Convex integral functionals of regular processes

This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be identified with the space of optional random measures with essentially bounded variation. Combined with classical Banach space techniques, our results allow for a systematic treatment of stochastic optimization problems over BV processes and, in particular, yields a maximum principle for a general class of singular stochastic control problems.     

Test of the Duh-Haymet-Henderson theory for mixtures: cavity correlation functions and excess volumes

The accuracy of the Duh-Haymet-Henderson (DHH) integral equation theory for predicting the cavity correlation functions of mixtures has been tested by comparison with molecular simulations. We have compared the cavity correlation functions, internal energies, and pressures computed for Lennard-Jones model mixtures of Ar/Kr, Ar/Ne, and Ar/Xe with these same quantities computed from the DHH theory and also, for reference, the Percus-Yevick (PY) integral equation theory. We found that DHH gave much better accuracy than PY at high densities. At low densities DHH and PY give essentially identical predictions. We have computed excess volumes for Ar/Kr mixtures at two pressures (10 and 20?MPa) at 132.32?K, for which experimentally derived data are available. The DHH theory predicts the correct trends and is quantitatively more accurate than the PY theory for predicting the excess volumes. We have tested the local optimality of the DHH theory for pure fluids by adding two adjustable parameters to the DHH bridge function expression to see if it is possible to improve the DHH predictions of the cavity correlation function empirically, holding the form of the bridge function constant. We found that no single set of adjustable parameter values could improve the accuracy of DHH over multiple different isotherms. Furthermore, perturbing DHH leads to a decrease in accuracy of the predictions of both the pressure and energy, although small improvements in the cavity correlation functions were achieved. Thus, the DHH theory is locally optimal, given the form of the bridge function.     

Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions

Some Hardy-type integral inequalities in general measure spaces, where the corresponding Hardy operator is replaced by a more general Volterra type integral operator with kernel , are considered. The equivalence of such inequalities on the cones of non-negative respective non-increasing functions are established and applied.

     

A perturbation of ring derivations on Banach algebras

Suppose A is a Banach algebra and suppose is an approximate ring derivation in the sense of Hyers-Ulam-Rassias. This stability phenomenon was introduced for the first time in the subject of functional equations by Th.M. Rassias [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300]. If A has an approximate identity, or if A is semisimple and commutative, then we prove that f is an exact ring derivation.     

Efficient thermal field computation in phase-field models

We solve the phase-field equations in two dimensions to simulate crystal growth in the low undercooling regime. The novelty is the use of a fast solver for the free space heat equation to compute the thermal field. This solver is based on the efficient direct evaluation of the integral representation of the solution to the constant coefficient, free space heat equation with a smooth source term. The computational cost and memory requirements of the new solver are reasonable and no artificial boundary conditions are needed. This allows one to solve for the thermal field in a computational domain whose size depends only on the size of the growing crystal and not on the extent of the thermal field, which can result in significant computational savings in the low undercooling regime.     

Integral Closures of Cohen-Macaulay Monomial Ideals

ABSTRACT

The purpose of this paper is to present a family of Cohen-Macaulay monomial ideals such that their integral closures have embedded components and hence are not Cohen-Macaulay.     

Palladium-Catalyzed Fluorinative Bifunctionalization of Aziridines and Azetidines with gem-Difluorocyclopropanes

An unprecedented Pd-catalyzed fluorinative bifunctionalization of aziridines and azetidines was successfully developed via regioselective C−C and C−F bond cleavage of gem-difluorocyclopropanes, leading to various β,β′-bisfluorinated amines and β,γ-bisfluorinated amines. This reaction was achieved by incorporating a 2-fluorinated allyl group and a fluorine atom scissored from gem-difluorocyclopropane in 100 % atom economy for the first time. The mechanistic investigations indicated that the reaction underwent amine attacking 2-fluorinated allyl palladium complex to generate η²-coordinated N-allyl aziridine followed by fluoride ligand transfer affording the final β- and γ-fluorinated amines.     

Synthesis, ring transformations, IR-, NMR and DFT study of heterocycles with two ferrocenyl units

Cyclization of 1,5-bis(ferrocenylmethylidene)thiocarbonohydrazide with DMAD afforded diastereomeric dimethyl-thiazole-4,5-dicarboxylates. The cis-isomer undergoes ring opening and recyclization to a thiazolone derivative. A further thiazolone was obtained from this precursor with ethyl chloroacetate employing a bifunctional organocatalyst. Due to its propensity to dehydrogenation evidenced by DFT calculations, the studied thiocarbonohydrazide underwent oxidative cyclizations under different conditions to yield a 1,3,4-thiadiazole and a 1,2,4-triazole derivative, respectively. Thermal isomerisation of 1,3,4-thiadiazole into 1,2,4-triazole was also observed. The DMAD-mediated cyclizations of the S-metylated thiocarbonohydrazide and the 1,5-bis(ferrocenylmethylideneamino)guanidine gave 1,2,4-triazole derivatives and a 4-pyrimidone, respectively. The structure of the new compounds was established by IR and NMR spectroscopy, including HMQC, HMBC and DEPT measurements. The solid state structure of a triazole was revealed by single crystal X-ray analysis.