Potential anomalies are analysed for the local spin-3 and spin-4 classically conserved currents in any two-dimensional sigma model on a compact symmetric space G/H, with G and H classical groups. Quantum local conserved charges are shown to exist in exactly those models which also possess quantum non-local (Yangian) charges. The possibility of larger sets of quantum local charges is discussed a...

Supergravities in four and higher dimensions are reviewed. We discuss the action and its local symmetries of N = 1 supergravity in four dimensions, possible types of spinors in various dimensions, field contents of supergravity multiplets, non-compact bosonic symmetries, non-linear sigma models, duality symmetries of antisymmetric tensor fields and super p-branes. An expanded version of a revie...

Every classical sigma-model with target space a compact symmetric space G/H (with G classical) is shown to possess infinitely many local, commuting, conserved charges which can be written in closed form. The spins of these charges run over a characteristic set of values, playing the role of exponents of G/H, and repeating modulo an integer h which plays the role of a Coxeter number.

‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is i...

Let $F/F_{\mathsf{o}}$ be a quadratic extension of non-archimedean locally compact fields odd residual characteristic and $\sigma$ its non-trivial automorphism. We show that any $\sigma$-self-dual cuspidal representation ${\rm GL}_n(F)$ contains Bushnell--Kutzko type. Using such type, we construct an explicit test vector for Flicker's local Asai $L$-function GL}_n(F_{\mathsf{o}})$-distinguished...

six sigma methodology is one of the most famous effective problem solving approaches that helps organizations to achieve their goals. despite the variety of its positive advantage, most companies have failed to implement six sigma successfully. the reason for this includes lack of the organizations attention to success or failure factors when implement six sigma projects. hence, while performin...

It is shown that a locally compact second countable group $G$ has the Haagerup property if and only there exists sharply weak mixing 0-type measure preserving free $G$-action $T=(T_g)_{g\in G}$ on an infinite $\sigma $-finite standard space $

We introduce the moduli space of quasi-parabolic $SL(2,\mathbb{C})$-Higgs bundles over a compact Riemann surface $\Sigma$ and consider natural involution, studying its fixed point locus when is $\mathbb{C} \mathbb{P}^1$ establishing an identification with null polygons in Minkowski $3$-space.

Let A be an abelian variety over the function field K of a compact Riemann surface B. Fix model $$f :{\mathcal {A}} \rightarrow B$$ A/K and effective horizontal divisor $${\mathcal {D}}\subset {\mathcal {A}}$$ . We give sufficient condition on {D}}$$ for finiteness set $$(S, {D}})$$ -integral sections every finite subset $$S \subset These integral $$\sigma $$ are algebraic satisfy geometric ( \...

This paper characterizes a compact piece of the helicoid $H_C$ in solid cylinder $C \subset \mathbb{R}^3$ from following two perspectives. First, under reasonable conditions, has smallest area among all immersed surfaces $\Sigma$ with $\partial \Sigma d_1 \cup d_2 S$, where $d_1$ and $d_2$ are diameters top bottom disks $C$ $S$ is side surface $C$. Second, other than $H_C$, there exists no mini...