The stochastic optimal control uses the differential equation of Bellman and its solution—the Bellman function. We show how the homonym function in harmonic analysis is (and how it is not) the same stochastic optimal control Bellman function. Then we present several creatures from Bellman’s Zoo: a function that proves the inverse Hölder inequality, as well as several other harmonic analysis Bel...

This paper presents the modified design that can reject harmonic components in the branch-line coupler. After adding open stubs at the center of branch lines of the traditional design, their new network parameters can be found in order to maintain the conventional function at an operating frequency and suppress its harmonic terms chosen. Experimental results show the second and third harmonic s...

The discrete harmonic wavelet transform was developed by Newland in 1993 1, 2 . Similar to the ordinary discrete wavelet transform, the classical harmonic wavelet transform can also perform multiresolution analysis of a function. In addition, it has a fast algorithm based on fast Fourier transform for numerical implementation. A distinct advantage of harmonic wavelets is that they are disjoint ...

To study the impact of fundamental flow and background harmonics on harmonic and resonance characteristics of high-speed train-network coupling systems, harmonic admittance matrix model for four quadrant converter is deduced with the method of FFT and Bessel function. Equivalent load of train and chain network model of multiple conductors was established to conduct the calculation of fundamenta...

The order of growth of a harmonic function is determined by the growth of its gradient and conversely. We extend these results to solutions of certain subelliptic equations in John domains in Carnot groups. The modulus of the gradient is replaced by a local average of the horizontal gradient. In the harmonic case these quantities are equivalent. The proof uses recent integral inequalities assoc...

Second-harmonic generation was produced in germanium-doped silica planar waveguides prepared by simulfaneous illumination with 1064- and 532-nm laser light. During preparation using prism coupling to specific waveguiding modes, the film-generated second-harmonic intensity grew as a function of preparation time until it saturated. The growth rate and saturation level for p-polarized second-harmo...

In this paper, we present a novel semi-supervised smooth harmonic transductive learning algorithm that can get closed-form solution. Our method introduces the unlabeled class information to the learning process and tries to exploit the similar configurations shared by the label distribution of data. After discovering the property of smooth harmonic function based on spectral clustering in class...

For a quantum harmonic oscillator, an explicit expression that describes the energy distribution as coordinate function is obtained. The presence of poles shown for system in domains where Wigner has negative values.

In this work, we present the analytical approach for evaluation of conditional measure Wiener path integral. We consider time-dependent model parameters. find differential equation variable, determining behavior harmonic as well an-harmonic parts oscillator. part result in form operator function.

In this paper we evaluate Euler-like sums involving harmonic/odd harmonic numbers and central binomial coefficients by using the expansion for powers of inverse sine function. We also a number integrals which in turn give rise to new coefficient identities.