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We consider a face of the polytope of doubly stochastic matrices, whose non-zero entries coincide with that of \[ V_{l,m,n}=\left[\begin{matrix} 0_{l,l} & 0_{l,m} & J_{l,n} \\ 0_{m,l} & I_{m} & J_{m,n}\\ J_{n,l} & J_{n,m} & J_{n,n}\\ \end{matrix}\right]. \] V l , m , n = [ 0 l , l 0 l , m J l , n 0 m , l I m J m , n J n , l J n , m J n , n ]. Here, $ 0_{r,s} $ 0 r , s is the $ r\times s $ r × s zero matrix, $ J_{u,v} $ J u , v denotes the $ u\times v $ u × v matrix all of whose entries are 1 and $ I_m $ I m is the identity matrix of order m. We determine the minimum permanent and minimizing matrices on this face of the polytope of doubly stochastic matrices. This research contributes towards solution of two problems from Minc's well-known lists of unsolved problems on permanents. [ABSTRACT FROM AUTHOR]

Let G be a graph with n vertices and m edges. A (G) and I denote, respectively, the adjacency matrix of G and an n by n identity matrix. For a graph G, the permanent of matrix (I + A (G)) is called the permanental sum of G. In this paper, we give a relation between the Hosoya index and the permanental sum of G. This implies that the computational complexity of the permanental sum is N P -complete. Furthermore, we characterize the graphs with the minimum permanental sum among all graphs of n vertices and m edges, where n + 3 ≤ m ≤ 2 n − 3 . [ABSTRACT FROM AUTHOR]

We provide a (strong) inductive proof of Borchardt's theorem for calculating the permanent of a Cauchy matrix via the determinants of auxiliary matrices. This result has implications for antisymmetric products of interacting geminals (APIG), and suggests that the restriction of the APIG coefficients to Cauchy form (typically called APr2G) is special in its tractability. [ABSTRACT FROM AUTHOR]

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 G be a graph, and let $ A(G) $ A (G) be the adjacency matrix of G. The computation of permanent of $ A(G) $ A (G) is #p-complete. Computing permanent of $ A(G) $ A (G) is of great interest in quantum chemistry, statistical physics, among other disciplines. In this paper, we characterize the ordering of permanents of adjacency matrices of all graphs obtained from regular complete bipartite graph $ K_{p, p} $ K p , p by deleting six edges. As an application, we show that all graphs with a perfect matching obtained from $ K_{p, p} $ K p , p with six edges deleted are determined by their permanental polynomials. [ABSTRACT FROM AUTHOR]

Matrix permanents are hard to compute or even estimate in general. It had been previously suggested that the permanents of Positive Semidefinite (PSD) matrices may have efficient approximations. By relating PSD permanents to a task in quantum state tomography, we show that PSD permanents are NP-hard to approximate within a constant factor, and so admit no polynomial-time approximation scheme (unless P = NP). We also establish that several natural tasks in quantum state tomography, even approximately, are NP-hard in the dimension of the Hilbert space. These state tomography tasks therefore remain hard even with only logarithmically few qubits. [ABSTRACT FROM AUTHOR]

A new direct torque control method for three-level direct matrix converter permanent magnet synchronous motor (TLDMC-PMSM) based on the modulation coefficient optimization method (MCOM) is proposed to address the problems of large torque chain pulsation, amplitude disorder and weak system robustness in matrix converter permanent magnet synchronous motor system (MC-PMSM) using direct torque control (DTC). In the paper, firstly, the principle of MC-PMSM-DTC system is described; secondly, the two-level MC is replaced by TLDMC, the speed loop is cascade spiral sliding mode control, the torque magnetic chain loop is super twisting sliding mode control-direct torque control to replace the traditional PI control, and the modulation coefficient optimal method is introduced to reduce the drawback of gradually increasing motor torque fluctuation, and then the accurate control of PMSM is realized; finally, the feasibility and superiority of the proposed method are verified by MATLAB/Simulink simulation software and hardware experiments. [ABSTRACT FROM AUTHOR]

