Any ordinary permutation τ ∈ Sn of size n, written as a word τ = τ1 . . . τn, can be locally classified according to the relative order of τj to its neighbours. This gives rise to four local order types called peaks (or maxima), valleys (or minima), double rises and double falls. By the correspondence between permutations and binary increasing trees the classification of permutations according ...

We show that, given a histogram with n bins—possibly non-contiguous or consisting of single points—there exists a unique polynomial histopolant (polynomial of order n with bin averages equal to the histogram’s). We also present histopolating cardinal functions for histograms with contiguous bins. The Hodge star operator from the theory of differential forms is the mapping which puts kand (d − k...

In this paper, we present a numerical method for solving Hallen’s integral equation based on radial basis functions (RBFs). This method will represent the solution of Hallen’s integral equation by interpolating the radial basis functions based on Legendre-Gauss-Lobatto(LGL) nodes and weights. The numerical results show that the proposed method for Hallen’s integral equation is very accurate and...

With the rapid development of information technology, blockchain technology has also been deeply impacted. When performing block verification in network, if all transactions are verified on chain, this will cause accumulation data resulting storage problems. At same time, security is challenged, which put enormous pressure block, extremely low communication efficiency block. The traditional sys...

In this paper, we introduce hybrid of block-pulse functions and Bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. Then, we utilize them to solve delay differential equations and time-delay system. The method is based upon e...

In this project, we study a randomized variant of Fibonacci heaps where instead of using mark bits, one flips coins in order to determine whether to cascade bringing nodes into the root list. Although it seems intuitive that such heaps should have the same expected performance as standard Fibonacci heaps—and Karger has conjectured as such—the only previous work was an O(log s) upper bound using...

A simple strategy for constructing a sequence of increasingly refined interpolation grids over the triangle or the tetrahedron is discussed with the goal of achieving uniform convergence and ensuring high interpolation accuracy. The interpolation nodes are generated based on a one-dimensional master grid comprised of the zeros of the Lobatto, Legendre, Chebyshev, and second-kind Chebyshev polyn...

In this paper, a cooperative algorithm to improve the orthogonal space-timefrequency block codes (OSTFBC) in frequency selective channels for 2*1, 2*2, 4*1, 4*2 MIMO-OFDM systems, is presented. The algorithm of three node, a source node, a relay node and a destination node is formed, and is implemented in two stages. During the first stage, the destination and the relay antennas receive the sym...

It is very difficult and expensive to replace sensor node battery in wireless sensor network in many critical conditions such as bridge supervising, resource exploration in hostile locations, and wildlife safety, etc. The natural choice in such situations is to maximize network lifetime. One such approach is to divide the sensing area of wireless sensor network into clusters to achieve high ene...

A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn polynomials, little q-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey–Wilson to Wilson polynomials and from q-Racah to Racah polynomials ar...