One of the effective items to reduce time for arriving fire fighters to place of event is determining the optimal location of fire stations. Ranking can define the best location of a fire station through the available options. The case of this study is the district ten of Tehran municipality. That is the smallest district of Tehran municipality in terms of size and is highest in terms of density, and population is quadruple the standard and twice the average density in Tehran. This research introduces a new ranking Technique called the “, Fibonacci Sequence Technique”, , then the results of this new Technique are compared to the TOPSIS method. In addition to the standard criteria of 6430, new criteria have been introduced for the location of fire stations. The results show that the ranking with the Fibonacci Sequence Technique is consistent with the TOPSIS method. It validates the Fibonacci Sequence Technique. Also, the new criteria get a high score in the evaluation by experts, which validates the new criteria.

The aim of this paper is to introduce the cyclic-Fibonacci hybrid Sequence and give some properties. By taking into account the cyclic-Fibonacci hybrid Sequence modulo m, the method will be given to determine the period lengths of this Sequence according to the different m values. In the final part of this paper, we study the cyclic-Fibonacci hybrid Sequence in groups and then we calculate the cyclic-Fibonacci hybrid lengths of polyhedral groups (2, 2, 2), (2, n, 2) and (n, 2, 2) as applications of the results produced.

In the present paper, we aim to generalize the notion of complex-type Fibonacci Sequences to complex-type cyclic Fibonacci Sequences. Firstly, we define the complex-type cyclic-Fibonacci Sequence and then we give miscellaneous  properties of this Sequence by using the matrix method. Also, we study the complex-type cyclic-Fibonacci Sequence modulo $m$. In addition, we describe the complex-type cyclic-Fibonacci Sequence in a $2$-generator group and investigate that in finite groups in details. Then, as our last result, we obtain the lengths of the periods of the complex-type cyclic-Fibonacci Sequences in dihedral groups $D_{2}$, $D_{3}$, $D_{4}$, $D_{5}$, $D_{6}$ and $D_{8}$ with respect to their generating sets.

This paper try to show that cling to the physical order that governs nature can be helpful in engineering application such as acoustical materials. In this regards, an innovative idea to the noise control problem for broader absorption bandwidth at low frequencies is presented in this paper. For this aim, Helmholtz resonator array (HRA) designed based on Fibonacci Sequence, which is addressed “, Fibonacci based-HRA”, . First, to validate the simulations which were performed through finite element method (FEM) as a numerical method in COMSOL Multi-physics software (Version 5. 2), the results have been compared with experimental results which obtained by other researchers for two cases: (1) one unit resonator, and (2) four resonators array block with equal size. Second, to examine the performance of sound absorption of Fibonacci based-HRA, the results obtained for HRA with equal sizes of the 4, 6, 8 and 10 component resonators, compared with those obtained for Fibonacci based-HRA with the same number of the component resonators and the same overall dimensions of HRA block. The comparison showed that Fibonacci based-HRA approach is a good candidate for broad-band low frequency noise control.

In this paper some properties of a generalization of Fibonacci Sequence are investigated. Then we solve the Diophantine equations x2±kxy-y2±x=0, where k is a positive integer, and describe the structure of solutions.

The purpose of the paper is to present a new generalization of the dual Fibonacci quaternions called the generalized dual bi-periodic Fibonacci quaternions. This new generalization allow us to state several number of dual quaternion Sequences in a unique Sequence. Furthermore, we give the generating function, the Binet formula, the norm value and some basic properties of these dual quaternions.

Digital watermarking technology is presented as one of the best solutions for solving unauthorized copying, content identification and authentication of digital media. Digital watermarking can be applied in the fields of image, text, audio, and video contents. Audio watermarking has recently attracted the attention of researchers because the human auditory system is much more sensitive than his vision system. Therefore, insertion of the data into audio signals in a transparent way is much more difficult than other watermarking species. An efficient audio watermarking system should be able to improve reconciliation of the three measures of transparency, strength and capacitance. Improving the compromise between these three measures is a challenging problem, due to the fact that increasing the capacity of the input signal, causes distortions in the signal which in turn causes a reduction in transparency and robustness. In this paper, a new method is proposed for watermarking of audio signals that is able to improve the three criteria of transparency, robustness and capacity in an appropriate manner. In order to improve the resilience of the hidden signal against signal processing attacks, the synergy of three efficient transforms in the field of signal processing namely, the graph-centric conversion (GBT), the discrete cosine transform (DCT) and the discrete wavelet transform (DWT), has been used. In addition, in order to maintain the transparency of the watermarked signal, the watermarked data in the high triangle matrix resulting from the LU decomposition of the approximation coefficients of the discrete wavelet are entered in an order which is based on the Fibonacci Sequence. The procedure is based on the value of the watermarked bit, the non-zero values of the upper triangular matrix are replaced by the nearest even or odd numbers in the Fibonacci Sequence. The latent extraction operation is completely blind. The results of the evaluation of the proposed method on audio files with Blue, Electronic, Classic and Jazz styles show that the proposed method, despite good resistance to various signal processing attacks, has an average signal rate of 45. 13 dB and a placement rate of 625. 75 bits per second.

Using a tight-binding model and transfer-matrix Technique, as well as Lanczos algorithm, we numerically investigate the nature of the electronic states and electron transmission in site, bond and mixing Fibonacci model chains. We rely on the Landauer formalism as the basis for studying the conduction properties of these systems. Calculating the Lyapunov exponent, we also study the localization properties of electronic eigenstates in the Fibonacci chains.. The focus is on the significance of the relationship between the transmission spectra and the nature of the electronic states. Our results show that, in contrast to Anderson's localization theorem, in the Fibonacci chains the electronic states are non-localized and the transparent states occurr near the Fermi level.

In this paper, a new interconnection network structure called hierarchical extended Fibonacci cubes interconnection networks HEFC1(n) is proposed, and its properties are evaluated. A set of the HEFC1(n)s constructed by the proposed method is a two level conventional hierarchical network. For each n (dimension of extended Fibonacci cube-EFC1(n)), a HEFC1(n)   interconnection network can be constructed. All EFC1(n) for n>4 are recursively constructible, hence HEFC1(n)s for n>4 are also recursively constructible with some extra EFC1(n-1)s and EFC1(n-2)s. Furthermore, since a HEFC1(n) has a hierarchically structured character and the feature of uniformity, a wide variety of inter-cluster connections are possible. The comparisons of HEFC1(n)s with some of the traditional cubic and hierarchical cubic networks are presented in this study. The routing in HEFC1(n+2)s is as easy as routing in HCN(n,n) and the scalability of HEFC1(n+2) is better than the scalability of HCN(n,n) and H(2n). H(2n) and HCN(n,n) are symmetric interconnection networks, however, HEFC1(n+2) is not a symmetric interconnection network and HEFC1(n+2)s have a recurrent structure as H(2n) and HCN(n,n). The cost of HEFC1(n+2) is better than the costs of HCN(n,n) and H(2n).The edge connectivity of HEFC1(n+2) is worse than the edge connectivity of H(2n) and HCN(n,n). This makes the VLSI design of HEFC1(n+2) simpler than the VLSI designs of H(2n) and HCN(n,n).

The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matrix multiplication. For creating this method, a new model for matrix multiplication with an algorithm for data distribution on Fibonacci Hypercube structure was provided. Other than this, another optimized algorithm was designed on Mesh structure. By running the algorithms on a simulative parallel system and giving the results in graphical mode, it has been found that these two algorithms have optimized value in parallel matrix multiplication and they are more efficient than the previous algorithms.