Showing papers by "Romanian Academy published in 1997"

Nonlinear Fractional Programming

Abstract: In this chapter we deal with the following nonlinear fractional programming problem: $$P:\mathop{{\max }}\limits_{{x \in s}} q(x) = (f(x) + \alpha )/((x) + \beta )$$ where f, g: R n → R, α, β ∈ R, S ⊆ R n . To simplify things, and without restricting the generality of the problem, it is usually assumed that, g(x) + β + 0 for all x ∈ S,S is non-empty and that the objective function has a finite optimal value.

Stability results on interpolation scales of quasi-Banach spaces and applications

Abstract: We investigate stability of Fredholm properties on interpolation scales of quasi-Banach spaces. This analysis is motivated by problems arising in PDE's and several applications are presented.

Some Propagation Properties of the Iwatsuka Model

Abstract: In this paper we study a two dimensional magnetic field Schrodinger Hamiltonian introduced in [7]. This model has some interesting propagation properties, as conjectured in [2] and at the same time is a special case of the class of analytically decomposable Hamiltonians [5]. Our aim is to start from a conjugate operator, intimately related to the band structure of the Hamiltonian and to prove existence of an asymptotic velocity in one spatial direction and a theorem giving minimal and maximal velocity bounds for the propagation associated to the Hamiltonian. A simple example of this model, with a very simple conjugate operator, has been given in [9]. At the same time, by using the Virial Theorem, we obtain a generalisation of the hypothesis in [7].

Molecular mechanisms of erythrophagocytosis: Flow cytometric quantitation of in vitro erythrocyte phagocytosis by macrophages

Abstract: A rapid, sensitive, and reproducible flow cytofluorimetric procedure is described for quantitation of erythrophagocytosis based on the use of red blood cells (RBCs) labeled with the fluorescent probe PKH-26. The procedure involves the following steps: i) incubation of PKH-26-labeled erythrocytes with macrophages, ii) removal of un-bound red blood cells, iii) lysis of membrane-bound RBCs, and iv) measurement of extent of phagocytosis by direct flow-cytometric analysis of intact macrophages. Each step was controlled by fluorescence microscopy. Use of fluorescent, instead of radio-labeled RBCs, makes the method more sensitive, rapid, and avoids radioactive hazards. Furthermore, this approach is multi-parametric and can distinguish different populations of macrophages with reference to their erythrophagocytic potential. This technology moreover, has broad applications from the initial step of contact (between effector and target cells to study the specific receptor mediated attachment) to the subsequent cascade of time-dependent changes resulting from that signal transduction.

On Very Ample Vector Bundles on Curves

Abstract: We study very ample vector bundles on curves. We first give numerical conditions for the existence of non-special such bundles. Then we prove the inequality \[ h^0(\det E)\ge h^0(E) + {\rm rank}(E)-2 \] over curves of genus at least two. We apply this to prove some special cases of a conjecture on scrolls of small codimension.

The structure of higher-dimensional noncommutative tori and metric diophantine approximation.

Abstract: We use the cut-down method and metric diophantine approximation techniques in order to prove that the set of elements Θ = (ejk)i^j 3 was studied in [17], where the Chern character has been computed, in [38], where the positive cone of K0 (A0) has been described and cancellation for projective modules over simple noncommutative tori proved and in [5], where simple noncommutative tori were shown to be approximately divisible. For our purpose it is convenient to regard noncommutative tori s twisted group C*-algebras C*(Z, /?), where β is a 2-cocycle on Z.. To construct projective modules over A&, Rieffei embeds D = Z. s a lattice in the abelian locally compact group G = M χ Μ (f denotes the topological dual of M) such that β lifts to the canonical Heisenberg bicharacter on G ([38]). This construction exhibits an explicit isomorphism between a corner of Αθ = C*(/), ) and the twisted group C*-algebra C*(D\\ /T) associated with the orthogonal lattice Z) of Z) in G with respect to *. This approach has been further exploited in [21] to give a new proof of the Elliott-Evans theorem and show that under some technical diophantine conditions on the triple Θ = ( 12, 013, Θ23) E [0, l), Αθ is an inductive limit of direct sums of four circle algebras. In this paper the problem of the structure of N-dimensional noncommutative tori for all 7V ̂ 3 is being considered. Using metric diophantine approximation techniques ([11], [25], [26], [40]) and an extension of the cut-down method ([21]) we show that \"almost all\" noncommutative tori decompose s inductive limits of circle algebras. More precisely, we prove the following general result: Theorem I. For all N 2> 3, the set {0 = (ejk)l^j l such that (ii) (co(^) = ω! («)··· ωΓ(«)}η^1 w decreasing monotonically and Σ ω(η) = oo. Ae 5ei $ of r-tuples ( 1? . . . , 0r) 6 7 iv//A ^Ae property that there exist infinitely many integers q,p^...,pr, 0 Σ\"% = Σ β« and Σ^αΓα5= ^ aras for any sequence {#9}9 and any subset ̂ c N*. Denote the number of integers 0 < m < n such that gcd (m, n) = l by φ (n). l l 7V Τνπ The first step consists in proving that μΓ(<Γ) > 0. Since £ Σ \"\" = Σ * — < , k£N p\\k P ρϊΝ P P 6 Lemma 4 in [40], Chap. l yields δ > 0 such that ^\"= {« 6 N* | φ (ή) ^ <5«} has positive density in N*. As (ω(ή)}η decreases and ]Γ ω(#) = oo, we still have ]T a)(q) = ao and = oo, where we set Q^(Q) = Σ^(ί)· Furthermore, if we consider ^ (1.1) β(θ) = χ _ ω ) , ) ( ) ̂ β»(θ) ^ χ ο (θ),

