A mixed stochastic user equilibrium model considering influence of advanced traveller information systems in degradable transport network

Advanced traveler information systems （ATIS） can not only improve drivers＇ accessibility to the more accurate route travel time information, but also can improve drivers＇ adaptability to the stochastic network capacity degradations. In this paper, a mixed stochastic user equilibrium model was proposed to describe the interactive route choice behaviors between ATIS equipped and unequipped drivers on a degradable transport network. In the proposed model the information accessibility of equipped drivers was reflected by lower degree of uncertainty in their stochastic equilibrium flow distributions, and their behavioral adaptability was captured by multiple equilibrium behaviors over the stochastic network state set. The mixed equilibrium model was formulated as a fixed point problem defined in the mixed route flows, and its solution was achieved by executing an iterative algorithm. Numerical experiments were provided to verify the properties of the mixed network equilibrium model and the efficiency of the iterative algorithm.

Crossing Limit Cycles of Planar Piecewise Hamiltonian Systems with Linear Centers Separated by Two Parallel Straight Lines

In this paper, we have studied several classes of planar piecewise Hamiltonian systems with three zones separated by two parallel straight lines. Firstly, we give the maximal number of limit cycles in these classes of systems with a center in two zones and without equilibrium points in the other zone (or with a center in one zone and without equilibrium points in the other zones). In addition, we also give examples to illustrate that it can reach the maximal number.

Study on Phase Equilibrium Properties for CO_(2)^+ Cosolvent Binary Systems

In this study, the constant volume, visual method is used to measure the critical point of CO2+toluene, CO2+cyclohexane, CO2+n-butyraldehyde, CO2+i-butyraldehyde, CO2+methanol and CO2+alcohol binary systems. The relationship between critical point and the concentration of the entrainer for different substances has been discussed, and the comparison of the phase behavior of single component system and that of binary systems have been carried out.

A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems

Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, have been adopted to define thermodynamic entropy by means of the impossibility of Perpetual Motion Machine of the Second Kind (PMM2) which is a consequence of the Second Law. Equality of temperature, chemical potential and pressure in many-particle systems are proved to be necessary conditions for the stable equilibrium. The proofs assume the stable equilibrium and derive, by means of the Highest-Entropy Principle, equality of temperature, chemical potential and pressure as a consequence. A first novelty of the present research is to demonstrate that equality is also a sufficient condition, in addition to necessity, for stable equilibrium implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality of temperature potential and pressure addressed to as generalized potential. The second novelty is that the proof of sufficiency of equality, or necessity of stable equilibrium, is achieved by means of a generalization of entropy property, derived from a generalized definition of exergy, both being state and additive properties accounting for heat, mass and work interactions of the system underpinning the definition of Highest-Generalized-Entropy Principle adopted in the proof.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

Fractional-order systems without equilibria:The first example of hyperchaos and its application to synchronization

A challenging topic in nonlinear dynamics concerns the study of fractional-order systems without equilibrium points.In particular, no paper has been published to date regarding the presence of hyperchaos in these systems. This paper aims to bridge the gap by introducing a new example of fractional-order hyperchaotic system without equilibrium points. The conducted analysis shows that hyperchaos exists in the proposed system when its order is as low as 3.84. Moreover, an interesting application of hyperchaotic synchronization to the considered fractional-order system is provided.

A New Algorithm for Resource Constraint Project Scheduling Problem Based on Multi-Agent Systems

The resource constrained project scheduling problem (RCPSP) and a decision-making model based on multi-agent systems (MAS) and general equilibrium marketing are proposed. An algorithm leading to the resource allocation decision involved in RCPSP has also been developed. And this algorithm can be used in the multi-project scheduling field as well.Finally, an illustration is given.

Stability for manifolds of equilibrium states of generalized Birkhoff system

Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

Preliminary Analysis of Advanced Equilibrium Configuration for the Fusion-Driven Subcritical System

The Fusion-Driven Subcritical System(FDS)is a subcritical nuclear energy systemdrived by fusion neutron source.In this paper,an advanced plasma configuration for FDS systemhas been proposed,which aims at high beta,high bootstrap current and good confinement.Afixed-boundary equilibrium code has been used to obtain ideal equilibrium configuration.In order

Phase Equilibrium of Quaternary System Cd^(2+)//Cl^-,SO_4^(2-),NO_3^--H_2O at 298 K

Solid-liquid equilibrium of quaternary system Cd2＋//Cl–, SO42–, NO3–-H2O at 298 K was studied by means of an isothermal solution saturation method. Experimental results indicate that there are three univariant curves BE, AE and CE, one invariant point E and three crystallization fields in the quaternary system. The quaternary system belongs to a simple type, and there are no double salts or solid solution existing. The crystallization zones of equilibrium solid phases are CdCl2·5/2H2O（AEB field）, 3CdSO4·8H2O（AEC field） and Cd（NO3）2·4H2O（BEC field）, respectively. The composition of the invariant point is CdCl2, Cd（NO3）2, CdSO4 and H2O and the contents of which are 17.02%, 45.50%, 4.52% and 32.96%, respectively. The physico-chemical properties of solution in the quaternary system show regular changes along with the increased cadmium concentration. The results indicate that Cd（NO3）2 possessed the highest solubility among those three salts, which means a strong transfer of Cd ion and a high pollution risk of soil environment. And the solubility of CdSO4 would be restrained as the salts existing together.

