Synthesis of a Systematic 64-Membered Heparan Sulfate Tetrasaccharide Library

Heparan sulfate (HS) has multifaceted biological activities. To date, no libraries of HS oligosaccharides bearing systematically varied sulfation structures are available owing to the challenges in synthesizing a large number of HS oligosaccharides. To overcome the obstacles and expedite the synthesis, a divergent approach was designed, where 64 HS tetrasaccharides covering all possible structures of 2-O-, 6-O- and N-sulfation with the glucosamine-glucuronic acid-glucosamine-iduronic acid backbone were successfully produced from a single strategically protected tetrasaccharide intermediate. This extensive library helped identify the structural requirements for HS sequences to have strong fibroblast growth factor-2 binding but a weak affinity for platelet factor-4. Such a strategy to separate out these two interactions could lead to new HS-based potential therapeutics without the dangerous adverse effect of heparin-induced thrombocytopenia.     

Modeling the adsorption of U(VI) onto animal chitin using coupled mass transfer and surface complexation

This paper reports the development of a treatment system, using animal chitin as a passive biosorbent, for removing U(VI) from aqueous waste streams. An integral part of this system is a model that provides for the optimization of the treatment system through simulation of U(VI) removal efficiency based on the characteristics of the influent waste stream. The model accounts for changing solution matrix conditions through the coupling of surface complexation and mass transfer models. Complexation of U(VI) by chitin surface sites was modeled using FITEQL. Application of FITEQL in the “forward” mode provided the sorbed and aqueous phase concentrations needed for the mass transfer model. The mass transfer model was derived for both batch and continuously stirred tank reactor (CSTR) configurations using Fick's Law, reactor mass balances and rate law expressions. The coupled model was successfully validated using CSTR data at pH 6.5 and rate constants determined from batch sorption experiments. The CSTR configuration yields a steady-state, eighty percent U(VI) removal for 1 μM influent U(VI) with a solution-phase pH of 6.5 and 3.9 g l⁻¹ chitin.     

Übergangsmetall—methylen-komplexe : XXXI. Primärkomplexierung von diazoalkanen an metall—metall-mehrfachbindungen; ein weiterer koordinationstyp

An unexpected novel coordination mode of diazoalkanes has been verified via addition of 2-diazopropane to the metal—metal triple bond of bis[dicarbonyl(η⁵-pentamethylcyclopentadienyl)molybdenum] (MoMo). The dinuclear 1:1 addition product isolated in nearly quantitative yield is structurally characterized by a bent, 4-electron type η¹:η²-diazoalkane ligand, with the terminal nitrogen atom symmetrically bridging the metal-metal “single bond” (d(MoMo) 305.0(2) pm; d(Mo---N(1)) 212.0(12) and 212.6(10) pm, respectively) and the second nitrogen atom being bonded to one molybdenum atom only (d(Mo---N(2)) 213.4(13) pm).     

Integrating on-line process control and imperfect corrective maintenance: An economical design

Existing studies of on-line process control are concerned with economic aspects, and the parameters of the processes are optimized with respect to the average cost per item produced. However, an equally important dimension is the adoption of an efficient maintenance policy. In most cases, only the frequency of the corrective adjustment is evaluated because it is assumed that the equipment becomes “as good as new” after corrective maintenance. For this condition to be met, a sophisticated and detailed corrective adjustment system needs to be employed. The aim of this paper is to propose an integrated economic model incorporating the following two dimensions: on-line process control and a corrective maintenance program. Both performances are objects of an average cost per item minimization. Adjustments are based on the location of the measurement of a quality characteristic of interest in a three decision zone. Numerical examples are illustrated in the proposal.     

Minimal Degree and (k, m)-Pancyclic Ordered Graphs

Given positive integers k m n, a graph G of order n is (k, m)-pancyclic ordered if for any set of k vertices of G and any integer r with m r n, there is a cycle of length r encountering the k vertices in a specified order. Minimum degree conditions that imply a graph of sufficiently large order n is (k, m)-pancylic ordered are proved. Examples showing that these constraints are best possible are also provided.     

Degree conditions for 2-factors

For any positive integer k, we investigate degree conditions implying that a graph G of order n contains a 2-factor with exactly k components (vertex disjoint cycles). In particular, we prove that for k ≤ (n/4), Ore's classical condition for a graph to be hamiltonian (k = 1) implies that the graph contains a 2-factor with exactly k components. We also obtain a sufficient degree condition for a graph to have k vertex disjoint cycles, at least s of which are 3-cycles and the remaining are 4-cycles for any s ≤ k. © 1997 John Wiley & Sons, Inc.     

A bivariate interval censorship model for partnership formation

We consider a statistical problem of estimating a bivariate age distribution of newly formed partnership. The study is motivated by a type of data that consist of uncensored, right-censored, left-censored, interval-censored and missing observations in the coordinates of a bivariate random vector. A model is proposed for formulating such type of data. A feasible algorithm to estimate the generalized MLE (GMLE) of the bivariate distribution function is also proposed. We establish asymptotic properties for the GMLE under a discrete assumption on the underlying distributions and apply the method to the data set.     

Using Concept Maps and Interpretive Essays for Assessment in Mathematics

This study explored the use of student-constructed concept maps in conjunction with written interpretive essays as an additional method of assessment in three undergraduate mathematics courses. The primary objectives of this study were to evaluate the benefits of using concept maps and written essays to assess the “connectedness” of students' knowledge; to measure the correlation between students' scores on the concept maps and written essays, course exams, and final grade; and to document students' perception of the effect of this approach on their mathematical knowledge. Results indicated that concept maps, when combined with written essays, are viable tools for assessing students' organization of mathematical knowledge. In addition, students perceive this approach as enhancing their mathematical knowledge.     

Convergence and finite determination of formal CR mappings

It is shown that a formal mapping between two real-analytic hypersurfaces in complex space is convergent provided that neither hypersurface contains a nontrivial holomorphic variety. For higher codimensional generic submanifolds, convergence is proved e.g. under the assumption that the source is of finite type, the target does not contain a nontrivial holomorphic variety, and the mapping is finite. Finite determination (by jets of a predetermined order) of formal mappings between smooth generic submanifolds is also established.