On the deformation of abelian integrals

We consider the deformation of abelian integrals which arose from the study of SG form factors. Besides the known properties they are shown to satisfy Riemann bilinear identity. The deformation of intersection number of cycles on hyperelliptic curve is introduced.Comment: 8 pages, AMSTE

Derivations in the Banach ideals of τ\tau-compact operators

Let $\mathcal{M}$ be a von Neumann algebra equipped with a faithful normal semi-finite trace $\tau$ and let $S_0(\tau)$ be the algebra of all $\tau$-compact operators affiliated with $\mathcal{M}$. Let $E(\tau)\subseteq S_0(\tau)$ be a symmetric operator space (on $\mathcal{M}$) and let $\mathcal{E}$ be a symmetrically-normed Banach ideal of $\tau$-compact operators in $\mathcal{M}$. We study (i) derivations $\delta$ on $\mathcal{M}$ with the range in $E(\tau)$ and (ii) derivations on the Banach algebra $\mathcal{E}$. In the first case our main results assert that such derivations are continuous (with respect to the norm topologies) and also inner (under some mild assumptions on $E(\tau)$). In the second case we show that any such derivation is necessarily inner when $\mathcal{M}$ is a type $I$ factor. As an interesting application of our results for the case (i) we deduce that any derivation from $\mathcal{M}$ into an $L_p$-space, $L_p(\mathcal{M},\tau)$, ($1<p<\infty$) associated with $\mathcal{M}$ is inner

Commutator estimates in W∗W^*-factors

Let $\mathcal{M}$ be a $W^*$-factor and let $S\left( \mathcal{M} \right)$ be the space of all measurable operators affiliated with $\mathcal{M}$. It is shown that for any self-adjoint element $a\in S(\mathcal{M})$ there exists a scalar $\lambda_0\in\mathbb{R}$, such that for all $\varepsilon > 0$, there exists a unitary element $u_\varepsilon$ from $\mathcal{M}$, satisfying $|[a,u_\varepsilon]| \geq (1-\varepsilon)|a-\lambda_0\mathbf{1}|$. A corollary of this result is that for any derivation $\delta$ on $\mathcal{M}$ with the range in an ideal $I\subseteq\mathcal{M}$, the derivation $\delta$ is inner, that is $\delta(\cdot)=\delta_a(\cdot)=[a,\cdot]$, and $a\in I$. Similar results are also obtained for inner derivations on $S(\mathcal{M})$.Comment: 21 page

The Competitive Advantage of Outstanding the Products and Services of the Nigerian Service Industry

The study examines the concept of outsourcing and the possible impact it has on the competitive advantage it has on a company in Nigerian economy. Outsourcing is the practice in which companies move or contract out some or all of their products or service operations to other companies that specialize in those operations or to companies in other countries. The problems indentified in the Nigeria service industry are high operating cost having negative impact on return on capital employed, sub-optimality in production because of ineffective utilization of resources and inability of organization to identify areas of core competence for competitive advantage. The main objective of this paper is to evaluate the competitive advantag

Raising and lowering operators and their factorization for generalized orthogonal polynomials of hypergeometric type on homogeneous and non-homogeneous lattice

We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal polynomials, namely, those difference of orthogonal polynomials that satisfy a similar difference equation of hypergeometric type.Comment: LaTeX, 19 pages, (late submission to arXiv.org

Application of crossflow ultrafiltration for scaling up the purification of a recombinant ferritin

Ferritin proteins are taking center stage as smart nanocarriers for drug delivery due to their hollow cage-like structures and their unique 24-meric assembly. Among all ferritins, the chimeric Archaeoglobus ferritin (HumFt) is able assemble/disassemble varying the ionic strength of the medium while recognizing human TfR1 receptor overexpressed in cancer cells. In this paper we present a highly efficient, large scale purification protocol mainly based on crossflow ultrafiltration, starting from fermented bacterial paste. This procedure allows one to obtain about 2 g of purified protein starting from 100 g of fermented bacterial paste. The current procedure can easily remove contaminant proteins as well as DNA molecules in the absence of expensive and time consuming chromatographic steps

Observational Features of Black Holes

Recently considered a very attracting possibility to detect retro-MACHOs, i.e. retro-images of the Sun by a Schwarzschild black hole. In this paper we discuss glories (mirages) formed near rapidly rotating Kerr black hole horizons and propose a procedure to measure masses and rotation parameters analyzing these forms of mirages. In some sense that is a manifestation of gravitational lens effect in the strong gravitational field near black hole horizon and a generalization of the retro-gravitational lens phenomenon. We analyze the case of a Kerr black hole rotating at arbitrary speed for some selected positions of a distant observer with respect to the equatorial plane of a Kerr black hole. We discuss glories (mirages) formed near rapidly rotating Kerr black hole horizons and propose a procedure to measure masses and rotation parameters analyzing these forms of mirages. Some time ago suggested to search shadows at the Galactic Center. In this paper we present the boundaries for shadows calculated numerically. We also propose to use future radio interferometer RADIOASTRON facilities to measure shapes of mirages (glories) and to evaluate the black hole spin as a function of the position angle of a distant observer.Comment: Plenary talk presented at Workshop on High Energy Physics&Field Theory (Protvino, Russia, 2004

Baxter equations and Deformation of Abelian Differentials

In this paper the proofs are given of important properties of deformed Abelian differentials introduced earlier in connection with quantum integrable systems. The starting point of the construction is Baxter equation. In particular, we prove Riemann bilinear relation. Duality plays important role in our consideration. Classical limit is considered in details.Comment: 28 pages, 1 figur