The impact of disaster on the strategic interaction between company and government

A company allocates a resource between safety effort and production. The government earns taxes on production. The disaster probability is modeled as a contest between the disaster magnitude and the two players’ safety efforts. The model illustrates that safety efforts are strategic substitutes and inverse U shaped in the disaster magnitude. The company’s safety effort increases, and the government’s safety effort decreases, in taxation. Taxation can ameliorate companies’ free riding on governments’ safety efforts. With sufficiently large production, the government prefers, and the company does not prefer, raising taxation above 0%. For the government, an upper limit usually exists above which taxation cannot be profitably increased. The model shows how both or no players exert safety efforts when the disaster magnitude is small and large respectively, and how they free ride on each other’s safety efforts when the disaster magnitude is intermediate. The company free rides when the unit production cost is low so that the large profits outweigh the negative impact of the disaster. With endogenized taxation determined by the government, the tax rate decreases in the disaster magnitude, the unit production cost, the government’s unit cost of safety effort, and how the company is negatively affected by the disaster. The tax rate increases in the company’s resource and how the government is negatively affected by the disaster. The tax rate is weakly U shaped in the company’s unit safety effort. The model is illustrated with numerical examples and with the oil spill disasters by BP in 2010 and by Exxon Valdez in 1989.     

The analysis and application of an HBV model

A mathematical model is formulated to describe the spread of hepatitis B. The stability of equilibria and persistence of disease are analyzed. The results shows that the dynamics of the model is completely determined by the basic reproductive number ρ₀. If ρ₀ < 1, the disease-free equilibrium is globally stable. When ρ₀ > 1, the disease-free equilibrium is unstable and the disease is uniformly persistent. Furthermore, under certain conditions, it is proved that the endemic equilibrium is globally attractive. Numerical simulations are conducted to demonstrate our theoretical results. The model is applied to HBV transmission in China. The parameter values of the model are estimated based on available HBV epidemic data in China. The simulation results matches the HBV epidemic data in China approximately.     

On the quiver-theoretical quantum Yang–Baxter equation

Quivers over a fixed base set form a monoidal category with tensor product given by pullback. The quantum Yang–Baxter equation, or more properly the braid equation, is investigated in this setting. A solution of the braid equation in this category is called a “solution” for short. Results of Etingof–Schedler–Soloviev, Lu–Yan–Zhu and Takeuchi on the set-theoretical quantum Yang–Baxter equation are generalized to the context of quivers, with groupoids playing the role of groups. The notion of “braided groupoid” is introduced. Braided groupoids are solutions and are characterized in terms of bijective 1-cocycles. The structure groupoid of a non-degenerate solution is defined; it is shown that it is a braided groupoid. The reduced structure groupoid of a non-degenerate solution is also defined. Non-degenerate solutions are classified in terms of representations of matched pairs of groupoids. By linearization we construct star-triangular face models and realize them as modules over quasitriangular quantum groupoids introduced in papers by M. Aguiar, S. Natale and the author.     

A deterministic particle method for the Vlasov–Fokker–Planck equation in one dimension

The Vlasov–Fokker–Planck equation is a model for a collisional, electrostatic plasma. The approximation of this equation in one spatial dimension is studied. The equation under consideration is linear in that the electric field is given as a known function that is not internally consistent with the phase space distribution function. The approximation method applied is the deterministic particle method described in Wollman and Ozizmir [Numerical approximation of the Vlasov–Poisson–Fokker–Planck system in one dimension, J. Comput. Phys. 202 (2005) 602–644]. For the present linear problem an analysis of the stability and convergence of the numerical method is carried out. In addition, computations are done that verify the convergence of the numerical solution. It is also shown that the long term asymptotics of the computed solution is in agreement with the steady state solution derived in Bouchut and Dolbeault [On long time asymptotics of the Vlasov–Fokker–Planck equation and of the Vlasov–Poisson–Fokker–Planck system with coulombic and Newtonian potentials, Differential Integral Equations 8(3) (1995) 487–514].     

Some properties of the bivariate lognormal distribution for reliability applications

In this paper, we study the bivariate lognormal distribution from a reliability point of view. The conditional distribution of X given Y > y is found to be log‐skew normal. The monotonicity of the hazard rates of the univariate as well as the conditional distributions is discussed. Clayton's association measure is obtained in terms of the hazard gradient, and its value in the case of our model is derived. The probability distributions, in the case of series and parallel systems, are derived, and the monotonicity of their failure rates is discussed. Three real applications of the bivariate lognormal distribution are provided, two from financial economics and one from reliability. Copyright © 2012 John Wiley & Sons, Ltd.     

