Information systems: On queries involving cardinalities

A query language is considered allowing queries which ask for the cardinality of a set of objects satisfying specified conditions, or ask whether or not some relations (equalities, inequalities, etc.) hold between the cardinalities of sets of objects satisfying some conditions. We describe a precise semantics of this language, and we give a complete axiom system for equivalent transformations of queries. By using these axioms we are able to transform any query into a normal form which makes the retrieval process more efficient.     

Lucky labelings of graphs

Suppose the vertices of a graph G were labeled arbitrarily by positive integers, and let S(v) denote the sum of labels over all neighbors of vertex v. A labeling is lucky if the function S is a proper coloring of G, that is, if we have S(u)≠S(v) whenever u and v are adjacent. The least integer k for which a graph G has a lucky labeling from the set {1,2,…,k} is the lucky number of G, denoted by η(G).Using algebraic methods we prove that η(G)?k+1 for every bipartite graph G whose edges can be oriented so that the maximum out-degree of a vertex is at most k. In particular, we get that η(T)?2 for every tree T, and η(G)?3 for every bipartite planar graph G. By another technique we get a bound for the lucky number in terms of the acyclic chromatic number. This gives in particular that for every planar graph G. Nevertheless we offer a provocative conjecture that η(G)?χ(G) for every graph G.     

CAM pilot plant for Mexico

The need for economic progress in the less developed countries is becoming increasingly obvious. The threat to the global economy due to their heavy indebtedness, combined with intensifying social unrest affecting a shrinking world are palpable signs of such a need. At the same time, a growing urgency is felt for balancing foreign trade and to increase U.S. exports.     

Chemical structure of poly(β‐cyclodextrin‐co‐citric acid)

We synthesized water‐insoluble polymers, poly(β‐cyclodextrin‐co‐citric acid)s, by heating a mixture of citric acid, cyclodextrin (CD), and Na₂HPO₄ as a catalyst with a 6 : 1 : 2 molar ratio at 160, 170, and 180°C for 10 and 20 min. The chemical composition of the polyesters was determined by high pressure liquid chromatography (HPLC) analysis of the polymer hydrolysates. The crosslinking mechanisms and thermal degradation of the polymers were also investigated. The polyesters contained 30–35% citric acid, 1–4% unsaturated carboxylic acids (i.e., itaconic, cis‐aconitic, trans‐aconitic, and mesaconic acids), and 60–70% CD, whereas about 40% of them were able to form inclusion complexes. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Identification of selective inhibitors of the potassium channel kv1.1-1.2((3)) by high-throughput virtual screening and automated patch clamp

Two voltage-dependent potassium channels, Kv1.1 (KCNA1) and Kv1.2 (KCNA2), are found to co-localize at the juxtaparanodal region of axons throughout the nervous system and are known to co-assemble in heteromultimeric channels, most likely in the form of the concatemer Kv1.1-1.2((3)) . Loss of the myelin sheath, as is observed in multiple sclerosis, uncovers the juxtaparanodal region of nodes of Ranvier in myelinated axons leading to potassium conductance, resulting in loss of nerve conduction. The selective blocking of these Kv channels is therefore a promising approach to restore nerve conduction and function. In the present study, we searched for novel inhibitors of Kv1.1-1.2((3)) by combining a virtual screening protocol and electrophysiological measurements on a concatemer Kv1.1-1.2((3)) stably expressed in Chinese hamster ovary K1 (CHO-K1) cells. The combined use of four popular virtual screening approaches (eHiTS, FlexX, Glide, and Autodock-Vina) led to the identification of several compounds as potential inhibitors of the Kv1.1-1.2((3)) channel. From 89 electrophysiologically evaluated compounds, 14 novel compounds were found to inhibit the current carried by Kv1.1-1.2((3)) channels by more than 80?% at 10?μM. Accordingly, the IC(50) values calculated from concentration-response curve titrations ranged from 0.6 to 6?μM. Two of these compounds exhibited at least 30-fold higher potency in inhibition of Kv1.1-1.2((3)) than they showed in inhibition of a set of cardiac ion channels (hERG, Nav1.5, and Cav1.2), resulting in a profile of selectivity and cardiac safety. The results presented herein provide a promising basis for the development of novel selective ion channel inhibitors, with a dramatically lower demand in terms of experimental time, effort, and cost than a sole high-throughput screening approach of large compound libraries.     

Reactions taking place in the system N,N,N′,N′,N″‐ pentakis(hydroxymethyl)melamine–oxirane in aqueous media

The results of studies on effects of the amount and type of oxirane, amount of catalyst and water, and temperature on the course of reactions taking place in the system N,N,N′,N′,N″‐pentakis(hydroxymethyl)melamine (PHMM)–oxirane carried out in aqueous media are reported. Quantitative determination of the content of functional groups present in the system and of side products formed in reactions of oxirane with water, made it possible to analyze in detail the processes taking place in the system. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 824–836, 2000