A theoretical relation is presented between the seismological Fourier amplitude spectrumand the mean squared value of the elastic response, which is defined by Gaussian distribution. Byshifting a general process to its mean value, spectrum of the mean squared value of the displacementis computed from the Fourier amplitude spectrum and the real part of the relative displacementtransfer function ...

We address the problem of reducing edge lengths a network within given budget so that sum weighted distances from each vertex to others is minimized. call this reverse total distance on networks. first show NP-hard by set cover it in polynomial time. Particularly, we develop linear time algorithm solve tree. For cycles, devise an iterative approach without mentioning exact complexity. Additiona...

In this paper, we give a matrix construction method for designing DNA codes that come from group rings. We show with our one can obtain reversible $$G^k$$ -codes of length kn, where $$k, n \in \mathbb {N},$$ over the finite commutative Frobenius ring R. employ to many $$\mathbb {F}_4$$ satisfy Hamming distance, reverse, reverse-complement and fixed GC-content constraints. Moreover, improve lowe...

In this paper, we develop the theory for constructing DNA cyclic codes of odd length over R = Z4[u]/〈u 2 − 1〉 based on the deletion distance. Firstly, we relate DNA pairs with a special 16 elements of ring R. Cyclic codes of odd length over R satisfy the reverse constraint and the reverse-complement constraint are discussed in this paper. We also study the GC-content of these codes and their de...

1. Introduction. In the problem of bounding the size of codes in compact homogeneous spaces, Del-sarte's polynomial method gives rise to the most powerful universal bounds on codes. Many overviews of the method exist in the literature; see for instance Levenshtein (1998). The purpose of this talk is to present a functional perspective of this method and give some examples. Let X be a compact me...