A particular model of tumor progression (extended Perumpanani’s model), assuming that the invasive cells, the connective tissue and the proteases are moving through a non-differential medium governed by the Non-Standard Scale Relativity Theory (Scale Relativity Theory with arbitrary constant fractal dimension) is analyzed. In such context an action-reaction type law acting on the complex system...

In this paper we treat some fractal and statistical features of the DNA sequences. First, a fractal record model of DNA sequence is proposed by mapping DNA sequences to integer sequences, followed by R/S analysis of the model and computation of the Hurst exponents. Second, we consider transition between the four kinds of bases within DNA. The transition matrix analysis of DNA sequences shows th...

In this paper, the fuzzy matrix equation $Awidetilde{X}B=widetilde{C}$ in which $A,B$ are $n times n$crisp matrices respectively and $widetilde{C}$ is an $n times n$ arbitrary LR fuzzy numbers matrix, is investigated. A new numerical procedure for calculating the fuzzy solution is designed and a sufficient condition for the existence of strong fuzzy solution is derived. Some examples are ...

We find that the IIA Matrix models defined on the non-compact C/Z6, C /Z2 and C/Z4 orbifolds preserve supersymmetry where the fermions are on-massshell Majorana-Weyl fermions. In these examples supersymmetry is preserved both in the orbifolded space and in the non-orbifolded space at the same time. The Matrix model on C/Z6 orbifold has the same N = 2 supersymmetry as the case of C/Z3 orbifold, ...

‎‎‎This paper presents a remarkable formula for spectral distance of a given block normal matrix $G_{D_0} = begin{pmatrix}‎ ‎A & B \‎ ‎C & D_0‎ ‎end{pmatrix} $ to set of block normal matrix $G_{D}$ (as same as $G_{D_0}$ except block $D$ which is replaced by block $D_0$)‎, ‎in which $A in mathbb{C}^{ntimes n}$ is invertible‎, ‎$ B in mathbb{C}^{ntimes m}‎, ‎C in mathbb{C}^{mti...

Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...

let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(r, s)$-symmetric and $(r, s)$-skew symmetric matrices have a number of special properties and widely used in engi...

Abstract The dependence of the chaotic phase Bose–Hubbard Hamiltonian on particle number N , system size L and density is investigated in terms spectral eigenstate features. We analyse development as limit infinite Hilbert space dimension approached along different directions, show that fastest route to chaos path at fixed n ≲ 1. → ∞ constant leads a slower convergence towards random matrix the...

In this study, a fractal, Y-shaped dual-mode resonator bandpass filter (BPF) with input-output cross-coupling is introduced. A parallel-coupling feed structure with a cross coupling has been used to generate two transmission zeroes (TZs) near the lower and upper cutoff frequency that can effectively improve the passband edge selectivity. Also, a fractal shaped based on conventional diamond and ...