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.

The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics

We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and ID NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of polynomial reproduction whilst deriving the shape functions. Nevertheless, given the higher complexity in forming the knotclouds for tetrahedral elements especially when higher demand is placed on the order of continuity of the shape functions across inter-element boundaries, we presently emphasize an exploration of the triangular prism based formulation in the context of several benchmark problems of interest in linear solid mechanics. In the absence of a more rigorous study on the convergence analyses, the numerical exercise, reported herein, helps establish the method as one of remarkable accuracy and robust performance against numerical ill-conditioning (such as locking of different kinds) vis-a-vis the conventional FEM.

Mobile Base Stations Placement and Energy Aware Routing in Wireless Sensor Networks

Increasing network lifetime is important in wireless sensor/ad-hoc networks. In this paper, we are concerned with algorithms to increase network lifetime and amount of data delivered during the lifetime by deploying multiple mobile base stations in the sensor network field. Specifically, we allow multiple mobile base stations to be deployed along the periphery of the sensor network field and develop algorithms to dynamically choose the locations of these base stations so as to improve network lifetime. We propose energy efficient low-complexity algorithms to determine the locations of the base stations; they include i) Top-K-max algorithm, ii) maximizing the minimum residual energy (Max-Min-RE) algorithm, and iii) minimizing the residual energy difference (MinDiff-RE) algorithm. We show that the proposed base stations placement algorithms provide increased network lifetimes and amount of data delivered during the network lifetime compared to single base station scenario as well as multiple static base stations scenario, and close to those obtained by solving an integer linear program (ILP) to determine the locations of the mobile base stations. We also investigate the lifetime gain when an energy aware routing protocol is employed along with multiple base stations.

Study Of Acoustic Source Localization Algorithm For Planar Arrays

The source localization algorithms in the earlier works, mostly used non-planar arrays. If we consider scenarios like human-computer communication, or human-television communication where the microphones need to be placed on the computer monitor or television front panel, i.e we need to use the planar arrays. The algorithm proposed in 1], is a Linear Closed Form source localization algorithm (LCF algorithm) which is based on Time Difference of Arrivals (TDOAs) that are obtained from the data collected using the microphones. It assumes non-planar arrays. The LCF algorithm is applied to planar arrays in the current work. The relationship between the error in the source location estimate and the perturbation in the TDOAs is derived using first order perturbation analysis and validated using simulations. If the TDOAs are erroneous, both the coefficient matrix and the data matrix used for obtaining source location will be perturbed. So, the Total least squares solution for source localization is proposed in the current work. The sensitivity analysis of the source localization algorithm for planar arrays and non-planar arrays is done by introducing perturbation in the TDOAs and the microphone locations. It is shown that the error in the source location estimate is less when we use planar array instead of the particular non-planar array considered for same perturbation in the TDOAs or microphone location. The location of the reference microphone is proved to be important for getting an accurate source location estimate if we are using the LCF algorithm.

Variable Elimination in Linear Constraints

Gauss and Fourier have together provided us with the essential techniques for symbolic computation with linear arithmetic constraints over the reals and the rationals. These variable elimination techniques for linear constraints have particular significance in the context of constraint logic programming languages that have been developed in recent years. Variable elimination in linear equations (Guassian Elimination) is a fundamental technique in computational linear algebra and is therefore quite familiar to most of us. Elimination in linear inequalities (Fourier Elimination), on the other hand, is intimately related to polyhedral theory and aspects of linear programming that are not quite as familiar. In addition, the high complexity of elimination in inequalities has forces the consideration of intricate specializations of Fourier's original method. The intent of this survey article is to acquaint the reader with these connections and developments. The latter part of the article dwells on the thesis that variable elimination in linear constraints over the reals extends quite naturally to constraints in certain discrete domains.

