EXTENSIONS OF VECTOR BUNDLES WITH APPLICATION TO NOETHER-LEFSCHETZ THEOREMS

Given a smooth, projective variety Y over an algebraically closed field of characteristic zero, and a smooth, ample hyperplane section X subset of Y, we study the question of when a bundle E on X, extends to a bundle epsilon on a Zariski open set U subset of Y containing X. The main ingredients used are explicit descriptions of various obstruction classes in the deformation theory of bundles, together with Grothendieck-Lefschetz theory. As a consequence, we prove a Noether-Lefschetz theorem for higher rank bundles, which recovers and unifies the Noether-Lefschetz theorems of Joshi and Ravindra-Srinivas.

Role of predictors in downscaling surface temperature to river basin in India for IPCC SRES scenarios using support vector machine

In this paper, downscaling models are developed using a support vector machine (SVM) for obtaining projections of monthly mean maximum and minimum temperatures (T-max and T-min) to river-basin scale. The effectiveness of the model is demonstrated through application to downscale the predictands for the catchment of the Malaprabha reservoir in India, which is considered to be a climatically sensitive region. The probable predictor variables are extracted from (1) the National Centers for Environmental Prediction (NCEP) reanalysis dataset for the period 1978-2000, and (2) the simulations from the third-generation Canadian Coupled Global Climate Model (CGCM3) for emission scenarios A1B, A2, B1 and COMMIT for the period 1978-2100. The predictor variables are classified into three groups, namely A, B and C. Large-scale atmospheric variables Such as air temperature, zonal and meridional wind velocities at 925 nib which are often used for downscaling temperature are considered as predictors in Group A. Surface flux variables such as latent heat (LH), sensible heat, shortwave radiation and longwave radiation fluxes, which control temperature of the Earth's surface are tried as plausible predictors in Group B. Group C comprises of all the predictor variables in both the Groups A and B. The scatter plots and cross-correlations are used for verifying the reliability of the simulation of the predictor variables by the CGCM3 and to Study the predictor-predictand relationships. The impact of trend in predictor variables on downscaled temperature was studied. The predictor, air temperature at 925 mb showed an increasing trend, while the rest of the predictors showed no trend. The performance of the SVM models that are developed, one for each combination of predictor group, predictand, calibration period and location-based stratification (land, land and ocean) of climate variables, was evaluated. In general, the models which use predictor variables pertaining to land surface improved the performance of SVM models for downscaling T-max and T-min

A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization

While frame-invariant solutions for arbitrarily large rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a rotation vector parametrization, which uses only three parameters and provides a parsimonious storage of rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative rotations and a new rotation vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired rotation vector or its complement. This rules out an additive interpolation of total rotation vectors at the nodes. Hence, interpolations of relative rotation vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.

Prediction of Ultimate Capacity of Laterally Loaded Piles in Clay: A Relevance Vector Machine Approach

This study investigates the potential of Relevance Vector Machine (RVM)-based approach to predict the ultimate capacity of laterally loaded pile in clay. RVM is a sparse approximate Bayesian kernel method. It can be seen as a probabilistic version of support vector machine. It provides much sparser regressors without compromising performance, and kernel bases give a small but worthwhile improvement in performance. RVM model outperforms the two other models based on root-mean-square-error (RMSE) and mean-absolute-error (MAE) performance criteria. It also stimates the prediction variance. The results presented in this paper clearly highlight that the RVM is a robust tool for prediction Of ultimate capacity of laterally loaded piles in clay.

Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

Reduced complexity two stage vector quantization

We address the issue of complexity for vector quantization (VQ) of wide-band speech LSF (line spectrum frequency) parameters. The recently proposed switched split VQ (SSVQ) method provides better rate-distortion (R/D) performance than the traditional split VQ (SVQ) method, even at the requirement of lower computational complexity. but at the expense of much higher memory. We develop the two stage SVQ (TsSVQ) method, by which we gain both the memory and computational advantages and still retain good R/D performance. The proposed TsSVQ method uses a full dimensional quantizer in its first stage for exploiting all the higher dimensional coding advantages and then, uses an SVQ method for quantizing the residual vector in the second stage so as to reduce the complexity. We also develop a transform domain residual coding method in this two stage architecture such that it further reduces the computational complexity. To design an effective residual codebook in the second stage, variance normalization of Voronoi regions is carried out which leads to the design of two new methods, referred to as normalized two stage SVQ (NTsSVQ) and normalized two stage transform domain SVQ (NTsTrSVQ). These two new methods have complimentary strengths and hence, they are combined in a switched VQ mode which leads to the further improvement in R/D performance, but retaining the low complexity requirement. We evaluate the performances of new methods for wide-band speech LSF parameter quantization and show their advantages over established SVQ and SSVQ methods.

The dipole moments and molecular structure of substituted acetamides

Thioacetamide has a dipole moment substantially higher than the vector sum of the normal characteristic moments of its constituent bonds. However, the effect can reasonably be accounted for on the scheme of alterations in charge distribution and hence of bond moments proposed by Smith, Ree, Magee and Eyring. The same is probably true for chloroacetamide even though the problem of rotation about the C-C single bond renders the conclusion less certain. For cyanoacetamide, the observed moment cannot be accounted for satisfactorily on this basis.

