Search

Abstract: Remark on Polickýʼs paper on circular units of a compositum of quadratic number fields is given. [Copyright &y& Elsevier]

This review paper gives an overview of the method of multipliers for partial differential equations (PDEs). This method has made possible a lot of solutions to PDEs that are of interest in many areas such as applied mathematics, mathematical physics, engineering, etc. Looking at the history of the method and synthesizing the newest developments, we hope to give it the attention that it deserves to help develop the vast amount of work still needed to understand it and make the best use of it. It is also an interesting and a relevant method in itself that could possibly give interesting results in areas of mathematics such as modern algebra, group theory, topology, etc. The paper will be structured in such a manner that the last review known for this method will be presented to understand the theoretical framework of the method and then later work done will be presented. The information of four recent papers further developing the method will be synthesized and presented in such a manner that anyone interested in learning this method will have the most relevant information available and have all details cited for checking. [ABSTRACT FROM AUTHOR]

In 1975, Symons [[5]] introduced a subsemigroup of HT ht , defined as HT ht , for a nonempty subset I Y i of I X i , determining all its automorphisms. The first paper [[21]] introduces a construction of a new graph associated with a semihypergroup, using the fundamental relation HT ht . In particular, it is shown that the Cayley graphs generated by transposition trees on the set HT ht are HT ht -extendable and their extendability number is HT ht for any integer HT ht . Connections between algebraic structure theory and graph theory have been established in order to solve open problems in one theory with the help of the tools existing in the other, emphasizing the remarkable properties of one theory with techniques involving the second. [Extracted from the article]

In this paper, we examine the notions of mj-clean ring and strongly mj-clean ring. And we will provide some of its basic properties. We examine the relationship of mj-clean ring with m-clean ring and j-clean ring. We prove that R is strongly mj-clean ring if and only if Mn(R) is strongly mj-clean ring. We prove that mj-clean ring is Dedekind-finite; i.e., ab = 1 implies that ba = 1. [ABSTRACT FROM AUTHOR]

The primary motivation for this work is to develop the concept of Marshall's quotient applicable to non-commutative multi-rings endowed with involution, expanding upon the main ideas of the classical case—commutative and without involution—presented in Marshall's seminal paper. We define two multiplicative properties to address the involutive case and characterize their Marshall quotient. Moreover, this article presents various cases demonstrating that the "multi" version of rings with involution offers many examples, applications, and relatives in (multi)algebraic structures. Therefore, we established the first steps toward the development of an expansion of real algebra and real algebraic geometry to a non-commutative and involutive setting. [ABSTRACT FROM AUTHOR]

The study delves into the relationship between symmetry groups and automorphism groups in polyhedral graphs, emphasizing their interconnected nature and their significance in understanding the symmetries and structural properties of fullerenes. It highlights the visual importance of symmetry and its applications in architecture, as well as the mathematical structure of the automorphism group, which captures all of the symmetries of a graph. The paper also discusses the significance of groups in Abstract Algebra and their relevance to understanding the behavior of mathematical systems. Overall, the findings offer an inclusive understanding of the relationship between symmetry groups and automorphism groups, paving the way for further research in this area. [ABSTRACT FROM AUTHOR]

Leibniz algebras are non-antisymmetric generalizations of Lie algebras. In this paper, we investigate the properties of complete Leibniz algebras under certain conditions on their extensions. Additionally, we explore the properties of derivations and direct sums of Leibniz algebras, proving several results analogous to those in Lie algebras. [ABSTRACT FROM AUTHOR]

In this paper, we consider the q-analog of Kostant’s Partition Function of Lie algebras sl4(C) and sp6(C) and present a closed formula for the values of these functions. [ABSTRACT FROM AUTHOR]

