The aim of this paper is to obtain Karush-Kuhn-Tucker optimality conditions for weakly efficient solutions to vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient solutions to the constrained vector optimization problem are presented. As well as some examples. The results presented in this paper generalize results obtained by Gong (2008) and Wei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces and real Banach spaces to Hadamard manifolds, respectively.

In this study, we investigate the form of solutions, stability character and asymptotic behavior of the following four rational difference equations x_{n+1} = (1/(x_{n}(x_{n-1}±1)±1)), x_{n+1} = ((-1)/(x_{n}(x_{n-1}±1)∓1)), such that their solutions are associated with Tribonacci numbers.

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations x_{n+1} = ((±1)/(x_{n}(x_{n-1}±1)-1)) x_{n+1} = ((±1)/(x_{n}(x_{n-1}∓1)+1)).

The Boltzmann-Gibbs (BG) entropy has been used in a wide variety of problems for more than a century. It is well known that BG entropy is extensive, but for certain systems such as those dictated by long-range interactions, the entropy must be non-extensive. Tsallis entropy possesses non-extensive characteristics, which is parametrized by a variable q (q = 1 being the classic BG limit), but unless q is determined from microscopic dynamics, the model remains but a phenomenological tool. To this date very few examples have emerged in which q can be computed from first principles. This paper shows that the space plasma environment, which is governed by long-range collective electromagnetic interaction, represents a perfect example for which the q parameter can be computed from micro-physics. By taking the electron velocity distribution function measured in the heliospheric environment into account, and considering them to be in quasi equilibrium state with electrostatic turbulence known as the quasi-thermal noise, it is shown that the value corresponding to q = 9/13 = 0.6923 may be deduced. This prediction is verified against observation made by spacecraft, and it is shown to be in excellent agreement.

In this study, the multi-relaxation-time lattice Boltzmann method is applied to investigate the oscillatory instability of lid-driven flows in two-dimensional semi-elliptical cavities with different vertical to horizontal aspect ratios K in the range of 1.0--3.0. The program implemented in this study is parallelized using CUDA (compute unified device architecture), a parallel computing platform, and computations are carried out on NVIDIA Tesla K40c GPU. To carry out precise calculations, the CUDA algorithm is extensively investigated, and its parallel efficiency indicates that the maximum speedup is 47.6 times faster. Furthermore, the steady--oscillatory Reynolds numbers are predicted by implementing the CUDA-based programs. The amplitude coefficient is defined to quantify the time-dependent oscillation of the velocity magnitude at the monitoring point. The simulation results indicate that the transition Reynolds numbers correlate negatively with the aspect ratio of the semi-elliptical cavity, and are smaller than those of the rectangular cavity at the same aspect ratio. In addition, the detailed vortex structures of the semi-elliptical cavity within a single period are also investigated when the Reynolds number is larger than the steady--oscillatory value to determine the effects of periodic oscillation of the velocity magnitude.

A Wireless Body Area Sensor Network (WBASN) is combination of numerous sense nodes, positioned onto/close or inside a person body. Wireless Body Area Sensor Networks (WBASN) is a developing automation trend that exploits wireless sensor nodes to put instantaneous wearable well-being of ill person to improve individual’s existence. The sensor nodes might be used outwardly to observe abundant health parameters (like heart activity, blood pressure and cholesterol) of an ill person at a vital site within hospital. Hence the goal of WBASN is much crucial, enhancing the lifetime of nodes is compulsory to sustain many issues such as utility and efficiency. It is essential to evaluate time that when the first node will die it we want to refresh or change the battery reason is that loss of crucial information is not tolerable. The lifetime is termed as the time interval when a first node dies out due to battery exhaustion. In our proposed protocol life time of a network is the main concern as well other protocol related issues such as throughput, path loss, and residual energy. Bio-sensors are used for deployment on human body. Poisson distribution and equilibrium model techniques have been used for attaining the required results. Multi-hop network topology and random network node deployment used to achieve minimum energy consumption and longer network lifetime.

