuniform payoff allocation mechanism is proposed for spatial public goods games where individuals are nodes on a scale-free network. Each individual is assigned a weight k_i ^α, where k_i is the degree of individual i and α is an adjustable parameter that controls the degree of diversity in individuals’ profits. During the evolution progress, the allocation of payoff on individual i is assumed to be proportional to its weight. Individuals synchronously update their strategies according to the stochastic rule with a fixed noise level. It is found that there exists an optimal value of α which yields the highest level of cooperation. Other pertinent quantities, including the payoff and the probability of finding a node playing as cooperator versus the degree, are also investigated computationally and analytically. Our results suggest that a suitable degree of diversity among individuals can promote the emergence of cooperation.     

Inverse scattering with non-overdetermined data

Let A(β,α,k) be the scattering amplitude corresponding to a real-valued potential which vanishes outside of a bounded domain D⊂R³. The unit vector α is the direction of the incident plane wave, the unit vector β is the direction of the scattered wave, k>0 is the wave number. The governing equation for the waves is [∇²+k²−q(x)]u=0 in R³. For a suitable class M of potentials it is proved that if Aq₁(−β,β,k)=Aq₂(−β,β,k),∀β∈S², ∀k∈(k₀,k₁), and q₁, q₂∈M, then q₁=q₂. This is a uniqueness theorem for the solution to the inverse scattering problem with backscattering data. It is also proved for this class of potentials that if , ∀k∈(k₀,k₁), and q₁, q₂∈M, then q₁=q₂. Here is an arbitrarily small open subset of S², and |k₀−k₁|>0 is arbitrarily small.     

A multi-channel scattering theory for some time dependent Hamiltonians,charge transfer problem

Scattering theory for time dependent HamiltonianH(t)=?(1/2) Δ+ΣV _j (x?q _j (t)) is discussed. The existence, asymptotic orthogonality and the asymptotic completeness of the multi-channel wave operators are obtained under the conditions that the potentials are short range: |V _j (x)|≦C _j (1+|x|)^?2?ε, roughly spoken; and the trajectoriesq _j (t) are straight lines at remote past and far future, and |q _j (t)?q _k (t)| → ∞ ast → ± ∞ (j≠k).     

A model for cascading failures in scale-free networks with a breakdown probability

Considering that not all overload nodes will be removed from networks due to some effective measures to protect them, we propose a new cascading model with a breakdown probability. Adopting the initial load of a node j to be L_j=[k_j(∑_m∈Γjk_m)]^α with k_j and Γ_j being the degree of the node j and the set of its neighboring nodes, respectively, where α is a tunable parameter, we investigate the relationship between some parameters and universal robustness characteristics against cascading failures on scale-free networks. According to a new measure originated from a phase transition from the normal state to collapse, the numerical simulations show that Barabási-Albert (BA) networks reach the strongest robustness level against cascading failures when the tunable parameter α=0.5, while not relating to the breakdown probability. We furthermore explore the effect of the average degree 〈k〉 for network robustness, thus obtaining a positive correlation between 〈k〉 and network robustness. We then analyze the effect of the breakdown probability on the network robustness and confirm by theoretical predictions this universal robustness characteristic observed in simulations. Our work may have practical implications for controlling various cascading-failure-induced disasters in the real world.     

Reconstruction of singularities for solutions of Schrödinger's equation

We determine the behavior in time of singularities of solutions to some Schrödinger equations onR ⁿ . We assume the Hamiltonians are of the formH ₀+V, where \(H_0 = 1/2\Delta + 1/2 \sum\limits_{k = 1}^n { \omega _k^2 x_k^2 } \) , and whereV is bounded and smooth with decaying derivatives. When all ω _k =0, the kernelk(t,x,y) of exp (?itH) is smooth inx for every fixed (t,y). When all ω₁ are equal but non-zero, the initial singularity “reconstructs” at times \(t = \frac{{m\pi }}{{\omega _1 }}\) and positionsx=(?1) ^m y, just as ifV=0;k is otherwise regular. In the general case, the singular support is shown to be contained in the union of the hyperplanes \(\{ x|x_{js} = ( - 1)^l js_{y_{js} } \} \) , when ω _j t/π=l _j forj=j ₁,...,j _r .     

Quantization and meaning of observables linear in momentum

A detailed study is made of the observablesξ ^j(x^k)p_i+f(x^k) linear in momentum on a Riemannian manifold: their quantization and (through quantum unitary transformations) physical meaning are discussed using geometrical methods.     

