Abstract We study a system of n Abelian vector fields coupled to $$\frac{1}{2} n(n+1)$$ 1 2 n ( + ) complex scalars parametrising the Hermitian symmetric space $${\textsf{Sp}}(2...

let $mathcal{a}$ be a banach algebra and $mathcal{m}$ be a banach $mathcal{a}$-bimodule. we say that a linear mapping $delta:mathcal{a} rightarrow mathcal{m}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{a} rightarrow mathcal{m}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{a}$. giving some facts concerning general...

We derive the coherent state representation of the integrable spin chain Hamil-tonian with non-compact supersymmetry group G =SU(1, 1|1). By passing to the continuous limit, we find a spin chain sigma model describing a string moving on the supercoset G/H, H being the stabilizer group. The action is written in a manifestly G-invariant form in terms of the Cartan forms and the string coordinates...

Investigated in this paper are the uniform approximation capabilities of sum-of-product (SOPNN) and sigma-pi-sigma (SPSNN) neural networks. It is proved that the set of functions that are generated by an SOPNN with its activation function in C(R) is dense in C(K) for any compact K ∈ R , if and only if the activation function is not a polynomial. It is also shown that if the activation function ...

The target space of a nonlinear sigma model is usually required to be positive definite to avoid ghosts. We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, thus the associated group being non-compact. We show that the would-be ghost associated with the negative direction is fully projected out by 2 second-class constraints, and there ...

In this article‎, ‎we have characterized ideals in $C(X)$ in which‎ ‎every ideal is also an ideal (a $z$-ideal) of $C(X)$‎. ‎Motivated by‎ ‎this characterization‎, ‎we observe that $C_infty(X)$ is a regular‎ ‎ring if and only if every open locally compact $sigma$-compact‎ ‎subset of $X$ is finite‎. ‎Concerning prime ideals‎, ‎it is shown that‎ ‎the sum of every two prime (semiprime) ideals of e...

Abstract We prove that the solid ergodicity property is stable with respect to taking coinduction for a fairly large class of coinduced action. More precisely, assume $\Sigma <\Gamma $ are countable groups such $g\Sigma g^{-1}\cap \Sigma finite any $g\in \Gamma \setminus $. Then measure preserving action \curvearrowright X_0$ gives rise solidly ergodic equivalence relation if and only as...

We use an extension of Gordon-Litherland pairing to thickened surfaces give a topological characterization alternating links in surfaces. If $\Sigma$ is closed oriented surface and $F$ compact unoriented $\Sigma \times I$, then the defines symmetric bilinear on first homology $F$. A I$ called definite if its form. prove that non-split link $L$ only it bounds two opposite sign.