Formation of complex Langmuir and Langmuir-Blodgett films of water soluble rosebengal

This communication reports the formation of complex Langmuir monolayer at the air-water interface by charge transfer types of interaction with the water soluble N- cetyl N, N, N trimethyl ammonium bromide (CTAB) molecules doped with rosebengal (RB), with the stearic acid (SA) molecules of a preformed SA Langmuir monolayer. The reaction kinetics of the formation of RB-CTAB-SA complex monolayer was monitored by observing the increase in surface pressure with time while the barrier was kept fixed. Completion of interaction kinetics was confirmed by FTIR study. This complex Langmuir films at the air-water interface was transferred onto solid substrates at a desired surface pressure to form multilayered Langmuir-Blodgett films. Spectroscopic characterizations reveal some molecular level interactions as well as formation of microcrystalline aggregates depending upon the molar ratios of CTAB and RB within the complex LB films. Presence of two types of species in the complex LB films was confirmed by fluorescence spectroscopy.Comment: 13 pages, figures

Compactness of the space of causal curves

We prove that the space of causal curves between compact subsets of a separable globally hyperbolic poset is itself compact in the Vietoris topology. Although this result implies the usual result in general relativity, its proof does not require the use of geometry or differentiable structure.Comment: 15 page

Identification of BV/ODV-C42, an Autographa californica Nucleopolyhedrovirus orf101-Encoded Structural Protein Detected in Infected-Cell Complexes with ODV-EC27 and p78/83

orf101 is a late gene of Autographa californica nucleopolyhedrovirus (AcMNPV). It encodes a protein of 42 kDa which is a component of the nucleocapsid of budded virus (BV) and occlusion-derived virus (ODV). To reflect this viral localization, the product of orf101 was named BV/ODV-C42 (C42). C42 is predominantly detected within the infected-cell nucleus: at 24 h postinfection (p.i.), it is coincident with the virogenic stroma, but by 72 h p.i., the stroma is minimally labeled while C42 is more uniformly located throughout the nucleus. Yeast two-hybrid screens indicate that C42 is capable of directly interacting with the viral proteins p78/83 (1629K) and ODV-EC27 (orf144). These interactions were confirmed using blue native gels and Western blot analyses. At 28 h p.i., C42 and p78/83 are detected in two complexes: one at approximately 180 kDa and a high-molecular-mass complex (500 to 600 kDa) which also contains EC27

On the quasi-component of pseudocompact abelian groups

In this paper, we describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component q(\widetilde G) of its completion. Specifically, we characterize the pairs (C,A) of compact connected abelian groups C and subgroups A such that A \cong q(G) and C \cong q(\widetilde G). As a consequence, we show that for every positive integer n or n=\omega, there exist plenty of abelian pseudocompact perfectly minimal n-dimensional groups G such that the quasi-component of G is not dense in the quasi-component of the completion of G.Comment: minor revisio

A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube

We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $\lambda_s$ (the algebraic convergence) and $\lambda_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov cube respectively. In particular we show that $\lambda_{ls}$ is a topological convergence iff forcing by B does not produce new reals and that $\lambda_{ls}$ is weakly topological if B satisfies condition $(\hbar)$ (implied by the ${\mathfrak t}$-cc). On the other hand, if $\lambda_{ls}$ is a weakly topological convergence, then B is a $2^{\mathfrak h}$-cc algebra or in some generic extension the distributivity number of the ground model is greater than or equal to the tower number of the extension. So, the statement "The convergence $\lambda_{ls}$ on the collapsing algebra B=\ro ((\omega_2)^{<\omega}) is weakly topological" is independent of ZFC

On two-dimensional surface attractors and repellers on 3-manifolds

We show that if $f: M^3\to M^3$ is an $A$-diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal B$ and $M^2_ \mathcal B$ is a supporting surface for $\mathcal B$, then $\mathcal B = M^2_{\mathcal B}$ and there is $k\geq 1$ such that: 1) $M^2_{\mathcal B}$ is a union $M^2_1\cup...\cup M^2_k$ of disjoint tame surfaces such that every $M^2_i$ is homeomorphic to the 2-torus $T^2$. 2) the restriction of $f^k$ to $M^2_i$ $(i\in\{1,...,k\})$ is conjugate to Anosov automorphism of $T^2$

Functions of several Cayley-Dickson variables and manifolds over them

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are proved in the new generalized form for functions of Cayley-Dickson variables instead of complex. Moreover, analogs of Stein manifolds over Cayley-Dickson graded algebras are defined and investigated

Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers

In this paper we study the ergodic properties of mathematical billiards describing the uniform motion of a point in a flat torus from which finitely many, pairwise disjoint, tubular neighborhoods of translated subtori (the so called cylindric scatterers) have been removed. We prove that every such system is ergodic (actually, a Bernoulli flow), unless a simple geometric obstacle for the ergodicity is present.Comment: 24 pages, AMS-TeX fil

Robots That Do Not Avoid Obstacles

The motion planning problem is a fundamental problem in robotics, so that every autonomous robot should be able to deal with it. A number of solutions have been proposed and a probabilistic one seems to be quite reasonable. However, here we propose a more adoptive solution that uses fuzzy set theory and we expose this solution next to a sort survey on the recent theory of soft robots, for a future qualitative comparison between the two.Comment: To appear in the Handbook of Nonlinear Analysis, Edt Th. Rassias, Springe

Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proven, that they are finite dimensional Lie groups for compact manifolds. Their examples are given. Many charactersitic features are found in comparison with commutative geometry over $\bf R$ or $\bf C$.Comment: 55 pages, 53 reference