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The design performance of real-time operating gas turbine power plants (GTPPs) deteriorates in terms of efficiency, reliability, and commercial availability due to aging, rubbing, contamination, and other similar problems. A manager minimizes operation and maintenance (O&M) expenses, consociating about the function of its basic structure (i.e., layout and design), availability (maintenance aspects), operation efficiency (trained workforce), safety and security, and other regulatory elements. Understanding plant structure improves performance, economical design, maintenance planning, etc. For a better understanding of design, a technique comprising graph theory, matrix method, and combinatorics is developed to determine the performance of GTPP. Detailed methodology for developing a system structure graph, various system structure matrices, and their permanent functions are described for the GTPP. For accessible and appropriate performance analysis, GTPP is divided into seven sub-systems. Structural interconnections between seven sub-systems of GTPP are as per real-time GTPP. The gas turbine system structure is developed in the form of a digraph. Matrix representation corresponding to digraph representation is developed, which is processed with the help of combinatorics. With the help of a computer programming tool developed in C++ for calculating the permanent of a matrix, the result comes out as a numerical value called the GTPP index. The methodology applied in the present work can be incorporated with standard computer programming tools developed for the performance assessment. In this way, it is easy to assess the dynamic behavior of the gas turbine system, as the methodology of the present work can incorporate tangible and intangible factors. Results obtained from the present methods agree with the available information in the literature. • The framework for exploring the dynamic behaviour of gas turbine systems is presented. • Graph theory, matrix method, and combinatorics are united into a single methodology. • Evaluations of efficiency, reliability, availability and maintainability are offered. • Recommendations for the ERAM evaluation of gas turbine systems are provided. [ABSTRACT FROM AUTHOR]

Let H be a subgroup of a group G. Then we say that H is w- s-permutable in G if G has a normal subgroup K such that HK is s-permutable in G and $$H\cap K$$ is nearly s-permutable in G. In this article, we analyse the structure of a group G by using the properties of w- s-permutable subgroups and obtain some new characterizations of p-nilpotent groups and supersoluble groups. Some known results are generalized. [ABSTRACT FROM AUTHOR]

The role of double space is essential in the new interpretation of T-duality and consequently in an attempt to construct M-theory. The case of the open string is missing in such an approach because until now there has been no appropriate formulation of open string T-duality. In the previous paper (Sazdović, From geometry to non-geometry via T-duality, arXiv:1606.01938, 2017), we showed how to introduce vector gauge fields AaN and AiD at the end-points of an open string in order to enable open string invariance under local gauge transformations of the Kalb–Ramond field and its T-dual “restricted general coordinate transformations”. We demonstrated that gauge fields AaN and AiD are T-dual to each other. In the present article we prove that all above results can be interpreted as coordinate permutations in double space. [ABSTRACT FROM AUTHOR]

A Lyndon word is a primitive string which is lexicographically smallest among cyclic permutations of its characters. Lyndon words are used for constructing bases in free Lie algebras, constructing de Bruijn sequences, finding the lexicographically smallest or largest substring in a string, and succinct suffix-prefix matching of highly periodic strings. In this paper, we extend the concept of the Lyndon word to two dimensions. We introduce the 2D Lyndon word and use it to capture 2D horizontal periodicity of a matrix in which each row is highly periodic, and to efficiently solve 2D horizontal suffix-prefix matching among a set of patterns. This yields a succinct and efficient algorithm for 2D dictionary matching. We present several algorithms that compute the 2D Lyndon word that represents a matrix. The final algorithm achieves linear time complexity even when the least common multiple of the periods of the rows is exponential in the matrix width. [ABSTRACT FROM AUTHOR]

The classical results by Kräuter and Seifter concerning the divisibility of permanents for (±1)-matrices by large powers of 2 are useful in testing whether the permanent function is nonvanishing. This paper suggests a new approach to this problem, allowing one to obtain a short combinatorial proof of the results by Kräuter and Seifter. [ABSTRACT FROM AUTHOR]

We calculate the partition function of the q-state Potts model on arbitrary-length cyclic ladder graphs of the square and triangular lattices, with a generalized external magnetic field that favors or disfavors a subset of spin values $$\{1,\ldots ,s\}$$ with $$s \le q$$ . For the case of antiferromagnet spin-spin coupling, these provide exactly solved models that exhibit an onset of frustration and competing interactions in the context of a novel type of tensor-product $$S_s \otimes S_{q-s}$$ global symmetry, where $$S_s$$ is the permutation group on s objects. [ABSTRACT FROM AUTHOR]

This paper presents a permutation test for the incomplete pairs setting. This situation arises in both observational and experimental studies when some of the data are in the form of a paired sample and the rest of the data comprise two independent samples. The proposed method uses the data from the two types of samples to test the difference between the mean responses. Our test statistic combines the observed mean difference for the complete pairs with the difference between the two means of the independent samples. The randomizations are carried out as is typically done with standard permutation tests for paired and independent samples. We show by a simulation study that our statistic performs well in comparison to other methods. [ABSTRACT FROM AUTHOR]

