Nonnegative integral solution of linear equations

A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.

A High Pressure Study of the Phase Diagram and the Critical Exponent β of Binary Liquid Systems

The pressure dependence of critical parameters xc, Tc, and β have been analysed in four systems namely cyclohexane + acetic anhydride, n-heptane + acetic anhydride, methanol + n-heptane, and carbon disulphide + acetonitrile. The separation temperature was found to increase linearly with pressure the value of dTc/dP being 28 mK, 11 mK, 22 mK, and 25 mK respectively. These are in fair agreement with earlier measurements available for two systems. For the methanol + n-heptane system dTc/dP is apparently not consistent with the value predicted from the specific heat and thermal expansion data.Die Druckabhängigkeit der kritischen Parameter xc, Tc und β ist in den vier Systemen Cyclohexan + Essigsäureanhydrid, n-Heptan + Essigsäureanhydrid, Methanol + n-Heptan und Schwefelkohlenstoff + Acetonitril analysiert worden. Es wurde gefunden, daß die kritische Temperatur linear mit dem Druck ansteigt. Die Werte für dTc/dP betragen 28 mK, 11 mK, 22 mK und 25 mK. Sie sind in guter überein-stimmung mit früheren Messungen an zweien dieser Systeme. Für Methanol + n-Heptan stimmt der Wert für dT/dP offensichtlich nicht mit Werten, die mit Hilfe von Daten für die spezifische Wärme und die thermische Ausdehnung vorhergesagt wurden, überein.

An efficient algorithm for linear programming

A simple but efficient algorithm is presented for linear programming. The algorithm computes the projection matrix exactly once throughout the computation unlike that of Karmarkar’s algorithm where in the projection matrix is computed at each and every iteration. The algorithm is best suitable to be implemented on a parallel architecture. Complexity of the algorithm is being studied.

An optimal parallel algorithm for sparse matrix bandwidth reduction on a linear array

A simple and efficient algorithm for the bandwidth reduction of sparse symmetric matrices is proposed. It involves column-row permutations and is well-suited to map onto the linear array topology of the SIMD architectures. The efficiency of the algorithm is compared with the other existing algorithms. The interconnectivity and the memory requirement of the linear array are discussed and the complexity of its layout area is derived. The parallel version of the algorithm mapped onto the linear array is then introduced and is explained with the help of an example. The optimality of the parallel algorithm is proved by deriving the time complexities of the algorithm on a single processor and the linear array.

2-Dimensional Linear-Stability of Premixed Laminar Flames Under Zero-Gravity

This paper reports on the numerical study of the linear stability of laminar premixed flames under zero gravity. The study specifically addresses the dependence of stability on finite rate chemistry with low activation energy and variable thermodynamic and transport properties. The calculations show that activation energy and details of chemistry play a minor role in altering the linear neutral stability results from asymptotic analysis. Variable specific heat makes a marginal change to the stability. Variable transport properties on the other hand tend to substantially enhance the stability from critical wave number of about 0.5 to 0.20. Also, it appears that the effects of variable properties tend to nullify the effects of non-unity Lewis number. When the Lewis number of a single species is different from unity, as will happen in a hydrogen-air premixed flame, the stability results remain close to that of unity Lewis number.

A note on resolving infeasibility in linear programs by constraint relaxation

We study the problem of finding a set of constraints of minimum cardinality which when relaxed in an infeasible linear program, make it feasible. We show the problem is NP-hard even when the constraint matrix is totally unimodular and prove polynomial-time solvability when the constraint matrix and the right-hand-side together form a totally unimodular matrix.

Crystal structures, spectral and magnetic properties of (µ-hydroxo)(µ-acetato)dicopper(II) complexes containing chelating amines

The reaction of [Cu2(O2CMe)4(H2O)2] with N, N, N′, N′-tetramethylethane- 1,2-diamine (tmen) in ethanol yielded the dicopper(II) complex [Cu2(OH)(O2CMe)(tmen)2][ClO4]21. A similar reaction with N, N- dimethylethane- 1,2-diamine (dmen) afforded a crystalline product 2 in which two dicopper(II) complexes, [Cu2(OH)(O2CMe)(dmen)2][ClO4]22a and [Cu2(OH)(O2CMe)(H2O)2(dmen)2][ClO4]22b, are cocrystallized in a 1 : 1 molar ratio along with 2NaClO4. The crystal structures of 1 and 2 have been determined. The complexes have an asymmetrically dibridged [Cu2(µ-OH)(µ-O2CMe)]2+ core. The co-ordination geometry of the metal is square planar (CuO2N2). The copper atoms in 2b have a square-pyramidal CuO3N2 co-ordination sphere. The Cu Cu distances and Cu–O–Cu angles in 1, 2a and 2b are 3.339(2), 3.368(3), 3.395(7)Å, 120.1(2), 116.4(1) and 123.6(2)°, respectively. Complex 1 exhibits an axial ESR spectrum in a methanol glass giving g∥= 2.26 (A∥= 164 × 10–4 cm–1) and g⊥= 2.04. The ESR spectra obtained from the bulk material of the dmen product are indicative of the presence of two dimers, viz. complex 2a(g∥= 2.25, A∥= 165 × 10–4 cm–1; g⊥= 2.03) and 2b(g∥= 2.19, A∥= 184 × 10–4 cm–1; g⊥= 2.0). Variable-temperature magnetic susceptibility measurements on these complexes show an intramolecular antiferromagnetic coupling in the dimeric core. The fitting parameters are J=–27.8 cm–1, g= 2.1 for complex 1 and J=–10.1 cm–1, g= 2.0 for 2. The magnetostructural properties of the complexes are discussed. There is a linear correlation of the –2J values with the Cu Cu distances among dibridged complexes having square-planar copper(II) centres.

