Local approximability of max-min and min-max linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0. In a min-max LP, the objective is to minimise ρ subject to Ax ≤ ρ1, Cx ≥ 1, and x ≥ 0. The matrices A and C are nonnegative and sparse: each row ai of A has at most ΔI positive elements, and each row ck of C has at most ΔK positive elements. We study the approximability of max-min LPs and min-max LPs in a distributed setting; in particular, we focus on local algorithms (constant-time distributed algorithms). We show that for any ΔI ≥ 2, ΔK ≥ 2, and ε > 0 there exists a local algorithm that achieves the approximation ratio ΔI (1 − 1/ΔK) + ε. We also show that this result is the best possible: no local algorithm can achieve the approximation ratio ΔI (1 − 1/ΔK) for any ΔI ≥ 2 and ΔK ≥ 2.

A new classification and linear sequence of extant gymnosperms

A new classification and linear sequence of the gymnosperms based on previous molecular and morphological phylogenetic and other studies is presented. Currently accepted genera are listed for each family and arranged according to their (probable) phylogenetic position. A full synonymy is provided, and types are listed for accepted genera. An index to genera assists in easy access to synonymy and family placement of genera.

A linear sequence of extant families and genera of lycophytes and ferns

Throughout the history of the classification of extant ferns (monilophytes) and lycophytes, familial and generic concepts have been in great flux. For the organisation of lycophytes and ferns in herbaria, books, checklists, indices and spore banks and on the internet, this poses a problem, and a standardized linear sequence of these plants is therefore in great need. We provide here a linear classification to the extant lycophytes and ferns based on current phylogenetic knowledge; this provides a standardized guide for organisation of fern collections into a more natural sequence. Two new families, Diplaziopsidaceae and Rhachidosoraceae, are here introduced.

Incipient motion design of sand bed channels affected by bed suction

Seepage through sand bed channels in a downward direction (suction) reduces the stability of particles and initiates the sand movement. Incipient motion of sand bed channel with seepage cannot be designed by using the conventional approach. Metamodeling techniques, which employ a non-linear pattern analysis between input and output parameters and solely based on the experimental observations, can be used to model such phenomena. Traditional approach to find non-dimensional parameters has not been used in the present work. Parameters, which can influence the incipient motion with seepage, have been identified and non-dimensionalized in the present work. Non-dimensional stream power concept has been used to describe the process. By using these non-dimensional parameters; present work describes a radial basis function (RBF) metamodel for prediction of incipient motion condition affected by seepage. The coefficient of determination, R-2 of the model is 0.99. Thus, it can be said that model predicts the phenomena very well. With the help of the metamodel, design curves have been presented for designing the sand bed channel when it is affected by seepage. (C) 2010 Elsevier B.V. All rights reserved.

Effect of wall thickness on the end corrections of the extended inlet and outlet of a double-tuned expansion chamber

Simple expansion chambers, the simplest of the muffler configurations, have very limited practical application due to the presence of periodic troughs in the transmission loss spectrum which drastically lower the overall transmission loss of the muffler. Tuned extended inlet and outlet can be designed to nullify three-fourths of these troughs, making use of the plane wave theory. These cancellations would not occur unless one altered the geometric lengths for the extended tube in order to incorporate the effect of evanescent higher-order modes (multidimensional effect) through end corrections or lumped inertance approximation at the area discontinuities or junctions. End corrections of the extended inlet and outlet have been studied by several researchers. However the effect of wall thickness of the inlet/outlet duct on end correction has not been studied explicitly. This has significant effect on the tuning of an extended inlet/outlet expansion chamber. It is investigated here experimentally as well as numerically (through use of 3-D FEM software) for stationary medium. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.

On duality in linear fractional programming

In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.

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.

Improved Inverted V-Notch or Chimney Weir

This paper is devoted to the improvement of the measuring range of inverted V-notch (IVN) weir, a practical linear sharp-crested weir, designed earlier by the writers. The range of linearity of IVN can be considerably enhanced (by more than 200%) by the addition of a retangular weir of width 0.265W (W = half crest width) at a depth of 0.735d (d = altitude of IVN), above the crest of the weir, which is equivalent to providing at this depth two vertical straight lines to the IVN, resulting in a chimney-shaped profile; hence, the modified weir is named chimney weir. The design parameters of the weir, that is, the linearity range, base flow depth, and datum constant, which fixes the reference plane of the weir, are estimated by solving the nonlinear programming problem using a numerical optimization procedure. For flows through this weir above a depth of 0.22d, the discharges are proportional to the depth of flow measured above a reference plane situated at 0.08d above the weir crest for all heads in the range 0.22d <= h <= 2.43d, within a maximum percentage deviation of ±1.5 from the theoretical discharge. A significant result of the analysis is that the same linear head-discharge relationship governing the flow through the IVN is also valid for the extended chimney weir. Experiments with three different chimney weirs show excellent agreement with the theory by giving a constant average coefficient of discharge for each weir.

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.

A Novel Method for the Uniform Incorporation of Grain-Boundary Layer Modifiers in Positive Temperature Coefficient of Resistivity Barium Titanate

The presently developed two-stage process involves diping the prefired porous disks of n-BaTiO3 in nonaqueous solutions containing Al-buty rate, Ti-isopropoxide, and tetraethyl silicate and subsequent sintering. This leads to uniform distribution of the grain-boundary layer (GBL) modifiers (Al2O3+ TiO2+ SiO2) and better control of the grain size as well as the positive temperature coefficient of resistivity characteristics. The technique is particularly suited for GBL modifiers in low concentrations (< 1%).

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.