On the stability of equilibria of nonholonomic systems with nonlinear constraints

Lyapunov＇s first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The mo- tion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin＇s series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three eases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints （V. V. Kozlov （1986）） is generalized to the case of nonlin- ear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov （1994） to nonholonomic systems with nonlinear constraints.

Alloy Gene Gibbs Energy Partition Function and Equilibrium Holographic Network Phase Diagrams of AuCu-Type Sublattice System

Taking AuCu-sublattice system as an example, we present two discoveries and a method. First, the alloy gene sequences are the central characteristic atom sequences in the basic coordination cluster sequences. Second, the transmission mode of the information about structures and properties of the alloy genes is described by the alloy gene Gibbs energy partition function. The most valuable method in the system sciences is “the whole obtained from a few parts”. We have established the alloy gene database and holographic alloy positioning system of the Au-Cu system, as well as alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of the AuCu-type sublattice system. It means that a standard way for researchers to share predictive algorithms and computational methods may be produced during designing advanced alloys.

Effective temperature and fluctuation-dissipation theorem in athermal granular systems:A review

The definition and the previous measurements of a dynamics-relevant temperature-like quantity in granular media are reviewed for slow and fast particle systems. Especially, the validity of the fluctuation-dissipation theorem in such an athermal system is explored. Experimental evidences for the fluctuation-dissipation theorem relevant effect temperature support the athermal statistical mechanics, which has been widely explored in recent years by physicists. Difficulties encountered in defining temperature or establishing thermodynamics or statistical mechanics in non-equilibrium situations are discussed.

A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

This paper reports a new simple four-dimensional（4 D） hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.

Equilibrium of hydroxyl complex ions in Pb^(2+)-H_2O system

The thermodynamics equilibrium principle was used to construct the diagrams for the concentration of complex ions(pc) vs pH,the distribution ratio of lead hydroxyl complex ions(αn) vs pH,and the conditional solubility product of Pb(OH)2 vs pH in the Pb2+-H2O system. The relationship between the equilibrium concentration of each kind of lead hydroxyl complex ions in equilibrium with Pb(OH)2(s) and pH value was shown in the system. The minimum solubility of lead is at the pH value of 10.096-10.997. The distribution ratio of each kind of the lead hydroxyl complex ions is determined as a function of the pH value and the total lead concentration([Pb]T). The diagram for the conditional solubility product,pKSP vs pH,shows that each kind of lead hydroxyl complex ions existing in the system is dependent upon an optimized pH value at the established concentration of [Pb]T,and that pKSP reaches the minimum at the pH value of 10.3-11.2. The results can provide a theoretical basis for removing lead ions from wastewater by the neutralization and hydrolyzation technology.

Generation of countless embedded trumpet-shaped chaotic attractors in two opposite directions from a new three-dimensional system with no equilibrium point

A new three-dimensional （3D） continuous autonomous system with one parameter and three quadratic terms is presented firstly in this paper. Countless embedded trumpet-shaped chaotic attractors in two opposite directions are generated from the system as time goes on. The basic dynamical behaviors of the strange chaotic system are investigated. Another more complex 3D system with the same capability of generating countless embedded trumpet-shaped chaotic attractors is also put forward.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

Developing architecture of a traveler information system for dynamic equilibrium in traffic networks

Having criticized the current architecture of Advanced Traveler Information Systems （ATISs）, this work discusses a new base of requirements to develop a new paradigm for traffic information systems. It mainly integrates three dimensions within a traffic system： drivers＇ pattern of behavior and preferences, urban traffic desires, and capabilities of traffic information service providers. Based on the above, functional segments from several related backgrounds are brought together to structure a new architecture, called Interactive Traveler Information System （ITIS）. The main interactive feature of this new architecture is a two-way communication track between drivers and the traffic information system provider-in fact, a decision on choosing a road at a particular time for an individual will be made based on the utility of both sides. This new configuration consists of driver-side smartphone application, centric traffic prediction, and decision-maker units, which will shape a new approach of decision-making processes. These all work together to satisfy the designated goal of ITIS, which is preserving the Wardrop equilibrium condition in the traffic network level. Finally, we concentrate on a comparison study, which shows a differentiation between performance of the proposed ITIS and the current ATIS model in a real situation. This has been done with simulations of analogical scenarios. The most noticeable advantage of the proposed architecture is not being limited to a saturation limit, and the positive effect of increasing system penetration in the performance of the newly introduced information system. In conclusion, new research subjects are suggested to be carried out.

Classification of Stably Dissipative 3D Lotka-Volterra Systems and Their Necessary and Sufficient Condition for Being Stably Dissipative

By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipative 3D Lotka-Volterra systems and five classes of maximal stably dissipative graphs were obtained for these systems. Finally, the necessary and sufficient condition of being stably dissipative for every class was studied, under which the matrix associated with the graph is stably dissipative.