We present a finite-order system of recurrence relations for the permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1 , 2 and 3) and the method for deriving such recurrence relations, which is based on the permanents of the matrices with defects. The proposed system of linear recurrence equations with variable coefficients provides a powerful tool for the analysis of the circulant permanents, their fast, linear-time computing; and finding their asymptotics in a large-matrix-size limit. The latter problem is an open fundamental problem. Its solution would be tremendously important for a unified analysis of a wide range of the nature's ♯ P -hard problems, including problems in the physics of many-body systems, critical phenomena, quantum computing, quantum field theory, theory of chaos, fractals, theory of graphs, number theory, combinatorics, cryptography, etc. [ABSTRACT FROM AUTHOR]

The article offers a solution to the mathematical problem on the automorphisms of semitriangular graphs. It notes that an undirected graphs without loops or multiple edges were being considered. It adds that the proof of the theorem has been coordinated on Higman's method in dealing with automorphisms of a strongly regular graph. Furthermore, the number of vertices in the equation are eigenvalues of I multiplicities as permutation representation of the group at vertices provides a matrix representation.

Let p be a permutation of the set Nn = {1,2,…,n}. We introduce techniques for counting N(n; k; r; I); the number of Lehmer's strongly restricted permutations of Nn satisfying the conditions -k ≥ p(i)-i ≤ r (for arbitrary natural numbers k and r) and p(i) - ϵ I (for some set I). We show that N(n; 1, r, θ) is the Fibonacci (r + 1)-step number. [ABSTRACT FROM AUTHOR]

Permutation tests are often presented in a rather casual manner, in both introductory and advanced statistics textbooks. The appeal of the cleverness of the procedure seems to replace the need for a rigorous argument that it produces valid hypothesis tests. The consequence of this educational failing has been a widespread belief in a "permutation principle", which is supposed invariably to give tests that are valid by construction, under an absolute minimum of statistical assumptions. Several lines of argument are presented here to show that the permutation principle itself can be invalid, concentrating on the Fisher-Pitman permutation test for two means. A simple counterfactual example illustrates the general problem, and a slightly more elaborate counterfactual argument is used to explain why the main mathematical proof of the validity of permutation tests is mistaken. Two modifications of the permutation test are suggested to be valid in a very modest simulation. In instances where simulation software is readily available, investigating the validity of a specific permutation test can be done easily, requiring only a minimum understanding of statistical technicalities. [ABSTRACT FROM AUTHOR]

In this article, there are presented the substitution tables used in cryptosystems (DES and AES) and their role in increasing the security of the cryptographic algorithms. The substituting tables are non-linear permutation functions and they are mathematically formalized using the Boolean functions. The easiest way to obtain new cryptographic algorithms is to use random S-boxes. The research directions are concentrated on the constructions of Boolean functions that have good cryptographic properties. [ABSTRACT FROM AUTHOR]

The quadratic assignment problem (QAP) is a well-known combinatorial optimization problem with a wide variety of applications, prominently including the facility location problem. The acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this paper, we show the benefit of utilizing strategic diversification within the tabu search (TS) framework for the QAP, by incorporating several diversification and multistart TS variants. Computational results for an extensive and challenging set of QAP benchmark test problems demonstrate the ability of our TS variants to improve on a classic TS approach that is one of the principal and most extensively used methods for the QAP. We also show that our new procedures are highly competitive with the best recently introduced methods from the literature, including more complex hybrid approaches that incorporate the classic TS method as a subroutine. [ABSTRACT FROM AUTHOR]

We introduce and study a new class of lattice ordered algebras. [ABSTRACT FROM AUTHOR]

We explore p-wave pairing in a single-channel two-component Fermi system with unequal population near Feshbach resonance. Our analytical and numerical study reveal a rich superfluid (SF) ground state structure as a function of imbalance. In addition to the state Δ±1 ∝ Y1±1, a multitude of “mixed” SF states formed of linear combinations of Y1m's give global energy minimum under a phase stability condition; these states exhibit variation in energy with the relative phase between the constituent gap amplitudes. States with local energy minimum are also obtained. We provide a geometric representation of the states. A T = 0 polarization vs. p-wave coupling phase diagram is constructed across the BEC-BCS regimes. With increased polarization, the global minimum SF state may undergo a quantum phase transition to the local minimum SF state. [ABSTRACT FROM AUTHOR]

Abstract  We investigate binary sequences which can be obtained by concatenating the columns of (0,1)-matrices derived from permutation sequences. We then prove that these binary sequences are subsets of a surprisingly diverse ensemble of codes, namely the Levenshtein codes, capable of correcting insertion/deletion errors; spectral null codes, with spectral nulls at certain frequencies; as well as being subsets of run-length limited codes, Nyquist null codes and constant weight codes. [ABSTRACT FROM AUTHOR]