DNA Computing: Distributed Splicing Systems

Abstract: Because splicing systems with a finite set of rules generate only regular languages, it is necessary to supplement such a system with a control mechanism on the use of rules. One fruitful idea is to use distributed architectures suggested by the grammar systems area. Three distributed computability (language generating) devices based on splicing are discussed here. First, we improve a result about the so-called communicating distributed H systems (systems with seven components are able to characterize the recursively enumerable languages — the best result known up to now is of ten components), then we introduce two new types of distributed H systems: the separated two-level H systems and the periodically time-varying H systems. In both cases we prove characterizations of recursively enumerable languages — which means that in all these cases we can design universal “DNA computers based on splicing”.

The Schwarzschild Problem in Astrophysics

Abstract: The Schwarzschild problem (the two-body problem associated to apotential of the form A/r + B/r3 has been qualitativelyinvestigated in an astrophysical framework, exemplified by two likelysituations: motion of a particle in the photogravitational field ofan oblate, rotating star, or in that of a star which generates aSchwarzschild field Using McGehee-type transformations, regularizedequations of motion are obtained, and the collision singularity isblown up and replaced by the collision manifold λ (a torus)pasted on the phase space The flow on λ is fullycharacterized Then, reducing the 4D phase space to dimension 2, theglobal flow in the phase plane is depicted for all possible values ofthe energy and for all combinations of nonzero A and B Eachphase trajectory is interpreted in terms of physical motion,obtaining in this way a telling geometric and physical picture of themodel

A Comparison between Hydrophobically End-Capped Poly(ethylene oxide) with Ether and Urethane Bonds

Abstract: Two models of HEUR (hydrophobically modified ethylene oxide urethane) associative polymers (AP) are compared. The two polymers are polyethyleneoxides simply end-capped with dodecyl groups, one thro ...

TiO2-Based Porous Materials Obtained from Gels, in Different Experimental Conditions

Abstract: The gels which are precursors of TiO2 porous materials are prepared by the controlled hydrolysis-condensation of titanium isopropoxide by polymeric method. In the present work, a study of the influence of different experimental conditions (water/alkoxide ratio, solvent/alkoxide ratio and temperature) on the structure and texture of the polymeric gels obtained with the same type of alkoxide has been investigated. The structural and textural modifications for the unsupported materials have been detected using DTA/TGA, XRD, specific surface area and pore size computerized measurements. The optical properties of the supported materials deposited on silicon wafers have been investigated using ellipsometric method. Supported and unsupported porous materials with different structure and texture have been obtained depending on different experimental and thermal treatment conditions.

Bismaleimide Resins Containing Urethanic Moieties

Abstract: A series of novel bismaleimide (BMIs) resins were prepared from 4-maleimidophenyl isocyanate and oligoether diols and oligoester diols. All the BMIs were characterized by IR, 1H-NMR spectra and elemental analysis. DSC studies indicated that the thermal polymerization of the BMIs carried out in the 80–260°C range, and their curing behavior was significantly affected by the molecular weight of the BMIs. The poly(aminobismaleimide) resins (V1a-e, V2a-e) obtained by Michael addition of 4,4′-diaminodiphenylmethane and 4,4′-oxydianiline in 1-methyl-2-pyrrolidinone, led to elastic films showing good mechanical properties and better thermal stability than the traditional polyurethane elastomers.

Network algebra for asynchronous dataflow

Abstract: Network algebra is proposed as a uniform algebraic framework for the description and analysis of dataflow networks. An equational theory of networks, called BNA (Basic Network Algebra), is presented. BNA, which is essentially a part of the algebra of flownomials, captures the basic algebraic properties of networks. For asynchronous dataflow networks, additional constants and axioms are given; and a corresponding process algebra model is introduced. This process algebra model is compared with previous models for asynchronous dataflow.

