Reactivity of Aliphatic and Phenolic Hydroxyl Groups in Kraft Lignin towards 4,4′ MDI

Several efforts have been dedicated to the development of lignin-based polyurethanes (PU) in recent years. The low and heterogeneous reactivity of lignin hydroxyl groups towards diisocyanates, arising from their highly complex chemical structure, limits the application of this biopolymer in PU synthesis. Besides the well-known differences in the reactivity of aliphatic and aromatic hydroxyl groups, experimental work in which the reactivity of both types of hydroxyl, especially the aromatic ones present in syringyl (S-unit), guaiacyl (G-unit), and p-hydroxyphenyl (H-unit) building units are considered and compared, is still lacking in the literature. In this work, the hydroxyl reactivity of two kraft lignin grades towards 4,4′-diphenylmethane diisocyanate (MDI) was investigated. ³¹P NMR allowed the monitoring of the reactivity of each hydroxyl group in the lignin structure. FTIR spectra revealed the evolution of peaks related to hydroxyl consumption and urethane formation. These results might support new PU developments, including the use of unmodified lignin and the synthesis of MDI-functionalized biopolymers or prepolymers.     

On the Analytic Type of Artin Algebras

In this paper we give a complete analytic classification of Artin Gorenstein almost stretched algebras, i.e., Artin Gorenstein algebras with Hilbert function {1, n, 2,…, 2, 1,…, 1}.     

On dominant poles and model reduction of second order time-delay systems

The method known as the dominant pole algorithm (DPA) has previously been successfully used in combination with model order reduction techniques to approximate standard linear time-invariant dynamical systems and second order dynamical systems. In this paper, we show how this approach can be adapted to a class of second order delay systems, which are large scale nonlinear problems whose transfer functions have an infinite number of simple poles. Deflation is a very important ingredient for this type of methods. Because of the nonlinearity, many deflation approaches for linear systems are not applicable. We therefore propose an alternative technique that essentially removes computed poles from the system?s input and output vectors. In general, this technique changes the residues, and hence, modifies the order of dominance of the poles, but we prove that, under certain conditions, the residues stay near the original residues. The new algorithm is illustrated by numerical examples.     

Utilization and maintenance in a model with scrapping

We consider a productive asset, called equipment or capital good, and we examine the properties of, as well as the interactions between, the operating policies, which are determined by its optimal utilization and maintenance, and the capital policy of scrapping, which defines the optimal time when the productive asset is retired from its current use. Starting with an abstract model and using the approach of optimal control, initially we characterize the various types of equipment by assigning to them a single total profit index, which indicates how the above policies affect the flow of operating revenues plus capital gains or losses. This index is a function of market-determined prices. So using it we then investigate how the operating and capital policies are influenced by the rate of discount, the price of new equipment, and the rise or fall of the price of new equipment relative to the value of its output. Among other interesting results, we find that the effects of these prices on the nature and interactions of optimal policies depend crucially on whether the equipment is of the usual profit making type, where output is the main source of revenue, or of the antique type, where the main source of revenue is capital gains.     

Asymptotic behavior of the distribution of the stock price in models with stochastic volatility: the Hull–White model

In the present Note, we study the asymptotic behavior of the distribution density of the stock price process in the Hull–White model. The leading terms in the asymptotic expansions at zero and infinity are found for such a density and the corresponding error estimates are given. Similar problems are solved for time averages of the volatility process, which are also of interest in the study of Asian options. To cite this article: A. Gulisashvili, E.M. Stein, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Applications of the Wold decomposition to the study of row contractions associated with directed graphs

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid algebras, and show that joint similarity implies joint unitary equivalence for such families. For each graph we prove a generalization of von Neumann's inequality which applies to row contractions of operators on Hilbert space which are related to the graph in a natural way. This yields a functional calculus determined by quiver algebras and free semigroupoid algebras. We establish a generalization of Coburn's theorem for the -algebra of a CKT family, and prove a universality theorem for -algebras generated by these families. In both cases, the -algebras generated by quiver algebras play the universal role.

     

Group-wise sufficient dimension reduction with principal fitted components

Sufficient dimension reduction methodologies in regressions of Y on a p-variate X aim at obtaining a reduction \(R(X) \in {\mathbb R}^{d}, d \le p\), that retains all the regression information of Y in X. When the predictors fall naturally into a number of known groups or domains, it has been established that exploiting the grouping information often leads to more effective sufficient dimension reduction of the predictors. In this article, we consider group-wise sufficient dimension reduction based on principal fitted components, when the grouping information is unknown. Principal fitted components methodology is coupled with an agglomerative clustering procedure to identify a suitable grouping structure. Simulations and real data analysis demonstrate that the group-wise principal fitted components sufficient dimension reduction is superior to the standard principal fitted components and to general sufficient dimension reduction methods.     

On the Local Convergence Analysis of the Gradient Sampling Method for Finite Max-Functions

The gradient sampling method is a recently developed tool for solving unconstrained nonsmooth optimization problems. Using just first-order information about the objective function, it generalizes the steepest descent method, one of the most classical methods for minimizing a smooth function. This study aims at determining under which circumstances one can expect the same local convergence result of the Cauchy method for the gradient sampling algorithm under the assumption that the problem is stated by a finite max-function around the optimal point. Additionally, at the end, we show how to practically accomplish the required hypotheses during the execution of the algorithm.