Grid based ionospheric error correction is an effective method in GNSS. Apart from critical applications, like SBAS, the grid ionospheric data disseminated through GNSS signal are also used for various non-critical ap...
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Grid based ionospheric error correction is an effective method in GNSS. Apart from critical applications, like SBAS, the grid ionospheric data disseminated through GNSS signal are also used for various non-critical applications, like near real-time ionospheric mapping etc. However, the grid-based correction approach and the related applications may experience deterioration in performance, if one or more source reference receivers fail to measure the TEC, or experience poor measurement quality over an extended time, rendering some of the grid data unavailable. This situation is more probable at the equatorial ionospheric regions, due to its high dynamics and sensitivity to external disturbances. This work uses simple feed forward neural network with 30 days training period to predict the grid VTEC values during this period of unavailability. The results show that, if aided with discrete VTEC measurements at only 3 or more grid points (α-points) as inputs during the period of prediction, the network can predict the grid VTEC values over considerably large spatial area with adequate accuracy over extended time periods. In this work, the network has been tested for continuous 07 and 30 days of predictions and found to be performing appreciably well. The errors were bound within 5 TECU with 95 % confidence. The prediction performance showed seasonal variability with best performance during the summer. Over a day, the accuracy was found to get worse during afternoon. Upon comparing with persistence type prediction, the performance of this approach was found to give accuracy improvement of 6 – 12 TECU. The prediction accuracy was observed to deteriorate for reduced α-points, which in general, cannot be compensated with increased training period. However, it showed good enough accuracy in predicting the VTEC values on a geomagnetically disturbed day, generating confidence to be used as an alternative source for VTEC data quite satisfactorily. This alternate determination of
Using block-pulse functions (BPFs)/shifted Legendre polynomials (SLPs) a unified approach for computing optimal control law of linear time-varying time-delay systems with reverse time terms and quadratic performance i...
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Using block-pulse functions (BPFs)/shifted Legendre polynomials (SLPs) a unified approach for computing optimal control law of linear time-varying time-delay systems with reverse time terms and quadratic performance index is discussed in this paper. The governing delay-differential equations of dynamical systems are converted into linear algebraic equations by using operational matrices of orthogonal functions (BPFs and SLPs). The problem of finding optimal control law is thus reduced to the problem of solving algebraic equations. One example is included to demonstrate the applicability of the proposed approach. (C) 2010 The Franklin Institute. Published by Elsevier Ltd L All rights reserved.
The rational Cherednik algebra H is a certain algebra of differential-reflection operators attached to a complex reflection group W and depending on a set of central parameters. Each irreducible representation S-lambd...
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The rational Cherednik algebra H is a certain algebra of differential-reflection operators attached to a complex reflection group W and depending on a set of central parameters. Each irreducible representation S-lambda of W corresponds to a standard module M(lambda) for H. This paper deals with the infinite family G(r, 1, n) of complex reflection groups;our goal is to study the standard modules using a commutative subalgebra t of H discovered by Dunkl and Opdam. In this case, the irreducible W-modules are indexed by certain sequences lambda of partitions. We first show that t acts in an upper triangular fashion on each standard module M(lambda), with eigenvalues determined by the combinatorics of the set of standard tableaux on lambda. As a consequence, we construct a basis for M(lambda) consisting of orthogonal functions on C-n with values in the representation S-lambda. For G(1, 1, n) with lambda = (n) these functions are the non-symmetric Jack polynomials. We use intertwining operators to deduce a norm formula for our orthogonal functions and give an explicit combinatorial description of the lattice of submodules of M(lambda) in the case in which the orthogonal functions are all well-defined. A consequence of our results is the construction of a number of interesting finite dimensional modules with intricate structure. Finally, we show that for a certain choice of parameters there is a cyclic group of automorphisms of H so that the rational Cherednik algebra for G(r, p, n) is the fixed subalgebra. Our results therefore descend to the rational Cherednik algebra for G(r, p, n) by Clifford theory.