强激光场中原子团簇的电离和光辐射

通过数值求解一维含时薛定谔方程,研究了原子与原子围簇的电离、电子的时间演化和光辐射现象。结果表明,原子团簇比原子更易于电离,原子团簇中电子的时间演化和原子中电子的时间演化不同,光辐射频率也要高很多。     

On a soluble model of an antiferromagnetic chain with Dzyaloshinsky interactions. I

The one-dimensional anisotropic XY model with antisymmetric nearest-neighbour interactions (Dzyaloshinsky interactions) in the presence of a magnetic field B in the z direction is investigated. Special attention is given to the critical behaviour of the system. In the ground state, the susceptibility χ^zz has a logarithmic singularity as B → 1 provided that the strength Δ of the Dzyaloshinsky interaction obeys the inequality |Δ| ≤ |γ|, where γ is the anisotropy parameter. However, if |Δ| #62; |γ|, χ^zz diverges with a power -$\text{1}\text{2}$ singularity as B ↑ (1 + Δ² - γ²)^{$\text{1}\text{2}$}. The specific heat is studied for low temperatures. Furthermore for a few special values of γ and B the static correlation functions 〈S^α_jS^β_k〉 are evaluated in the low-temperature limit, for α, β = x, y, z and |j - k| = 1, 2. Finally we consider the chain with Dzyaloshinsky interactions only.     

Anionic conductivity and thermal stability of single crystals of solid solutions based on calcium fluoride

The temperature and composition dependencies of the anionic conductivity in the temperature range from ambient to 1073 K were studied for single crystals of Ca_1−xGd_xF_2+x (x=1×10⁻⁴, 1×10⁻³, 1×10⁻² and 1×10⁻¹) and of Ca_0.8R_0.2F_2.2 (R=La, Ce, Pr, Nd, Gd, Dy, Er, Tm, Yb, Lu and Y), having the fluorite structure. The conductivity plots for the concentrated Ca_0.8R_0.2F_2.2 solid solutions display the low-temperature and high-temperature linear (Arrhenius) regions with the knee temperature T_k∼770 K. The values of the conductivity activation enthalpy obey the relation ΔH_HT(T>T_k)>ΔH_LT(T<T_k). The conductivity mechanism in heavily doped Ca_1−xR_xF_2+x crystals is associated with the clusters of the point defects which decrease the potential barriers for fluoride anions moving by hops over the structural sites of the anion sub-lattice. We studied the effect of the dimensional factor (doped cation radii) on the anionic transport in these crystals. A correlation between anionic transport and atomic structure of the studied crystals is discussed.     

Mössbauer study of Nd2Fe14B and Nd2(Fe1−xCox)14B compounds

The Mössbauer spectra of Nd₂Fe₁₄B and Nd₂(Fe_1?xCo_x)₁₄B compounds (x=0.0.05, 0.10 and 0.16) have been investigated at room temperature and at 77 K. Taking advantage of combined ME and NMR investigations of the Nd₂Fe₁₄B compund, the hyperfine field values and their assignment to the six Fe sites have been determined to be the following sequence: 378(j₂), 346(k₂), 334(j₁), 325(k₁), 322(c), 306(e) kOe. The substitution of Co for Fe decreases the hyperfine fields at all Fe sites. The intensity variations of the subspectra with Co content show that Co atoms have a strong preference to occupy the k₂ site, but have a rather less tendency to enter the j₂ site, which is preferred by Fe atoms.     

On the topological charge concentrated at a point

For SU(2) gauge fields over the 4-dimensional sphere with a finite number of points x₁, x₂, ..., and x_N removed, there are gauge transformations which modify the topological charge concentrated at x_j by adding n_j, where n₁, n₂, …, and n_N. are integers such that Σ^N_{j = 1}n_j = 0. However, the reduction modulo Z of the topological charge at a point is well defined, being given in terms of the secondary characteristic classes of Chern and Simons, except when the topological charge is indeterminate.     

Dielectric relaxation of ethanol and N-methyl acetamide polar mixture in C 6 H 6 at 9.90 GHz

Debye relaxation times (τ _{j k} ) and dipole moments (μ _{j k} ) of binary (j k) polar mixtures of ethanol (EtOH) and N-methyl acetamide (NMA) dissolved in benzene(i) are studied by studying conductivity of solution at 9.90 GHz for different temperatures, different mole fractions (x _j ) of ethanol and different weight fractions (w _{j k} ) of the mixtures, respectively. The variation of τ _{j k} ?x _j from linear slope of imaginary \((\sigma _{ijk}^{\prime \prime } )\) against real \((\sigma _{ijk}^{\prime })\) part of total conductivity \((\sigma _{ijk}^{\ast })\) curve reveals solute–solute (dimer) or solute–solvent (monomer) molecular associations up to x _j = 0.0?0.3 and thereafter, solute–solvent molecular associations. τ _{j k} s from the ratio of slopes of \(\sigma _{ijk}^{\prime \prime }-w_{jk} \) and \(\sigma _{ijk}^{\prime }-w_{jk} \) curves exhibit solute–solvent molecular association for all x _j s which are consistent with the μ _{j k} ?x _j curves at all temperatures except at 35^°C. This signifies the validity of both the proposed methods in estimating τ and μ. The molecular dynamics of the polar mixture are ascertained from Eyring rate theory. Theoretical dipole moments from bond angles and bond moments (μ _theo) are also calculated to predict associational aspects.     