Catalytic hydrogen evolution in the presence of sulfide and cobalt ions. A study by cathodic stripping voltammetry on the hanging mercury drop electrode

Abstract: Traces of sulfide ion produce a cathodic peak on the HMDE at about −1.50 V (vs. SCE) after preconcentration at −0.5 V in the borax buffer containing 0.01 mM CoII. This peak is due to the catalytic hydrogen evolution, as demonstrated by the influence of the buffer concentration, the effect of water substitution by deuterium oxide and by the formation of hydrogen bubbles on the electrode. The effect of sulfide ion concentration, deposition time and deposition potential demonstrate that a positively charged cobalt complex is adsorptively accumulated during the deposition step. The reduction of CoII in this species produces a catalytically active compound which is involved in the reduction of the hydrogen ion according to the proposed mechanism. The potential analytical applications of this process for the determination of the sulfide ion have been assessed. The peak current is directly proportional to the concentration of the sulfide ion enabling the application of the standard addition method. The detection limit (using either normal or derivative LSV) is about 1 nM for 10 min accumulation time. The accuracy and reproducibility are fairly good and some of the common interferences in CSV of sulfide ion are removed or at least diminished.

On the Lojasiewicz exponent at infinity for polynomial functions

Abstract: The Lojasiewicz exponent at infinity of an entire function measures of the infimal rate of growth of its gradient. The authors compute the Lojasiewicz exponents at infinity of the 3-variable complex polynomials x - 3 x^{2n+1} y^{2q} + 2 x^{3n+1} y^{3q} + y z

Fractional Programming in The Complex Space

Abstract: In this chapter, we present several results which were obtained in fractional programming in complex space. The idea of studying the mathematical programming in complex space belongs to N. Levinson (“Linear programming in complex space”,J. Math. Anal. Appl., 14, 44-62 (1966)) who extended to the complex space the basic theorems of linear programming. In particular, using a variant in the complex space of Farcas’ Lemma from real space, he generalizes duality theorems from real linear programming. Since then, over 160 works of mathematical programming in the complex space (See Dorel I. Duca and I.M. Stancu -Minasian, “Mathematical programming in complex space: a comprehensive bibliography”,Rev. Anal. Numer. Theor. Approx. 17(2), 1988, 133-140) have appeared. Several works refer to fractional programming. A synthesis of these was given by Stancu-Minasian [908].

Phase-transfer catalytic activity of polymer-supported ammonium and phosphonium salts in oxidation of benzyl alcohol with hydrogen peroxide

Abstract: Quaternary ammonium or phosphonium salts, immobilized on polymeric support, were obtained by polymer-analogous reactions on ‘gel-type’ styrene-divinylbenzene copolymers and by trans-quatemization of the ammonium groups to phosphonium groups. Polymeric catalysts with degrees of functionalization of 0.15–2.78 mmole g−1 were used in the oxidation of benzyl alcohol with hydrogen peroxide. The activity of the single -onium salts increases as a consequence of association of ammonium and phosphonium salts on the polymeric support. The activity of polymer-supported ammonium and phosphonium salts increases with the number of carbon atoms contained in the alkyl radicals of the -onium and of the functionalization degree with phosphonium groups. Addition of RuCl3·3H2O to the reaction media increases the activity of the phase-transfer catalysts.

Some remarks on nef and good divisors on an algebraic variety

Abstract: Let X be a complete normal algebraic variety defined over a field k algebraically closed and let D be a Cartier divisor on X. Under the assumption that D is nef and good, we describe boundedness properties of base locus of the systems |nD|, algebraic convexity properties of X \ supp(D), and a criterium for semiampleness.

Stable rank-2 vector bundles over ruled surfaces

Abstract: We give necessary and sufficient numerical conditions for a 2-vector bundle over a ruled surface to be H -stable for some ample line bundle H . Then one solves the problem of the non-emptiness of moduli spaces of stable 2-vector bundles over ruled surfaces in almost all cases.

Deformation retracts of Stein spaces

Abstract: Let X be an n-dimensional Stein space. It was proved in [4, 5, 3] that X has the homotopy type of a CW-complex of dimension5n; in the algebraic case this was proved in [8] with the additional conclusion that the CW-complex is nite. It is therefore natural to ask if there exists a subset Q of X with the same topological properties as X , for instance Q is a strong deformation retract of X , and Q is a CW-complex of dimension5 n. The main result of the paper is:

Topological quantum field theory with corners based on the Kauffman bracket

Abstract: We describe the construction of a topological quantum field theory with corners based on the Kauffman bracket, that underlies the smooth theory of Lickorish, Blanchet, Habegger, Masbaum and Vogel. We also exhibit some properties of invariants of 3-manifolds with boundary.