Existence and regularity of solution of mixed boundary value problem of a Busemann-equation with nonlinear absorb term

The Busemann-equation is a classical equation coming from fluid dynamics. The well-posed problem and regularity of solution of Busemann-equation with nonlinear term are interesting and important. The Busemann-equation is elliptic in y>0 and is degenerate at the line y=0 in R². With a special nonlinear absorb term, we study a nonlinear degenerate elliptic equation with mixed boundary conditions in a piecewise smooth domain. By means of elliptic regularization technique, a delicate prior estimate and compact argument, we show that the solution of mixed boundary value problem of Busemann-equation is smooth in the interior and Lipschitz continuous up to the degenerate boundary on some conditions. The result is better than the result of classical boundary degenerate elliptic equation.     

The harmonic dirichlet problem for a cracked domain with jump conditions on cracks

The harmonic problem in a cracked domain is studied in R ^m , m?>?2. The boundary of the domain is assumed to be nonsmooth, while cracks are smooth. The Dirichlet condition is specified on the boundary of the domain. Jumps of the unknown function and its normal derivative are specified on the cracks. Uniqueness and solvability results are obtained. The problem is reduced to the uniquely solvable integral equation, its solution is given explicitely in the form of a series. The estimates of the solution of the problem depending on the boundary data are obtained.     

Evolution of a semilinear parabolic system for migration and selection without dominance

The semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus without dominance is investigated. The population occupies a finite habitat of arbitrary dimensionality and shape (i.e., a bounded, open domain in Rd). The selection coefficients depend on position; the drift and diffusion coefficients may depend on position. The primary focus of this paper is the dependence of the evolution of the gene frequencies on λ, the strength of selection relative to that of migration. It is proved that if migration is sufficiently strong (i.e., λ is sufficiently small) and the migration operator is in divergence form, then the allele with the greatest spatially averaged selection coefficient is ultimately fixed. The stability of each vertex (i.e., an equilibrium with exactly one allele present) is completely specified. The stability of each edge equilibrium (i.e., one with exactly two alleles present) is fully described when either (i) migration is sufficiently weak (i.e., λ is sufficiently large) or (ii) the equilibrium has just appeared as λ increases. The existence of unexpected, complex phenomena is established: even if there are only three alleles and migration is homogeneous and isotropic (corresponding to the Laplacian), (i) as λ increases, arbitrarily many changes of stability of the edge equilibria and corresponding appearance of an internal equilibrium can occur and (ii) the conditions for protection or loss of an allele can both depend nonmonotonically on λ. Neither of these phenomena can occur in the diallelic case.     

An Inventory System with Postponed Demands

Abstract

In this article we consider a continuous review perishable inventory system in which the demands arrive according to a Markovian arrival process (MAP). The items in the inventory have shelf life times that are assumed to follow an exponential distribution. The inventory is replenished according to an (s, S) policy and the replenishing times are assumed to follow a phase type distribution. The demands that occur during stock out periods either enter a pool which has capacity N (<∞) or leave the system. Any demand that arrives when the pool is full and the inventory level is zero, is also assumed to be lost. The demands in the pool are selected one by one, if the replenished stock is above s, with interval time between any two successive selections is distributed as exponential with parameter depending on the number of customers in the pool. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady state case. The measures of system performance in the steady state are derived and the total expected cost rate is also calculated. The results are illustrated numerically.     

Monitoring process for attributes with quality deterioration and diagnosis errors

The aim of this paper is to present an online economical quality-control procedure for attributes in a process subject to quality deterioration after random shift and misclassification errors during inspections. The process starts in control (State I) and, in a random time, it shifts to out of control (State II). Once at State II, the non-conforming fraction increases according to a non-decreasing function ψ(z), where z is the number of items produced after a shift. The monitoring procedure consists of inspecting a single item at every m produced items, which is examined r times independently to decide its condition. Once an inspected item is declared non-conforming, the process is stopped and adjusted. A direct search technique is used to find the optimum parameters which minimize the expected cost function. The proposed model is illustrated by a numerical example. Copyright © 2007 John Wiley & Sons, Ltd.     

Shape coexistence in188Pb

The shape coexistence in¹⁸⁸Pb is investigated in terms of the projected shell model. Analyzing the experimental data with the calculated results, it is shown that the three shapes, sphere, oblate and prolate, coexist with each other in the low-lying excited states. The prolate band exhibits a mixture between two kinds of multi-particle-hole configuration. The mixing is discussed and the mixing coefficients are given, meaning the vi_12/2 pair alignment happens gradually in this case. The oblate (ϕh _9/22p2h) band structure is predicted and the 2⁺ prolate state is in the range of 804-880 keV.     

Heat transfer in a peristaltic flow of MHD fluid with partial slip

In the present note, we have discussed the effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel. The governing equations of motion and energy are simplified using a long wave length approximation. A closed form solution of the momentum equation is obtained by Adomian decomposition method and an exact solution of the energy equation is presented in the presence of viscous dissipation term. The expression for pressure rise is calculated using numerical integration. The trapping phenomena is also discussed. The graphical results are presented to interpret various physical parameter of interest. It is found that the temperature field decreases with the increase in slip parameter L, and magnetic field M, while with the increase in P_r and E_c, the temperature field increases.     

