We present well-known interpretations of Lagrange multipliers in physical and economic applications, and introduce a new interpretation in nonlinear pricing problem. The multipliers can be interpreted as a network of directed flows between the buyer types. The structure of the digraph and the fact that the multipliers usually have distinctive values can be used in solving the optimization probl...

This work presents novel multipliers for Montgomery multiplication defined on binary fields GF(2). Different to state of the art Montgomery multipliers, this work uses a Linear Feedback Shift Register (LFSR) as the main building block. We studied different architectures for bit-serial and digit-serial Montgomery multipliers using the LFSR and the Montgomery factors x and x. The proposed multipl...

Using Bessel-Muirhead system, we can express the K-bessel function defined on a Jordan algebra as linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a reduction to the rank two. The main tools are some algebraic identities developed for the occasion.

In a simple picture, a Bessel beam is viewed as a transverse standing wave formed in the interference region between incoming and outgoing conical waves. Based on this interpretation we propose an optical resonator that supports modes that are approximations to Bessel-Gauss beams. The Fox-Li algorithm in two transverse dimensions is applied to confirm the conlcusion.

Nondiffractive Bessel beams were generated experimentally and their propagation was characterized using the self-convergent width method. By the use of this criterion for the calculation of the truncated second-moment of the irradiance, the invariant propagation of the generated Bessel beams is confirmed.

We numerically investigate the possibility to generate freely accelerating or decelerating pulses. In particular it is shown that acceleration along the propagation direction z may be obtained by a purely spatial modulation of an input Gaussian pulse in the form of finite-energy Bessel pulses with a cone angle that varies along the radial coordinate.We discuss simple practical implementations o...

It is shown that the tail probability of a Bessel process is the distributio function of a random time which is related to first and last passage times of Bessel processes. AMS Classification 60 J 25, 60 J 60, 60 E 15, 60 G 44, 60 H 10.

We give a shorter proof of Kanter's (1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions I 0 (x) + I 1 (x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due toČekanavičius

We study the heat equation in n dimensional by Diamond Bessel operator. We find the solution by method of convolution and Fourier transform in distribution theory and also obtain an interesting kernel related to the spectrum and the kernel which is called Bessel heat kernel.

We put forward the concept of reconfigurable structures optically induced by mutually incoherent nondiffracting Bessel beams in Kerr-type nonlinear media. We address collinear couplers and X junctions and show how one can tune the switching properties of such structures by varying the intensity of the Bessel beams.