A 14N NMR study of the isomeric structures of urea and its analogues

In urea and its structural analogues differences in excess of 100 ppm are found in the nitrogen screening constants for the amide- and isoamide-type structures. The nitrogen chemical shifts are interpreted within the framework of Pople's gauge dependent atomic orbital approximation using INDO molecular orbitals. It is demonstrated that this method provides reasonable values for nitrogen absolute screening constants. The experimental data reported should be useful in examinations of tautomeric equilibria in amides and related structures.     

Determining Optimum Fertilizer Combinations Through Goal Programming with Penalty Functions: An Application to Sugar Beet production in Spain

A goal programming model was used to analyse optimum fertilizer combinations. Under this approach, the fertilizer requirements, instead of being fixed values as in traditional linear programming, are considered targets which may or may not be achieved. A penalty system coupled to the goal programming model makes the specified lower and upper levels of nutrients more flexible and realistic. A simple example is used to expound the model, and then applied to real data to give optimum combinations of fertilizers for sugar beet in Western Andalusia (Spain).     

The Painleve Ping-Pong P IV

We construct a transformation which generates new solutions for a one-parameter family of the fourth Painlevé equations. We obtain solutions with the same parameter values as in the given equation. Also we obtain new relations between two Painlevé transcendents of the fourth kind with different free parameters.     

Chromatographic method for the isolation of active 40S and 60S subunits from rat liver polyribosomes

A rapid and simple procedure for isolation of 40S and 60S ribosomal subunits by ion-exchange column chromatography is described. The dissociated ribosomes can be separated and non-ribosomal proteins and low-molecular-weight substances removed. An assessment by physicochemical and functional criteria showed that the ribosomal subunits obtained are active and sufficiently homogeneous.     

Discriminant versus rough sets approach to vague data analysis

This paper presents a comparative study of the use of two different methods of data analysis on a common set of data. The first is a method based on rough sets theory and the second is the location model method from the field of discriminant analysis. To investigate the comparative performance of these methods, a set of real medical data has been used. The data considered are of both discrete and continuous character. During the comparison, particular attention is paid to data reduction and to the derivation of decision rules and classification functions from the reduced set.     

Geometry and ergodic theory of non-recurrent elliptic functions

We explore the class of elliptic functions whose critical points all contained in the Julia set are non-recurrent and whose ω-limit sets form compact subsets of the complex plane. In particular, this class comprises hyperbolic, subhyperbolic and parabolic elliptic maps. Leth be the Hausdorff dimension of the Julia set of such an elliptic functionf. We construct an atomlessh-conformal measurem and show that theh-dimensional Hausdorff measure of the Julia set off vanishes unless the Julia set is equal to the entire complex plane ℂ. Theh-dimensional packing measure is positive and is finite if and only if there are no rationally indifferent periodic points. Furthermore, we prove the existence of a (unique up to a multiplicative constant) σ-finitef-invariant measure μ equivalent tom. The measure μ is shown to be ergodic and conservative, and we identify the set of points whose open neighborhoods all have infinite measure μ. In particular, we show that ∞ is not among them. The research of the first author was supported in part by the Foundation for Polish Science, the Polish KBN Grant No 2 PO3A 034 25 and TUW Grant no 503G 112000442200. She also wishes to thank the University of North Texas where this research was conducted. The research of the second author was supported in part by the NSF Grant DMS 0100078. Both authors were supported in part by the NSF/PAN grant INT-0306004.     

Photoreflectance study of energy level structure of self-assembled InAs/GaAs quantum dots emitting at 1.3 μm

Photoreflectance and photoluminescence measurements were performed on the ensemble of self assembled InAs/GaAs quantum dots designed to emit at 1.3 μm. As many as six QDs-related optical transitions were observed in PR spectra, the energies of which were confirmed by high-excitation PL results. Numerical calculations allowed estimating the average size of the dots, which is larger than for standard InAs/GaAs QDs. This result is in agreement with structural data. Additionally, the energy level structure for such QDs was derived and compared with the electronic structure of standard InAs/GaAs dots. It was shown that the energy level structure of such large dots qualifies them for the active region of a laser emitting at 1.3 μm.     

Endpoints of set-valued dynamical systems of asymptotic contractions of Meir–Keeler type and strict contractions in uniform spaces

In this paper, we introduce the concepts of the set-valued dynamical systems of asymptotic contractions of Meir–Keeler type and set-valued dynamical systems of strict contractions in uniform spaces and we present a method which is useful for establishing conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions. The result, concerning the investigations of problems of the set-valued asymptotic fixed point theory, include some well-known results of Meir and Keeler, Kirk and Suzuki concerning the asymptotic fixed point theory of single-valued maps in metric spaces. The result, concerning set-valued strict contractions (in which the contractive coefficient is not constant), is different from the result of Yuan concerning the existence of endpoints of Tarafdar–Vyborny generalized contractions (in which the contractive coefficient is constant) in bounded metric spaces and provides some examples of Tarafdar–Yuan topological contractions in compact uniform spaces. Definitions and results presented here are new for set-valued dynamical systems in uniform, locally convex and metric spaces and even for single-valued maps. Examples show a fundamental difference between our results and the well-known ones.     

Degrees in a digraph whose nodes are graphs

By an f-graph we mean an unlabeled graph having no vertex of degree greater than f. Let D(n, f) denote the digraph whose node set is the set of f-graphs of order n and such that there is an arc from the node corresponding to graph H to the node corresponding to the graph K if and only if K is obtainable from H by the addition of a single edge. In earlier work, algorithms were developed which produce exact results about the structure of D(n, f), nevertheless many open problems remain. For example, the computation of the order and size of D(n, f) for a number of values of n and f have been obtained. Formulas for the order and size for f = 2 have also been derived. However, no closed form formulas have been determined for the order and size of D(n, f) for any value of f. Here we focus on questions concerning the degrees of the nodes in D(n,n − 1) and comment on related questions for D(n,f) for 2 f < n − 1.