Interruption and Uncooperativeness in Academic ELF Group Work : An Application of Linear Unit Grammar

This study addresses the challenge of analyzing interruption in spoken interaction. It begins with my observation of eight hours of academic group work among speakers of English as a lingua franca (ELF) in a university course. Unlike the common findings of ELF research which underscore the cooperative orientation of ELF users, this particular group gave strong impressions of interruption and uncooperativeness as they prepared a scientific group presentation. In the effort to investigate these impressions, I found that no satisfactory method exists for systematically identifying and analyzing interruptions. A useful tool was found in Linear Unit Grammar or LUG (Sinclair & Mauranen 2006), which analyzes spoken interaction prospectively as linear text. In the course of transcribing one of the early group work meetings, I developed a model of LUG-based criteria for identifying individual instances of interruption. With this system in place, I was then able to evaluate the aggregate occurrences of interruption in the group work and identify co-occurring interactive features which further influenced the perception of uncooperativeness. Finally, these aggregate statistics directed a return to the data and a contextually sensitive, qualitative analysis. This research cycle illuminates the interactive features which contributed to my own impressions of uncooperativeness, as well as the group members orientations to their own interruptive practice.

Field-dependent changeover from current-to voltage-limiting characteristics by non-linear n-type BaTiO3 ceramics

Non-linear resistors having current-limiting capabilities at lower field strengths, and voltage-limiting characteristics (varistors) at higher field strengths, were prepared from sintered polycrystalline ceramics of (Ba0.6Sr0.4)(Ti0.97Zr0.03)O3+0.3 at % La, and reannealed after painting with low-melting mixtures of Bi2O3 + PbO +B2O3. These types of non-linear characteristics were found to depend upon the non-uniform diffusion of lead and the consequent distribution of Curie points (T c) in these perovskites, resulting in diffuse phase transitions. Tunnelling of electrons across the asymmetric barrier at tetragonak-cubic interfaces changes to tunnelling across the symmetric barrier as the cubic phase is fully stabilized through Joule heating at high field strengths. Therefore the current-limiting characteristics switch over to voltage-limiting behaviour because tunnelling to acceptor-type mid-bandgap states gives way to band-to-band tunnelling.

Heat capacity measurements on Ge20Se80−xBix glasses

The specific heat Cp of glassy Ge20Se80−xBix (0 ≤ × ≤ 12) samples is investigated. The Cp at 323K and the ΔCp at glass transition temperature Tg1 show anomalous features around x = 8 at.%, where p−n conduction type inversion also take place. These features are discussed in the light of Phillips model of phase separation in these glasses at the microscopic level.

Intercalation of n-alkylamines in iron thiohypophosphate (FePS3)

The intercalation of linear alkylamines (C1-C4) in the two-dimensional (2D) Ising antiferromagnet, FePS3, has been investigated. Intercalation proceeds with a dilation of the interlayer distance. The expansion (approximately 3.8 angstrom) is the same for all four amine molecules, suggesting that they are oriented flat with respect to the layers. From an analysis of the products of deintercalation, it is concluded that the intercalated species are the alkylammonium cations and neutral amine molecules. The intercalated compounds are highly moisture sensitive, as reflected in the chemical nature of the intercalated species. Charge neutrality of the lattice after intercalation is preserved by the loss of Fe2+ ions from the lattice. These Fe2+ ions are further oxidized to form superparamagnetic Fe2O3 clusters, as confirmed by Mossbauer spectra and magnetic measurements. This was further corroborated by in situ EPR studies. The Fe-57 Mossbauer spectra of the intercalated compounds showed evidence for two species other than Fe2O3. On the basis of the observed isomer shifts and quadrupole splittings, they have been assigned to Fe2+ in an environment similar to that in FePS3 and in a distorted FePS3 environment. The temperature and field dependence of the magnetic susceptibility of single crystals of the amine-intercalated FePS3 have been measured. Their magnetic behavior shows many of the features expected of a 2D Ising antiferromagnet with random defects, Fe1-xPS3, in agreement with the mechanism of intercalation.

Polarimetric Measurements in a Severe Hailstorm

This study explores the utility of polarimetric measurements for discriminating between hydrometeor types with the emphasis on (a) hail detection and discrimination of its size, (b) measurement of heavy precipitation, (c) identification and quantification of mixed-phase hydrometeors, and (d) discrimination of ice forms. In particular, we examine the specific differential phase, the backscatter differential phase, the correlation coefficient between vertically and horizontally polarized waves, and the differential reflectivity, collected from a storm at close range. Three range–height cross sections are analyzed together with complementary data from a prototype WSR-88D radar. The case is interesting because it demonstrates the complementary nature of these polarimetric measurands. Self-consistency among them allows qualitative and some quantitative discrimination between hydrometeors.