Visakhapatnam, poised to become the executive capital of Andhra Pradesh, is confronting escalating population growth and water scarcity challenges. With over 19 lakh residents and an 11.96% growth rate, the city’s water demand is expected to outstrip its current supply capacity. The Greater Visakhapatnam Municipal Corporation relies on diverse water sources, but encroachments on water bodies and industrial pollution exacerbate the scarcity issue. Against this backdrop, desalination emerges as a sustainable solution, leveraging the city’s extensive coastline. This study explores the technical, economic, environmental, social, and political dimensions of implementing a solar-powered Reverse Osmosis (RO) desalination plant in Visakhapatnam. While various desalination methods exist, solar-powered RO is highlighted for its ecological sustainability, utilizing abundant and renewable solar energy. The study employs the Multi-Criteria Decision-making Approach (MCDA) to comprehensively evaluate the proposed solution. The application of fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) aids in identifying the optimal solution under uncertain conditions. Furthermore, a graph theory and matrix approach are introduced to analyze the decision-making problem. The attribute digraph visually represents the relationships between different criteria, while the permanent matrix quantifies the relative importance of these criteria. The study location selection process involves linear normalization and a permanent matrix computation, ultimately ranking Chinna Rushikonda as the top choice for implementing a solar photovoltaic-powered RO desalination plant. The integration of MCDA, fuzzy TOPSIS, and graph theory provides a comprehensive and robust methodology for decision-making in complex projects, ensuring sustainable and well-informed choices. [ABSTRACT FROM AUTHOR]

A356 alloy based composites are extensively used in different component industries like components of automobile parts owing to pronounced strength to weight ratio. In the current paper, A356/Si3N4 nanocomposites are fabricated by means of stir casting by varying Si3N4 reinforcement nanoparticles. Silicon Nitride (Si3N4) nanoparticle is intermixed to Al powder mechanically to develop their wettability among the particles of A356/Si3N4 nanocomposites. The Si3N4 nanoparticle is integrated by altering weight percentage. The electomechanical stirring process to produce the vortex is taken up to spread Si3N4 nanoparticles in the liquefied matrix dispensed into a permanent mould. Morphological investigation of the composite specimen is accomplished by TEM. Based on the study, it can be acquired that the strengthening by Si3N4 nanoparticles promotes the strength and hardness of the fabricated nanocomposites. The maximum tensile strength is depicted to be 319 MPa for A356/5%Si3N4 nanocomposites whereas hardness is increased from 43 HBN to 86 HBN. The physical properties such as density and porosity are also increased due to the presence of Si3N4 nanoparticles. The maximum porosity of 1.12% was predicted at 5 wt. % of Si3N4. The TEM examination discloses the presence of Si3N4 nanoparticles in the fabricated composites. Additionally, the current research guidance has ability to afford a monitor to the industrialized preparation of A356/Si3N4 nanocomposites. [ABSTRACT FROM AUTHOR]

The permanent is a multilinear function that is a "symmetric" analog of the determinant. In the present paper, we consider several properties of the permanent of matrices of small orders. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we define the k-step generalized Balancing sequences and study the Binet formula of these sequences. Also, we find families of super-diagonal matrices such that the permanents of these matrices are the elements of the k-step generalized Balancing sequences. Finally, we examine the periods of the k-step Balancing sequences in the semi-direct product presented by G = (x,y | ... = y² = 1, yxy = x-1 for the generating pair (x,y). [ABSTRACT FROM AUTHOR]

In the present paper, we evaluate the permanent and determinant of some Toeplitz-Hessenberg matrices with generalized Fibonacci and generalized Lucas numbers as entries.We develop identities involving sums of products of generalized Fibonacci numbers and generalized Lucas numbers with multinomial coefficients using the matrix structure, and then we present an application of the determinant of such matrices. [ABSTRACT FROM AUTHOR]

