Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Involutions for upper triangular matrix algebras

In this paper we describe completely the involutions of the first kind of the algebra UT_n(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UT_n(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT₂(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT₃(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UT_n(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities.     

Continuous reaction system to investigate the dispersion polymerization of vinyl monomers in supercritical carbon dioxide

A laboratory‐scale continuous reaction system using a stirred tank reactor was assembled in our laboratory to study the dispersion polymerization of vinyl monomers in supercritical carbon dioxide (scCO₂). The apparatus was equipped with a suitable downstream separation section to collect solid particles entrained in the effluent stream from the reactor, whose monomer concentration could be measured online with a gas chromatograph. The dispersion polymerization of methyl methacrylate in scCO₂ was selected as a model process to be investigated in the apparatus. The experiments were performed at 65 °C and 25 MPa with 2,2′‐azobisisobutyronitrile as the initiator and a reactive polysiloxane macromonomer as a surfactant to investigate the effect of the mean residence time of the reaction mixture on the monomer conversion, polymerization rate, polymer molecular weight, and particle size distribution. The results were compared with those obtained in batch polymerizations carried out under similar operative conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4122–4135, 2006     

New synthesis of some 1,2,5-benzothiadiazcpinc 1,1-dioxide derivatives. I

2-Nitrobenzenesulfonyl chloride reacts with ω-aminoacetophenone and 4-amino-3,5-dimethyl-isoxazole to give 3 and 7, respectively. Reduction of 3 with zinc powder and acetic acid afforded the 2,5-dihydro- and 2,3,4,5-tetrahydro-1,2,5-benzothiadiazepine I,1-dioxide derivatives (4 and 5). Catalytic hydrogenolysis of 7 and successive cyclization of the intermediate 8 gave the 3-ace-thyl-2,5-dihydro-4-methyl-1,2,5-benzothiadiazepine 1,1-dioxide (9). The structures were assigned on the basis of correct elemental data and spectroscopic evidences.     

Development of an apparatus for cooling <Superscript>6</Superscript>Li-<Superscript>87</Superscript>Rb Fermi-Bose mixtures in a light-assisted magnetic trap

We describe an experimental setup designed to produce ultracold trapped gas clouds of fermionic ⁶Li and bosonic ⁸⁷Rb. This combination of alkali metals has the potential to reach deeper Fermi degeneracy with respect to other mixtures since it allows for improved heat capacity matching which optimizes sympathetic cooling efficiency. Atomic beams of the two species are independently produced and then decelerated by Zeeman slowers. The slowed atoms are collected into a magneto-optical trap and then transferred into a quadrupole magnetic trap. An ultracold Fermi gas with temperature in the 10^?3 T _F range should be attainable through selective confinement of the two species via a properly detuned laser beam focused in the center of the magnetic trap.     

Carbon-13 NMR characterisation of carboxyl derivatives of 1-ureidopyrroles

1-Ureido-5-methyl-2,3-dicarbethoxypyrrole under acidic conditions afforded different partially hydrolyzed or decarboxylated products. It has been possible to characterize two isomeric monoethyl esters of dicarboxylic acids of 1-ureidopyrroles by proton gated decoupled carbon-13 nmr spectra on the basis of multiplicities of the carbonyl carbons resonances.     

∗-Polynomial Identities of a Nonsymmetric ∗-Minimal Algebra

Let F be an infinite field of characteristic ≠?2. We study the ?-polynomial identities of the ?-minimal algebra R?=?UT _?(F?⊕?F, F). We describe the generators of T _?(R) and a linear basis of the relatively free algebra of R. When char.F?=?0, these results allow us to provide a complete list of polynomials generating irreducible GL × GL-modules decomposing the proper part of the relatively free algebra of R. Finally, the ?-codimension sequence of R is explicitly computed.