Francis Sowerby Macaulay began his career working on Brill and Noether's theory of algebraic plane curves and their interpretation of the Riemann–Roch and Cayley–Bacharach theorems; in fact it is Macaulay who first stated and proved the modern form of the Cayley–Bacharach theorem. Later in his career Macaulay developed ideas and results that have become important in modern commutative algebra, such as the notions of unmixedness, perfection (the Cohen–Macaulay property), and super-perfection (the Gorenstein property), work that was appreciated by Emmy Noether and the people around her. He also discovered results that are now fundamental in the theory of linkage, but this work was forgotten and independently rediscovered much later. The name of a computer algebra program (now Macaulay2) recognizes that much of his work is based on examples created by refined computation. Though he never spoke of the connection, the threads of Macaulay's work lead directly from the problems on plane curves to his later theorems. In this paper we will explain what Macaulay did, and how his results are connected. [ABSTRACT FROM AUTHOR]

Copyright of Ñawi: Arte, Diseño y Comunicación is the property of Escuela Superior Politecnica del Litoral and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Phainomena is the property of Phenomenological Society of Ljubljana and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Algebraic topology studies topological spaces with the help of tools from abstract algebra. The main focus of this paper is to show that many concepts from algebraic topology can be conveniently expressed in terms of (normal) factor graphs. As an application, we give an alternative proof of a classical duality result of Kramers and Wannier, which expresses the partition function of the 2-D Ising model at a low temperature in terms of the partition function of the 2-D Ising model at a high temperature. Moreover, we discuss analogous results for the 3-D Ising model and the Potts model. [ABSTRACT FROM AUTHOR]

The idea of integrating the history of mathematics content in mathematics teaching and learning is not new. Researchers stress many benefits of using history of mathematics in mathematics education. They suggest that it is very important for mathematics teachers to be familiar with the genesis of mathematical concepts and statements, since these might help them to better understand the difficulties students face. As a matter of fact, history of mathematics shows us that students very often form mathematical concepts in the similar way these concepts have been formed through the history of mankind. The main purpose of this study is to introduce some pre-algebra concepts, such as systems of linear equations, to primary-grade students by using an ancient Chinese method. In the first part of the paper we give an overview of the Fangcheng method. The Fangcheng method is presented in chapter 8 of the book The Nine Chapters on the Art and Calculation which is one of the most important and most influential mathematical works in the long history of China. Originally, the method was used for solving some real-life problems, such as calculating the yields of rice, prices of different products and numbers of animals. It deals with the solution of simultaneous linear equations with two to five unknowns by placing them in a table, and operating with columns in a way identical to the row transformations of the modern matrix algebra. In Serbia, students do not learn how to solve systems of linear equations until the 8th grade of primary school. The aim of the study was to investigate the possibility for fourth grade students to use an adapted Fangcheng method as a tool for solving word problems. The second part of the paper consists of the research methodology, results and discussion. We used the quasi-experimental one-group design with post-test only. There was no justified reason to include a control group since the comparison would not be possible considering that the contents presented to the experimental group were not usually taught in first four primary school grades. Furthermore, the pre-test could not be monitored since no student had had previous experience in using the presented method for solving systems of linear equations. The first research task was to determine if fourth grade students were able to learn, understand, and use the Fangcheng method when solving systems of linear equations with two unknowns. The second research task was to examine if students were able to learn, understand, and use the same method in solving systems of linear equations with three unknowns. The sample included 48 fourth grade students. The research had two phases, and at the end of each phase post-tests were conducted. In the first phase, all students participated in the intervention program, while the second phase included only those students who performed well on the first post-test (14 students). The study results indicate that students who show greater interest in mathematics successfully adopt the procedures necessary for the performance of the Fangcheng method. Furthermore, the majority of students use the Fangcheng method without any difficulties when solving text-based systems of linear equations with two unknowns within the given formed initial table. Difficulties arise when students need to mark the values and form a table on their own. A large number of students manages to understand the technique used, but due to frequent computational errors, they are unable to accurately determine the values of the unknowns. The findings of the study cannot be generalized considering the fact that there are certain limitations, such as a small sample size and quasi-experimental design. Therefore, some further research should be performed with a larger sample of students. However, since there are not many empirical researches which explore the effects of applying the history of mathematics in math teaching, we believe that our study contributes to the field. In this regard, it would be important in future studies to examine the views of teachers as to whether they apply some segments of the history of mathematics in their teaching work, for what purpose, in what parts of the class, whether their application sufficiently arouses students' interest. [ABSTRACT FROM AUTHOR]