By definition, a rigid graph in R d (or on a sphere) has a finite number of embeddings up to rigid motions for a given set of edge length constraints. These embeddings are related to the real solutions of an algebraic system. Naturally, the complex solutions of such systems extend the notion of rigidity to C d . A major open problem has been to obtain tight upper bounds on the number of embeddings in C d , for a given number |V| of vertices, which obviously also bound their number in R d . Moreover, in most known cases, the maximal numbers of embeddings in C d and R d coincide. For decades, only the trivial bound of O (2 d | V |) was known on the number of embeddings. Recently, matrix permanent bounds have led to a small improvement for d ≥ 5 . This work improves upon the existing upper bounds for the number of embeddings in R d and S d , by exploiting outdegree-constrained orientations on a graphical construction, where the proof iteratively eliminates vertices or vertex paths. For the most important cases of d = 2 and d = 3 , the new bounds are O (3. 7764 | V |) and O (6. 8399 | V |) , respectively. In general, we improve the exponent basis in the asymptotic behavior with respect to the number of vertices of the recent bound mentioned above by the factor of 2 . Besides being the first substantial improvement upon a long-standing upper bound, our method is essentially the first general approach relying on combinatorial arguments rather than algebraic root counts. [ABSTRACT FROM AUTHOR]

Epithelial cells secrete apical extracellular matrices to form protruding structures such as denticles, ridges, scales, or teeth. The mechanisms that shape these structures remain poorly understood. Here, we show how the actin cytoskeleton and a provisional matrix work together to sculpt acellular longitudinal alae ridges in the cuticle of adult C. elegans. Transient assembly of longitudinal actomyosin filaments in the underlying lateral epidermis accompanies deposition of the provisional matrix at the earliest stages of alae formation. Actin is required to pattern the provisional matrix into longitudinal bands that are initially offset from the pattern of longitudinal actin filaments. These bands appear ultrastructurally as alternating regions of adhesion and separation within laminated provisional matrix layers. The provisional matrix is required to establish these demarcated zones of adhesion and separation, which ultimately give rise to alae ridges and their intervening valleys, respectively. Provisional matrix proteins shape the alae ridges and valleys but are not present within the final structure. We propose a morphogenetic mechanism wherein cortical actin patterns are relayed to the laminated provisional matrix to set up distinct zones of matrix layer separation and accretion that shape a permanent and acellular matrix structure. Author summary: Animal surfaces are often decorated with intricately shaped structures such as denticles, ridges, or scales that are composed of extracellular matrix materials. We don't understand how those extracellular materials get sculpted into appropriate shapes, but most models propose that cellular protrusions initiate the process. Here we investigated the formation of nematode adult alae, which are three racing stripe-like cuticle ridges that run along the left and right sides of the body. We found that alae development requires the actin cytoskeleton and a set of temporary matrix components, both of which organize into longitudinal stripes that presage the final structure. Using electron microscopy, we saw no evidence for cell membrane protrusion or folding that would explain a ridged matrix pattern. Instead, we observed that the first sign of alae formation is the appearance of four small separations between different layers of the temporary matrix. We propose that cytoskeletal patterns are relayed to the to the temporary matrix to trigger delamination and subsequent zonal differences in matrix accumulation that establish the alternating valley and ridge pattern of the alae. [ABSTRACT FROM AUTHOR]

The Matrix Converter–fed Finite Control Set–Model Predictive Control is an efficient drive control approach that exhibits numerous advantageous features. However, it is computationally expensive as it employs all the available matrix converter voltage vectors for the prediction and estimation. The computational complexity increases further with respect to the inclusion of additional control objectives in the cost function which degrades the potentiality of this technique. This paper proposes two computationally effective switching tables for simplifying the calculation process and optimizing the matrix converter active prediction vectors. Here, three prediction active vectors are selected out of 18 vectors by considering the torque and flux errors of the permanent magnet synchronous motor. In addition, the voltage vector location segments are modified into 12 sectors to boost the torque dynamic control. The performance superiority of the proposed concept is analyzed using the MATLAB/Simulink software and the real-time validation is conducted by implementing in the real-time OPAL-RT lab setup. [ABSTRACT FROM AUTHOR]

