Triangular line graphs and word sense disambiguation

Linguists often represent the relationships between words in a collection of text as an undirected graph G=(V,E), where V is the vocabulary and vertices are adjacent in G if and only if the words that they represent co-occur in a relevant pattern in the text. Ideally, the words with similar meanings give rise to the vertices of a component of the graph. However, many words have several distinct meanings, preventing components from characterizing distinct semantic fields. This paper examines how the structural properties of triangular line graphs motivate the use of a clustering coefficient on the triangular line graph, thereby helping to identify polysemous words. The triangular line graph of G, denoted by T(G), is the subgraph of the line graph of G where two vertices are adjacent if the corresponding edges in G belong to a K₃.     

The problem of recovering the temperature and moisture fields in a porous body from incomplete initial data

We propose a statement and computational scheme for the inverse problem of recovering the temperature field and the moisture distribution in a body with incompletely known initial conditions. We give additional relations on the integral values of the unknown functions and introduce a test for the choice of a unique solution of the problem from the set of admissible temperature and moisture functions. We state conditions for independence of the additional data and obtain systems of equations and conditions that close the initial indeterminate problem. We study in detail the example of heat-moisture conduction in a layer. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 66–73.     

Control of damped vibrations of a rod by means of a concentrated force or moment loading

The optimal local loading regimes of a vibrating rod (one endpoint of the rod is fixed, while the second is stress-free), which ensure the damping of certain modes of elastic vibration over a minimal time interval, for a minimal norm of the control function and also under the simultaneous minimization of the time and the norm of the load function are given.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 71–75, 1987.     

2-Substituted hexahydroacylanthranils: Synthesis and selective reactions with amines

Summary In contrast to their aromatic analogues, the corresponding saturated diamides5–9 are formed exclusively when hexahydro-3,1,4-benzoxazinones (3,4) are reacted with amines. The cyclodehydration reaction of the diamides5–9 cannot be carried out at arbitrarily high temperatures.Saturated Heterocycles, Part 217. Part 216: L. Simon, S. G. Talpas, F. Fülöp, G. Bernáth, G. Argay, A. Kálmán, P. Sohár (1995) J Heterocyclic Chem32: 161     

Stereochemical studies—XXXVII: Saturated heterocycles—XIII Configuration and conformation of Z- and E-N-methyl- and -N- benzyl-2-p-nitrophenyl-4,5- and -5,6-tetramethylenetetrahydro-1,3-oxazines

The configuration and conformation of Z- and E-N-methyl- and -N-benzyl-2-p-nitrophenyl-4,5-, and -5,6-tetramethylenetetrahydro-1,3-oxazines were determined by ¹H and ¹³C NMR spectroscopy. The Z isomers were proved to be conformationally homogeneous, having the heteroatom in axial and equatorial position, respectively, in the case of the 5,6- and 4,5-tetramethylene compounds. Consequently, the p-nitrophenyl group and the anellated cyclohexyl ring are all-cis arranged in the Z-5,6-tetramethylene compounds while in the case of the Z-4,5-tetramethylene isomers the p-nitrophenyl group and the cyclohexyl ring are trans arranged to the hetero ring.     

Mapping prefer-opposite to prefer-one de Bruijn sequences

We present a mapping of the binary prefer-opposite de Bruijn sequence of order n onto the binary prefer-one de Bruijn sequence of order \(n-1\). The mapping is based on the differentiation operator \(D(\langle {b_1,\ldots ,b_l}\rangle ) = \langle b_2-b_1, b_3-b_2,\ldots , b_{l}-b_{l-1} \rangle \) where bit subtraction is modulo two. We show that if we take the prefer-opposite sequence \(\langle {b_1,b_2,\ldots ,b_{2^n}}\rangle \), apply D to get the sequence \(\langle {\hat{b}_1, \ldots , \hat{b}_{2^n-1}}\rangle \) and drop all the bits \(\hat{b}_i\) such that \(\langle {\hat{b}_i,\ldots ,\hat{b}_{i+n-1}}\rangle \) is a substring of \(\langle {\hat{b}_1,\ldots ,\hat{b}_{i+n-2}}\rangle \), we get the prefer-one de Bruijn sequence of order \(n-1\).     

Closed 3-stop center and periphery in graphs

A delivery person must leave the central location of the business, deliver packages at a number of addresses, and then return. Naturally, he/she wishes to reduce costs by finding the most efficient route. This motivates the following: Given a set of k distinct vertices S = { x1, x2, . . . , xk } in a simple graph G, the closed k-stop-distance of set S is defined to be dk( S) = min θ∈P (S ) (d(θ(x1), θ(x2)) + d(θ(x2), θ(x3)) + ··· + d(θ(xk), θ(x1))), where P (S) is the set of all permutations of S. That is the same as saying that dk( S) is the length of a shortest closed walk through the vertices { x1, . . . , xk }. The closed 2-stop distance is twice the standard distance between two vertices. We study the closed k-stop center and closed k-stop periphery of a graph, for k = 3.     

Preparative reversed-phase liquid chromatography of peptides. Isocratic two-step elution system for high loads on analytical columns

We have developed further our novel sample displacement chromatography (SDC) methodology to carry out preparative separations on analytical equipment and 15-cm analytical columns for sample loads < or = 200 mg. Thus, a two-step isocratic SDC protocol was developed and applied to the purification of important biologically active peptides, i.e. bradykinin antagonists of 10 and 11 residues. Following sample loading in 100% aqueous solvent at a concentration of approximately 7-10 mg/ml (with sample loads varying from 67 to 200 mg) onto a small C18 column (150 x 4.6 mm I.D., made up of three 50-mm columns attached in series), we applied isocratic elution with aqueous acetonitrile at two concentrations, the first (lower concentration) to displace hydrophilic impurities off the column and the second (higher concentration) to displace pure product from the column; hydrophobic impurities remain trapped on the column. This modified SDC approach promises to allow great flexibility in purifying peptides, at high yield of pure product (> 99% purity), and encompassing a range of sample hydrophobicities as well as sample loads (< or = 200 mg) varying by as much as a factor of three.     

2D numerical simulation of passive autocatalytic recombiner for hydrogen mitigation

Resolving hydrogen related safety issues, pertaining to nuclear reactor safety has been an important area of research world over for the past decade. The studies on hydrogen transport behavior and development of hydrogen mitigation systems are still being pursued actively in various research labs, including Bhabha Atomic Research Centre (BARC), in India. The passive autocatalytic recombiner (PAR) is one of such hydrogen mitigating device consisting of catalyst surfaces arranged in an open-ended enclosure. In the plate type recombiner design sheets made of stainless steel and coated with platinum catalyst material are arranged in parallel inside a flow channel. The catalyst elements are exposed to a constant flow of a mixture of air, hydrogen and steam, a catalytic reaction occurs spontaneously at the catalyst surfaces and the heat of reaction produces natural convection flow through the enclosure. Numerical simulation and experiments are required for an in-depth knowledge of such plate type PAR. Specific finite volume based in-house 2D computational fluid dynamics (CFD) code has been developed to model and analyse the working of these recombiners and has been used to simulate one literature quoted experiment. The validation results were in good agreement against literature quoted German REKO experiments. Parametric study has been performed for particular recombiner geometry for various inlet conditions. Salient features of the simplified CFD model developed at BARC and results of the present model calculations are presented in this paper.