This paper is concerned with the hyperbolic conservation law M i\ Sxa . db(u) _ St + ^ x ^ ~ ° (1.2) u(x,O) = f (x) . By means of the Crandall-Liggett theory of nonlinear semigroups ([1]), it will be shown that the operator A : u H-> ——b(u) Q. X generates a semigroup S = {Sfc; t ;> 0} of contraction operators on L (IR). The function t h-» S.f may then be thought of as a generalized solution of ...

In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute directly the partial derivatives of functions defined on triangular meshes which are the discretization of regular surfaces under consideration. Most import...

We investigate an idealized model of microtubule dynamics that involves: (i) attachment of guanosine triphosphate (GTP) at rate λ, (ii) conversion of GTP to guanosine diphosphate (GDP) at rate 1, and (iii) detachment of GDP at rate μ. As a function of these rates, a microtubule can grow steadily or its length can fluctuate wildly. For μ = 0, we find the exact tubule and GTP cap length distribut...

Consider a probability measure μ supported by a regular geodesic ball in a manifold. For any p ≥ 1 we define a stochastic algorithm which converges almost surely to the p-mean ep of μ. Assuming furthermore that the functional to minimize is regular around ep, we prove that a natural renormalization of the inhomogeneous Markov chain converges in law into an inhomogeneous diffusion process. We gi...

Abstract. For a finite typed graph on n nodes and with type law μ, we define the socalled spectral potential ρλ( ·, μ), of the graph.From the ρλ( ·, μ) we obtain Kullback action or the deviation function, Hλ(π ‖ ν), with respect to an empirical pair measure, π, as the Legendre dual. For the finite typed random graph conditioned to have an empirical link measure π and empirical type measure μ, w...

Let {X,Xn}n∈N be a sequence of independent and identically distributed i.i.d. positive random variables with a nondegenerate distribution function and EX μ > 0. For each n ≥ 1, the symbol Sn/Vn denotes self-normalized partial sums, where Sn ∑n i 1 Xi and V 2 n ∑n i 1 Xi − μ . We say that the random variable X belongs to the domain of attraction of the normal law if there exist constants an > 0,...

The use of the symbolic software package GeM for Maple is illustrated with examples of computation of nonlocal symmetries and nonlocal conservation laws of nonlinear partial differential equations. In the considered examples, the nonlocal symmetries and conservation laws arise as local symmetries and conservation laws of potential systems. FullMaple codewith detailed comments is presented. Exam...

We show that the Schrödinger equation is a lift of Newton’s third law of motion ∇μ̇ μ̇ = −∇WF (μ) on the space of probability measures, where derivatives are taken w.r.t. the Wasserstein Riemannian metric. Here the potential μ → F (μ) is the sum of the total classical potential energy 〈V, μ〉 of the extended system and its Fisher information ~2 8 ∫ |∇ ln μ|2dμ. The precise relation is established ...

In this paper, an approach for the computation of bounds on parametric model uncertainty for robust control design is proposed. The approach uses μ sensitivities to identify which uncertain parameters in the model are most critical in terms of closed-loop robustness objectives. Using skewed μ analysis tools, the maximum possible uncertainty bounds for model parameters which are most difficult o...

Abstract—In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem ...