This paper deals with an inverse problem of determining the shape and location of inhomogeneity D in an elliptic equation with a Neumann boundary condition ∂u ∂ν = g on ∂Ω −∆u(x) + pχD(x)u(x) = 0, x ∈ Ω, where D ⊂ Ω and χD is the characteristic function of a subdomain D. We prove the global uniqueness in this inverse problem by a single measurement of Dirichlet data u on ∂Ω.

This note is a supplement to some recent work of R.B. Bapat on Moore-Penrose inverses of set inclusion matrices. Among other things Bapat constructs these inverses (in case of existence) forH(s, k) mod p, p an arbitrary prime, 0 ≤ s ≤ k ≤ v − s. Here we restrict ourselves to p = 2. We give conditions for s, k which are easy to state and which ensure that the Moore-Penrose inverse of H(s, k) mod...

In this article, we have considered Wick-type stochastic Korteweg de Vries (KdV) equation with conformable derivatives. By the help of white noise analysis, Hermit transform and extended G?/G- expansion method, obtained exact travelling wave solutions KdV We applied inverse for soliton then shown how can be presented as Brownian motion functional by an application example.

We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions f ,g. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to quaternion fields to conform with the OPS determined by f ,g, or by only one pure unit quaternion f , comment on their geometric meaning, and establish invers...

We give some extensions of the classical chain rule rg(u)] = g 0 (u)ru and of the chain rule for transport operators a rg(u)] = g 0 (u) a ru, a 2 W 1;1 , via an inverse Sard lemma. Coeecients a of bounded variation are also treated in the case of a Vlasov operator.

We present an algorithm which, for any given black box group G isomorphic to Sp(d, q), constructs explicit inverse isomorphisms between G and the standard copy of Sp(d, q). We also report on the performance of an implementation of this algorithm in the group theory system GAP.

The purpose of this note is to define a graph whose vertex set finite group G $G$ , edge contained in that the commuting and contains enhanced power . We call deep Two elements are joined if only their inverse images every central extension commute. give conditions for be equal either graph, show automorphisms act as graph.

For a graph $G$, we associate family of real symmetric matrices, $\mathcal{S}(G)$, where for any $M \in \mathcal{S}(G)$, the location nonzero off-diagonal entries $M$ is governed by adjacency structure $G$. The ordered multiplicity Inverse Eigenvalue Problem Graph (IEPG) concerned with finding all attainable lists eigenvalue multiplicities matrices in $\mathcal{S}(G)$. connected graphs order si...

Recursive modelling for the kinematics and dynamics of the known 3-PRR planar parallel robot is established in this paper. Three identical planar legs connecting to the moving platform are located in a vertical plane. Knowing themotion of the platform,we develop first the inverse kinematics and determine the positions, velocities and accelerations of the robot. Further, the principle of virtual...

In this paper, by considering the g-circulant matrix Cn,g(H) = gcirc(Hk,1,Hk,2, . . . ,Hk,n) whose entries are the generalized k-Horadam numbers, we present a new generalization to compute spectral norm, determinant and inverse of Cn,g(H). In fact the results in here are the most general statements to obtain the inverses and determinants in such matrices having the elements of all second order ...