Finite Projective Geometries and Classification of the Weight Hierarchies of Codes （Ⅰ）

The weight hierarchy of a binary linear [n,κ] code C is the sequence (d1,d2,...,dκ), where dr is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries.The possible weight hierarchies in class A, B, C, D are determined in Part (Ⅰ). The possible weight hierarchies in class E, F, G, H, I are determined in Part (Ⅱ).     

Analysis of flow and thermal field in nanofluid using a single phase thermal dispersion model

Flow and thermal field in nanofluid is analyzed using single phase thermal dispersion model proposed by Xuan and Roetzel [Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer 43 (2000) 3701–3707]. The non-dimensional form of the transport equations involving the thermal dispersion effect is solved numerically using semi-explicit finite volume solver in a collocated grid. Heat transfer augmentation for copper–water nanofluid is estimated in a thermally driven two-dimensional cavity. The thermo-physical properties of nanofluid are calculated involving contributions due to the base fluid and nanoparticles. The flow and heat transfer process in the cavity is analyzed using different thermo-physical models for the nanofluid available in literature. The influence of controlling parameters on convective recirculation and heat transfer augmentation induced in buoyancy driven cavity is estimated in detail. The controlling parameters considered for this study are Grashof number (10³ < Gr < 10⁵), solid volume fraction (0 < ? < 0.2) and empirical shape factor (0.5 < n < 6). Simulations carried out with various thermo-physical models of the nanofluid show significant influence on thermal boundary layer thickness when the model incorporates the contribution of nanoparticles in the density as well as viscosity of nanofluid. Simulations incorporating the thermal dispersion model show increment in local thermal conductivity at locations with maximum velocity. The suspended particles increase the surface area and the heat transfer capacity of the fluid. As solid volume fraction increases, the effect is more pronounced. The average Nusselt number from the hot wall increases with the solid volume fraction. The boundary surface of nanoparticles and their chaotic movement greatly enhances the fluid heat conduction contribution. Considerable improvement in thermal conductivity is observed as a result of increase in the shape factor.     

Revenue management approach to stochastic capacity allocation problem

To formulate stochastic capacity allocation problems in a manufacturing system, the concept and techniques of revenue management is applied in this research. It is assumed the production capacity is stochastic and hence its exact size cannot be forecasted in advance, at the time of planning. There are two classes of “frequent” and “occasional” customers demanding this capacity. The price rate as well as the penalty for order cancellation caused by overbooking is different for each class. The model is developed mathematically and we propose an analytical solution method. The properties of the optimal solution as well as the behavior of objective function are also analyzed. The objective function is not concave, in general. However, we prove it is a unimodal function and by taking advantage of this property, the optimal solution is determined.     

The Third Problem for the Laplace Equation with a Boundary Condition from L p

The third problem for the Laplace equation is studied on an open set with Lipschitz boundary. The boundary condition is in L_p and it is fulfilled in the sense of the nontangential limit. The existence and the uniqueness of a solution is proved and the solution is expressed in the form of a single layer potential. For domains with C¹ boundary the explicit solution of the problem is calculated.     

Fisher information under restriction of Shannon information in multi-terminal situations

Fisher information generally decreases by summarizing observed data into encoded messages. The present paper studies the amount of Fisher information included in independently summarized messages from correlated information sources; that is, the amount of Fisher information when sequences x ^N and y ^N of N independent observations of random variables x and y are encoded (summarized) independently of each other into meassages m _X and m _Y . The problem is to obtain the maximal amount of Fisher information when the size of the summarized data or Shannon message information is limited. The problem is solved in the case of completely compressed symmetric data summarization. An achievable bound is given in the general case. Information geometry, which is a powerful new differential geometrical method applicable to statistics and systems theory, is applied to this problem, proving its usefulness in information theory as well.The present work is supported in part by Grant-in-Aid for Scientific Research #61030014, Ministry of Education, Science and Culture of Japan.     

Equivalence between modified symplectic Gram-Schmidt and Householder SR algorithms

The SR factorization for a given matrix A is a QR-like factorization A=SR, where the matrix S is symplectic and R is J-upper triangular. This factorization is fundamental for some important structure-preserving methods in linear algebra and is usually implemented via the symplectic Gram-Schmidt algorithm (SGS). There exist two versions of SGS, the classical (CSGS) and the modified (MSGS). Both are equivalent in exact arithmetic, but have very different numerical behaviors. The MSGS is more stable. Recently, the symplectic Householder SR algorithm has been introduced, for computing efficiently the SR factorization. In this paper, we show two new and important results. The first is that the SR factorization of a matrix A via the MSGS is mathematically equivalent to the SR factorization via Householder SR algorithm of an embedded matrix. The later is obtained from A by adding two blocks of zeros in the top of the first half and in the top of the second half of the matrix A. The second result is that MSGS is also numerically equivalent to Householder SR algorithm applied to the mentioned embedded matrix.