Localized tachyon mass and a g-theorem analogue

We study the localized tachyon condensation (LTC) of non-supersymmetric orbifold backgrounds in their mirror Landau-Ginzburg picture. Using he existence of four copies of (2,2) worldsheet supersymmetry, we show at the CFT level, that the minimal tachyon mass in twisted sectors shows somewhat analogous properties of c- or g-function. Namely, $m := |\alpha' M^2_{min}|$ satisfies $m(M) \geq m(D_1\oplus D_2)={\rm max} \{m(D_1),m(D_2)\}$. $c$- $g$- $m$- functions share the common property $f(M)\geq f(D_1\oplus D_2)$ for $f=c,g,m$, although they have different behavior in detail.Comment: 15 pages, no figure, to appear in NP

Uniqueness theorem for inverse scattering problem with non-overdetermined data

Let $q(x)$ be real-valued compactly supported sufficiently smooth function, $q\in H^\ell_0(B_a)$, $B_a:=\{x: |x|\leq a, x\in R^3$ . It is proved that the scattering data $A(-\beta,\beta,k)$ $\forall \beta\in S^2$, $\forall k>0$ determine $q$ uniquely. here $A(\beta,\alpha,k)$ is the scattering amplitude, corresponding to the potential $q$

Uniqueness of the solution to inverse scattering problem with scattering data at a fixed direction of the incident wave

Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(\beta,\alpha_0,k)$ $\forall \beta\in S^2$, $\forall k>0,$ determine $q$ uniquely. Here $\alpha_0\in S^2$ is a fixed direction of the incident plane wave

Energy Distribution of a G\"{o}del-Type Space-Time

We calculate the energy and momentum distributions associated with a G\"{o}del-type space-time, using the well-known energy-momentum complexes of Landau and Lifshitz and M{\o}ller. We show that the definitions of Landau and Lifshitz and M{\o}ller do not furnish a consistent result.Comment: LaTex, no figure