Degree Complexity of Birational Maps Related to Matrix Inversion

For a q × q matrix x = (x _{i, j} ) we let ${J(x)=(x_{i,j}^{-1})}For a q × q matrix x = (x _{i, j} ) we let J(x)=(x_i,j^-1){J(x)=(x_{i,j}^{-1})} be the Hadamard inverse, which takes the reciprocal of the elements of x. We let I(x)=(x_i,j)^-1{I(x)=(x_{i,j})^{-1}} denote the matrix inverse, and we define K=I°J{K=I\circ J} to be the birational map obtained from the composition of these two involutions. We consider the iterates Kⁿ=K°?°K{K^n=K\circ\cdots\circ K} and determine the degree complexity of K, which is the exponential rate of degree growth d(K)=lim_n?￥( deg(Kⁿ) )^1/n{\delta(K)=\lim_{n\to\infty}\left( deg(K^n) \right)^{1/n}} of the degrees of the iterates. Earlier studies of this map were restricted to cyclic matrices, in which case K may be represented by a simpler map. Here we show that for general matrices the value of δ(K) is equal to the value conjectured by Anglès d’Auriac, Maillard and Viallet.     

Magnetic structure of TmCu2Ge2

TmCu₂Ge₂ compound crystallizes in the tetragonal ThCr₂Si₂-type crystal structure. The neutron diffraction reveals the presence of an incommensurate antiferromagnetic order below T_N=2.5 K. The Tm magnetic moment of 5.0(1) μ_B at 0.47 K is parallel to the c-axis. The order is described by the propagation vector k=[k_x, k_x, 0], where k_x=0.117(3). The increase of the values of the components k_x near the Néel temperature is observed.     

Critical parameters near the ferromagnetic-paramagnetic phase transition in La0.7A0.3(Mn1−xbx)O3 (A=Sr; B=Ti and Al; x=0.0 and 0.05) compounds

The critical parameters provide important information concerning the interaction mechanisms near the paramagnetic-to-ferromagnetic transition. In this paper, we present a thorough study for the critical behavior of La_0.7A_0.3(Mn_1−xB_x)O₃ (A=Sr; B=Ti and Al; x=0.0 and 0.05) polycrystalline samples near ferromagnetic-paramagnetic phase transition temperature by analyzing isothermal magnetization data. We have analyzed our dc-magnetization data near the transition temperature with the help of the modified Arrot plot, Kouvel-Fisher method. We have determined the critical temperature T_C and the critical parameters β, γ and δ. With the values of T_C, β and γ, we plot M×(1−T/T_C)^−β vs. H×(1−T/T_C)^−γ. All the data collapse on one of the two curves. This suggests that the data below and above T_C obey scaling, following a single equation of state. Critical parameters for x=0 and x_Ti=0.05 samples are between those predicted for a 3D-Heisenberg model and mean-field theory and for x_Al=0.05 samples the values obtained for the critical parameters are close to those predicted by the mean-field theory.     

Edge-based-attack induced cascading failures on scale-free networks

Most previous existing works on cascading failures only focused on attacks on nodes rather than on edges. In this paper, we discuss the response of scale-free networks subject to two different attacks on edges during cascading propagation, i.e., edge removal by either the descending or ascending order of the loads. Adopting a cascading model with a breakdown probability p of an overload edge and the initial load (k_ik_j)^α of an edge ij, where k_i and k_j are the degrees of the nodes connected by the edge ij and α is a tunable parameter, we investigate the effects of two attacks for the robustness of Barabási-Albert (BA) scale-free networks against cascading failures. In the case of α<1, our investigation by the numerical simulations leads to a counterintuitive finding that BA scale-free networks are more sensitive to attacks on the edges with the lowest loads than the ones with the highest loads, not relating to the breakdown probability. In addition, the same effect of two attacks in the case of α=1 may be useful in furthering studies on the control and defense of cascading failures in many real-life networks. We then confirm by the theoretical analysis these results observed in simulations.     

Ion conduction in proton- and related defect (super) ionic conductors: Mechanical,electronic and structure parameters

We find the relationships among optical dielectric constant ε_∞, activation energy E_ac, averaged atomic mass per a formula unit, ∑_jm_j / N, volume V and transition temperature T_c for various type ion conductors with forms of E_ac = α / (ε_∞ ? β), E_ac = A₀ + δ / [(∑_jm_j / N) ? d], E_ac = A_v / V^2/3, and ln(T_c) = g ? hln(∑_jm_j), where α, β, δ, A₀, d, A_v, g and h are constants depending on the kinds of conduction elements. We derive those proportional forms from a simple equation of motion under the assumption of ion hopping assisted by enhanced vibration displacement of host lattice. The enhancement is induced from the large fourth-order term of the host lattice potential originating from the electronic shielding effect of Coulomb force, heavy atomic mass of constituent ion, and volume expansion under the long-range periodicity of crystal structure. This mechanism is ascertained from characteristic phenomena of various kinds of conduction elements. For impurity-type H⁺-ion or defect conductor, the proportional form is shifted from that of superionic conductor because of weakened effect of host lattice vibration mode on H⁺-ion or O-ion defect. Photo-induced spectra of mobile ion in AgCl are understood, and a small quantum effect of H⁺ -ion is suggested.