We consider a compact perturbation $H_0 = S + K_0^* K_0$ of self-adjoint operator $S$ with an eigenvalue $\lambda^\circ$ below its essential spectrum and the corresponding eigenfunction $f$. The is assumed to be "along" $f$, namely $K_0f=0$. belongs spectra both $H_0$ $S$. Let have $\sigma$ more eigenvalues than $H_0$; known as spectral shift at $\lambda^\circ$. now allow vary in suitable space...

We present an exact duality transformation in the framework of Statistical Mechanics for various lattice models with non-Abelian global or local symmetries. The transformation applies to sigma models with variables in a compact Lie group G with global G×G-symmetry (the chiral model) and with variables in coset spaces G/H and a global G-symmetry (for example, the non-linear O(N) or RPN models) i...

This paper presents a new design of a discrete time Delta-Sigma (∆Σ) oversampled ultrasound beamformer which integrates individual channel apodization by means of variable feedback voltage in the Delta-Sigma analog to digital (A/D) converters. The output bit-width of each oversampled A/D converter remains the same as in an unmodified one. The outputs of all receiving channels are delayed and su...

‎given a finite non-cyclic group $g$‎, ‎call $sigma(g)$ the smallest number of proper subgroups of $g$ needed to cover $g$‎. ‎lucchini and detomi conjectured that if a nonabelian group $g$ is such that $sigma(g) < sigma(g/n)$ for every non-trivial normal subgroup $n$ of $g$ then $g$ is textit{monolithic}‎, ‎meaning that it admits a unique minimal normal subgroup‎. ‎in this paper we show how thi...

Let ${\mathcal M}\subset {\mathbb R}^n$ be a $C^2$-smooth compact submanifold of dimension $d$. Assume that the volume M}$ is at most $V$ and reach (i.e. normal injectivity radius) greater than $\tau$. Moreover, let $\mu$ probability measure on which density strictly positive Lipschitz-smooth function. $x_j\in {\mathcal M}$, $j=1,2,\dots,N$ $N$ independent random samples from distribution $\mu$...

let $g$ be a simple graph with an orientation $sigma$‎, ‎which ‎assigns to each edge a direction so that $g^sigma$ becomes a‎ ‎directed graph‎. ‎$g$ is said to be the underlying graph of the‎ ‎directed graph $g^sigma$‎. ‎in this paper‎, ‎we define a weighted skew‎ ‎adjacency matrix with rand'c weight‎, ‎the skew randi'c matrix ${bf‎ ‎r_s}(g^sigma)$‎, ‎of $g^sigma$ as the real skew symmetric mat...

Let $A$ be a Banach ternary algebra over a scalar field $Bbb R$ or $Bbb C$ and $X$ be a ternary Banach $A$--module. Let $sigma,tau$ and $xi$ be linear mappings on $A$, a linear mapping $D:(A,[~]_A)to (X,[~]_X)$ is called a Lie ternary $(sigma,tau,xi)$--derivation, if $$D([a,b,c])=[[D(a)bc]_X]_{(sigma,tau,xi)}-[[D(c)ba]_X]_{(sigma,tau,xi)}$$ for all $a,b,cin A$, where $[abc]_{(sigma,tau,xi)}=ata...

Let $\Sigma$ be a compact oriented surface. The Dehn twist along every simple closed curve $\gamma \subset \Sigma$ induces an automorphism of the fundamental group $\pi$ $\Sigma$. There are two possible ways to generalize such automorphisms if $\gamma$ is allowed have self-intersections. One way consider `generalized twist' $\gamma$: Malcev completion whose definition involves intersection oper...

We establish the long time existence of complete non-compact weakly convex and smooth hypersurfaces $$\Sigma _t$$ evolving by $$Q_k$$ -flow. show that maximum T depends on dimension $$d_W$$ vector space $$W{:}{=}\{w \in \mathbb {R}^{n+1}: \sup _{X\in \Sigma _0} |\langle X,w\rangle | = +\infty \}$$ which contains each direction in our initial data _0$$ is infinite. If $$d_W=\text {dim}(W) \ge n-...