On second order degree of graphs

Given a vertex v of a graph G the second order degree of v denoted as d 2(v) is defined as the number of vertices at distance 2 from v.In this paper we address the following question:What are the sufficient conditions for a graph to have a vertex v such that d2(v) ≥ d(v),where d(v) denotes the degree of v? Among other results,every graph of minimum degree exactly 2,except four graphs,is shown to have a vertex of second order degree as large as its own degree.Moreover,every K-4-free graph or every maximal planar graph is shown to have a vertex v such that d2(v) ≥ d(v).Other sufficient conditions on graphs for guaranteeing this property are also proved.     

Theoretical study of AlC3+

A theoretical study of the AlC₃⁺ species has been carried out. Predictions have been made for some of the molecular properties (geometries, dipole moments, and harmonic vibrational frequencies) which could help in their possible experimental detection. In addition, a topological analysis of the electron density and its associated Laplacian has also been carried out. The global ground state is predicted to be a linear species with ¹Σ electronic state, but a rhombic four‐membered ring (¹A₁) lies close in energy. It seems that both isomers could be accessible to experimental detection. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Optimization of Biodegradable Nanocomposites Based on aPLA/PCL Blends for Food Packaging Applications

Biodegradable blends of amorphous poly(lactic acid) (aPLA) and polycaprolactone (PCL) and nanocomposites of these blends were developed by melt blending. A morphological study of the bioblends was carried out by means of WAXS and SEM showing immiscible behavior. The nanocomposites were also characterized morphologically by WAXS, TEM and SEM, revealing high degree of interaction of the nanoclays with the aPLA. Mechanical, thermal and gas barrier properties of the different blends and nanocomposites were studied and the effect of blending and clay addition on the above-mentioned properties was evaluated.     

Tensor Characterizations of Summing Polynomials

Operators T that belong to some summing operator ideal can be characterized by means of the continuity of an associated tensor operator \({\overline{T}}\) that is defined between tensor products of sequences spaces. In this paper, we provide a unifying treatment of these tensor product characterizations of summing operators. We work in the more general frame provided by homogeneous polynomials, where an associated “tensor” polynomial—which plays the role of \({\overline{T}}\)—, needs to be determined first. Examples of applications are shown.     

Simultaneous-fluorimetric methods for the determination of ammonia and urea by use of flow injection configurations with dual injection valves

Summary Two fluorimetric methods are proposed for the simultaneous determination of ammonia and urea based on the reaction of the former with o-phthalaldehyde/2-mercaptoethanol and on the use of a dual injection system in which the valves are coupled in series or in parallel. An enzymatic reactor converts urea into ammonia which is determined by the same reaction. These configurations provide very similar results with a linear determination range between 0.5 and 10.0 g ml^–1 and a sampling frequency of 60 h^–1. The proposed methods are very tolerant to foreign species commonly found in water, as shown by applying them to samples of different origins.     

I2-Catalyzed enantioselective ring expansion of beta-lactams to gamma-lactams through a novel C3-C4 bond cleavage. Direct entry to protected 3,4-dihydroxypyrrolidin-2-one derivatives

Molecular iodine (10 mol%) efficiently catalyzes the ring expansion of 4-oxoazetidine-2-carbaldehydes in the presence of tert-butyldimethyl cyanide to afford protected 5-cyano-3,4-dihydroxypyrrolidin-2-ones with good yield and high diastereoselectivity, through a novel C3-C4 bond cleavage of the beta-lactam nucleus.     

Economic lot scheduling with deliberated and controlled coproduction

This paper presents an algorithm to define the optimal parameters for deliberated and controlled coproduction in an economic lot scheduling problem setting (DCCELSP). Coproduction is said to be deliberated and controlled because it is possible to decide whether or not to coproduce when all the parameters associated with the process are known. The aim is to determine how to produce two products most economically where deliberated coproduction is an option. For this purpose, a procedure for defining optimal lot periods is introduced. Two models are proposed for this procedure and a numerical illustration is provided to gain insight into their dynamics. The cost advantages of coproduction were found to depend on the relationship between setup and holding costs, production rates, and demand for products. The more similar these system parameters are and the higher the machine usage ratio is, the more favourable coproduction is. Additionally, if coproduction is not deliberated appropriately, costs soar.     

Determination of the free activation energy for the breaking of the P---Ag bond in [(η-p-cymene)Ru(μ-pz)3Ag(PPh3)]

The Arrhenius equation corresponding to the process P---Ag+P*---Ag*→---P---Ag*+P*---Ag has been determined for [(η⁶-p-cymene)Ru(μ-pz)₃Ag(PPh₃)] (1) by complete line-shape analysis of the ³¹P NMR spectra between −40°C and +30°C. It has the form K = 10^11.8± e^{(−46±5 kJ mol−1/RT)}. The preexponential term, log A = 11.8 corresponds to a small activation entropy, whereas the activation energy, 46 kJ mol⁻¹ is comparable to those determined for other phosphorus—metal compounds.