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     

Accurate mass measurements by Fourier transform mass spectrometry in the study of advanced glycation end products/peptides

The Maillard reaction occurring between sugars and amino groups is important in living systems. When amino groups belonging to protein chains are involved, the Maillard reaction has been invoked as responsible for protein cross-linking and the production of 'toxic' compounds. The reaction leads to the production of a heterogeneous group of substances, usually called advanced glycation end products (AGEs). Classical analytical approaches, such as spectroscopic (ultraviolet, fluorescence) and mass spectrometric (matrix-assisted laser desorption/ionization, liquid chromatography/electrospray ionization mass spectrometry) methods, have shown that the digestion mixture is highly complex. However, there are clear differences between the digestion mixtures of glycated and unglycated human serum albumin (HSA). In the former case, possible glycated peptides belonging to the AGE peptide class may be identified. Tandem mass spectrometric experiments on selected species seemed to be promising as regards structural information, but it was thought of interest to undertake the present investigation, based on liquid chromatography/electrospray ionization Fourier transform mass spectrometry, in order to obtain definitive results on their elemental composition. Using this approach, about 20 glycated peptides were detected and their possible structures were postulated by examining the known sequence of HSA.     

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.     

The Chemistry of Coumarin Derivatives. Part 5. Unusual course of the reaction of 4-hydroxycoumarin and aliphatic aldehydes

The reaction of 4-hydroxycoumarin and certain aliphatic aldehydes affords 1:1 or complex 2:2 adducts besides (or in place) of the expected 2:1 bis(coumarin) adducts. Reaction with heptanal, cyclohexanecarbaldehyde, and pivalaldehyde are reported as representative. The structure of the reaction products was established by spectroscopical techniques, including X-ray analysis, and their formation was mechanistically rationalized. Some of the 1:1 adducts are synthetically useful for the preparation of 3-alkyl-4-hydroxycoumarins.     

4(1H)-Quinolinone Alkaloids. An Efficient Synthesis of Graveoline by Palladium-Catalysed Reductive N-Heterocyclisation

An efficient synthesis of the 4H-quinolone alkaloid graveoline has been achieved by a route featuring an Pd(II)-catalysed reductive N-hetero-cyclisation [CO(3 MPa), Pd(TMB)₂, TMPhen, 170°C, 3h] of 2′-nitrochalcone as a key step.     

An effective and rapid determination by MALDI/TOF/TOF of methionine sulphoxide content of ApoA‐I in type 2 diabetic patients

Increased oxidation of low density lipoprotein (LDL) is characteristic of atherosclerosis. In this frame, high density lipoproteins (HDL) play an important role, being able to remove lipid peroxides (LPOs) and cholesterol from oxidized LDL, so exhibiting a protective role against atherosclerosis. A wide range of reactive compounds lead to the oxidation of methionine (Met) residues with the formation of methionine sulphoxide (MetO) in apolipoprotein A‐I (ApoA‐I). Consequently, the determination of MetO level can give both an evaluation of oxidative stress and the reduced capability of ApoA‐I in LPOs and cholesterol transport. For these reasons, the development of analytical methods able to determine the MetO level is surely of interest, and we report here the results obtained by MALDI mass spectrometry. Copyright © 2013 John Wiley & Sons, Ltd.