On the Aumann–Shapley value

Let L be a D-lattice, i.e. a lattice ordered effect algebra, and let BV be the Banach space of all real-valued functions of bounded variation on L (vanishing at 0) endowed with the variation norm. We prove the existence of a continuous Aumann–Shapley value φ on NA, the subspace of BV spanned by all functions of the form , where  is a non-atomic σ-additive modular measure and is of bounded variation and continuous at 0 and at 1.      

A boundary value approach to the numerical solution of initial value problems by multistep methos †

A boundary value appraoch to the numerical solution of initial value problems by means of linear multistep methods is presented. This theory is based on the study of linear difference equations when their general solution is computed by imposing boundary conditions. All the main stability and convergence properties of the obtained methods are investigated abd compared to those of the classical multistep methods. Then, as an example, new itegration formulas, called extended trapezoidal rules, are derived. For any order they have the same stability properties (in the sense of the definitions given in this paper) of the trapezoidal rule, which is the first method in this class. Some numerical examples are presented to confirm the theoretical expectations and to allow us to trust a future code based on boundary value methods.     

The Central value of the Rankin–Selberg L-Functions

Let f be a Maass form for SL which is fixed and u _j be an orthonormal basis of even Maass forms for SL , we prove an asymptotic formula for the average of the product of the Rankin–Selberg L-function of f and u _j and the L-function of u _j at the central value 1/2. This implies simultaneous nonvanishing results of these L-functions at 1/2. Received: November 2006, Revision: March 2007, Accepted: March 2007     

Solvability in the large on (0, ∞) of the fundamental initial-boundary value problem for the two-dimensional equations of the motion of Oldroyd fluids

The unqiue global solvability for t (0, ) is proved for the system describing the two-dimensional motion of an Oldroyd fluid.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 69–72, 1986.     

Scheduling projects to maximize net present value — the case of time-dependent,contingent cash flows

The problem of scheduling activities in a project to maximize its Net Present Value (NPV) has been solved for the case where net cash flow magnitudes are independent of the time of realization. This paper models a more realistic version of this problem — because of incentive payments and penalties for early and late event occurrences, respectively, and because of changing costs of resources over time, net cash flow magnitudes are dependent on the time of realization. We formulate an optimization program for this more general problem and present a simulated annealing solution approach. We test different implementation strategies for this algorithm and suggest a method for choosing neighborhood moves. We compare the NPVs of the solutions obtained from our formulation with the NPVs of early start schedules and with late start schedules for 168 different problems. These computational results show that the simulated annealing approach consistently produces substantially better solutions than the early start or late start schedules. Even poor simulated annealing neighborhood moves give improved solutions for most problems studied.     

Mean value estimates related to the Lindelöf hypothesis

We use an approach based on Fourier inversion formula and measure convolutions to obtain, in the setting of the Lindelöf hypothesis, new mean value results for the Riemann zeta function.     

What do the Chinese value in (mathematics) education?

The achievement in mathematics among the Chinese has aroused the interest of educationalists, sociologists and psychologists worldwide. The coining of the term Confucian Heritage Culture learner??s phenomenon mistakenly led researchers to look for direct attributions from Confucianism, without realizing that Confucianism is just one Chinese school of thought, and it is over-simplistic to draw causal relationships between schools of thought and social phenomena. This paper begins by introducing three major Chinese schools of thought??Confucianism, Daoism and Buddhism??and their views on education. The discussion will then focus on how these schools of thought might impact education in general and mathematics education in particular.     

Initial boundary value problems for the nonlinear Schrödinger equation

A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix $\bar \partial $ problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.     

Dirichlet problem for Schrödinger equation with the boundary value in the BMO space

Science China Mathematics - Let (X, d, μ) be a metric measure space satisfying a Q-doubling condition (Q &gt; 1) and an L2-Poincaré inequality. Let $${\cal L} = {\cal L} + V$$ be a...     

On the value distribution of f a(f')~n

Let f be a transcendental meromorphic function,a a nonzero finite complex number,and n 2 a positive integer.Then f a(f')n assumes every complex value infinitely often.This answers a question of Ye for n = 2.A related normality criterion is also given.     

Symplectic and contact properties of the Mañé critical value of the universal cover

We discuss several symplectic aspects related to the Mañé critical value c _u of the universal cover of a Tonelli Hamiltonian. In particular we show that the critical energy level is never of virtual contact type for manifolds of dimension greater than or equal to three. We also show the symplectic invariance of the finiteness of the Peierls barrier and the Aubry set of the universal cover. We also provide an example where c _u coincides with the infimum of Mather’s α function but the Aubry set of the universal cover is empty and the Peierls barrier is finite. A second example exhibits all the ergodic invariant minimizing measures with zero homotopy, showing, quite surprinsingly, that the union of their supports is not a graph, in contrast with Mather’s celebrated graph theorem.     

On the convergence at infinity of the Leray solution of the two-dimensional Navier–Stokes equations to the prescribed asymptotic value

In this Note we prove that $\text{v}{}_{\mathrm{L}}\text{～}$, the Leray velocity solution to the steady incompressible, two-dimensional Navier–Stokes equations, tends at infinity to the prescribed vector $\text{v}{}_{\mathrm{\infty }}\text{～}\text{.}$ We show also that the sequence of Leray solutions to the same boundary value problem in the bounded domains converges quasi-uniformly in $\text{Ω}$ to $\text{(}\text{v}{}_{\mathrm{L}}\text{～}\text{,p}{}_{\mathrm{L}}\text{).}$To cite this article: D. Socolescu, C. R. Acad. Sci. Paris, Ser. I 336 (2003).