A Combination of Hexagonal and 12-Sided Polygonal Voltage Space Vector PWM Control for IM Drives Using Cascaded Two-Level Inverters

This paper proposes a multilevel inverter configuration which produces a hexagonal voltage space vector structure in the lower modulation region and a 12-sided polygonal space vector structure in the overmodulation region. A conventional multilevel inverter produces 6n plusmn 1 (n = odd) harmonics in the phase voltage during overmodulation and in the extreme square-wave mode of operation. However, this inverter produces a 12-sided polygonal space vector location, leading to the elimination of 6n plusmn 1 (n = odd) harmonics in the overmodulation region extending to a final 12-step mode of operation with a smooth transition. The benefits of this arrangement are lower losses and reduced torque pulsation in an induction motor drive fed from this converter at higher modulation indexes. The inverter is fabricated by using three conventional cascaded two-level inverters with asymmetric dc-bus voltages. A comparative simulation study of the harmonic distortion in the phase voltage and associated losses in conventional multilevel inverters and that of the proposed inverter is presented in this paper. Experimental validation on a prototype shows that the proposed converter is suitable for high-power applications because of low harmonic distortion and low losses.

A Multilevel Inverter with Hexagonal and 12-sided Polygonal Space Vector Structure for Induction Motor Drive

This paper proposes a multilevel inverter which produces hexagonal voltage space vector structure in lower modulation region and a 12-sided polygonal space vector structure in the over-modulation region. Normal conventional multilevel inverter produces 6n +/- 1 (n=odd) harmonics in the phase voltage during over-modulation and in the extreme square wave mode operation. However, this inverter produces a 12-sided polygonal space vector location leading to the elimination of 6n 1 (n=odd) harmonics in over-modulation region extending to a final 12-step mode operation. The inverter consists of three conventional cascaded two level inverters with asymmetric dc bus voltages. The switching frequency of individual inverters is kept low throughout the modulation index. In the low speed region, hexagonal space phasor based PWM scheme and in the higher modulation region, 12-sided polygonal voltage space vector structure is used. Experimental results presented in this paper shows that the proposed converter is suitable for high power applications because of low harmonic distortion and low switching losses.

Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

Distance Relay Co-ordination Using Support Vector Machines in Power Transmission System

In this paper, a new approach to enhance the transmission system distance relay co-ordination is presented. The approach depends on the apparent impedance loci seen by the distance relay during all possible disturbances. In a distance relay, the impedance loci seen at the relay location is obtained by extensive transient stability studies. Support vector machines (SVMs), a class of patterns classifiers are used in discriminating zone settings (zone-1, zone-2 and zone-3) using the signals to be used by the relay. Studies on a sample 9-bus are presented for illustrating the proposed scheme.

The truncated dielectric-coated conducting sphere-radiation and gain characteristic

An exhaustive study of the radiation and gain characteristics of a truncated dielectric-coated conducting spherical antenna excited in the symmetric TM mode has been reported. The effect of the various structure parameters on the radiation and the gain characteristics for a few even and odd order TM., modes for different structures is shown. The theorctical radiation patterns and gain have been compared with experiment. It is found that there is good agreement between theory and experiment in the case of TM es and TM os,modes. A theoretical and experimental study of the radiation and gain characcteristics in the frequency range 8.0 to 12.0 GHz has been reported.

Nitrile Reversible ketenimine tautomerism in substituted alkylidene malononitriles and alkylidene cyanoacetates: A characteristic UV absorption band

Several alkylidene malononitriles (1b,1d,1e,2b and4b) and alkylidene cyanoacetates (1a,2a and4a) studied exhibit a long wavelength UV absorption band around 355 nm which shows a hyperchromic effect in the presence of ethanolic alkali. This band has been assigned to the ketenimine tautomer (5). Addition of water to1b,1e and2b gives the corresponding pyridine diols (7a,7b and8a) respectively. Similarly, addition of ethanol to1e and2b gave the corresponding ethoxypyridine derivatives (7c and8b). Mechanism of formation of these compounds is discussed. Structures, as well as mechanism of formation of1c,7c and10 obtained from1b,1e and2b respectively on standing at room temperature are also discussed.

Nitrileketenimine tautomerism in substituted alkylidene malononitriles and alkylidene cyanoacetates: A characteristic UV absorption band

Several alkylidene malononitriles (1b,1d,1e,2b and4b) and alkylidene cyanoacetates (1a,2a and4a) studied exhibit a long wavelength UV absorption band around 355 nm which shows a hyperchromic effect in the presence of ethanolic alkali. This band has been assigned to the ketenimine tautomer (5). Addition of water to1b,1e and2b gives the corresponding pyridine diols (7a,7b and8a) respectively. Similarly, addition of ethanol to1e and2b gave the corresponding ethoxypyridine derivatives (7c and8b). Mechanism of formation of these compounds is discussed. Structures, as well as mechanism of formation of1c,7c and10 obtained from1b,1e and2b respectively on standing at room temperature are also discussed.

Two Stage Transform Vector Quantization of LSFs for Wideband Speech Coding

We investigate the use of a two stage transform vector quantizer (TSTVQ) for coding of line spectral frequency (LSF) parameters in wideband speech coding. The first stage quantizer of TSTVQ, provides better matching of source distribution and the second stage quantizer provides additional coding gain through using an individual cluster specific decorrelating transform and variance normalization. Further coding gain is shown to be achieved by exploiting the slow time-varying nature of speech spectra and thus using inter-frame cluster continuity (ICC) property in the first stage of TSTVQ method. The proposed method saves 3-4 bits and reduces the computational complexity by 58-66%, compared to the traditional split vector quantizer (SVQ), but at the expense of 1.5-2.5 times of memory.