Fluctuation theorems are a class of equalities each of which links a thermodynamic path functional such as heat and work to a state function such as entropy and free energy. Jinwoo and Tanaka [L. Jinwoo and H. Tanaka, Sci. Rep. 5, 7832 (2015)] have shown that each microstate of a fluctuating system can be regarded as an ensemble (or a 'macrostate') if we consider trajectories that reach each microstate. They have revealed that local forms of entropy and free energy are true thermodynamic potentials of each microstate, encoding heat, and work, respectively, within an ensemble of paths that reach each state. Here we show that information that is characterized by the local form of mutual information between two subsystems in a heat bath is also a true thermodynamic potential of each coupled state and encodes the entropy production of the subsystems and heat bath during a coupling process. To this end, we extend the fluctuation theorem of information exchange [T. Sagawa and M. Ueda, Phys. Rev. Lett. 109, 180602 (2012)] by showing that the fluctuation theorem holds even within an ensemble of paths that reach a coupled state during dynamic co-evolution of two subsystems.

The Rybczynski theorem describes the trade effect within production analyses between factor endowments and outputs. The Stolper-Samuelson theorem focuses on cost analyses between factor reward and commodity price. This paper examines the trade effect of changes of factor endowments on prices, based on general equilibrium. The study shows that changes of factor endowments cause domestic output changes (the Rybczynski effect), which affect output prices and factor prices (the Stolper-Samuelson effect). It is like a chain of effects that the Rybczynski’s trade effect triggers the Stolper-Samuelson’s trade effect. The analysis of this paper shows that a small increase of a factor endowment of any country rewards another factor and the commodity using the latter factor intensively. It displays a tuneful circle. Trade brings a well-balanced development to the world.

An SIRS (Susceptible–Infected–Removed-Susceptible) mathematical model for the transmission dynamics of the Transfusion–Transmitted Malaria (TTM) model with optimal control pair u₁(t) and u₂(t) was developed and studied in this research work. The model Transfusion–Transmitted Malaria disease–free equilibrium and endemic equilibriums points were determined. The model exhibited two equilibriums; disease-free and endemic equilibrium. It is shown that the disease–free equilibrium was locally asymptotically stable if the associated basic reproduction numbers R₀ is less than unity while the disease persists if R₀ is greater than unity. The global stability of the Transfusion–Transmitted Malaria model at the disease-free equilibrium was established using the comparison method. The optimality system was derived and an optimal control model of blood screening and drug treatment for the Transfusion–Transmitted Malaria model was investigated. Conditions for the optimal control were considered using Pontryagin’s Maximum Principle and solved numerically using the Forward and Backward Finite Difference Method (FBDM). Numerical results obtained are in perfect agreement with our analytical results.

I propose a dynamic evolution hypothesis regarding the evolution of organisms by incorporating both diminished fitness returns and mutation rate tuning during adaptation to a constant environment. Basically, accumulating evidence from life history studies conducted over the past 70 years suggests that the evolution of individual fitness is subject to ecological constraints, leading to the evolutionary existence of an upper limit of individual fitness (ULIF). Given the existence of the ULIF, organismal evolution, which might initially have relatively great fitness returns through primarily Darwinian evolution, will eventually be subject to diminished fitness returns towards zero. With the diminished fitness return, Darwinian selection strength may eventually become smaller than the power of random genetic drift, leading to the occurrence of neutral evolution at both phenotypic and molecular levels. Meanwhile, mutation rates may change from an initial increase, due to the relatively strong fitness return, to subsequent decreases, due to both the diminished fitness return of beneficial mutations and the cost of deleterious mutations. The diminished fitness returns with subsequently reduced mutation rates are two potential evolution barriers leading to eventual evolutionary stasis. These findings provide important insights for understanding the conditions for the occurrences of different evolutionary patterns. Darwinian evolution theory, neutral evolution theory and punctuated equilibrium theory can be unified in the context of the dynamic evolution hypothesis formulated in this study.

Thunderstorm electrification has been studied for hundreds of years. Several mechanisms have been proposed to elucidate the electrification, including convective charging, inductive precipitation charging, and ice crystal-graupel collision charging. Field observations and model studies have demonstrated the vital roles that graupel and ice crystals play in the electrification, but the mechanism of the collision charging is still unclear. The fundamental essence of relative growth rate theory used for explaining the tripole charge structure in thunderclouds also needs a further exploration. We analyze the processes of ice crystal-graupel collision charging from charge migration inside hydrometeors to charge separation between two hydrometeors. The driving effects of temperature gradient and chemical potential gradient in charge migration are clarified, as well as the applicability of the relative growth rate theory, thermoelectric effect and surface tension gradient in different humidities. Based on the understanding from these electrification mechanisms, we propose that the essence of charge separation is driven by non-thermal equilibrium, and future studies on thunderstorm electrification should focus on the dynamical non-thermal equilibrium of cloud particles.

