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This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles. [ABSTRACT FROM AUTHOR]

When decisions involve opting in or out of competition many decision makers will opt-in even when doing so leads to losses on average. In the current paper, we examine the generality of this effect in risky choices not involving competition. We found that re-framing a sure (certain) zero option as an option to observe the results of the other options without choosing would lead to increased consequential choice (i.e., increased selection of risky options rather than the zero option). Specifically, in two studies we compared the rate of consequential choice in a novel paradigm where decision makers decide to observe or to choose with consequence from a set of risky options (decisions-to-engage) to a full-feedback decisions-from-feedback paradigm where the choice set included a labeled sure zero option. Compared to decisions-from-feedback, participants were more likely to choose from mixed (risky) gambles with consequence (over a zero outcome) in decisions-to-engage. This occurred irrespective of whether doing so was advantageous (i.e., when choice led to monetary gains on average) or disadvantageous (i.e., when choice led to monetary losses on average), and when descriptions of the options outcomes and probabilities were provided (Study 2). These findings provide an important boundary condition for the positive effects of experience on the quality of choice, and suggest that decision makers' preference for agency can sometimes induce poorer choices. [ABSTRACT FROM AUTHOR]

In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent, identically distributed data. Under mild regularity conditions, we prove a law of large numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straightforward way to establish convergence with probability 1 of sample-based estimators of risk averse stochastic programming problems. [ABSTRACT FROM AUTHOR]

Bandit processes and the Gittins index have provided powerful and elegant theory and tools for the optimization of allocating limited resources to competitive demands. In this paper we extend the Gittins theory to more general branching bandit processes, also referred to as open bandit processes, that allow uncountable states and backward times. We establish the optimality of the Gittins index policy with uncountably many states, which is useful in such problems as dynamic scheduling with continuous random processing times. We also allow negative time durations for discounting a reward to account for the present value of the reward that was received before the present time, which we refer to as time-backward effects. This could model the situation of offering bonus rewards for completing jobs above expectation. Moreover, we discover that a common belief on the optimality of the Gittins index in the generalized bandit problem is not always true without additional conditions, and provide a counterexample. We further apply our theory of open bandit processes with time-backward effects to prove the optimality of the Gittins index in the generalized bandit problem under a sufficient condition. [ABSTRACT FROM AUTHOR]

This paper is concerned with the initial boundary value problem of a class of nonlinear wave equations and reaction–diffusion equations with several nonlinear source terms of different signs. For the initial boundary value problem of the nonlinear wave equations, we derive a blow up result for certain initial data with arbitrary positive initial energy. For the initial boundary value problem of the nonlinear reaction–diffusion equations, we discuss some probabilities of the existence and nonexistence of global solutions and give some sufficient conditions for the global and nonglobal existence of solutions at high initial energy level by employing the comparison principle and variational methods. [ABSTRACT FROM AUTHOR]

The notion of completeness between two random elements has been considered recently to provide identification in nonparametric instrumental problems. This condition is quite abstract, however, and characterizations have been obtained only in special cases. This paper considers a nonparametric model between the two variables with an additive separability and a large support condition. In this framework, different versions of completeness are obtained, depending on which regularity conditions are imposed. This result allows one to establish identification in an instrumental nonparametric regression with limited endogenous regressor, a case where the control variate approach breaks down. [ABSTRACT FROM AUTHOR]

This paper presents a sharp boundary growth estimate for all positive superharmonic functions u in a smooth domain Ω in ℝ2 satisfying the nonlinear inequality -Δu(x) ≤ cδΩ(x)-αu(x)p for all x ϵ Ωwhere c > 0, α ϵ ℝ and p > 0, and δΩ(x) stands for the distance from a point x to the boundary of Ω. A result is applied to show the existence of nontangential limits of such superharmonic functions. [ABSTRACT FROM AUTHOR]