High-Rate Space-Time Coded Large MIMO Systems: Low-Complexity Detection and Performance

Large MIMO systems with tens of antennas in each communication terminal using full-rate non-orthogonal space-time block codes (STBC) from Cyclic Division Algebras (CDA) can achieve the benefits of both transmit diversity as well as high spectral efficiencies. Maximum-likelihood (ML) or near-ML decoding of these large-sized STBCs at low complexities, however, has been a challenge. In this paper, we establish that near-ML decoding of these large STBCs is possible at practically affordable low complexities. We show that the likelihood ascent search (LAS) detector, reported earlier by us for V-BLAST, is able to achieve near-ML uncoded BER performance in decoding a 32x32 STBC from CDA, which employs 32 transmit antennas and sends 32(2) = 1024 complex data symbols in 32 time slots in one STBC matrix (i.e., 32 data symbols sent per channel use). In terms of coded BER, with a 16x16 STBC, rate-3/4 turbo code and 4-QAM (i.e., 24 bps/Hz), the LAS detector performs close to within just about 4 dB from the theoretical MIMO capacity. Our results further show that, with LAS detection, information lossless (ILL) STBCs perform almost as good as full-diversity ILL (FD-ILL) STBCs. Such low-complexity detectors can potentially enable implementation of high spectral efficiency large MIMO systems that could be considered in wireless standards.

Linear electro‐optic dispersion in (‐)‐2‐(α‐methylbenzylamino)‐5‐nitropyridine single crystals

The variation of the linear electro-optic effect in (-)-2-(alpha-methylbenzylamino)-5-nitropyridine with the wavelength of the incident light at room temperature has been measured. The reduced half-wave voltages have been found to have the values 2.1, 2.8, and 6.0 kV at 488, 514.5, and 632.8 nm respectively and the corresponding values of the linear electro-optic coefficient have been evaluated.;The interpretation of the results in terms of the structures of the molecule and the crystal is discussed. The thermal variation of the birefringence has also been investigated and the coefficient for the temperature variation of the refractive index difference is found to have the value (d Delta n/dT)=9.3X10(-5) K-1.

Practical constant-accuracy linear weir

This paper is concerned with the modifications of the Extended Bellmouth Weir (EBM weir) earlier designed by Keshava Murthy. It is shown that by providing inclined sides (equivalent to providing an inward-trapezoidal weir) over a sector of a circle of radius R, separated by a distance 2t, and depth d, the measurable range of EBM can be considerably enhanced (over 375%). Simultaneously, the other parameters of the weir are optimized such that the reference plane of the weir coincides with its crest making it a constant-accuracy linear weir. Discharge through the aforementioned weir is proportional to the depths of flow measured above the crest of the weir for all heads in the range of 0.5R less-than-or-equal-to h less-than-or-equal-to 7.9R, within a maximum deviation of +/-1% from the theoretical discharge. Experiments with two typical weirs show excellent agreement with the theory by giving a constant-average coefficient of discharge of 0.619

Soft-chemical synthesis of new non-linear optical materials, K0.5M0.5Ti0.5OPO4(M = Nb, Ta),related to KTiOPO4

Soft-chemical oxidation of KTiOPO4-like KM(0.5)(V)Ti(0.5)(III)OPO(4) (M = Nb, Ta) using chlorine in CHCl3 is accompanied by partial deintercalation of potassium, yielding K(0.5)MV(0.5)Ti(0.5)(IV)OPO(4) compounds which are new non-linear optical materials that exhibit efficient second-harmonic generation of 1064 nm radiation, as does KTiOPO4.

Linear electro-optic effect and temperature coefficient of birefringence in 4-nitro-4script-methylbenzylidene aniline single crystals

A study of the linear electro?optic effect in single crystals of the organic compound, 4?nitro�4??methylbenzylidene aniline is reported. The reduced half?wave voltages have been found to have values 2.8, 1.3, and 1.1 kV at 632.8, 514.5, and 488.0 nm, respectively and the corresponding values of the largest linear electro?optic coefficient have been calculated. The thermal variation of the birefringence has also been investigated and the temperature variation of the refractive index difference is found to have the value, d?n/dT = 15.8 × 10?5 K?1.

On the dual head-discharge characteristics of a modified chimney weir

This paper is concerned with the dual head-discharge characteristics of a modified chimney weir. It is shown by an optimization procedure that the modified chimney weir having an inward trapezoidal weir over an inverted V-notch can produce discharges proportional to both the logarithm of the head as well as the linear power of the head reckoned independently over two different reference planes, within a prefixed maximum allowable percentage error from the theoretical discharge. A new technique is adopted to optimize the weir parameters, in order to obtain the maximum ranges of measurement under logarithmic, linear as well as combined characteristics. In the case of linear weir it is shown that it is possible to enhance the linearity range of the chimney weir by more than 540% and for a weir with constant indication accuracy by more than 350%. In addition, about 86% of the overall depth of the designed linear weir and over 90% of the logarithmic weir is converted as the corresponding measurable ranges. Experiments with four typical weirs give consistent constant average coefficient of discharge for each weir confirming the theory. The practical application of the weir in minor irrigation, hydraulic and other engineering fields is highlighted.

