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Statistical characterizations of complex network structures can be obtained from both the Ihara Zeta function (in terms of prime cycle frequencies) and the partition function from statistical mechanics. However, these two representations are usually regarded as separate tools for network analysis, without exploiting the potential synergies between them. In this paper, we establish a link between the Ihara Zeta function from algebraic graph theory and the partition function from statistical mechanics, and exploit this relationship to obtain a deeper structural characterisation of network structure. Specifically, the relationship allows us to explore the connection between the microscopic structure and the macroscopic characterisation of a network. We derive thermodynamic quantities describing the network, such as entropy, and show how these are related to the frequencies of prime cycles of various lengths. In particular, the n-th order partial derivative of the Ihara Zeta function can be used to compute the number of prime cycles in a network, which in turn is related to the partition function of Bose–Einstein statistics. The corresponding derived entropy allows us to explore a phase transition in the network structure with critical points at high and low-temperature limits. Numerical experiments and empirical data are presented to evaluate the qualitative and quantitative performance of the resulting structural network characterisations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel series of second-order Backward Differentiation Formulas (BDFs) specifically designed to address phase-lag and its first derivative in the numerical resolution of Initial Value Problems (IVPs) with orbital solutions. Our methodology commences with an in-depth analysis of phase-lag phenomena associated with second-order BDFs. Following this, we construct a suite of equations by embedding algebraic functions into the operational framework of the 3-step second-order BDF (SOBDF) method. Additionally, we elaborate on equations that precisely describe the phase-lag and its derivatives, with a concentrated focus on the 3-step SOBDF method. The culmination of this work is the presentation of six distinct methods, each methodically crafted to negate both the real and imaginary elements of phase-lag and its derivatives in numerical computations. The study advances with a meticulous examination of the local truncation error and the stability regions pertinent to the six phase-fitted methods introduced. Furthermore, we scrutinize their computational performance by deploying these methods across a spectrum of initial value problems, offering valuable insights into their effectiveness in varying contexts. [ABSTRACT FROM AUTHOR]

Permutation codes have received a great attention due to various applications. For different applications, one needs permutation codes under different metrics. The generalized Cayley metric was introduced by Chee and Vu (in: 2014 IEEE international symposium on information theory, Honolulu, June 29–July 4, 2014, pp 2959–2963, 2014) and this metric includes several other metrics as special cases. However, the generalized Cayley metric is not easily computable in general. Therefore the block permutation metric was introduced by Yang et al. (IEEE Trans Inf Theory 65(8):4746–4763, 2019) as the generalized Cayley metric and the block permutation metric have the same magnitude. In this paper, by introducing a novel metric closely related to the block permutation metric, we build a bridge between some advanced algebraic methods and codes in the block permutation metric. More specifically, based on some techniques from algebraic function fields originated in Xing (IEEE Trans Inf Theory 48(11):2995–2997, 2002), we give an algebraic-geometric construction of codes in the novel metric with reasonably good parameters. By observing a trivial relation between the novel metric and block permutation metric, we then produce non-systematic codes in block permutation metric that improve all known results given in Xu et al. (Des Codes Cryptogr 87(11):2625–2637, 2019) and Yang et al. (2019). More importantly, based on our non-systematic codes, we provide an explicit and systematic construction of codes in the block permutation metric which improves the systematic result shown in Yang et al. (2019). In the end, we demonstrate that our codes in the novel metric itself have reasonably good parameters by showing that our construction beats the corresponding Gilbert–Varshamov bound. [ABSTRACT FROM AUTHOR]

We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of N 1 N 2 -automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the N 1 N 2 -automorphism group in the general case and the N 1 N 2 -automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction. [ABSTRACT FROM AUTHOR]

This paper presents a study of the thermal and thermal stress state of a methane pyrolysis reactor for hydrogen recovery which has the form of a quartz cylinder filled with tin. To determine the temperature state, the problem for the two-layer (quartz–tin) structure using the Heaviside function was reduced to the problem for a single-layer structure with variable (piecewise homogeneous) properties of the material. An analytical solution including algebraic polynomial functions with coefficients exponentially stabilizing in time was obtained by determining the position of the temperature perturbation front and additional boundary conditions using the integral heat balance method. The obtained solution was used to determine quasi-static temperature stresses in the case where the structure is a two-layer hollow cylinder (flat deformation). The layer matching method was used to obtain an exact analytical solution of the thermoelasticity problem, from which it follows that at the point of contact of the layers, the hoop and axial stresses have a jump (discontinuity) with a change of sign at it. It is found that in some startup modes, the hoop and axial stresses can exceed the tensile strength of the quartz layer. The results were used to determine startup modes in which the stresses do not exceed permissible values. [ABSTRACT FROM AUTHOR]

