نتایج جستجو برای: fully normalized legendre functions

تعداد نتایج: 747502  

2012
B. M. Mohan Sanjeeb Kumar Kar

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed....

Journal: :Computer Physics Communications 2006
Simone Taioli Jonathan Tennyson

The WATERWAVES program suite performs complex scattering calculations by propagating a wave packet in a complex, full-dimensional potential for non-rotating (J = 0) but vibrating triatomic molecules. Potential energy and decay probability surfaces must be provided. Expectation values of geometric quantities can be calculated, which are useful for following the wave packet motion. The programs u...

Journal: :Proceedings of the American Mathematical Society 1974

1984
V. V. Goryunov V. M. Zakalyukin

We show that Lagrangian and Legendre varieties associated with matrix singularities and singularities of composite functions are stable in a sense which is a natural modification of Givental’s notion of stability of Lagrangian projections. The study of singular Lagrangian and Legendre varieties was initiated about twenty five years ago by Arnold when he was investigating singularities in the va...

2005
Hugo Touchette Christian Beck

We discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as Legendre-Fenchel transforms of functions analogous to free energy functions. We show that the Legendre-Fenchel transform of a free energy function yields the correct multifractal spectrum only when the latter is wholly concave. If the spectrum has no definite concavity, then the transform yield...

Journal: :Journal of Classical Analysis 2016

2001
Nobuhiro Asai

In this paper we will develop a systematic method to answer the questions (Q1)(Q2)(Q3)(Q4) (stated in Section 1) with complete generality. As a result, we can solve the difficulties (D1)(D2) (discussed in Section 1) without uncertainty. For these purposes we will introduce certain classes of growth functions u and apply the Legendre transform to obtain a sequence which leads to the weight seque...

Journal: :European Journal of Combinatorics 2016

2012
Jonathan M. Borwein Liangjin Yao

In this paper, we study the properties of integral functionals induced on LE(S, μ) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and...

Journal: :Pattern Recognition 2004
Chee-Way Chong Raveendran Paramesran Ramakrishnan Mukundan

By convention, the translation and scale invariant functions of Legendre moments are achieved by using a combination of the corresponding invariants of geometric moments. They can also be accomplished by normalizing the translated and/or scaled images using complex or geometric moments. However, the derivation of these functions is not based on Legendre polynomials. This is mainly due to the fa...

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