Abstract: The past decade has seen a flurry of research into pattern avoiding permutations but little of it is concerned with their exhaustive generation. Many applications call for exhaustive generation of permutations subject to various constraints or imposing a particular generating order. In this paper we present generating algorithms and combinatorial Gray codes for several families of pattern avoiding permutations. Among the families under consideration are those counted by Catalan, large Schröder, Pell, even-index Fibonacci numbers and the central binomial coefficients. We thus provide Gray codes for the set of all permutations of avoiding the pattern for all and the Gray codes we obtain have distances 4 or 5. [Copyright &y& Elsevier]

A permutation algorithm and associated FORTRAN program are provided for weighted kappa. Program EWK provides the weighted kappa test statistic and the exact one-sided upper-tail probability values. [ABSTRACT FROM AUTHOR]

The article examines the refinement of alternating permutations by inversions. According to the author, involution can be refined by inversions and may be used to understand generalizations of alternating permutations. He asserts that a frequently given proof an equation, which involves solving a nonlinear differential equation, cannot be easily be extended. In addition, he stresses that other known proofs include Mȍbius inversion on posets or the combinatories of the ring of symmetric functions.

Distance-increasing maps from binary vectors to permutations, namely DIMs, are useful for the construction of permutation arrays. While a simple mapping algorithm defining DIMs of even lengths is known, existing DIMs of odd lengths are defined either by recursively merging DIMs of shorter lengths or by complicated mapping algorithms. In this paper, simple mapping algorithms defining DIMs of all lengths are presented. [ABSTRACT FROM AUTHOR]

By calculating the permanents for all Hadamard matrices of orders up to and including 28 we answer a problem posed by E.T.H. Wang and a similar question asked by H. Perfect. Both questions are answered by the existence of Hadamard matrices of order 20 which do not seem to be simply related but nevertheless have the same permanent. For orders up to and including 20 we also settle several other existence questions involving permanents of (+1,  -1)-matrices. Specifically, we establish the lowest positive value taken by the permanent in these cases and find matrices which have equal permanent and determinant when such a matrix exists. Our results address Conjectures 19 and 36 and Problems 5 and 7 in Minc's well known catalogue of unsolved problems on permanents. We also include a little-known proof that there exists a (+1,  -1)-matrix A of order n such that per( A )  =  0 if and only if n   +  1 is not a power of 2. [ABSTRACT FROM AUTHOR]

This article develops statistical methods useful for comparing the marginals F and G of a bivariate distribution. Such comparisons are appropriate in the analysis of matched-pair data involving a treatment and a control (or two treatments). The quantile comparison function q = G-1 (F), proposed by Lehmann as a generalized measure of treatment effect in fully randomized experiments, is shown to be applicable and also useful in the analysis of matched-pair data. Nonparametric simultaneous confidence bands for q are constructed using asymptotic and permutation methods. The copula of the bivariate distribution plays a significant role in the methodology. Application of the results is illustrated on a dataset from an industrial experiment. [ABSTRACT FROM AUTHOR]

I derive analytically the spectrum of the CMB fluctuations. The final result forCl is presented in terms of elementary functions with an explicit dependence on the basic cosmological parameters. This result is in a rather good agreement with CMBFAST for a wide range of parameters around concordance model. This allows us to understand the physical reasons for dependence of the particular features of the CMB spectrum on the basic cosmological parameters and to estimate the possible accuracy of their determination. I also analyze the degeneracy of the spectrum with respect to certain combinations of the cosmological parameters. [ABSTRACT FROM AUTHOR]

The article discusses the main objective of the journal which is to cover the latest research on random structure and to provide a forum for ideas on future studies in randomness. Includes topics covered such as random graphs, hypergraphs, matroids, tree, mapping, permutations, matrices and also mentions the focus of journal on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography

Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light’s orbital angular momentum degree of freedom. By exploiting the spatial mode of photons, our scheme provides a more elegant way to understand the principle of quantum permutation algorithm and shows that the high dimension characteristic of light’s orbital angular momentum may be useful in quantum algorithms. Our scheme can be extended to higher dimension by introducing more spatial modes and it paves the way to trace the source of quantum speedup. [ABSTRACT FROM AUTHOR]

The article focuses on the paper "Sudoku Squares and Chromatic Polynomials," by Agnes M. Herzog and M. Ram Murty, published in the periodical "Notices of the American Mathematical Society." Here, the authors explained how mathematicians perceived the numerical puzzle, Sudoku. They also discussed, the classical concepts in combinatory analysis which come into play when a mathematician considers Sudoku, which include graphs, chromatic polynomials, Mö bius inversion, Latin squares, scheduling, permanents and Hall's Theorem.