Dynamic tomography reconstructs a time activity curve (TAC) for every voxel assuming that the algebraic form of the function is known a priori. The algebraic form derived from the analysis of compartmental models depends nonlinearly on the nonnegative parameters to be determined. Direct methods apply fitting in every iteration step. Because of the iterative nature of the maximum likelihood–expectation maximization (ML–EM) reconstruction, the fitting result of the previous step can serve as a good starting point in the current step; thus, after the first iteration we have a guess that is not far from the solution, which allows the use of gradient-based local optimization methods. However, finding good initial guesses for the first ML–EM iteration is a critical problem since gradient-based local optimization algorithms do not guarantee convergence to the global optimum if they are started at an inappropriate location. This paper examines the robust solution of the fitting problem both in the initial phase and during the ML–EM iteration. This solution is implemented on GPUs and is built into the 4D reconstruction module of the TeraTomo software. [ABSTRACT FROM AUTHOR]

In his biography of Emil Artin, Richard Brauer describes the years from 1931-1941 as a time when 'Artin spoke through his students and through the members of his mathematical circle' rather than through written publications. This paper explores these seemingly quiet years when Artin immigrated to America and disseminated ideas about algebraic number theory during this time in his collaboration with George Whaples, a young American mathematician who had just completed his Ph.D. at the University of Wisconsin. The main result of their work is the use of the product formula for valuations to come up with an axiomatic characterization of both algebraic number fields and algebraic function fields with a finite field of constants. These two families of fields are exactly the fields for which class field theory is known to hold. We situate their mathematical work in the broader context of algebraic number theory and their lives within the broader historical context. [ABSTRACT FROM AUTHOR]

In this paper, we study the algebraic degree evaluation of NFSR-based cryptosystems. The degree evaluation method based on the numeric mapping proposed by Liu at CRYPTO 2017 is very fast and could be applied to a cube of any size. The numeric degree of f 1 (x , v) × f 2 (x , v) is estimated as D 1 + D 2 , where D 1 and D 2 are the numeric degrees of f 1 and f 2 respectively and the algebraic degree of a function is no more than its numeric degree. It can be observed that some variables may be counted twice in D 1 + D 2 and the precise of the numerical mapping heavily depends on how many variables are counted redundantly. When applied to an iterative cryptosystem, such redundances will accumulate during iteratively computing numeric degrees. This is an important factor accounting for the difference between the numeric degree and the algebraic degree of a cryptosystem. To reduce this difference, a new framework on the degree evaluation algorithm based on the numeric mapping is proposed. The main idea is to identify variables which are repeatedly counted in the numeric mapping and eliminate the redundant degrees on these variables. As illustrations, a concrete algorithm on Trivium-like ciphers is given which is shown to be useful in correlation cube attacks and the zero-sum distinguisher search. For correlation cube attacks on 835-round Trivium, we find some more useful cubes so that we could recover about 1.5 more bits at a cost of 2 40.7 . Furthermore, we find several cubes leading to zero-sum distinguishers for Kreyvium variants with from 875 to 880 initialization rounds. [ABSTRACT FROM AUTHOR]

In this paper, a modified generalized Newton method is presented to solve absolute value equations, when all the singular values of the system matrix exceed 1. The convergence properties of the proposed method are given. [ABSTRACT FROM AUTHOR]

A four stages twelfth algebraic order symmetric two-step method with vanished phase-lag and its first and second derivative is developed in this paper for the first time in the literature. More specifically in this paper the following will be investigated: (i) the phase-lag analysis for the development of the new method, (ii) the construction of the new method, (iii) the local truncation error analysis which is based on the radial Schrödinger equation, (iv) the interval of periodicity analysis and the stability analysis which is based on a scalar test equation with frequency not equal with the frequency of the scalar test equation used for the phase-lag analysis, (v) the error estimation procedure based on the algebraic order, (vi) the numerical results from our numerical tests for the study of the efficiency of the new obtained method. The numerical tests are based on the numerical solution of the Schrödinger equation. [ABSTRACT FROM AUTHOR]

