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1.
AbstractRealistic 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. 相似文献
2.
Onofrio Mario Di Vincenzo Plamen Koshlukov Roberto La Scala 《Advances in Applied Mathematics》2006,37(4):541
In this paper we describe completely the involutions of the first kind of the algebra UTn(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 UTn(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 UTn(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities. 相似文献
3.
Alberto Giaconia Giuseppe Filardo Onofrio Scialdone Alessandro Galia 《Journal of polymer science. Part A, Polymer chemistry》2006,44(13):4122-4135
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 相似文献
4.
Lopez-Martens A Hannachi F Dossing T Schück C Collatz R Gueorguieva E Vieu C Leoni S Herskind B Khoo TL Lauritsen T Ahmad I Blumenthal DJ Carpenter MP Gassmann D Janssens RV Nisius D Korichi A Bourgeois C Astier A Ducroux L Le Coz Y Meyer M Redon N Sharpey-Schafer JF Wilson AN Korten W Bracco A Lucas R 《Physical review letters》1996,77(9):1707-1710
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6.
The catalytic constants for the -butylaminolysis of sultones in aprotic-apolar solvents are linearly correlated with a combination of the hydrogen-bonding parameter and the polarity parameter of the catalyst. 相似文献
7.
Fabrizi de Biani F Ienco A Laschi F Leoni P Marchetti F Marchetti L Mealli C Zanello P 《Journal of the American Chemical Society》2005,127(9):3076-3089
The reaction between equimolar amounts of Pt(3)(mu-PBu(t)()(2))(3)(H)(CO)(2), Pt(3)()H, and CF(3)SO(3)H under CO atmosphere affords the triangular species [Pt(3)(mu-PBu(t)()(2))(3)(CO)(3)]X, [Pt(3)()(CO)(3)()(+)()]X (X = CF(3)SO(3)(-)), characterized by X-ray crystallography, or in an excess of acid, [Pt(6)(mu-PBu(t)()(2))(4)(CO)(6)]X(2), [Pt(6)()(2+)()]X(2)(). Structural determination shows the latter to be a rare hexanuclear cluster with a Pt(4) tetrahedral core formed by joining the unbridged sides of two orthogonal Pt(3) triangles. The dication Pt(6)()(2+)() features also extensive redox properties as it undergoes two reversible one-electron reductions to the congeners [Pt(6)(mu-PBu(t)()(2))(4)(CO)(6)](+) (Pt(6)()(+)(), E(1/2) = -0.27 V) and Pt(6)(mu-PBu(t)()(2))(4)(CO)(6) (Pt(6)(), E(1/2) = -0.54 V) and a further quasi-reversible two-electron reduction to the unstable dianion Pt(6)()(2)()(-)() (E(1/2) = -1.72 V). The stable radical (Pt(6)()(+)()) and diamagnetic (Pt(6)()) species are also formed via chemical methods by using 1 or 2 equiv of Cp(2)Co, respectively; further reduction of Pt(6)()(2+)() causes fast decomposition. The chloride derivatives [Pt(6)(mu-PBu(t)()(2))(4)(CO)(5)Cl]X, (Pt(6)()Cl(+)())X, and Pt(6)(mu-PBu(t)()(2))(4)(CO)(4)Cl(2), Pt(6)()Cl(2)(), observed as side-products in some electrochemical experiments, were prepared independently. The reaction leading to Pt(3)()(CO)(3)()(+)() has been analyzed with DFT methods, and identification of key intermediates allows outlining the reaction mechanism. Moreover, calculations for the whole series Pt(6)()(2+)() --> Pt(6)()(2)()(-)()( )()afford the otherwise unknown structures of the reduced derivatives. While the primary geometry is maintained by increasing electron population, the system undergoes progressive and concerted out-of-plane rotation of the four phosphido bridges (from D(2)(d)() to D(2) symmetry). The bonding at the central Pt(4) tetrahedron of the hexanuclear clusters (an example of 4c-2e(-) inorganic tetrahedral aromaticity in Pt(6)()(2+)()) is explained in simple MO terms. 相似文献
8.
The use of Tenax GC for the extraction of organic micro-pollutants such as pesticides and polynuclear aromatic hydrocarbons from water has been studied. In the absence of other contaminants and under conditions standardized at the time as optimal, the recovery of such substances is, on average, over 90%, both for the organochlorine and organophosphorus pesticides and for polynuclear aromatic hydrocarbons. Research into the effectiveness of extraction with Tenax from natural waters and water artificially contaminated with surfactants, fats and oils etc., in the laboratory is now being carried out. 相似文献
9.
Onofrio Migliara Salvatore Petruso Vincenzo Sprio 《Journal of heterocyclic chemistry》1979,16(5):835-837
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. 相似文献
10.