We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite (HPSD) matrices. By analyzing a constructive randomized rounding algorithm, we obtain an improved multiplicative approximation factor to the permanent of HPSD matrices, as well as computationally efficient certificates for this approximation. We also propose an analog of van der Waerden's conjecture for HPSD matrices, where the polynomial optimization problem is interpreted as a relaxation of the permanent. [ABSTRACT FROM AUTHOR]

We study the range of the permanent function for the multidimensional matrices of 0 and 1. The main result is a multidimensional version for the Brualdi–Newman upper bound on the consecutive values of the permanent (1965). Moreover, we deduce a formula for the permanent of the multidimensional (0,1)-matrices through the number of partial zero diagonals. Using the formula, we evaluate the permanents of the -matrices with a few zeros and estimate the permanents of the matrices whose all zero entries are located in several orthogonal hyperplanes. We consider some divisibility properties of the permanent and illustrate the results by studying the values of the permanent for the -dimensional -matrices of order . [ABSTRACT FROM AUTHOR]

Necessary and sufficient conditions for the equality of the determinant and permanent for all powers of a given matrix are provided. The characterisation is based on a condition on merely one power. [ABSTRACT FROM AUTHOR]

Let G be a simple undirected graph, I the identity matrix, and A(G) an adjacency matrix of G. Then the permanental sum of G equals to the permanent of the matrix I + A (G) . Since the computation of the permanental sum of a graph is #P-complete, it is desirable to have good bounds. In this paper, we affirm a sharp upper bound for general graphs conjectured by Wu and So. Moreover, we prove a sharp lower bound for connected tricyclic graphs. Lastly, several unsolved problems about permanental sum are presented. [ABSTRACT FROM AUTHOR]

Dirichlet matrices are strongly connected to some important problems in Number Theory, such as the Prime Number Theorem, the Riemann Hypothesis and Kalmár's Factorisatio Numerorum problem. In this note, we obtain some recurrences for the determinants and permanents of Dirichlet matrices that allows us to obtain information about the asymptotic behavior of the permanents of certain classes of Dirichlet matrices. A generalization of Kalmár's Factorisatio Numerorum problem is obtained. [ABSTRACT FROM AUTHOR]

The matching polynomials and permanental polynomials have been investigated extensively, but no investigations focus on the relations between them. In this paper, we establish first two equalities on the signless matching polynomial and signless permanental polynomials. Then we show that the number of perfect matchings of a graph is the mean value of the permanents of skew-adjacency matrices. Moreover, we find that the matching polynomial of a graph is the expectation of skew-permanental polynomials of orientation graphs. Finally, we derive that the variance of the permanents of skew-adjacency matrices of orientation graphs can be expressed in terms of the number of matching alternating cycles in a graph. [ABSTRACT FROM AUTHOR]

An inhomogeneity into a conductive matrix deforms the flow pattern of an applied electric current. A usual current cloak can be defined as a permanent modification of the matrix properties around the inhomogeneity guaranteeing that the current flow pattern is similar before and after passing by the modified zone, so it implies the 'electrical invisibility' of the inhomogeneous region. Here we introduce the concept of a current cloak that can be tuned by means on an external field. We demonstrate analytically and using finite elements simulations that a current cloak can be constructed and manipulated by an external magnetic field for a concrete system consisting in a magneto-resistive matrix with an inclusion of larger conductivity. [ABSTRACT FROM AUTHOR]

We show that each perfect matching in a bipartite graph G intersects at least half of the perfect matchings in G. This result has equivalent formulations in terms of the permanent of the adjacency matrix of a graph, and in terms of derangements and permutations on graphs. We give several related results and open questions. [ABSTRACT FROM AUTHOR]