This is a sequel of previous papers of the authors on Weierstrass semigroups at ramification points of double coverings of algebraic curves of genus three. In this paper they give a list of possible numerical semigroups when the covering curve is of genus six and show that all of such semigroups are actually of double covering type. This result completes a classification of numerical semigroups of double covering type obtained by ramified double coverings of curves of genus three. [ABSTRACT FROM AUTHOR]

The analysis of compositions of Runge-Kutta methods involves manipulations of functions defined on rooted trees. Existing formulations due to Butcher [1972], Hairer and Wanner [1974], and Murua and Sanz-Serna [1999], while equivalent, differ in details. The subject of the present paper is a new recursive formulation of the composition rules. This both simplifies and extends the existing approaches. Instead of using the order conditions based on trees, we propose the construction of the order conditions using a suitably chosen basis on the tree space. In particular, the linear structure of the tree space gives a representation of the U and D simplifying assumptions on trees which is not restricted to Runge-Kutta methods. A proof of the group structure of the set of elementary weight functions satisfying the D simplifying assumptions is also given is this paper. [ABSTRACT FROM AUTHOR]

Schlesinger (S) transformations can be combined with a direct rational (R) pull-back of a hypergeometric 2 × 2 system of ODEs to obtain RS 4 2 -pullback transformations to isomonodromic 2 × 2 Fuchsian systems with 4 singularities. The corresponding Painlevé VI solutions are algebraic functions, possibly in different orbits under Okamoto transformations. The paper demonstrates direct computations (involving polynomial syzygies) of Schlesinger transformations that affect several singular points at once, and presents an algebraic procedure of computing algebraic Painlevé VI solutions without deriving full RS-pullback transformations. [ABSTRACT FROM AUTHOR]

Symbol alphabets of n-particle amplitudes in N = 4 super-Yang-Mills theory are known to contain certain cluster variables of G(4, n) as well as certain algebraic functions of cluster variables. In this paper we solve the C Z = 0 matrix equations associated to several cells of the totally non-negative Grassmannian, combining methods of arXiv:2012.15812 for rational letters and arXiv:2007.00646 for algebraic letters. We identify sets of parameterizations of the top cell of G+(5, 9) for which the solutions produce all of (and only) the cluster variable letters of the 2-loop nine-particle NMHV amplitude, and identify plabic graphs from which all of its algebraic letters originate. [ABSTRACT FROM AUTHOR]

Let $$G$$ be a graph of order $$n$$ and size $$m$$ . Suppose that $$f:V(G)\rightarrow {\mathbb {N}}$$ is a function such that $$\sum _{v\in V(G)}f(v)=m+n$$ . In this paper we provide a criterion for $$f$$ -choosability of $$G$$ . Using this criterion, it is shown that the choice number of the complete $$k$$ -partite graph $$K_{2,2,\ldots ,2}$$ is $$k$$ , which is a well-known result due to Erdös, Rubin and Taylor. Among other results we study the $$f$$ -choosability of the complete $$k$$ -partite graphs with part sizes at most $$2$$ , when $$f(v)\in \{k-1,k\}$$ , for every vertex $$v\in V(G)$$ . [ABSTRACT FROM AUTHOR]

In this paper we develop an effective procedure for expressing Stark units in real quadratic extensions of totally real fields as values of the Barnes multiple Gamma function at algebraic points. This procedure is used to explicitly generate non-abelian extensions of Q by special Gamma values. As a main component of our work, we develop an algorithm to compute Shintani sets in all dimensions. [ABSTRACT FROM AUTHOR]

This paper investigates non coherent localization of an unknown target node in presence of a symmetrically opposite mirror node while the transmitter anchor node is perturbed under duress from external factors in a wireless sensor network. By limiting the transmitter anchor node translocation to a straight line, the resulting anchor-target geometry is exploited to mitigate the effects of mirror node and the perturbations of the transmitter node. Signal model for unperturbed and perturbed scenario is described. Fisher information vector expression is derived with respect to the polygonal geometry. Multistatic technique is utilized to extract fisher information from every possible link between the transmitter, receiver and unknown target node. The loss of location information due to undesirable aspect of the polygonal geometry is derived, following which a suitable expression is obtained to mitigate these effects. Solutions to algebraic functions involving perturbed anchor and symmetric geometry are developed. Geometric dilution of precision in terms of internodal angles is established. Numerical results corroborate theoretical analysis to achieve localization error comparable to sensor networks devoid of such perturbations. [ABSTRACT FROM AUTHOR]