This paper is concerned with basic concepts and some results on regular Γ-nearness semigroup and ideals of a Γ-nearness semigroup. Also, it is given some properties about ideals of a regular Γ-nearness semigroup and an example about the subject. Furthermore, we study relations among ideals of a Γ-nearness semigroup. [ABSTRACT FROM AUTHOR]

Modulo lattice additive noise (MLAN) channels appear in the analysis of structured binning codes for Costa's dirty-paper channel and of nested lattice codes for the additive white Gaussian noise (AWGN) channel. In this paper, we derive a new lower bound on the error exponents of the MLAN channel. With a proper choice of the shaping lattice and the scaling parameter, the new lower bound coincides with the random-coding lower bound on the error exponents of the AWGN channel at the same signal-to-noise ratio (SNR) in the sphere-packing and straight-line regions. This result implies that, at least for rates close to channel capacity, 1) writing on dirty paper is as reliable as writing on clean paper; and 2) lattice encoding and decoding suffer no loss of error exponents relative to the optimal codes (with maximum-likelihood decoding) for the AWGN channel. [ABSTRACT FROM AUTHOR]

This paper presents a PVS development of relevant results of the theory of rings. The PVS theory includes complete proofs of the three classical isomorphism theorems for rings, and characterizations of principal, prime and maximal ideals. Algebraic concepts and properties are specified and formalized as generally as possible allowing in this manner their application to other algebraic structures. The development provides the required elements to formalize important algebraic theorems. In particular, the paper presents the formalization of the general algebraic-theoretical version of the Chinese remainder theorem (CRT) for the theory of rings, as given in abstract algebra textbooks, proved as a consequence of the first isomorphism theorem. Also, the PVS theory includes a formalization of the number-theoretical version of CRT for the structure of integers, which is the version of CRT found in formalizations. CRT for integers is obtained as a consequence of the general version of CRT for the theory of rings. [ABSTRACT FROM AUTHOR]

Nowadays, mathematicians are very interested in discovering new and advanced methods for determining the solution of Diophantine equations. Diophantine equations are those equations that have more unknowns than equations. Diophantine equations appear in astronomy, cryptography, abstract algebra, coordinate geometry and trigonometry. Congruence theory plays an important role in finding the solution of some special type Diophantine equations. The absence of any generalized method, which can handle each Diophantine equation, is challenging for researchers. In the present paper, the authors have discussed the existence of the solution of exponential Diophantine equation ( ) ( ) where are whole numbers. Results of the present paper show that the exponential Diophantine equation ( ) ( ) where are whole numbers, has no solution in the whole number. [ABSTRACT FROM AUTHOR]