Structural dependence of density in high molecular weight esters

The effect of molecular structure on density has been examined in high molecular weight esters (molecular weight 300-900), having varying degrees of branching. Densities were calculated from an empirical equation, which agrees well with the experimental values (error +/-1.5%), irrespective of branching. Since density is related to molecular packing and hence to the molecular rotation, in n-alkanes, the glass transition temperature (T(g)) and density both increase with molecular weight, and hence T(g) is directly related to the density. The esters exhibit a complex behavior. In linear esters the T(g) decreases with molecular weight which is explained from group contribution and molecular interactions. In the +-branched esters, however, T(g) decreases with molecular weight until the molecular weight reaches 600 and increases sharply thereafter. The Y-branched esters show an intermediate behavior. The dependence of T(g) on molecular weight has been explained from the segmental motion.

A Rotor Flux Estimation During Zero and Active Vector Periods Using Current Error Space Vector From a Hysteresis Controller for a Sensorless Vector Control of IM Drive

This paper proposes a sensorless vector control scheme for general-purpose induction motor drives using the current error space phasor-based hysteresis controller. In this paper, a new technique for sensorless operation is developed to estimate rotor voltage and hence rotor flux position using the stator current error during zero-voltage space vectors. It gives a comparable performance with the vector control drive using sensors especially at a very low speed of operation (less than 1 Hz). Since no voltage sensing is made, the dead-time effect and loss of accuracy in voltage sensing at low speed are avoided here, with the inherent advantages of the current error space phasor-based hysteresis controller. However, appropriate device on-state drops are compensated to achieve a steady-state operation up to less than 1 Hz. Moreover, using a parabolic boundary for current error, the switching frequency of the inverter can be maintained constant for the entire operating speed range. Simple sigma L-s estimation is proposed, and the parameter sensitivity of the control scheme to changes in stator resistance, R-s is also investigated in this paper. Extensive experimental results are shown at speeds less than 1 Hz to verify the proposed concept. The same control scheme is further extended from less than 1 Hz to rated 50 Hz six-step operation of the inverter. Here, the magnetic saturation is ignored in the control scheme.

New La2CuO4 derivatives La(2-2x)Sr(2x)Cu(1-x)M(x)O(4) (M=Ti, Mn, Fe, or Ru): A study of linear Cu-O-M electronic interaction in two dimensions

Oxides of the general formula La2-2xSr2xCu1-xII,M(x)(IV)O(4) (M = Ti, Mn, Fe, or Ru), crystallizing in the tetragonal K,NIF, structure, have been synthesized. For M=Ti, only the x=0,5 member could be prepared, while for M=Mn and Fe, the composition range is 0 Cu(III)-O-Fe(III) valence degeneracy. Increasing the strontium content at the expense of lanthanum in La2-2xSr2xCu1-xFexO4 for x less than or equal to 0.20 renders the samples metallic but not superconducting. (C) 1997 Academic Press.

On the improvement of chimney weirs

This paper is devoted to the improvement in the range of operation (linearity range) of chimney weir (consisting of a rectangular weir or vertical slot over an inward trapezium), A new and more elegant optimization procedure is developed to analyse the discharge-head relationship in the weir. It is shown that a rectangular weir placed over an inverted V-notch of depth 0.90d gives the maximum operating range, where d is the overall depth of the inward trapezoidal weir (from the crest to the vertex). For all flows in the rectangular portion, the discharge is proportional to the linear power of the head, h, measured above a reference plane located at 0.292d below the weir crest, in the range 0.90d less than or equal to h less than or equal to 7.474: within a maximum error of +/-1.5% from the theoretical discharge. The optimum range of operation of the newly designed weir is 200% greater than that in the chimney weir designed by Keshava Murthy and Giridhar, and is nearly 950% greater than that in the inverted V-notch. Experiments with two weirs having half crest widths of 0.10 and 0.12 m yield a constant average coefficient of discharge of 0.634 and confirm the theory. The application of the weir in the design of rectangular grit chamber outlet is emphasized, in that the datum for the linear discharge-head relationship is below the crest level of the weir.