This paper concerns global existence and finite time blow-up behavior of positive solutions for a nonlinear reaction-diffusion system with different diffusion coefficients. By use of algebraic matrix theory and modern analytical theory, we extend results of Wang (Z. Angew. Math. Phys. 51:160-167, 2000) to a more general system. Furthermore, we give a complete answer to the open problem which was brought forward in Wang (Z. Angew. Math. Phys. 51:160-167, 2000). [ABSTRACT FROM AUTHOR]

The fuzzy object-oriented databases have been proposed to meet the need of dealing with fuzzy as well as complex objects. In this paper, we present a formal fuzzy object-oriented database model. Based on the semantic measure of fuzzy data, we first identify two kinds of fuzzy object redundancies, which are inclusion redundancy and equivalence redundancy, and then define three kinds of merging operation for redundancy removal. On the basis, we define some fuzzy algebraic operations for fuzzy classes and fuzzy objects. Finally, in the paper, we discuss fuzzy querying strategies and give the form of SQL-like fuzzy querying for the fuzzy object-oriented databases. [ABSTRACT FROM AUTHOR]

The investigation of the impact of the vanishing of the phase-lag and its first and second derivatives on the efficiency of a four-step Runge-Kutta type method of sixth algebraic order is presented in this paper. Based on the above mentioned investigation, a Runge-Kutta type of two level four-step method of sixth algebraic order is produced. The error and the stability of the new obtained method are also studied in the present paper. The obtained new method is applied to the resonance problem of the Schrödinger equation the efficiency of the method to be examined. [ABSTRACT FROM AUTHOR]

Polynomial factorization is a classical algorithmic algebra problem with a wide range of applications. Of particular interest is factorization over finite fields, among which fields of order two are probably the most important ones when representing Boolean functions by Zhegalkin polynomials. In particular, factorization of Boolean polynomials corresponds to conjunctive decomposition of Boolean functions given in algebraic normal form. In addition, factorization enables decomposition of functions given in full disjunctive normal form (DNF) and positive DNF, as well as Cartesian decomposition of relational data. These applications demonstrate the importance of developing fast factorization algorithms. In this paper, we consider some recently proposed factorization algorithms of polynomial complexity and describe a parallel MIMD implementation that takes advantage of both task-level and data-level parallelism. We conduct some experiments on logic synthesis benchmarks and synthetic (random) polynomials to demonstrate significant factorization speedup. In conclusion, we discuss results of testing a parallel implementation of the algorithm on a massively parallel multicore architecture (REDEFINE). [ABSTRACT FROM AUTHOR]

Rotation symmetric Boolean functions incorporate a super-class of symmetric functions which represent an attractive corpus for computer investigation. These functions have been investigated from the viewpoints of bentness and correlation immunity and have also played a role in the study of nonlinearity. In the literature, many constructions of balanced odd-variable rotation symmetric Boolean functions with optimal algebraic immunity have been derived. While it seems that the construction of balanced even-variable rotation symmetric Boolean functions with optimal algebraic immunity is very hard work to breakthrough. In this paper, we present for the first time a construction of balanced rotation symmetric Boolean functions on an arbitrary even number of variables with optimal algebraic immunity by modifying the support of the majority function. The nonlinearity of the newly constructed rotation symmetric Boolean functions is also derived. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of constructing lower and upper estimators for univariate functions. This problem is of crucial importance in global optimization, where such bounds are used to reduce the search area. We propose to use piecewise linear estimators for bounding univariate functions and show how such estimators can be derived from the function's algebraic expression. The basic properties of such estimators are formulated and proved. We implemented the algorithms for the automated construction of lower and upper piecewise linear estimators and experimentally compared the proposed approach with the first-order interval bounds, Pijavskij method, and slope arithmetic. Numerical examples demonstrate that the piecewise linear estimators are more accurate with respect to the mentioned approaches. We also show that global optimization algorithms can significantly benefit from using piecewise linear estimators. Another advantage of the proposed approach is that the objective function does not have to be differentiable. This feature can favorably distinguish this method from other methods where the first and second derivatives are used. [ABSTRACT FROM AUTHOR]

The presentation, development and analysis of a new two-stages tenth algebraic order symmetric six-step method is introduced, for the first time in the literature, in this paper. More specifically, we present the development of the new method (requesting the highest algebraic order and the elimination of the phase-lag and its first and second derivatives), the analysis (error analysis and stability and interval of periodicity analysis) and the evaluation of the new developed method comparing its efficiency with the efficiency of well known methods and very recently produced methods in the literature on the approximate solution of the resonance problem of the one dimensional (or radial) Schrödinger equation. From the developments achieved and the results presented, we prove that the new obtained method is most more effective than other well known or recently developed methods of the literature. [ABSTRACT FROM AUTHOR]