We study a random permutation of a lattice box in which each permutation is given a Boltzmann weight with energy equal to the total Euclidean displacement. Our main result establishes the band structure of the model as the box-size N tends to infinity and the inverse temperature β tends to zero; in particular, we show that the mean displacement is of order min { 1 / β , N } . In one dimension our results are more precise, specifying leading-order constants and giving bounds on the rates of convergence. Our proofs exploit a connection, via matrix permanents, between random permutations and Gaussian fields; although this connection is well-known in other settings, to the best of our knowledge its application to the study of random permutations is novel. As a byproduct of our analysis, we also provide asymptotics for the permanents of Kac–Murdock–Szegő matrices. [ABSTRACT FROM AUTHOR]

Abstract The q -permanent linear preservers are described. We give several expansion formulas for the q -permanent of a square matrix, based on the cycle factorization of permutations. Some of these formulas are valid for all matrices, but others are not; for each such formula Φ we determine all digraphs D such that Φ holds for all matrices with digraph D. Proof techniques are based on combinatorial results, relating the length (number of inversions) of a permutation, the lengths of its cycles, and a delicate counting of crossings, jumps, and arc-under-arc relations in digraphs. We get new algebraic characterizations of noncrossing [acyclic] graphs. [ABSTRACT FROM AUTHOR]

Abstract We provide an upper bound on the number of n 2 × n 2 Sudoku squares, and explain intuitively why there is reason to believe that the bound is tight up to a multiplicative factor of a much smaller order of magnitude. A similar bound is established for Sudoku squares with rectangular regions. [ABSTRACT FROM AUTHOR]

We introduce a discrete delayed exponential depending on sequence of matrices. This discrete matrix gives a representation of a solution to the Cauchy problem for a discrete linear system with pure delay with sequence of matrices. We discard the commutativity condition used in recent works related to the representation of solutions for discrete delay linear systems. [ABSTRACT FROM AUTHOR]

In this work, phase selection, microstructure and mechanical properties of Mg-Al-Ca-Mn alloys with three different Ca/Al ratios (0.58, 0.79 and 0.91) were studied. The Mn content of the alloys was kept constant at ∼0.30 wt%. Thermodynamic non-equilibrium (Scheil) simulations, X-Ray Diffraction (XRD) analyses and Scanning Electron Microscopy/Electron Dispersive Spectroscopy (SEM/EDS) determined that all three alloys contain α-Mg solid solution phase, Al 8 Mn 5 intermetallics and, depending on the Ca/Al ratio, combinations of C36-(Mg,Al) 2 Ca (hP24 a = 0.577–0.586 nm, c = 1.819–1.835 nm), binary C14-Mg 2 Ca (hP12, a = 0.620 nm c = 1.023 nm), ternary C14-Mg 2 Ca (hP12, a = 0.561–0.599 nm, c = 1.025–1.051 nm), and/or C15-Al 2 Ca (cF24, a = 0.793 nm) Laves phases. It is observed that Ca/Al ratio shows a direct relationship with the total amounts of Laves intermetallics and the amount of the C36 phase, and an indirect relationship with the amount of C14 phase. Microhardness measurements, room and elevated temperature (150 °C and 200 °C) tensile tests, as well as tensile creep tests (175 °C/50 MPa), were carried out to determine the mechanical properties of the alloys. Results show that the hardness and room temperature yield and ultimate tensile strengths (UTS) increase while the ductility at all temperatures decreases with increasing Ca/Al ratio. At elevated temperatures, in the range of Ca/Al ratios investigated, the UTS has a relationship with the dissolved amount of Ca and Mn in the α-Mg phase. Creep strain was found to decrease from 0.35% to 0.05% as Ca/Al increases from 0.6 to 0.9 and as the amount of the C36 phase which can strengthen grain boundaries increases. One order of magnitude improvement seen in creep resistance as the Ca/Al ratio increases from 0.6 to 0.8 is attributable to the presence of C36 and C14 phases rather than C36 and thermally unstable C15 phase in the alloys and to the increased amounts of dissolved Mn and Ca in the α-Mg matrix. [ABSTRACT FROM AUTHOR]

In this paper, we present various results for permanents and determinants of some Hessenberg matrices. Also, some special cases for permanents are given. [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]