In scenarios such as natural disasters and military strike, it is common for unmanned aerial vehicles (UAVs) to form groups to execute reconnaissance and surveillance. To ensure the effectiveness of UAV communications, repeated resource acquisition issues and transmission mechanism design need to be addressed urgently. In this paper, we build an information interaction scenario in a Flying Ad-hoc network (FANET). The data transmission problem with the goal of throughput maximization is modeled as a coalition game framework. Then, a novel mechanism of coalition selection and data transmission based on group-buying is investigated. Since large-scale UAVs will generate high transmission overhead due to the overlapping resource requirements, we propose a resource allocation optimization method based on distributed data content. Comparing existing works, a data transmission and coalition formation mechanism is designed. Then the system model is classified into graph game and coalition formation game. Through the design of the utility function, we prove that both games have stable solutions. We also prove the convergence of the proposed approach with coalition order and Pareto order. Binary log-linear learning based coalition selection algorithm (BLL-CSA) is proposed to explore the stable coalition partition of system model. Simulation results show that the proposed data transmission and coalition formation mechanism can achieve higher data throughput than the other contrast algorithms.

UAV cooperative control has been an important issue in UAV-assisted sensor network, thanks to the considerable benefit obtained from cooperative mechanism of UAVs being applied as a flying base station. In coverage scenario, the tradeoff between coverage performance and transmission performance often makes deployment of UAVs fall into a dilemma, since both indexes are related to the distance between UAVs. To address this issue, UAV coverage and data transmission mechanism is analyzed in this paper, then an efficient multi-UAV cooperative deployment model is proposed. The problem is also modeled as a coalition formation game (CFG). The CFG with Pareto order is proved to have a stable partition. Then, an effective approach consisting of coverage deployment and coalition selection is designed, wherein UAVs can decide strategies cooperatively to achieve better coverage performance. Combining analysis of game approach, a coalition selection and position deployment algorithm based on Pareto order (CSPDA-PO) is designed to execute coverage deployment and coalition selection. Finally, simulation results are shown to validate the proposed approach based on efficient multi-UAV cooperative deployment model.

Normally, the Nernst voltage calculated from the concentration of the reaction gas in the flow channel is considered to be the ideal voltage (reversible voltage) of the oxyhydrogen fuel cell, but actually it will cause a concentration gradient when the reaction gas flows from the flow channel through the gas diffusion layer to the catalyst layer. The Nernst voltage loss in fuel cells in most of the current literature is thought to be due to the difference in concentration of reaction gas in the flow channel and concentration of reaction gas on the catalyst layer at the time when the high net current density is generated. Based on the Butler-Volmer equation in oxyhydrogen fuel cell, this paper demonstrates that the Nernst voltage loss is caused by the concentration difference of reaction gas in flow channel and on the catalytic layer at the time when equilibrium potential (Galvanic potential) of each electrode is generated.

Recently, the properties of bouncing oil droplets, also known as `walkers', have attracted much attention because they are thought to offer a gateway to a better understanding of quantum behaviour. They indeed constitute a macroscopic realization of wave-particle duality, in the sense that their trajectories are guided by a self-generated surrounding wave. The aim of this paper is to try to describe walker phenomenology in terms of de Broglie-Bohm dynamics and of a stochastic version thereof. In particular, we first study how a stochastic modification of the de Broglie pilot-wave theory, à la Nelson, affects the process of relaxation to quantum equilibrium, and we prove an H-theorem for the relaxation to quantum equilibrium under Nelson-type dynamics. We then compare the onset of equilibrium in the stochastic and the de Broglie-Bohm approaches and we propose some simple experiments by which one can test the applicability of our theory to the context of bouncing oil droplets. Finally, we compare our theory to actual observations of walker behavior in a 2D harmonic potential well.

Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several statements --such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness-- are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment.

