Abstract Let $\Sigma $ be a compact surface with boundary. For given conformal class c on the functional $\sigma _k^*(\Sigma ,c)$ is defined as supremum of k th normalized Steklov eigenvalue over all metrics in . We consider behavior this moduli space classes A precise formula for limit ,c_n)$ when sequence $\{c_n\}$ degenerates obtained. apply to study natural analogs Friedlander–Nadirashvili ...

We discuss the relationship between the phase diagram of the Q = 0 state Potts model, the arboreal gas model, and the supersphere sigma model S = OSP (1/2)/OSP (0/2). We identify the Potts antiferromagnetic critical point with the critical point of the arboreal gas (at negative tree fugacity), and with a critical point of the sigma model. We show that the corresponding conformal theory on the s...

In this work we study the issue of geodesic extendibility on complete and locally compact metric length spaces. We focus geometric structure space $(\Sigma (X),d_H)$ balls endowed with Hausdorff distance give an explicit isometry between closed half-space $ X\times \mathbb{R}_{\ge 0}$ a taxicab metric. Among applications establish group $\mbox{Iso} (X,d)$ (\Sigma when $(X,d)$ is Hadamard space.

We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (“quantum mechanical path integrals in curved space”) dimensional regularization requires only a covariant finite two-loop counterterm. This counterterm is nonvanishing and given by 1 8 h̄R. E-mail: [email protected] E-...

We discuss new methods for non-compact sigma models with and without RR fluxes.The methods include reduction to one dimensional supermagnets,supercoset constructions and supertwistors.This work is a first step towards the solution of these models,which are important in several areas of physics. I dedicate it to the memory of Volodya Gribov.

Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $sigma$ be a semi-prime operation, different from the identity map on the set of all ideals of $A$. Results of Essan proved that the sets of associated prime ideals of $sigma(I^n)$, which denoted by $Ass(A/sigma(I^n))$, stabilize to $A_{sigma}(I)$. We give some properties of the sets $S^{sigma}_{n}(I)=Ass(A/sigma(I^n))setminus A_{sigma}(I...

let $g$ be a simple graph‎, ‎and $g^{sigma}$‎ ‎be an oriented graph of $g$ with the orientation ‎$sigma$ and skew-adjacency matrix $s(g^{sigma})$‎. ‎the $k-$th skew spectral‎ ‎moment of $g^{sigma}$‎, ‎denoted by‎ ‎$t_k(g^{sigma})$‎, ‎is defined as $sum_{i=1}^{n}( ‎‎‎lambda_{i})^{k}$‎, ‎where $lambda_{1}‎, ‎lambda_{2},cdots‎, ‎lambda_{n}$ are the eigenvalues of $g^{sigma}$‎. ‎suppose‎ ‎$g^{sigma...

We consider the focusing inhomogeneous nonlinear Schrödinger (INLS) equation in $${\mathbb {R}}^N$$ $$\begin{aligned} i \partial _t u +\Delta + |x|^{-b} |u|^{2\sigma }u = 0, \end{aligned}$$ where $$N\ge 2$$ and $$\sigma $$ , $$b>0$$ . first obtain a small data global result $$H^1$$ which, two spatial dimensional case, improves third author [22] on range of b. For 3$$ $$\frac{2-b}{N}<\sigma <\fr...