Many boundary value problems occur in a natural way while studying fluid flow problems in a channel. The solutions of two such boundary value problems are obtained and analysed in the context of flow problems involving three layers of fluids of different constant densities in a channel, associated with an impermeable bottom that has a small undulation. The top surface of the channel is either bounded by a rigid lid or free to the atmosphere. The fluid in each layer is assumed to be inviscid and incompressible, and the flow is irrotational and two-dimensional. Only waves that are stationary with respect to the bottom profile are considered in this paper. The effect of surface tension is neglected. In the process of obtaining solutions for both the problems, regular perturbation analysis along with a Fourier transform technique is employed to derive the first-order corrections of some important physical quantities. Two types of bottom topography, such as concave and convex, are considered to derive the profiles of the interfaces. We observe that the profiles are oscillatory in nature, representing waves of variable amplitude with distinct wave numbers propagating downstream and with no wave upstream. The observations are presented in tabular and graphical forms. [ABSTRACT FROM AUTHOR]

“Testing Theories of Congressional-Presidential Interaction with Veto Override Rates” (henceforth “Veto Override Rates”) offers several tests of two models of vetoes and finds the models wanting. The paper concludes that something is seriously amiss with the models. In my view, the problem lies not in the models but in the tests. Understanding why the tests miss the mark is helpful in understanding models of veto politics, and more generally in thinking about testing strategies when multiple models analyze different causal mechanisms that hold under different circumstances. I should note immediately that the effort in the paper to think hard about override rates is admirable; it simply does not go far enough. [ABSTRACT FROM PUBLISHER]

A preconditioned iterative method for the two-dimensional Helmholtz equation with Robbins boundary conditions is discussed. Using a finite-difference method to discretize the Helmholtz equation leads to a sparse system of equations which is too large to solve directly. The approach taken in this paper is to precondition this linear system with a sine transform based preconditioner and then solve it using the generalized minimum residual method (GMRES). An analytical formula for the eigenvalues of the preconditioned matrix is derived and it is shown that the eigenvalues are clustered around 1 except for some outliers. Numerical results are reported to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

Let {(Xn, Sn), n ≥ 0} be a Markov random walk in which Xn takes values in a general state space and Sn takes values on the real line ℝ. In this paper we present some results that are useful in the study of asymptotic approximations of boundary crossing problems for Markov random walks. The main results are asymptotic expansions on moments of the first ladder height in Markov random walks with small positive drift. In order to establish the asymptotic expansions we study a uniform Markov renewal theorem, which relates to the rate of convergence for the distribution of overshoot, and present an analysis of the covariance between the first passage time and the overshoot. [ABSTRACT FROM AUTHOR]

Corrected random walk approximations to continuous-time optimal stopping boundaries for Brownian motion, first introduced by Chernoff and Petkau, have provided powerful computational tools in option pricing and sequential analysis. This paper develops the theory of these second-order approximations and describes some new applications. [ABSTRACT FROM AUTHOR]

We use an integral equation formulation approach to value shout options, which are exotic options giving an investor the ability to “shout” and lock in profits while retaining the right to benefit from potentially favourable movements in the underlying asset price. Mathematically, the valuation is a free boundary problem involving an optimal exercise boundary which marks the region between shouting and not shouting. We also find the behaviour of the optimal exercise boundary for one- and two-shout options close to expiry. [ABSTRACT FROM AUTHOR]

We study bound states in weakly deformed and heterogeneous waveguides, and compare analytical predictions using a recently developed perturbative method with precise numerical results for three different configurations: a homogeneous asymmetric waveguide, a heterogenous asymmetric waveguide and a homogeneous broken strip. We have found excellent agreement between the analytical and numerical results in all the examples; this provides a numerical verification of the analytical approach. [ABSTRACT FROM AUTHOR]

We interpret a boundary-value problem arising in a cell growth model as a singular Sturm–Liouville problem that involves a functional differential equation of the pantograph type. We show that the probability density function of the cell growth model corresponds to the first eigenvalue and that there is a family of rapidly decaying eigenfunctions. [ABSTRACT FROM AUTHOR]

In this paper, we provide a novel approach to studying the heavy-tailed asymptotic s of the stationary probability vector of a Markov chain of GI/G/I type, whose transition matrix is constructed from two matrix sequences referred to as a boundary matrix sequence and a repeating matrix sequence, respectively. We first provide a necessary and sufficient condition under which the stationary probability vector is heavy tailed. Then we derive the long-tailed asymptotics of the R-measure in terms of the RG-factorization of the repeating matrix sequence, and a Wiener-Hopf equation for the boundary matrix sequence. Based on this, we are able to provide a detailed analysis of the subexponential asymptotics of the stationary probability vector. [ABSTRACT FROM AUTHOR]