We employ the solution concept of ex post Nash equilibrium to predict the interaction of a finite number of agents competing in a finite number of basic games simultaneously. The competition is called a multi-game. For each agent, a specific weight, considered as private information, is allocated to each basic game representing its investment in that game and the utility of each agent for any strategy profile is the weighted sum, i.e., convex combination, of its utilities in the basic games. Multi-games can model decision making in multi-environments in a variety of circumstances, including decision making in multi-markets and decision making when there are both material and social utilities for agents as, we propose, in the Prisoner's Dilemma and the Trust Game. Given a set of pure Nash equilibria, one for each basic game in a multi-game, we construct a pure Bayesian Nash equilibrium for the multi-game. We then focus on the class of so-called uniform multi-games in which each agent is constrained to play in all games the same strategy from an action set consisting of a best response per game. Uniform multi-games are equivalent to multi-dimensional Bayesian games where the type of each agent is a finite dimensional vector with non-negative components. A notion of pure type-regularity for uniform multi-games is developed and it is shown that a multi-game that is pure type-regular on the boundary of its type space has a pure ex post Nash equilibrium which is computed in constant time with respect to the number of the types and is independent of prior probability distributions. We then develop an algorithm, linear in the number of types of the agents, which tests if a multi-game is pure type-regular on the boundary of its type space in which case it returns a pure ex post Nash equilibrium for the multi-game.

In this work α-synuclein amyloid fibrils, formation of which is a biomarker of the Parkinson’s disease, were investigated with the use of fluorescent probe thioflavin T (ThT). Experimental conditions of the protein fibrillogenesis were chosen so that a sufficient number of continuous measurements can be performed to characterize and analyze all stages of this process. The reproducibility of fibrillogenesis and the structure of the obtained aggregates (that is a critical point for their further investigation) were proved using a wide range of physical-chemical methods. For determination of ThT—α-synuclein amyloid fibrils binding parameters sample and reference solutions were prepared with the use of equilibrium microdialysis. By absorption spectroscopy of these solutions ThT—fibrils binding mode with the binding constant about 10⁴ M⁻¹ and stoichiometry of ThT per protein molecule about 1:8 was observed. Fluorescence spectroscopy of the same solutions with the subsequent correction of the recorded fluorescence intensity on the primary inner filter effect allowed to determine another mode of ThT binding to fibrils with the binding constant about 10⁶ M⁻¹ and stoichiometry about 1:2500. Analysis of photophysical characteristics of the dye molecules bound to the sites of different binding modes allowed to assume the possible localization of these sites. Obtained differences in the ThT binding parameters to amyloid fibrils formed from α-synuclein and other amyloidogenic proteins, as well as in the photophysical characteristics of the bound dye, confirmed the hypothesis of amyloid fibrils polymorphism.

This paper contains theoretical fundamentals of strut and tie models, used in unreinforced horizontal shear walls. Depending on support conditions and wall loading, we can distinguish models with discrete bars when point load is applied to the wall (type I model) or with continuous bars (type II model) when load is uniformly distributed at the wall boundary. The main part of this paper compares calculated results with the own tests on horizontal shear walls made of solid brick, silicate elements and autoclaved aerated concrete. The tests were performed in Poland. The model required some modifications due to specific load and static diagram.

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

This article puts forward the bi-matrix games with crisp parametric payoffs based on interval value function approach. We conclude that the equilibrium solution of the game model can converted into optimal solutions of the pair of the non-linear optimization problem. Finally, experiment results show the efficiency of the model.

In this paper we present an application of the dynamic tracking games framework to a monetary union. We use a small stylized nonlinear three-country macroeconomic model of a monetary union to analyse the interactions between fiscal (governments) and monetary (common central bank) policy makers, assuming different objective functions of these decision makers. Using the OPTGAME algorithm we calculate solutions for several games: a noncooperative solution where each government and the central bank play against each other (a feedback Nash Equilibrium solution), a fully cooperative solution with all players following a joint course of action (a Pareto optimal solution), and three solutions where various coalitions (subsets of the players) play against coalitions of the other players in a noncooperative way. It turns out that the fully cooperative solution yields the best results, the noncooperative solution fares worst, and the coalition games lie in between, with a broad coalition of the fiscally more responsible countries and the central bank against the less thrifty country coming closest to the Pareto optimum.

This work is a generalization of the Lopez-Ruiz, Mancini and Calbet (LMC); and Shiner, Davison and Landsberg (SDL) complexity measures, considering that the state of a system or process is represented by a dynamical variable during a certain time interval. As the two complexity measures are based on the calculation of informational entropy, an equivalent information source is defined and, as time passes, the individual information associated to the measured parameter is the seed to calculate instantaneous LMC and SDL measures. To show how the methodology works, an example with economic data is presented.

