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...

Let (M,g,Ω) be the conformal rescaling of a 3+1 dimensional vacuum spacetime (M̃, g̃), with g = Ωg̃, where Ω is a smooth function on M vanishing on the boundary ∂M. If M has smooth null boundary I , with connected components of topology S2×R, it follows that the Weyl tensor of (M,g) vanishes on I . From this follows peeling properties for (M̃, g̃). This picture of isolated systems in general relativ...

The nature of elastic deformation is examined in the light of the potential theory. The concepts and mathematical treatment of elasticity and the choice of equilibrium conditions are adopted from the mechanics of discrete bodies, e. g., celestial mechanics; they are not applicable to a change of state. By nature, elastic deformation is energetically a Poisson problem since the buildup of an ela...

Statistical convergence has been a prominent research area in mathematics since this concept was independently introduced by Fast and Steinhaus 1951. Afterward, the statistical of double sequences metric spaces fuzzy widely studied. The main goal present study is to introduce concepts Cauchy for intuitionistic spaces. Moreover, characterizes sequence an ordinary convergent subsequence sequence....

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...

We propose an optimization methodology suitable for the design of various antenna structures. This methodology includes a rapidly-converging iterative scheme. In each iteration stage, the algorithm generates a parameterized Cauchy model using the available results from previous iterations. Optimization is then applied to this Cauchy model to obtain better design parameters that are also used in...

What is the stability of recovering the location of xj . Suppose the number of point sources is known as m. Or we formulate the stability argument as following statement. Statement 1.1 If ul for l = 1, 2 be the solutions of equation 1 associated with Cauchy data (f , g) and sources F l = ∑m j=1 P l jδ(x − xj), if we have ‖(f, g) − (f, g)‖ ≤ , can we find a permutation π of {1, 2, . . . ,m} such...

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.