Vector linear solvability of non-multicast networks depends upon both the characteristic of the finite field and the dimension of the vector linear network code. In the literature, the dependency on the characteristic of the finite field and the dependency on the dimension have been studied separately. In this paper, we show the interdependency between the characteristic of the finite field and the dimension of the vector linear network code that achieves a vector linear network coding (VLNC) solution in non-multicast networks. For any given network $\mathcal {N}$ , we define $P(\mathcal {N},d)$ as the set of all characteristics of finite fields over which the network $\mathcal {N}$ has a $d$ -dimensional VLNC solution. To the best of our knowledge, for any network $\mathcal {N}$ shown in the literature, if $P(\mathcal {N},1)$ is non-empty, then $P(\mathcal {N},1) = P(\mathcal {N},d)$ for any positive integer $d$. We show that, for any two non-empty sets of primes $P_{1}$ and $P_{2}$ , there exists a network $\mathcal {N}$ such that $P(\mathcal {N},1) = P_{1}$ , but $P(\mathcal {N},2) = \{P_{1},P_{2} \}$. We also show that there are networks exhibiting a similar advantage (the existence of a VLNC solution over a larger set of characteristics) if the dimension is increased from 2 to 3. However, such behaviour is not universal, as there exist networks which admit a VLNC solution over a smaller set of characteristics of finite fields when the dimension is increased. Using the networks constructed in this paper, we further demonstrate that: (i) a network having an $m_{1}$ -dimensional VLNC solution over a finite field of some characteristic and an $m_{2}$ -dimensional VLNC solution over a finite field of some other characteristic may not have an $(m_{1} + m_{2})$ -dimensional VLNC solution over any finite field; (ii) there exist a class of networks for which scalar linear network coding (SLNC) over non-commutative rings has some advantage over SLNC over finite fields: the least sized non-commutative ring over which each network in the class has an SLNC solution is significantly lesser in size than the least sized finite field over which it has an SLNC solution. [ABSTRACT FROM AUTHOR]

This paper investigates the solutions (if any) of the Diophantine equation 3x + 35y = Z², where x, y, and are whole numbers. Diophantine equations are drawing the attention of researchers in diversified fields over the years. These are equations that have more unknowns than a number of equations. Diophantine equations are found in cryptography, chemistry, trigonometry, astronomy, and abstract algebra. The absence of any generalized method by which each Diophantine equation can be solved is a challenge for researchers. In the present communication, it is found with the help of congruence theory and Catalan's conjecture that the Diophantine equation 3x + 35y = Z² has only two solutions of (x, y, z) as (1, 0, 2) and (0, 1, 6) in non-negative integers. [ABSTRACT FROM AUTHOR]

Most studies on the switching game Lights Out and its variants focus on the solvability of given games or the number of solvable games, but when the game is viewed in a coding-theoretical perspective, more interesting questions with special symbolizations in coding theory will naturally pop up, such as finding the minimal number of lit lights among all solvable games apart from the solved game, or finding the minimal number of lit lights that the player can achieve from a given unsolvable game, etc. However, these problems are usually hard to solve in general from the perspective of algorithmic complexity. This study considers a Lights Out variant called two-state Alien Tiles, which toggles all the lights in the same row and those in the same column of the clicked light. We investigate its properties, discuss several coding-theoretical problems about this game, and explore this game as an error-correcting code and investigate its optimality. The purpose of this paper is to propose ways of playing switching games in a think-outside-the-box manner, which benefits the recreational mathematics community. [ABSTRACT FROM AUTHOR]

Let RG be the gruop ring of the group G over ring R and (RG) be its unit group. In this paper, The structure of the unit group of a group ring F2nD14 of the group D14 over a field of characteristic 2 is determined. [ABSTRACT FROM AUTHOR]

Background: Mutation testing is a widely explored technique used to evaluate the quality of software tests, but little attention has been given to its mathematical foundations. Aim: We provide a formal description of the core concepts in mutation testing, relations between them and conclusions that can be drawn from the presented model. Method: We introduce concepts of mutant space and patch space, and refer to patch merging procedure from the patch theory. We explicitly present constraints, such as location-dependence, that affect mutation operators. We also present a way to use introduced formalism with traditional operators proposed in other papers. Results: The proposed formalism allows to describe interactions between separate mutations using well-known abstract algebra notation. Conclusion: The presented formalism may substantially decrease the number of tested weak mutants and increase the number of valuable ones, while giving tools to partially address the problem of equivalent mutants, particularly for higher-order mutation testing. However, additional empirical evaluation is still needed. [ABSTRACT FROM AUTHOR]

Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. When they are defined over finite fields, those codes have been intensively studied, especially in recent years, but they have been firstly partially characterized by Ashikhmin and Barg since 1998. Next, they were completely characterized in 2018 by Ding, Heng, and Zhou in terms of the minimum and maximum nonzero weights in the corresponding codes. Since then, many construction methods for minimal linear codes over finite fields throughout algebraic and geometric approaches have been proposed in the literature. In particular, the algebraic approach gives rise to minimal codes from (cryptographic) functions. Linear codes over finite fields have been expanded into the collection of acceptable alphabets for codes and study codes over finite commutative rings. A natural way to extend the known results available in the literature is to consider minimal linear codes over commutative rings with unity. In extending coding theory to codes over rings, several essential principles must be considered. Particularly extending the minimality property from finite fields to rings and creating such codes is not simple. Such an extension offers more flexibility in the construction of minimal codes. The present article investigates one-dimensional minimal linear codes over the rings $\mathbb {Z}_{p^{n}}$ (where $p$ is a prime) and $\mathbb {Z}_{p^{m}q^{n}}$ (where $p < q$ are distinct primes and $m\leq n$). Our ultimate objective is to characterize such codes’ minimality and design minimal linear codes over the considered rings. Given our objective, we first introduced the notion of minimal codes over (commutative) rings and succeeded in deriving simple characterization of one-dimensional minimal linear codes over the underlying rings mentioned above. Our new algebraic approach allows designing new minimal linear codes. Almost minimal codes over rings are also presented. To the best of our knowledge, the present paper offers a wide variety of minimal codes over (commutative) rings for the first time. Novel perspectives and developments in this direction are expected in the future. [ABSTRACT FROM AUTHOR]

In this paper, we propose a generalized greedy (G-greedy) algorithm based on zero-forcing beamforming (ZFBF) for the multiple-input multiple-output (MIMO) broadcast channel. This algorithm serves as a general mathematical framework that includes a number of existing greedy user selection methods as its realizations. As previous results only give the scaling law of the sum rate of dirty paper coding (DPC), with the help of the G-greedy structure, we are able to obtain the exact limit of the DPC sum rate for a large number of users. We also prove that the difference between the sum rates obtained by G-greedy user selection and by DPC goes to zero as the number number of users increases. In addition to this, we investigate one particular greedy user selection scheme called sequential water-filling (SWF). For this algorithm, a complexity reduction is achieved byan iterative procedure based on an LQ decomposition, which converts the calculation of the Moore-Penrose matrix inverse to one vector-matrix multiplication. A sufficient condition is given to prune the search space of this algorithm that results in further complexity reduction. With the help of the G-greedy algorithm, we prove that SWF achieves the full DPC sum rate for a large number of users. For a moderate number of users, simulation demonstrates that, compared with other user selection algorithms, SWF achieves a higher sum rate that is close to the maximal sum rate achievable by ZFBF with the same order of complexity. [ABSTRACT FROM AUTHOR]

This paper provides a description of how market competitiveness evaluations concerning mechanical equipment can be made in the context of multi-criteria decision environments. It is assumed that, when we are evaluating the market competitiveness, there are limited number of candidates with some required qualifications, and the alternatives will be pairwise compared on a ratio scale. The qualifications are depicted as criteria in hierarchical structure. A hierarchical decision model called PCbHDM was used in this study based on an analysis of its desirable traits. Illustration and comparison shows that the PCbHDM provides a convenient and effective tool for evaluating the market competitiveness of mechanical equipment. The researchers and practitioners might use findings of this paper in application of PCbHDM. [ABSTRACT FROM AUTHOR]

A class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤; such bands are known as right normal skew nearlattices. The poset (R, ≤) is relatively orthocomplemented; in particular, every initial segment in it is orthomodular. The order ≤ is actually a version of the so called right-star order. The one-sided star orders are well-investigated for matrices and recently have been generalized to bounded linear Hilbert space operators and to abstract Rickart *-rings. The paper demonstrates that they can successfully be treated also in Rickart rings without involution. [ABSTRACT FROM AUTHOR]