To date, several different approaches are available to study sediment dynamics at reach or watershed scale, based on very different hypothesis. One of such assumptions, the so-called “morphodynamic equilibrium hypothesis” is becoming little unpopular for its embedded simplifications. The aim of this work is to demonstrate how this approach proves yet effective in modelling landscape morphodynamics at the watershed scale, for what concerns the longitudinal profile of a river and the sedimentary aspects. The application of a 1-D model based on the equilibrium hypothesis has been implemented for several large rivers worldwide. Geomorphological parameters have been analysed, which describe the evolution of longitudinal profile (concavity) and sediments characteristics (aggrading and fining), and the results show a reasonably good correspondence with qualitative estimation of the same parameters. At the scale of analysis and for the chosen systems, which show high inertia to geomorphological changes likely owing to their longitudinal extension, the model can detect where the present conditions reflect a big disturbance to the “natural equilibrium” thus allowing water managers to identify present issues to be addressed.

This paper formulates the classic Monty Hall problem as a Bayesian game. Allowing Monty a small amount of freedom in his decisions facilitates a variety of solutions. The solution concept used is the Bayes Nash Equilibrium (BNE), and the set of BNE relies on Monty's motives and incentives. We endow Monty and the contestant with common prior probabilities (p) about the motives of Monty, and show that under certain conditions on p, the unique equilibrium is one where the contestant is indifferent between switching and not switching. This coincides and agrees with the typical responses and explanations by experimental subjects. Finally, we show that our formulation can explain the experimental results in Page (1998) [12]; that more people gradually choose switch as the number of doors in the problem increases.

Numerical models widely used for hydrocarbon phase behavior and compositional flow simulations are based on assumption of thermodynamic equilibrium. However, it is not uncommon for oil and gas-condensate reservoirs to exhibit essentially non-equilibrium phase behavior, e.g., in the processes of secondary recovery after pressure depletion below saturation pressure, or during gas injection, or for condensate evaporation at low pressures. In many cases the ability to match field data with equilibrium model depends on simulation scale. The only method to account for non-equilibrium phase behavior adopted by the majority of flow simulators is the option of limited rate of gas dissolution (condensate evaporation) in black oil models. For compositional simulations no practical yet thermodynamically consistent method has been presented so far except for some upscaling techniques in gas injection problems. Previously reported academic non-equilibrium formulations have a common drawback of doubling the number of flow equations and unknowns compared to the equilibrium formulation. In the paper a unified thermodynamically-consistent formulation for compositional flow simulations with non-equilibrium phase behavior model is presented. Same formulation and a special scale-up technique can be used for upscaling of an equilibrium or non-equilibrium model to a coarse-scale non-equilibrium model. A number of test cases for real oil and gas-condensate mixtures are given. Model implementation specifics in a flow simulator are discussed and illustrated with test simulations. A non-equilibrium constant volume depletion algorithm is presented to simulate condensate recovery at low pressures in gas-condensate reservoirs. Results of satisfactory model matching to field data are reported and discussed.

We introduce the Symplectic Structure of Information Geometry based on Souriau’s Lie Group Thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using Geometric (Planck) Temperature of Souriau model and Symplectic cocycle notion, the Fisher metric is identified as a Souriau Geometric Heat Capacity. Souriau model is based on affine representation of Lie Group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie Group Thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant-Kirillov-Souriau) 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of Information Geometry for the action of an affine Group for exponentiel families, and provide some illustrations of use cases for multivariate Gaussian densities. Information Geometry is presented in the context of seminal work of Fréchet and his Clairaut-Legendre equation. Souriau model of Statistical Physics is validated as compatible with Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

This article investigates a proposed new mathematical model that considers the infected individuals using various rate coefficients such as transmission, progression, recovery and vaccination. The fact that the dynamic analysis is completely determined by the basic reproduction number is established. More specifically, local and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved under certain parameter conditions when the basic reproduction number is below or above unity. A realistic computer simulation is performed for better understanding of the variations in trends of different compartments after the outbreak of the disease.

In this work model of mirror elements equilibrium of the micromechanical components is developed, the behavior analysis of the mirror element of micromechanical mirrors in case changing of control voltages of electrostatic actuators is carried out, an expression for determining the maximum value of deflection voltage at which the snap-down effect will take the following form is obtained in case of the influence of the coefficient of the electrostatic rigidity of electrostatic actuators. The developed equilibrium model of mirror elements and the obtained results of modeling can be used at design of micromechanical mirrors with internal suspensions.