In this paper, we first present a novel secondary construction of bent functions (building new bent functions from two already defined ones). Furthermore, the algebraic degree and algebraic immunity of the constructed functions are analysed. Finally, we apply the construction using as initial functions some specific bent functions and then specify sufficient conditions for the resulting bent functions not to be contained in the completed Maiorana-McFarland class. In the second part of the paper, we present a corrigendum of 'Constructions of bent-negabent functions and their relation to the completed Maiorana-McFarland Class' (IEEE Trans Inf Theory 61(3):1496-1506, 2015). [ABSTRACT FROM AUTHOR]

This paper aims at contributing to remedy the narrow treatment of functions at upper secondary level. Assuming that students make sense of functions by working on functional situations in distinctive settings, we propose to consider functional working spaces inspired by geometrical working spaces. We analyse a classroom situation based on a geometric optimization problem pointing out that no working space has been prepared by the teacher for students' tasks outside algebra. We specify a dynamic geometry space, a measure space and an algebra space, with artefacts in each space and means for connecting these provided by Casyopée. The question at stake is then the functionality of this framework for implementing and analyzing classroom situations and for analyzing students' and teachers' evolution concerning functions, in terms of geneses relative to each space. [ABSTRACT FROM AUTHOR]

This paper presents two algebraic criteria for the input-to-state stability of recurrent neural networks with time-varying delays. The criteria which also ensure global exponential stability when the input u( t) is equal to 0 and is easy to be verified only with the connection weights of the recurrent neural networks. Two numerical examples are given to demonstrate the effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]

This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler's upper bound of algebraic degree. Also a class of 1-resilient functions on any number n > 2 of variables with at least sub-optimal algebraic immunity is provided. [ABSTRACT FROM AUTHOR]

In our previous papers, a new geometric model has been proposed for calculating the thermodynamic properties of a multi-component system in terms of the properties of its three sub-binary systems. This new model can overcome the inherent defects of the traditional symmetrical and asymmetrical geometric models. Consequently, it is more reasonable theoretically and more reliable in practical applications. However, calculations using this new model involve a series of integration processes which make it complicated and affects its applications. Since a large number of real systems can be approximately fit through a Redlich-Kister polynomial, in this paper a new formalism is presented for the model, based on the binary Redlich-Kister type parameters. The advantage of this treatment is that the whole integration process is avoided by using algebraic operations, thereby simplifying the calculation. [ABSTRACT FROM AUTHOR]

The paper presents composite noncertainty-equivalence adaptive control (NCEA) systems for the closed orbit and hovering control of spacecraft in the vicinity of a uniformly rotating asteroid. In this study, the asteroid's mass and moment of inertia matrix, and the mass of the spacecraft are treated as unknown constant parameters. The objective is to control the orbit of the spacecraft, despite uncertainties in the gravitational force of asteroid. For the trajectory control of the spacecraft, first a generalized composite noncertainty-equivalence adaptive (NCEA) control system - based on the immersion and invariance theory - is developed. This system consists of a control module for stabilization and an identifier for the estimation of parameters. The identifier includes a dynamic integral type parameter adaptation law, which is formed by combining the update laws of the NCEA system, gradient algorithm-based identification scheme, and classical certainty-equivalence adaptive system. The classical component of the composite update law is used to cancel certain sign-indefinite functions in the derivative of a Lyapunov function. The full estimate of each unknown parameter is the sum of an algebraic function, and a signal generated by the composite integral type adaptation law. The gradient algorithm-based update rule is a function of the estimation model error. Then, by a proper choice of adaptation gains of the generalized control system, two additional composite control systems - (i) an NCEA system with gradient algorithm-based adaptation law, and (ii) an NCEA controller with classical update law - are derived. By the Lyapunov analysis, it is shown that in each composite closed-loop system, all of the signals are bounded, and the trajectory tracking error asymptotically converges to zero. Interestingly, composite systems, including gradient-based adaptation, have two attractive manifolds to which certain vector functions converge, but the composite system, without gradient-based update law, has a single attractive manifold. Numerical results are presented, which show that robust orbit control of the spacecraft around 433 Eros and hovering control in the vicinity of Ida are accomplished, despite parameter uncertainties and perturbing disturbance forces on the spacecraft. [ABSTRACT FROM AUTHOR]