We consider two ensembles of $$0-1$$ $$n\times n$$ matrices. The first is the set of all $$n\times n$$ matrices with entries zeroes and ones such that all column sums and all row sums equal r, uniformly weighted. The second is the set of $$n \times n$$ matrices with zero and one entries where the probability that any given entry is one is r / n, the probabilities of the set of individual entries being i.i.d.'s. Calling the two expectation values E and $$E_B$$ respectively, we develop a formal relation We use two well-known approximating ensembles to E, $$E_1$$ and $$E_2$$ . Replacing E by either $$E_1$$ or $$E_2$$ we can evaluate all terms in (A1). For either $$E_1$$ or $$E_2$$ the terms $$T_i$$ have amazing properties. We conjecture that all these properties hold also for E. We carry through a similar development treating $$E({{\mathrm{perm}}}_m(A))$$ , with m proportional to n, in place of $$E({{\mathrm{perm}}}(A))$$ . [ABSTRACT FROM AUTHOR]

We prove that the determinantal complexity of a hypersurface of degree $$d > 2$$ is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least 5. As a result, we obtain that the determinantal complexity of the $$3 \times 3$$ permanent is 7. We also prove that for $$n> 3$$ , there is no nonsingular hypersurface in $${\mathbb {P}}^n$$ of degree d that has an expression as a determinant of a $$d \times d$$ matrix of linear forms, while on the other hand for $$n \le 3$$ , a general determinantal expression is nonsingular. Finally, we answer a question of Ressayre by showing that the determinantal complexity of the unique (singular) cubic surface containing a single line is 5. [ABSTRACT FROM AUTHOR]

Permutation entropy and order patterns in an EEG signal have been applied by several authors to study sleep, anesthesia, and epileptic absences. Here, we discuss a new version of permutation entropy, which is interpreted as distance to white noise. It has a scale similar to the well-known χ2 distributions and can be supported by a statistical model. Critical values for significance are provided. Distance to white noise is used as a parameter which measures depth of sleep, where the vigilant awake state of the human EEG is interpreted as "almost white noise". Classification of sleep stages from EEG data usually relies on delta waves and graphic elements, which can be seen on a macroscale of several seconds. The distance to white noise can anticipate such emerging waves before they become apparent, evaluating invisible tendencies of variations within 40 milliseconds. Data segments of 30 s of high-resolution EEG provide a reliable classification. Application to the diagnosis of sleep disorders is indicated. [ABSTRACT FROM AUTHOR]

Let Detn denote the closure of the Gln2 (C)-orbit of the determinant polynomial detn with respect to linear substitution. The highest weights (partitions) of irreducible Gln2 (C)-representations occurring in the coordinate ring of Detn form a finitely generated monoid S(Detn). We prove that the saturation of S(Detn) contains all partitions λ with length at most n and size divisible by n. This implies that representation theoretic obstructions for the permanent versus determinant problem must be holes of the monoid S(Detn). [ABSTRACT FROM AUTHOR]

Current world economic recession and high competition in the market of ferrous metallurgy products make the issue of improving the efficiency of the steel-making process especially pressing. One of the ways to improve the efficiency of a steel-making unit is to provide the sufficient minimum content of furnace slag in a pouring ladle. It can be achieved by permanent real-time monitoring of the melt stream during tapping from the steel-making unit. The most efficient way to monitor the melt stream is the method based on control of infrared radiation from the steel being tapped. The article offers the analysis of arrays of infrared radiation values from operating steel-making units of the largest smelters of Russia. The authors give some practical design recommendations for monitoring systems of melt stream in the process of tapping from the steel-making unit. They also describe the rule of slag detection in the melt stream. [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]

Quantum determinants and Pfaffians or permanents and Hafnians are introduced on the two-parameter quantum general linear group. Fundamental identities among quantum Pf, Hf, and det are proved in the general setting. We show that there are two special quantum algebras among the quantum groups, where the quantum Pfaffians have integral Laurent polynomials as coefficients. As a consequence, the quantum Hafnian is computed by a closely related quantum permanent and identical to the quantum Pfaffian on this special quantum algebra. [ABSTRACT FROM AUTHOR]

