In this paper, an image encryption algorithm is proposed based on the Sn PERMUTATION GROUP and chaotic functions. The proposed algorithm consists of three steps. In the first step, by applying the hash functions to the plain image information and using the 256-bit external key, a 256-bit secret key is extracted and used to calculate the initial values and parameters of the chaotic functions. In the second step known as the confusion step, the pixel positions of the plain image are rearranged using a row and column level PERMUTATION based on the chaotic functions, such that the correlation between adjacent pixels of the plain image is significantly reduced. In the third step or the diffusion step, the gray value of each pixel is changed based on a bit level PERMUTATION using the S8 PERMUTATION GROUP and the chaotic functions. Finally, by applying the bit level transform using the S8Sbox and XOR operation, the security of the proposed image encryption algorithm is increased. The experimental results and security analysis show that the NPCR is, the UACI is, entropy is and the correlation coefficients of the encrypted images are close to 0. Also, the proposed image encryption algorithm has high resistance against common attacks such as the exhaustive search, cropping and noise attacks.

A square matrix over the complex field with non-negative integral trace is called a quasi-PERMUTATION matrix. For a given finite GROUP G, let c (G) be the minimal degree of a faithful representation of G by complex quasi-PERMUTATION matrices. Let r (G) denotes the minimal degree of a faithful rational valued complex character of G. In this paper, we will calculate c (G) and r (G) for the GROUP GL (2,q) when extended by a certain GROUP of order two.

The aim of this paper is to determine an upper bound for the number of non-co-spectral PERMUTATION graphs in terms of automorphism GROUP of a graph G. As a corollary, we determine the eigenvalues of all PERMUTATION graphs P (Cn), where  2 Aut(Cn).

If F is a subfield of C, then a square matrix over F with non-negative integral trace is called a quasi-PERMUTATION matrix over F. For a finite GROUP G, let p(G) denote the minimal degree of a faithful PERMUTATION representation of G and let q(G) and c(G) denote the minimal degree of a faithful representation of G by quasi-PERMUTATION matrices over the rationals and the complex numbers, respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. In this paper, p(G), q(G), c(G) and r(G) are calculated for the GROUPs SL(3,q) and PSL (3,q).

A PERMUTATION with no fixed points is called a derangement. The subset D of a PERMUTATION GROUP is derangement if all elements of D are derangement. Let G be a PERMUTATION GROUP, a derangement graph is one with vertex set G and derangement set D as connecting set. In this paper, we determine the spectrum of derangement graphs of order a product of three primes.

A square matrix over F with non-negative integral trace is called a quasi-PERMUTATION matrix over F. Let G be a finite linear GROUP of degree n, that is, a finite GROUP of authomorphisms of an n-dimensional complex vector space or, equivalently, a finite GROUP of non-singular matrices of order n with complex coefficients. We shall say that G is a quasi-PERMUTATION GROUP if the trace of every element of G is a non-negative rational integer. Thus a PERMUTATION GROUP of degree n has a representation as a quasi-PERMUTATION GROUP of degree n. In this paper we calculate the kernel and Galois GROUPs for the irreducible characters of the GROUP GL (3,q). These help us to obtain the PERMUTATION and quasi-PERMUTATION representations of the GROUP GL (3,q).

The political, social, and religious conflicts between the Church and the Protestants during the Renaissance and afterward gave a unique dimension to the works of a large number of European artists such as Shakespeare. A few decades later, art critics defined this style under the rubric of Baroque. The writers of this article conduct an explanatory analysis of Shakespeare’s Hamlet in the light of baroque aesthetics. The authors maintain that Hamlet’s behavioral instability and inconsistency is comparable to Baroque aesthetics. His madness also reflects the chaotic society of the seventeenth century Europe which was stricken by harsh religious controversies. Hamlet represents a generation lost between Catholicism and Protestantism. On the one hand, the ghost of Hamlet’s father draws Hamlet towards his ancestral religion, which is Catholicism; on the other hand, Claudius’ progressive opinions, along with Hamlet’s education at Wittenberg, the cradle of Protestantism, push Hamlet towards iconoclastic Protestantism. Moreover, like in Baroque aesthetics in which the artist tries to challenge the perception of Truth in the mind of the audience in order to create a sense of uncertainty, from the very beginning of the play, both the characters and the audience of the play become doubtful about the state of the world and their own selves. Also, similar to a baroque hero who wants to yoke both worlds of the material and the spiritual in order to convey a spiritual message by dint of material senses, Shakespeare endows an extraterrestrial dimension on the concept of revenge. For a baroque hero the world is infinite and worldly eyes are unable to identify a greater portion of it. In view of that, Hamlet’s obsession with the other-world prevents him from killing Claudius while he is repenting his sins to God. Furthermore, from among the reasons why Hamlet is reluctant about avenging his father is Hamlet’s proximity to Claudius’ socio-political opinions. Unlike Father Hamlet, Claudius is a politically progressive ruler. On the one hand, Father Hamlet asks his son to kill his uncle in order to retrieve family honor and dignity, but, on the other hand, Hamlet’s love for the new world forbids him from doing so. Nevertheless, he still suspects the innocence of the brave new world and the distrust is also responsible for his madness. Therefore, Hamlet is trapped in a limbo and has lost his way to his desired utopia. He ought to choose either his ancestors’ way of life or the progressive thinkers’ frame of mind. However, his madness exacerbates and he decides to commit suicide. Although he wishes to die, he avoids committing suicide because Catholicism forbids suicidal acts. But when Laertes invites him to a duel, Hamlet resorts to the discourse of predetermination which is an indispensable part of Protestantism. Thus, if he dies in a duel with Laertes, his wish to die is fulfilled without committing suicide. In this fashion, he victoriously finds a third way between Catholicism and Protestantism and becomes more of a triumphant hero than a tragic protagonist.

Multivariate data analysis in ecology and biodiversity research is very important. Ecologists often need to test hypotheses about the effects of experimental factors on the entire community composition. To analyze multivariate data, the use of classical statistical methods is based on assumptions such as the normal distribution of data that are not usually observed in ecological data. To analyze multivariate data, the use of classical statistical methods is based on assumptions such as the normal distribution of data that are not usually observed in ecological data. Therefore, in recent years, nonparametric tests, based on PERMUTATION tests and distance or dissimilarity matrix, have been widely used to test the existence of differences in species composition in ecology sciences. The purpose of this paper is to introduce and familiarization with new ecological non-parametric multivariate tests related to ecology sciences such as SIMPER, ANOSIM, PERMANOVA and PERMDISP, with the aim of analyzing the composition of plant communities. In order to introduce these analyzes, vegetation data of six sites of rangelands located in the surrounding area of Tehran province were used and the composition of the plant communities of the mentioned areas was analyzed. SIMPER analysis showed that Stipa hohenackeriana and Bromus tomentellus, respectively, had the largest role in differentiating among the sites studied in arid and semi-arid regions. ANOSIM and PERMANOVA analyzes showed a significant difference of plant composition among the sites. According to the results of these tests, Firouzkooh-Alborz, Damavand-Semnan and Saveh-Salafchegan sites had more similarity in terms of composition of vegetation. PERMDISP analysis showed that heterogeneity and multivariate dispersion of species coverage were significantly higher in Salafchegan and Saveh sampling sites. Therefore, according to the results, it can be stated that in order to preserve biodiversity in the study sites, at least three separate management plans are needed. Also, according to SIMPER analysis results, management plans to preserve the biodiversity of the areas studied can be supported by the distinct species identified in each site.