We consider the inverse boundary value problem in two dimensions of determining the coefficients of a general second-order elliptic operator from the Cauchy data measured on a nonempty arbitrary relatively open subset of the boundary. We give a complete characterization of the set of coefficients yielding the same partial Cauchy data. As a corollary we prove several uniqueness results in determ...

We obtain some results in both, Lorentz and Finsler geometries, by using a correspondence between the conformal structure of standard stationary spacetimes on M = R × S and Randers metrics on S. In particular: (1) For stationary spacetimes: we give a simple characterization on when R×S is causally continuous or globally hyperbolic (including in the latter case, when S is a Cauchy hypersurface),...

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

For sequences of fuzzy numbers, Nanda 1 studied the sequences of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers forms a complete metric space. Kwon 2 introduced the definition of strongly p-Cesàro summability of sequences of fuzzy numbers. Savaş 3 introduced and discussed double convergent sequences of fuzzy numbers and showed that the set of all double conve...

In this paper, we review two properties of completeness known as the Bourbaki-completeness and cofinal in setting metric spaces. These notions came from new classes generalized Cauchy sequences appearing when characterizing so-called Bourbaki-boundedness a similar way that characterize totally boundedness. For clustering Bourbaki–Cauchy cofinally sequences, have respectively what is call The to...

Let D be the sheaf of analytic differential operators of n variables x1, . . . , xn. We consider a left ideal I of D generated by {l1, . . . , lm} which are in the Weyl algebra D = C〈x1, . . . , xn, ∂1, . . . , ∂n〉. If no confusion arises, we also denote by I the left ideal D ·{l1, . . . , ln} in D. Assume that D/I is holonomic. It was proved by M.Kashiwara that the germs of the k-th extension ...

In this paper, we study some basic properties of bicomplex numbers. We introduce two different types partial order relations on numbers, discuss valued metric spaces with respect to orders, and compare them. also define a hyperbolic space, the density natural statistical convergence, Cauchy property sequence numbers investigate in space prove that is complete if only complex are complete.