Letanddenote the group ofrth roots of unity, the set of allmatrices over, thematrix with all entries 1 and thematrix within the (1, 1)-entry and 1 elsewhere, respectively. Let. Wang proved thatif and only ifAcan be obtained fromby a finite sequence of elementary operations. In this paper, we generalize this result for matrices overby showing that the absolute value of permanent function achieves the maximum value,n!, if and only ifAis the matrix obtained fromby the certain elementary operations. Also, we prove that if, thenand. Among other results we prove that for a complex Hadamard matrix. [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 present a deterministic algorithm, which, for any given $$0< \epsilon < 1$$ and an $$n \times n$$ real or complex matrix $$A=\left( a_{ij}\right) $$ such that $$\left| a_{ij}-1 \right| \le 0.19$$ for all $$i, j$$ computes the permanent of $$A$$ within relative error $$\epsilon $$ in $$n^{O\left( \ln n -\ln \epsilon \right) }$$ time. The method can be extended to computing hafnians and multidimensional permanents. [ABSTRACT FROM AUTHOR]

Performance degradation is one of the key issues hindering direct methanol fuel cell commercialization, caused by different mechanisms interplaying locally and resulting in both temporary and permanent contributions. This work proposes a systematic experimental investigation, coupling in-situ diagnostics (electrochemical and mass transport investigation) with ex-situ analyses of pristine, activated and aged components (X-ray photoelectron spectroscopy and transmission electron microscopy), with an in-plane and through-plane local resolution. Such a combined approach allows to identify on one hand the degradation mechanisms, the affected components and the presence of heterogeneities; on the other hand, it allows to quantify the effect of the major mechanisms on performance decay. Thanks to a novel procedure, temporary (21 μV h −1 ) and permanent degradation (59 μV h −1 ) are separated, distinguishing the latter in different contributions: the effects of active area loss at both at anode (9 μV h −1 ) and cathode (31 μV h −1 ), mass transport issue (15 μV h −1 ) and membrane decay (4 μV h −1 ). The post-mortem analysis highlights the effect of degradation mechanisms consistent with the in-situ analysis and reveals the presence of considerable in plane and through plane heterogeneities in: particle size growth in catalyst layers, Pt/Ru and polymer content in catalyst and diffusion layers, Pt/Ru precipitates in the membrane. [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]

Bobkov (J. Theoret. Probab. 18(2) (2005) 399-412) investigated an approximate de Finetti representation for probability measures, on product measurable spaces, which are symmetric under permutations of coordinates. One of the main results of that paper was an explicit approximation bound for permanents of complex rectangular matrices, which was shown by a somewhat complicated induction argument. In this paper, we indicate how to avoid the induction argument using an (asymptotic) expansion. Our approach makes it possible to give new explicit higher order approximation bounds for such permanents and in turn for the probability measures mentioned above. [ABSTRACT FROM AUTHOR]

Let us fix a function f ( n ) = o ( n ln n ) and real numbers 0 ≤ α < β ≤ 1 . We present a polynomial time algorithm which, given a directed graph G with n vertices, decides either that one can add at most β n new edges to G so that G acquires a Hamiltonian circuit or that one cannot add α n or fewer new edges to G so that G acquires at least e − f ( n ) n ! Hamiltonian circuits, or both. [ABSTRACT FROM AUTHOR]

The method of Sinkhorn balancing that starts with a non-negative square matrix and iterates to produce a related doubly stochastic matrix has been used with some success to estimate the values of the permanent in some cases of physical interest. However, it is often claimed that Sinkhorn balancing is slow to converge and hence not useful for efficient computation. In this paper, we explain how some simple, low cost pre-processing allows one to guarantee that Sinkhorn balancing always converges linearly. We illustrate this approach by efficiently and accurately computing permanents and $$\alpha $$ -permanents of some previously studied matrices. [ABSTRACT FROM AUTHOR]