In the present paper, a study is performed in an irregular earth crust, layered over a semi-infinite half-space under the effect of gravity. The irregularities at the interface are possible combinations of geometric shapes such as rectangular, paraboic and triangular notches. The aim of the study is to come up with the influence of these irregularities on the phase velocity of shear horizontal waves. The current work also explores how inhomogeneities affect SH-wave propagation. The medium is assumed to exhibit inhomogeneities as a function of depth. These functions are the product of a linear algebraic function and an exponential function of depth. By means of separation of variables and the substitution method, the equation of motion is reduced to the hypergeometric equation. Suitable boundary conditions are employed to derive a closed form of the dispersion equation. Numerical computations are performed to visualize the impact of irregularity and inhomogeneity. It is observed that the irregular interfaces and the inhomogeneity involved in the medium have a significant effect on SH-wave propagation. [ABSTRACT FROM AUTHOR]

In the present paper, we consider estimates for the orders of zeros of polynomials in functions satisfying a system of algebraic differential equations and possessing a special D-property defined in the paper. The main result obtained in the paper consists of two theorems for the two cases in which these estimates are given. These estimates are improved versions of a similar estimate proved earlier in the case of algebraically independent functions and a single point. They are derived from a more general theorem concerning the estimates of absolute values of ideals in the ring of polynomials, and the proof of this theorem occupies the main part of the present paper. The proof is based on the theory of ideals in rings of polynomials. Such estimates may be used to prove the algebraic independence of the values of functions at algebraic points. [ABSTRACT FROM AUTHOR]

The development of an immersion-and invariance-based adaptive state variable feedback control law for the closed orbit and hovering control of spacecraft in the vicinity of asteroids is the subject of this paper. The celestial body is assumed to be rotating with constant angular velocity about a fixed axis. Also, it is assumed that the mass and moments of inertia matrix of the asteroid, and the mass of the spacecraft are not known. The objective is to control the orbit of the spacecraft despite uncertainties in the system parameters. Based on the immersion and invariance theory, a noncertainty-equivalence adaptive control system is designed for steering the spacecraft along prescribe closed orbits or to fixed points for hovering control. The control system has a modular structure - consisting of an stabilizing control module and an parameter identifier. The control law is synthesized using filtered signals so as to circumvent the complexity of the immersion and immersion methodology. Unlike certainty-equivalence systems, the parameter estimates include judiciously selected nonlinear state-dependent algebraic functions and partial estimates derived from an integral update law. By the Lyapunov analysis, it is shown that the trajectory tracking error asymptotically converges to zero and all the signals in the closed-loop system are bounded. For illustration, numerical results are presented for control around 433 Eros and Ida asteroids. These results show that, despite uncertainties in the relative spacecraft dynamics, the adaptive law accomplishes closed orbit as well as hovering control. [ABSTRACT FROM AUTHOR]

Abstract.??In his landmark paper on amalgamation published in Algebra Universalis in 1971, Don Pigozzi posed some open questions in connection with amalgamation of subclasses of cylindric algebras. Some of these questions were originally raised by Comer, Daigneault, Johnson, McKenzie and others. In this paper we give answers to all these as well as a number of other related questions. Most of the solutions were found by the authors of this paper. However, a few were contributed by others who will of course be given due credit at the appropriate points. [ABSTRACT FROM AUTHOR]

Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize the chromatic polynomial and are related to Hessenberg varieties and diagonal harmonics. Motivated by the Stanley–Stembridge conjecture, we show that the allowable coloring weights for indifference graphs of Dyck paths are the lattice points of a permutahedron P λ , and we give a formula for the dominant weight λ . Furthermore, we conjecture that such chromatic symmetric functions are Lorentzian, a property introduced by Brändén and Huh as a bridge between discrete convex analysis and concavity properties in combinatorics, and we prove this conjecture for abelian Dyck paths. We extend our results on the Newton polytope to incomparability graphs of (3 + 1) -free posets, and we give a number of conjectures and results stemming from our work, including results on the complexity of computing the coefficients and relations with the ζ map from diagonal harmonics. [ABSTRACT FROM AUTHOR]