For each nonzero h ∈ F[E]?, where F is a field, let Ah be the unital associative algebra generated by elements x, y, satisfying the relation yx - xy = h. This gives a parametric family of subalgebras of the Weyl algebra A1, containing many well-known algebras which have previously been studied independently. In this paper, we give a full description of the Hochschild cohomology HH●.Ah/over a field of an arbitrary characteristic. In case F has a positive characteristic, the center Z.Ah/of Ah is nontrivial and we describe HH●.Ah/as a module over Z.Ah/. The most interesting results occur when F has a characteristic 0. In this case, we describe HH●.Ah/as a module over the Lie algebra HH1.Ah/and find that this action is closely related to the intermediate series modules over the Virasoro algebra. We also determine when HH●.Ah/is a semisimple HH1.Ah/-module. [ABSTRACT FROM AUTHOR]

In the paper [1], V. O. Manturov introduced the groups Gkn depending on two natural parameters n > k and naturally related to topology and to the theory of dynamical systems. The group G2n, which is the simplest part of Gkn, is isomorphic to the group of pure free braids on n strands. In the present paper, we study the groups G2n supplied with additional structures-parity and points; these groups are denoted by G2n,p and G2n,d. First,we define the groups G2n,p and G2n,d, then study the relationship between the groups G2n, G2n,p, and G2n,d. Finally, we give an example of a braid on n + 1 strands, which is not the trivial braid on n + 1 strands, by using a braid on n strands with parity. After that, the author discusses links in Sg × S1 that can determine diagrams with points; these points correspond to the factor S1 in the product Sg × S1. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the concepts of para and quasi topological MV -algebras, which was first introduced by Najafi et al. in 2017, to BL-algebras as para and quasi topological BL-algebras and elaborate these concepts via some examples. We further derive and prove some theorems by employing pre-filters and a fundamental system of neighborhoods. [ABSTRACT FROM AUTHOR]

In this paper we elaborated the concept that on what conditions left almost semigroup (LA-Semigroup), right almost semigroup (RA-Semigroup) and a groupoid become commutative and further extended these results on medial, LA-Group and RA-Group. We proved that the relation of LA-Semigroup with left double displacement semigroup (LDD-semigroup), RA-Semigroup with left double displacement semigroup (RDD-semigroup) is only commutative property. We highlighted the errors in the recently developed results on LA-Semigroup and semigroup [17, 1, 18] and proved that example discussed in [18] is semigroup with left identity but not paramedial. We extended results on locally associative LA-Semigroup explained in [20, 21] towards LA-Semigroup and RA-Semigroup with left zero and right zero respectively. We also discussed results on n-dimensional LA-Semigroup, n-dimensional RASemigroup, non commutative finite medials with three or more than three left or right identities and finite as well as infinite commutative idempotent medials not studied in literature. [ABSTRACT FROM AUTHOR]

In this paper, we define the conceps of complex fuzzy Lie subalgebras and complex fuzzy ideals of Lie algebras with respect to t-norms and investigate some of characteristics and relationship between them. Next, we introduce the concepos of quotient subalgebras, intersection, sum and direct product of them and prove some results about them. Finally, we introduce and study the image and the inverse image of them under Lie algebra homomorphisms. [ABSTRACT FROM AUTHOR]

In this paper, the concept of fuzzy bipolar soft set initiated by Naz and Shabir [22] is modified and strengthened. Consequently, the basic operations on fuzzy bipolar soft sets are redefined and their algebraic properties are studied. The notion of fuzzy bipolar soft ordered semigroup is defined and, furthermore, the concepts of fuzzy bipolar soft left (resp., right, two-sided) ideals over ordered semigroups are introduced and characterized. [ABSTRACT FROM AUTHOR]

In this paper, the concept of permuting tri-multiderivation on incline algebra is initiated and some results are proved by using this idea. [ABSTRACT FROM AUTHOR]

