Abstract:
Integrins mediate cell adhesion, migration, and survival by connecting intracellular machinery with the surrounding extracellular matrix. Previous studies demonstrated the importance of the interaction between β3 integrin and VEGF type 2 receptor (VEGFR2) in VEGF-induced angiogenesis. Here we present in vitro evidence of the direct association between the cytoplasmic tails (CTs) of β3 and VEGFR2. Specifically, the membrane-proximal motif around 801YLSI in VEGFR2 mediates its binding to non-phosphorylated β3CT, accommodating an α-helical turn in integrin bound conformation. We also show that Y747 phosphorylation of β3 enhances the above interaction. To demonstrate the importance of β3 phosphorylation in endothelial cell functions, we synthesized β3CT-mimicking Y747 phosphorylated and unphosphorylated membrane permeable peptides. We show that a peptide containing phospho-Y747 but not F747 significantly inhibits VEGF-induced signaling and angiogenesis. Moreover, phospho-Y747 peptide exhibits inhibitory effect only in WT but not in β3 integrin knock-out or β3 integrin knock-in cells expressing β3 with two tyrosines substituted for phenylalanines, demonstrating its specificity. Importantly, these peptides have no effect on fibroblast growth factor receptor signaling. Collectively these data provide novel mechanistic insights into phosphorylation dependent cross-talk between integrin and VEGFR2.

Abstract:
A study is made on the previously ignored problem of the dependence of a static fluorescence quenching Stern-Volmer constant K_{sv} on the initial concentration of [F]_{0} fluorophore F. This correlation is shown to exist. It is concluded that the Stern-Volmer quenching constant may be used as association constant K only with .

Abstract:
In conditions of monochromatic excitation (λ_{exc}=337.1), the spectral dependence of the efficiency of fluorescence quenching α_{λ} of humic acids samples by Cd^{2+} and Cu^{2+} ions was studied. The difference of α_{λ} dependencies for these ions was established. In the spectral range 350 - 650 nm, changes of the α_{λ} for Cd^{2+} ion are markedly different from the magnitude for changes α_{λ}, which occur for ion Cu^{2+}. The interpretation of mismatch dependences obtained α_{λ} ions Cd^{2+} and Cu^{2+} is carried out within the concept of the availability of different sites, due to the difference in ionic radii (0.108 nm and 0.08 nm for Cd^{2+} and Cu^{2+}, respectively).

Abstract:
We consider finite nilpotent groups of matrices over commutative rings. A general result concerning the diagonalization of matrix groups in the terms of simple conditions for matrix entries is proven. We also give some arithmetic applications for representations over Dedekind rings. 1. Introduction In this paper we consider representations of finite nilpotent groups over certain commutative rings. There are some classical and new methods for diagonalizing matrices with entries in commutative rings (see [1, 2]) and the classical theorems on diagonalization over the ring of rational integers originate from the papers by Minkowski; see [3–5]. We refer to [6–8] for the background and basic definitions. First we prove a general result concerning the diagonalization of matrix groups. This result gives a new approach to using congruence conditions for representations over Dedekind rings. The applications have some arithmetic motivation coming back to Feit [9] and involving various arithmetic aspects, for instance, the results by Bartels on Galois cohomologies [10] (see also [11–14] for some related topics) and Bürgisser [15] on determining torsion elements in the reduced projective class group or the results by Roquette [16]. Throughout the paper we will use the following notations. , , , , , , and denote the fields of complex and real numbers, rationals and -adic rationals, the ring of rational and -adic rational integers, and the ring of integers of a local or global field , respectively. denotes the general linear group over . denotes the degree of the field extension . denotes the unit matrix. is a diagonal matrix having diagonal components . denotes the order of a finite group . Theorem 1. Let be a commutative ring, which is an integral domain, and let be a finite nilpotent group indecomposable in . Let one suppose that every matrix is conjugate in to a diagonal matrix. Then any of the following conditions implies that is conjugate in to a group of diagonal matrices:(i)every matrix in has at least one diagonal element ,(ii) is not contained in , where is the identity matrix, and for any matrix in , there are 2 indices such that and . For the proof of Theorem 1 we need the following. Proposition 2. If the centre of a finite subgroup for a commutative ring , which is an integral domain, contains a diagonal matrix , then is decomposable. Proof. After a conjugation by a permutation matrix we can assume that where for and contains elements that equal , . For a matrix consider the system of linear equations determined by the conditions ; this immediately

Abstract:
The work presents studies
on the complex permittivity and permeability of composites based on
acrylonitrile butadiene rubber containing combinations of conductive fillers
which include carbon black and nickel powder. The properties of those
composites, containing each of the fillers at the same amount were compared.
The permittivity and permeability values of the composites are influenced
remarkably by their morphology and structure as well as by the morphological
and structural specifics of both fillers. As electron scanning microscopy
studies confirm, those parameters are predetermined by the nature of the
composites studied—particle size, particles arrangement in the matrix and their
tendency to clustering. Last but not least matrix-filler interface phenomena
also impact the characteristics in question. The possibilities for applications
of the composites in antennae have been studied, in particular, as substrates
and insulating layers in flexible antennae for body centric communications
(BCCs). The research results allow the conclusion that these materials can find
such applications indeed. Composites of higher conductivity can be used where
surface waves are generated to provide on-body communications, while composites
of lower conductivity may be used for antennae that will be on the body of a
person and will transmit to and receive from other antennas that are not on the body of the same person
(off-body communications). It is clear that one can engineer the properties of
antennae substrates at microwave frequencies by adjusting the filler content
and the type of filler and thus control and tailor the antenna performance
specific for a particular application.

Abstract:
We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If k is the minimal degree of a representation of the finite group G, then for every subset B of G with $|B| > |G| / k^{1/3}$ we have B^3 = G. We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan's theorem which implies that if k>1, then G has a proper subgroup of index at most ck^2 for some absolute constant c, hence a product-free subset of size at least $|G| / c'k$. This answers a question of Gowers.

Abstract:
The tunnel current of a Luttinger liquid with a finite density of strong impurities is calculated using an instanton approach. For very low temperatures $T$ or electric fields $E$ the (nonlinear) conductivity is of variable range hopping (VRH) type as for weak pinning. For higher temperatures or fields the conductivity shows power law behavior corresponding to a crossover from multi- to single-impurity tunneling. For even higher $T$ and not too strong pinning there is a second crossover to weak pinning. The determination of the position of the various crossover lines both for strong and weak pinning allows the construction of the global regime diagram.

Abstract:
The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the help of the effective algorithms without their preliminary plotting, etc. The examining of the transformation of the vertex graphs into the edge graph and the opposite operation illustrates the reasons of the appearance of the NP-completeness from the point of view of the graph theory. We suggest that it also illustrates the synchronous possibility and impossibility of the struggle with the NP-completeness.

Abstract:
The presented material continues the previous article (arxiv:1007.1059) and also is devoted to the equivalent conversion between the graphs. The examining of the transformation of the vertex graphs into the edge graphs (together with the opposite transformation) illustrates the reasons of the appearance of NP-completeness from the point of view of the graph theory. We suggest that it also illustrates the synchronous possibility and impossibility of the struggle with NP-completeness.