Let {phi(n)}(n=0)(infinity) be a sequence of functions satisfying a second-order differential equation of the form alphaphi(n)'' + betaphi(n)' + (sigma + lambda(n)tau)phi(n) = f(n), where alpha, beta, sigm...
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Let {phi(n)}(n=0)(infinity) be a sequence of functions satisfying a second-order differential equation of the form alphaphi(n)'' + betaphi(n)' + (sigma + lambda(n)tau)phi(n) = f(n), where alpha, beta, sigma, tau, and f(n) are smooth functions on the real line R, and lambda(n) is the eigenvalue parameter. Then we find a necessary and sufficient condition in order for {phi(n)}(n=0)(infinity) to be orthogonal relative to a distribution w and then-we give a method to find the distributional orthogonalizing weight w. For such an orthogonal function system, we also give a necessary and sufficient condition in order that the derived set {(pphi(n))'}(n=0)(infinity) is orthogonal, which is a generalization of Lewis and Hahn. We also give various examples. (C) 2002 Elsevier Science B.V. All rights reserved.
We construct examples of H-infinity functions f on the unit disk such that the push-forward of Lebesgue measure on the circle is a radially symmetric measure mu(f) in the plane, and we characterize which symmetric mea...
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We construct examples of H-infinity functions f on the unit disk such that the push-forward of Lebesgue measure on the circle is a radially symmetric measure mu(f) in the plane, and we characterize which symmetric measures can occur in this way. Such functions have the property that {f(n)} is orthogonal in H-2, and provide counterexamples to a conjecture of W. Rudin, independently disproved by Carl Sundberg. Among the consequences is that there is an f in the unit ball of H-infinity such that the corresponding composition operator maps the Bergman space isometrically into a closed subspace of the Hardy space.
A system of orthogonal functions is suggested, which allows a statistically optimal description of turbulent fluctuations of the spatial density of the distribution function of identical Lagrangian air particles.
A system of orthogonal functions is suggested, which allows a statistically optimal description of turbulent fluctuations of the spatial density of the distribution function of identical Lagrangian air particles.
There are advantages in viewing orthogonal functions as functions generated by a random variable from a basis set of functions. Let Y be a random variable distributed uniformly on [0, 1]. We give two ways of generatin...
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There are advantages in viewing orthogonal functions as functions generated by a random variable from a basis set of functions. Let Y be a random variable distributed uniformly on [0, 1]. We give two ways of generating the Zernike radial polynomials with parameter 1, {Z(l+2n)(l)(x), n >= 0}. The first is using the standard basis {x(n), n >= 0} and the random variable Y(1/(l+1)). The second is using the nonstandard basis {x(l+2n), n >= 0} and the random variable Y(1/2). Zernike polynomials are important in the removal of lens aberrations, in characterizing video images with a small number of numbers, and in automatic aircraft identification.
In this paper two new recursive algorithms are presented for computing optimal control law of linear time-invariant singular systems with quadratic performance index by using the elegant properties of block-pulse func...
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In this paper two new recursive algorithms are presented for computing optimal control law of linear time-invariant singular systems with quadratic performance index by using the elegant properties of block-pulse functions (BPFs) and shifted Legendre polynomials (SLPs). Also a unified approach is given to solve the optimal control problem of singular systems via BPFs or SLPs. Two numerical examples are included to demonstrate the validity of the proposed algorithms and approach.
The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been co...
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The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f(t) of Lebesgue measure. (c) 2005 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
The present work proposes a method for solving Fredholm integral equations. This is demonstrated by using a complementary pair of orthogonal triangular functions set derived from the well-known block pulse functions s...
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The present work proposes a method for solving Fredholm integral equations. This is demonstrated by using a complementary pair of orthogonal triangular functions set derived from the well-known block pulse functions set. The operational matrices for integration, product of two triangular functions and some formulas for calculating definite integral of them are derived and utilized to reduce the solution of Fredholm integral equation to the solution of algebraic equations. Illustrative examples are included to show the high accuracy of the estimation, and to demonstrate validity and applicability of the method. (c) 2007 Elsevier Inc. All rights reserved.
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