This article sets out two central theses. Both theses primarily involve a fundamental criticism of current contractarian business ethics (CBE), but if these can be sustained, they also constitute two boundary conditions for any future contractarian theory of business ethics. The first, which I label the self-discipline thesis, claims that current CBE would gain considerably in focus if more attention were paid to the logic of the social contract argument. By this I mean the aims set by the theorist and method of reasoning by which normative conclusions are drawn in the contract model. The second, to which I refer as the domain-specificity thesis, argues that current CBE needs to be better adapted to its field of application and the specific goals which it aims to establish. I will substantiate these two theses on the basis of a comparative analysis of CBE with two earlier families of social contract theories. [ABSTRACT FROM AUTHOR]

The Douglas–Rachford method has been employed successfully to solve many kinds of nonconvex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections of hypersurfaces. Motivated by these discoveries, we reformulate a second order boundary value problem (BVP) as a feasibility problem where the sets are hypersurfaces. We show that such a problem may always be reformulated as a feasibility problem on no more than three sets and is well suited to parallelization. We explore the stability of the method by applying it to several BVPs, including cases where the traditional Newton's method fails. [ABSTRACT FROM AUTHOR]

We investigate the appropriateness of calving or crevasse models from the literature using linear elastic fracture mechanics (LEFM). To this end, we compare LEFM model-predicted stress intensity factors (SIFs) against numerically computed SIFs using the displacement correlation method in conjunction with the finite element method. We present several benchmark simulations wherein we calculate the SIF at the tips of water-filled surface and basal crevasses penetrating through rectangular ice slabs under different boundary conditions, including grounded and floating conditions. Our simulation results indicate that the basal boundary condition significantly influences the SIF at the crevasse tips. We find that the existing calving models using LEFM are not generally accurate for evaluating SIFs in grounded glaciers or floating ice shelves. We also illustrate that using the 'single edge crack' weight function in the LEFM formulations may be appropriate for predicting calving from floating ice shelves, owing to the low fracture toughness of ice; whereas, using the 'double edge crack' or 'central through crack' weight functions is more appropriate for predicting calving from grounded glaciers. To conclude, we recommend using the displacement correlation method for SIF evaluation in real glaciers and ice shelves with complex geometries and boundary conditions. [ABSTRACT FROM AUTHOR]

We present a high-order upwind finite volume element method to solve optimal control problems governed by first-order hyperbolic equations. The method is efficient and easy for implementation. Both the semi-discrete error estimates and the fully discrete error estimates are derived. Optimal order error estimates in the sense of $L^{2}$-norm are obtained. Numerical examples are provided to confirm the effectiveness of the method and the theoretical results. [ABSTRACT FROM PUBLISHER]

To simulate a glacial lake outburst flood, we employ a comprehensive physically based general two-phase mass flow model (Pudasaini, 2012). This model accounts for a strong interaction between the solid and fluid phases and incorporates buoyancy and other dominant physical aspects of the mass flows such as enhanced non-Newtonian viscous stress, virtual mass force and generalized drag. Our real two-phase mass flow simulation describes explicit evolution of the solid and fluid phases and the debris bulk as a whole, akin to torrential debris flows or debris floods during glacial lake outburst floods (GLOFs). The emptying of a lake following rapid collapse of a restraining dam, the consequent downslope motion of a mixed solid–fluid mass, and the tendency of the mass to form extruding plumes are analyzed in detail for different flow configurations, volumes, conduit geometries and boundary conditions. The solid and fluid phases evolve completely differently and reveal fundamentally different dynamical behaviours. During the flow, the relatively long fluid tail follows the solid-rich dense frontal surge head. The bulk debris develops into a frontal and side levee as derived from the initial frontal moraine dam. Results show that our high-resolution, unified simulation strategies and the advanced model equations can be applied to study the flow dynamics of a wide range of geophysical mass flows such as snow and rock–ice avalanches, debris flows and flash floods as well as GLOFs. This may help substantially in forming a basis for appropriate mitigation measures against potential natural hazards in high mountain slopes and valleys. [ABSTRACT FROM PUBLISHER]