The notion of transparency order, proposed by Prouff (DPA attacks and S-boxes, FSE 2005, LNCS 3557, Springer, Berlin, 2005) and then redefined by Chakraborty et al. (Des Codes Cryptogr 82:95–115, 2017), is a property that attempts to characterize the resilience of cryptographic algorithms against differential power analysis attacks. In this paper, we give a tight upper bound on the transparency order in terms of nonlinearity, inferring the worst possible transparency order of those functions with the same nonlinearity. We also give a lower bound between transparency order and nonlinearity. We study certain classes of Boolean functions for their transparency order and find that this parameter for some functions of low algebraic degree can be determined by their nonlinearity. Finally, we construct two infinite classes of balanced semibent Boolean functions with provably relatively good transparency order (this is the first time that an infinite class of highly nonlinear balanced functions with provably good transparency order is given). [ABSTRACT FROM AUTHOR]

In this paper, we produce and examine several new notions such as soft topological soft groups and their subsystem. Also, soft topological soft rings and their subsystems are introduced. Furthermore, we introduce some new concepts like softly topological softly homomorphism and softly topological softly isomorphism. [ABSTRACT FROM AUTHOR]

In this paper, by using Fourier splitting method and the properties of decay character r∗, we consider the algebraic time decay rate of solutions to a new Hall-MHD system in Sobolev space Hm(R3)×Hm+1(R3) for m≥0. [ABSTRACT FROM AUTHOR]

It is well-known that all local minimum points of a semistrictly quasiconvex real-valued function are global minimum points. Also, any local maximum point of an explicitly quasiconvex real-valued function is a global minimum point, provided that it belongs to the intrinsic core of the function’s domain. The aim of this paper is to show that these “local min-global min” and “local max-global min” type properties can be extended and unified by a single general local-global extremality principle for certain generalized convex vector-valued functions with respect to two proper subsets of the outcome space. For particular choices of these two sets, we recover and refine several local-global properties known in the literature, concerning unified vector optimization (where optimality is defined with respect to an arbitrary set, not necessarily a convex cone) and, in particular, classical vector/multicriteria optimization. [ABSTRACT FROM AUTHOR]

In this paper, we establish a group of closed-form formulas for the maximal and minimal ranks of a nonlinear matrix expression with respect to two variant matrices by using a linearization method and some known formulas for extremal ranks of linear matrix expressions. In addition, by using some pure algebraic operations of matrices and their generalized inverses, we derive the maximal and minimal ranks of the above nonlinear matrix expression, where the two variant matrices are any solutions of two consistent matrix equations. As an application, we derive some sufficient and necessary conditions for the existence of the solution of a nonlinear matrix function. [ABSTRACT FROM AUTHOR]

In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories. For example, dp-small ordered groups are abelian divisible and dp-small ordered fields are real closed. [ABSTRACT FROM AUTHOR]

In this paper, we consider reducts of p-adically closed fields. We introduce a notion of shadows: sets $${M_f = \{(x,y) \in K^2 \mid |y| = |f(x)|\}}$$ , where f is a semi-algebraic function. Adding symbols for such sets to a reduct of the ring language, we obtain expansions of the semi-affine language where multiplication is nowhere definable, thus giving a negative answer to a question posed by Marker, Peterzil and Pillay. The second main result of this paper is the fact that in p-adic fields, full multiplication becomes definable if we add a rational function to the semi-affine language. [ABSTRACT FROM AUTHOR]

In this paper we present a new methodology for the development of four-step hybrid type methods of sixth algebraic order with vanished phase-lag and its derivatives. The methodology is based on the vanishing of the phase-lag and its derivatives on its level of the hybrid method. We present a comparative error and stability analysis for the produced new method. The efficiency of the new obtained methods is examined by application to the resonance problem of the Schrödinger equation. [ABSTRACT FROM AUTHOR]

It is well-known that the reachability graph of a sum of disjoint Petri nets is the disjoint product of the reachability graphs of the components. We shall consider here the converse problem, i.e., determine when and how a transition system may be decomposed in non-trivial concurrent factors, and extend the theory to more general labelled transition systems. Meanwhile, we shall develop interesting algebraic properties of disjoint products. The present paper is an extended version of Devillers (in: Desel, Yakovlev (eds) Proceedings 16th international conference on application of concurrency to system design (ACSD 2016), 2016). [ABSTRACT FROM AUTHOR]

