In this paper, we will give a simpler proof for the uniqueness in the following inverse problem which we have already discussed in Preprint UTMS 2001-30 (Graduate School of Mathematical Sciences, The University of Tokyo, 2001):We consider an inverse problem of identifying the support D of a source term in an elliptic equation −∆u(x) + q(x)χD(x)u(x) = 0, x ∈ Ω and u(x) = f(x), x ∈ ∂Ω. Here q is ...

There are two cases where it is well known that Schriidinger operators have non-degenerate eigenvalues: The lowest eigenvalue in general dimension and all one-dimensional eigenvalues. One can ask about making this quantitative, i.e., obtain explicit lower bounds on the distance to the nearest eigenvalues. Obviously, one cannot hope to do this without any restrictions on V since, for example, if...

Consider a function f : f0;1g n ! f0;1g. The sensitivity of a point v 2 f0;1g n is jfv 0 : f (v 0) 6 = f (v); dist(v; v 0) = 1gj, i.e. the number of neighbors of the point in the discrete cube on which the value of f diiers. The average sensitivity of f is the average of the sensitivity of all points in f0;1g n. (This can also be interpreted as the sum of the innuences of the n variables on f ,...

We study C0-operators relative to a multiply connected domain using a substitute of the characteristic function. This method allows us to prove certain relations between the Jordan model of an operator and that of its restriction to an invariant subspace.

We propose stochastic N -component synchronization models (x1(t), . . . , xN (t)), xj ∈ Rd, t ∈ R+, whose dynamics is described by Lévy processes and synchronizing jumps. We prove that symmetric models reach synchronization in a stochastic sense: differences between components d (N) kj (t) = xk(t)−xj(t) have limits in distribution as t → ∞. We give conditions of existence of natural (intrinsic)...

Let D be a bounded domain in Rn such that ∂D is a union of a finite number of smooth hypersurfaces in general position. The asymptotics of the Fourier transform of a piece-wise smooth function f(x) with discontinuities of the first kind on ∂D, in particular of the characteristic function of D, is found in almost all directions. The results are based on our recent work on the singularities of th...

We consider the convolution model where i.i.d. random variables Xi having unknown density f are observed with additive i.i.d. noise, independent of the X’s. We assume that the density f belongs to either a Sobolev class or a class of supersmooth functions. The noise distribution is known and its characteristic function decays either polynomially or exponentially asymptotically. We consider the ...

Recently K. Murota has introduced concepts of L-convex function and Mconvex function as generalizations of those of submodular function and base polyhedron, respectively, and has shown separation theorems for L-convex/concave functions and for M-convex/concave functions. The present note gives short alternative proofs of the separation theorems by relating them to the ordinary separation theore...

in this paper, we propose a new method for fuzzy numbers. in this method, we assume that ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. so, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. then, mic and mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. finally,...