We consider a two-layer fluid of finite depth with a free surface and, in particular, the surface tension at the free surface and the interface. The usual assumptions of a linearized theory are considered. The objective of this work is to analyse the effect of surface tension on trapped modes, when a horizontal circular cylinder is submerged in either of the layers of a two-layer fluid. By setting up boundary value problems for both of the layers, we find the frequencies for which trapped waves exist. Then, we numerically analyse the effect of variation of surface tension parameters on the trapped modes, and conclude that realistic changes in surface tension do not have a significant effect on the frequencies of these. [ABSTRACT FROM AUTHOR]

More and more experimental evidence demonstrates that the slip boundary condition plays an important role in the study of nano- or micro-scale fluid. We propose a homogenization approach to study the effective slippage problem. We show that the effective slip length obtained by homogenization agrees with the results obtained by the traditional method in the literature for the simplest Stokes flow; then we use our approach to deal with two examples which seem quite hard by other analytical methods. We also include some numerical results to validate our analytical results. [ABSTRACT FROM AUTHOR]

The current study tested the boundary conditions of ethical decision-making by increasing cognitive load. This manipulation is believed to hinder deliberation, and, as we argue, reduces the cognitive capacity needed for a self-serving bias to occur. As telling a lie is believed to be more cognitively taxing than telling the truth, we hypothesized that participants would be more honest under high cognitive load than low cognitive load. 173 participants anonymously rolled a die three times and reported their outcomes - of which one of the rolls would be paid out - while either under high or low cognitive load. For the roll that determined pay, participants under low cognitive load, but not under high cognitive load, reported die rolls that were significantly different from a uniform (honest) distribution. The reported outcome of this roll was also significantly higher in the low load condition than in the high load condition, suggesting that participants in the low load condition lied to get higher pay. This pattern was not observed for the second and third roll where participants knew the rolls were not going to be paid out and where therefore lying would not serve self-interest. Results thus indicate that having limited cognitive capacity will unveil a tendency to be honest in a situation where having more cognitive capacity would have enabled one to serve self-interest by lying. [ABSTRACT FROM AUTHOR]

We investigate Cartan subalgebras in nontracial amalgamated free product von Neumann algebras ${\mathop{M{}_{1} \ast }\nolimits}_{B} {M}_{2} $ over an amenable von Neumann subalgebra $B$. First, we settle the problem of the absence of Cartan subalgebra in arbitrary free product von Neumann algebras. Namely, we show that any nonamenable free product von Neumann algebra $({M}_{1} , {\varphi }_{1} )\ast ({M}_{2} , {\varphi }_{2} )$ with respect to faithful normal states has no Cartan subalgebra. This generalizes the tracial case that was established by A. Ioana [Cartan subalgebras of amalgamated free product ${\mathrm{II} }_{1} $factors, arXiv:1207.0054]. Next, we prove that any countable nonsingular ergodic equivalence relation $ \mathcal{R} $ defined on a standard measure space and which splits as the free product $ \mathcal{R} = { \mathcal{R} }_{1} \ast { \mathcal{R} }_{2} $ of recurrent subequivalence relations gives rise to a nonamenable factor $\mathrm{L} ( \mathcal{R} )$ with a unique Cartan subalgebra, up to unitary conjugacy. Finally, we prove unique Cartan decomposition for a class of group measure space factors ${\mathrm{L} }^{\infty } (X)\rtimes \Gamma $ arising from nonsingular free ergodic actions $\Gamma \curvearrowright (X, \mu )$ on standard measure spaces of amalgamated groups $\Gamma = {\mathop{\Gamma {}_{1} \ast }\nolimits}_{\Sigma } {\Gamma }_{2} $ over a finite subgroup $\Sigma $. [ABSTRACT FROM AUTHOR]

We propose and study a number of layer methods for Navier-Stokes equations (NSEs) with spatial periodic boundary conditions. The methods are constructed using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the layer methods are nevertheless deterministic. [ABSTRACT FROM AUTHOR]

For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state (i0, j0), we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive a certain integral representation for the probability of this event, and an asymptotic expression for the case when i0 becomes large, a situation in which the event becomes highly unlikely. The integral representation follows from the solution of a boundary value problem and involves a conformal gluing function. The asymptotic expression follows from the asymptotic evaluation of this integral. Our results find applications in a model for nucleosome shifting, the voter model, and the asymmetric exclusion process. [ABSTRACT FROM AUTHOR]

We give a systematic treatment of caloric measure for arbitrary open sets. The caloric measure is defined only on the essential boundary of the set. Our main result gives criteria for the resolutivity of essential boundary functions, and their integral representation in terms of caloric measure. We also characterize the caloric measure null sets in terms of the boundary singularities of nonnegative supertemperatures. [ABSTRACT FROM AUTHOR]

A theoretical investigation of the unsteady flow of a Newtonian fluid through a channel is presented using an alternative boundary condition to the standard no-slip condition, namely the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter called the slip length, and the most general case of a constant but different slip length on each channel wall is studied. An analytical solution for the velocity distribution through the channel is obtained via a Fourier series, and is used as a benchmark for numerical simulations performed utilizing a finite element analysis modified with a penalty method to implement the slip boundary condition. Comparison between the analytical and numerical solution shows excellent agreement for all combinations of slip lengths considered. [ABSTRACT FROM AUTHOR]

The creeping flow of an incompressible viscous liquid past a porous approximately spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier–Stokes equations. The flow within the porous annular region of the shell is governed by Brinkman’s model. The boundary conditions used at the interface are continuity of the velocity, continuity of the pressure and Ochoa-Tapia and Whitaker’s stress jump condition. An exact solution for the problem and an expression for the drag on the porous approximately spherical shell are obtained. The drag is evaluated numerically for several values of the parameters governing the flow. [ABSTRACT FROM PUBLISHER]

The problem of stagnation point flow with heat transfer of an electrically conducting fluid impinging normally on a permeable axisymmetric surface in the presence of a uniform transverse magnetic field is analysed. The governing nonlinear differential equations and their associated boundary conditions are reduced to dimensionless form using suitable similarity transformations. Comparison with previously published work shows good agreement. Effects of the injection–suction parameter, magnetic parameter and Prandtl number on the flow and thermal fields are presented. The investigations show that the wall shear stress and heat transfer rate from the surface increase with increased applied magnetic field. An increase in the velocity and thermal boundary layer thicknesses is observed with an increase in the wall injection, while the velocity and thermal boundary layers become thinner when increasing the wall suction and applied magnetic field. [ABSTRACT FROM PUBLISHER]

We investigate natural convection cooling of the fluid in a drink can placed in a refrigerator by simulating the full combined boundary layer system on the can wall. The cylindrical can is filled with water at initial nondimensional temperature 0, and located within a larger cylindrical container filled with air at initial temperature −1. The outer container walls are maintained at constant temperature −1. Initially both fluids are at rest. Two configurations are examined: the first has the inner can placed vertically in the middle of the outer container with no contact with the outer container walls, and the second has the inner can placed vertically at the bottom of the outer container. The results are compared to those obtained by assuming that the inner can walls are maintained at a constant temperature, showing similar basic flow features and scaling relations, but with very different proportionality constants. [ABSTRACT FROM PUBLISHER]

We establish new sampling representations for linear integral transforms associated with arbitrary general Birkhoff regular boundary value problems. The new approach is developed in connection with the analytical properties of Green's function, and does not require the root functions to be a basis or complete. Unlike most of the known sampling expansions associated with eigen-value problems, the results obtained are, generally speaking, of Hermite interpolation type. [ABSTRACT FROM AUTHOR]

AbstractLet R(n,?) denote the number of representations of the natural number nas the?sum?of four squares, each composed only with primes not exceeding n?/2. When ?>e?1/3?a?lower bound for R(n,?) of the expected order of magnitude is established, and when ?>365/592, it is shown that R(n,?)>0 holds for large n. A similar result is obtained for sums of three squares. An asymptotic formula is obtained for the related problem of representing an integer as the sum of two squares and two squares composed of small primes, as above, for any fixed ?>0. This last result is the key to bound R(n,?)?from?below. [ABSTRACT FROM AUTHOR]