A recent paper (Kuniba in Nucl Phys B 913:248-277, 2016) introduced the stochastic Uq(An(1)) vertex model. The stochastic S-matrix is related to the R-matrix of the quantum group Uq(An(1)) by a gauge transformation. We will show that a certain function Dm→+ intertwines with the transfer matrix and its space reversal. When interpreting the transfer matrix as the transition matrix of a discrete-time totally asymmetric particle system on the one-dimensional lattice Z, the function Dm→+ becomes a Markov duality function Dm→ which only depends on q and the vertical spin parameters {μx}. By considering degenerations in the spectral parameter, the duality results also hold on a finite lattice with closed boundary conditions, and for a continuous-time degeneration. This duality function had previously appeared in a multi-species ASEP(q, j) process (Kuan in A multi-species ASEP(q, j) and q-TAZRP with stochastic duality, 2017). The proof here uses that the R-matrix intertwines with the co-product, but does not explicitly use the Yang-Baxter equation. It will also be shown that the stochastic Uq(An(1)) is a multi-species version of a stochastic vertex model studied in Borodin and Petrov (Higher spin six vertex model and symmetric rational functions, 2016) and Corwin and Petrov (Commun Math Phys 343:651-700, 2016). This will be done by generalizing the fusion process of Corwin and Petrov (2016) and showing that it matches the fusion of Kulish and yu (Lett Math Phys 5:393-403, 1981) up to the gauge transformation. We also show, by direct computation, that the multi-species q-Hahn Boson process (which arises at a special value of the spectral parameter) also satisfies duality with respect to D∞, generalizing the single-species result of Corwin (Int Math Res Not 2015:5577-5603, 2015). [ABSTRACT FROM AUTHOR]

In this paper, we establish some relations involving q-Euler type sums, q-harmonic numbers and q-polylogarithms. Then, using the relations obtained with the help of q-analog of partial fraction decomposition formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit formulas for several classes of q-harmonic sums in terms of q-polylogarithms and q-harmonic numbers. The given representations are new. [ABSTRACT FROM AUTHOR]

Assume that a linear random-effects model $$\mathbf{y}= \mathbf{X}\varvec{\beta }+ \varvec{\varepsilon }= \mathbf{X}(\mathbf{A}\varvec{\alpha }+ \varvec{\gamma }) + \varvec{\varepsilon }$$ is transformed as $$\mathbf{T}\mathbf{y}= \mathbf{T}\mathbf{X}\varvec{\beta }+ \mathbf{T}\varvec{\varepsilon }= \mathbf{T}\mathbf{X}(\mathbf{A}\varvec{\alpha }+ \varvec{\gamma }) + \mathbf{T}\varvec{\varepsilon }$$ by pre-multiplying a given matrix $$\mathbf{T}$$ of arbitrary rank. These two models are not necessarily equivalent unless $$\mathbf{T}$$ is of full column rank, and we have to work with this derived model in many situations. Because predictors/estimators of the parameter spaces under the two models are not necessarily the same, it is primary work to compare predictors/estimators in the two models and to establish possible links between the inference results obtained from two models. This paper presents a general algebraic approach to the problem of comparing best linear unbiased predictors (BLUPs) of parameter spaces in an original linear random-effects model and its transformations, and provides a group of fundamental and comprehensive results on mathematical and statistical properties of the BLUPs. In particular, we construct many equalities for the BLUPs under an original linear random-effects model and its transformations, and obtain necessary and sufficient conditions for the equalities to hold. [ABSTRACT FROM AUTHOR]

In this paper, some classical estimates between the norms of α-Bloch spaces B and Lipschitz classes Lip, 0 < α < 1, are improved. [ABSTRACT FROM AUTHOR]

In this paper, a new yet simple reference logo watermarking scheme based on fractional Fourier transform (FrFT) and singular value decomposition (SVD) is proposed. The core idea of the proposed scheme is to segment host image into non-overlapping blocks by the means of Hilbert space filling curve and a reference image is formed by considering Human visual system (HVS). First, reference image is transformed into FrFT domain and embedding is done by modifying singular values of the reference image using singular values of watermark. After embedding, modified reference image is segmented into blocks and these modified blocks are mapped into their original places for constructing watermarked image. For extraction, a reliable watermark extraction scheme is proposed. The experimental results demonstrate better visual imperceptibility and resiliency of the proposed scheme against intentional or un-intentional variety of attacks. [ABSTRACT FROM AUTHOR]

This paper is concerned with a polynomial model (residue class ring) for a given q-valued propositional logic (where q is a power of a prime integer). This model allows to transfer logic problems into algebraic terms, resulting in an immediate computational approach to Knowledge Based Systems based on multi-valued logics. By means of this new approach, we have extended an already existent algebraic model to logics with a prime power number of truth values, while also getting more straightforward proofs and a more direct enunciation of the central theorem of this model. [ABSTRACT FROM AUTHOR]