Qualitative theorem proving in linear constraints

We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take place through the elimination of middle terms, and because the computational complexity of the proof is not an issue. Indeed what we need is the existence of the proof and not its mechanization. In this paper, we treat the linear case and illustrate the power of this paradigm by giving extremely simple proofs of two central theorems in the complexity and geometry of linear programming.

The validity of the Adler-Bardeen theorem in the supersymmetric U(1) gauge model

Using the dimensional reduction regularization scheme, we show that radiative corrections to the anomaly of the axial current, which is coupled to the gauge field, are absent in a supersymmetric U(1) gauge model for both 't Hooft-Veltman and Bardeen prescriptions for γ5. We also discuss the results with reference to conventional dimensional regularization. This result has significant implications with respect to the renormalizability of supersymmetric models.

Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Microprocessor-controlled automatic focusing of a lens

Maximum intensity contrast has been used as a measure of lens defocus. A photodiode array under the control of 8085 microprocessor is used to measure the maximum intensity contrast and to position the lens for best focus. The lens is moved by a stepper motor under processor control at a speed of 350 to 500 steps/s. At this speed, focusing time was found to be between 5 and 8 s. Under coherent illuminating conditions, an accuracy of ± 50 μm has been achieved.

Multi Pattern Dynamic Time Warping For Automatic Speech Recognition

We are addressing the problem of jointly using multiple noisy speech patterns for automatic speech recognition (ASR), given that they come from the same class. If the user utters a word K times, the ASR system should try to use the information content in all the K patterns of the word simultaneously and improve its speech recognition accuracy compared to that of the single pattern based speech recognition. T address this problem, recently we proposed a Multi Pattern Dynamic Time Warping (MPDTW) algorithm to align the K patterns by finding the least distortion path between them. A Constrained Multi Pattern Viterbi algorithm was used on this aligned path for isolated word recognition (IWR). In this paper, we explore the possibility of using only the MPDTW algorithm for IWR. We also study the properties of the MPDTW algorithm. We show that using only 2 noisy test patterns (10 percent burst noise at -5 dB SNR) reduces the noisy speech recognition error rate by 37.66 percent when compared to the single pattern recognition using the Dynamic Time Warping algorithm.

Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

Automatic phonetic transcription of Tamil in Roman script

Simple formalized rules are proposed for automatic phonetic transcription of Tamil words into Roman script. These rules are syntax-directed and require a one-symbol look-ahead facility and hence easily automated in a digital computer. Some suggestions are also put forth for the linearization of Tamil script for handling these by modern machinery.

Automatic Path Planning and Control Design for Autonomous Landing of UAVs using Dynamic Inversion

In this paper a nonlinear control has been designed using the dynamic inversion approach for automatic landing of unmanned aerial vehicles (UAVs), along with associated path planning. This is a difficult problem because of light weight of UAVs and strong coupling between longitudinal and lateral modes. The landing maneuver of the UAV is divided into approach, glideslope and flare. In the approach UAV aligns with the centerline of the runway by heading angle correction. In glideslope and flare the UAV follows straight line and exponential curves respectively in the pitch plane with no lateral deviations. The glideslope and flare path are scheduled as a function of approach distance from runway. The trajectory parameters are calculated such that the sink rate at touchdown remains within specified bounds. It is also ensured that the transition from the glideslope to flare path is smooth by ensuring C-1 continuity at the transition. In the outer loop, the roll rate command is generated by assuring a coordinated turn in the alignment segment and by assuring zero bank angle in the glideslope and flare segments. The pitch rate command is generated from the error in altitude to control the deviations from the landing trajectory. The yaw rate command is generated from the required heading correction. In the inner loop, the aileron, elevator and rudder deflections are computed together to track the required body rate commands. Moreover, it is also ensured that the forward velocity of the UAV at the touch down remains close to a desired value by manipulating the thrust of the vehicle. A nonlinear six-DOF model, which has been developed from extensive wind-tunnel testing, is used both for control design as well as to validate it.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Automatic Road Extraction using High Resolution Satellite Image Based on Texture Progressive Analysis and Normalized Cut Method

In this paper the approach for automatic road extraction for an urban region using structural, spectral and geometric characteristics of roads has been presented. Roads have been extracted based on two levels: Pre-processing and road extraction methods. Initially, the image is pre-processed to improve the tolerance by reducing the clutter (that mostly represents the buildings, parking lots, vegetation regions and other open spaces). The road segments are then extracted using Texture Progressive Analysis (TPA) and Normalized cut algorithm. The TPA technique uses binary segmentation based on three levels of texture statistical evaluation to extract road segments where as, Normalizedcut method for road extraction is a graph based method that generates optimal partition of road segments. The performance evaluation (quality measures) for road extraction using TPA and normalized cut method is compared. Thus the experimental result show that normalized cut method is efficient in extracting road segments in urban region from high resolution satellite image.