Ratios of ordered points of point processes with regularly varying intensity measures

We study limiting properties of ratios of ordered points of point processes whose intensity measures have regularly varying tails, giving a systematic treatment which points the way to “large-trimming” properties of extremal processes and a variety of applications. Our point process approach facilitates a connection with the negative binomial process of Gregoire (1984) and consequently to certain generalised versions of the Poisson–Dirichlet distribution.     

How mathematical impossibility changed welfare economics: A history of Arrow's impossibility theorem

During the 20th century, impossibility theorems have become an important part of mathematics. Arrow's impossibility theorem (1950) stands out as one of the first impossibility theorems outside of pure mathematics. It states that it is impossible to design a welfare function (or a voting method) that satisfies some rather innocent looking requirements. Arrow's theorem became the starting point of social choice theory that has had a great impact on welfare economics. This paper will analyze the history of Arrow's impossibility theorem in its mathematical and economic contexts. It will be argued that Arrow made a radical change of the mathematical model of welfare economics by connecting it to the theory of voting and that this change was preconditioned by his deep knowledge of the modern axiomatic approach to mathematics and logic.     

Traveling Wave Solutions of a Fourth-order Generalized Dispersive and Dissipative Equation

In this paper, we consider a generalized nonlinear forth-order dispersive-dissipative equation with a nonlocal strong generic delay kernel, which describes wave propagation in generalized nonlinear dispersive, dissipation and quadratic diffusion media. By using geometric singular perturbation theory and Fredholm alternative theory, we get a locally invariant manifold and use fast-slow system to construct the desire heteroclinic orbit. Furthermore we construct a traveling wave solution for the nonlinear equation. Some known results in the literature are generalized.     

Limit cycle bifurcations by perturbing piecewise smooth Hamiltonian systems with multiple parameters

This paper is concerned with the problem of limit cycle bifurcation for piecewise smooth near-Hamiltonian systems with multiple parameters. By the first Melnikov function, some novel criteria have been established for the existence of multiple limit cycles. Furthermore, an example is included to validate the obtained results by considering the maximum number of limit cycles for a piecewise quadratic system studied in Llibre and Mereu (2014) [12]. Compared with the result in the above reference, one more limit cycle is found by our method.     

MODELING AND FORECASTING MONTHLY AVERAGE WATER LEVELS BASED ON THE ELLIPTIC ORBIT MODEL

Evaluation and forecasting of water‐level fluctuation for one river is of increasing importance since it is intimately associated with human welfare and socioeconomic sustainability development. In this study, it is found that time series of monthly water‐level fluctuation exhibits annual cyclical variation. Then with annual periodic extension for monthly water‐level fluctuation, the so‐called “elliptic orbit model” is proposed for describing monthly water‐level fluctuation by mapping its time series into the polar coordinates. Experiments and result analysis indicate potentiality of the proposed method that it yields satisfying results in evaluating and forecasting monthly water‐level fluctuation at the monitoring stations in the Yangtze River of China. It is shown that the monthly water‐level fluctuation is well described by the proposed elliptic orbit model, which offers a vivid approach for modeling and forecasting monthly water‐level fluctuation in a concise and intuitive way.     

Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.     

2‐(v,k,1) Designs Admitting a Primitive Rank 3 Automorphism Group of Affine Type: The Extraspecial and the Exceptional Classes

2‐(v,k,1) designs admitting a primitive rank 3 automorphism group , where G₀ belongs to the Extraspecial Class, or to the Exceptional Class of Liebeck's Theorem in [23], are classified.     

O2 Binding to Heme is Strongly Facilitated by Near‐Degeneracy of Electronic States

This paper reports the computed O₂ binding to heme, which for the first time explains experimental enthalpies for this process of central importance to bioinorganic chemistry. All four spin states along the relaxed Fe? O₂‐binding curves were optimized using the full heme system with dispersion, thermodynamic, and scalar‐relativistic corrections, applying several density functionals. When including all these physical terms, the experimental enthalpy of O₂ binding (?59 kJ mol^?1) is closely reproduced by TPSSh‐D3 (?66 kJ mol^?1). Dispersion changes the potential energy surfaces and leads to the correct electronic singlet and heptet states for bound and dissociated O₂. The experimental activation enthalpy of dissociation (～82 kJ mol^?1) was also accurately computed (～75 kJ mol^?1) with an actual barrier height of ～60 kJ mol^?1 plus a vibrational component of ～10 and ～5 kJ mol^?1 due to the spin‐forbidden nature of the process, explaining the experimentally observed difference of ～20 kJ mol^?1 in enthalpies of binding and activation. Most importantly, the work shows how the nearly degenerate singlet and triplet states increase crossover probability up to ～0.5 and accelerate binding by ～100 times, explaining why the spin‐forbidden binding of O₂ to heme, so fundamental to higher life forms, is fast and reversible.     

PEAKED WAVE SOLUTIONS TO A GENERALIZED HYPERELASTIC-ROD WAVE EQUATION

We study peaked wave solutions of a generalized Hyperelastic-rod wave equation describing waves in compressible hyperelastic-rods by using the bifurcation theory of planar dynamical systems and numerical simulation method. The existence domain of the peaked solitary waves are found. The analytic expressions of peaked solitary wave solutions are obtained. Our numerical simulation and qualitative results are identical.