This paper explores the viability and development of the first edition of the researcher's mathematical card game, Groups, as a learning tool for elementary group theory, a topic in abstract algebra. Groups was play-tested by six undergraduate students in late 2016 who provided feedback on Groups from both utility-centric and design-centric perspectives. This paper addresses how well undergraduates with no prior group theory experience understand the fundamentals of group theory after playing several games of Groups, and how well undergraduates with prior knowledge of group theory related the Groups game play and mechanics to the fundamentals of group theory. Based on interview and questionnaire data, players found Groups to be an engaging and effective learning tool with both strengths and weaknesses in the tested iteration. [ABSTRACT FROM AUTHOR]

In this paper, new construction methods for self-dual codes are given. The methods use the short Kharaghani array and its variation. They are applicable to any commutative Frobenius ring. We apply the constructions over the ring F2 + uF2 and self- dual Type I [64, 32, 12]2-codes with various weight enumerators obtained as Gray images. By using an extension theorem for self-dual codes we were able to construct 27 new extremal binary self-dual codes of length 68. The existence of extremal binary self-dual codes with these weight enumerators was previously unknown. [ABSTRACT FROM AUTHOR]

Copyright of Canadian Journal of Physics is the property of Canadian Science Publishing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Layout methods for dense and sparse data are often seen as two separate problems with their own particular techniques. However, they are based on the same basic concepts. This paper studies how to integrate automatic data-layout and partition techniques for both dense and sparse data structures. In particular, we show how to include support for sparse matrices or graphs in Hitmap, a library for hierarchical tiling and automatic mapping of arrays. The paper shows that it is possible to offer a unique interface to work with both dense and sparse data structures. Thus, the programmer can use a single and homogeneous programming style, reducing the development effort and simplifying the use of sparse data structures in parallel computations. Our experimental evaluation shows that this integration of techniques can be effectively done without compromising performance. [ABSTRACT FROM AUTHOR]

The paper deals with functional properties of three-valued logics. We consider the family of regular three-valued Kleene's logics (strong, weak, intermediate) and it's extensions by adding an implicative connectives ("natural" implications). The main result of our paper is the lattice that describes the relations between implicative extensions of regular logics. [ABSTRACT FROM AUTHOR]

In this paper we study the inequalities of the determinants of the positive definite matrices and the invertible matrices by applying the integral method and matrix theory such that extensions of Fan Ky's inequality are established. And then an improvement of Fan Ky's inequality is given by using the positive definiteness of Gram matrix. [ABSTRACT FROM AUTHOR]

Locales, the module system of the theorem prover Isabelle, were designed so that developments in abstract algebra could be represented faithfully and concisely. Whether these goals were met is assessed through a case study. Parts of an algebra textbook, Jacobson's Basic Algebra, that are challenging structurally were formalised. Key parts of the formalisation are presented in greater detail. An analysis of the work from both qualitative and quantitative perspectives substantiates that the design goals were met. In particular, the size ratio of formal to "pen and paper" text does not increase when going further into the book. The analysis also yields guidance on locales including patterns of use, which are identified and described. [ABSTRACT FROM AUTHOR]

In this paper, the fuzzy analytic network process (FANP) is proposed. For achieving this purpose, two problems are highlighted and overcome in this paper. First, the postulate of the reciprocal matrix should be released, because this property is not satisfied in the fuzzy comparison matrix. Second, the convergent problem for raising the fuzzy supermatrix to limiting power should be appropriately handled. In this paper, we directly fuzzify Cogger and Yu's method for obtaining the fuzzy local vectors, because their method releases the postulate of the reciprocal matrix in the analytic hierarchy process (AHP). Then, we derive the particular matrix problem for obtaining the fuzzy global weight vector so that the convergent problem in a fuzzy limiting supermatrix can be overcome. [ABSTRACT FROM AUTHOR]

The conventional image-based visual servoing leads to image singularities that might cause control instabilities. To avoid this problem, in this paper, the image moments are used as features for visual servoing, where the Jacobian matrix is full rank and upper triangular. Thus, it has the maximal decoupled structure and simplifies the controller. The general analytical form of the interaction matrix or the Jacobian matrix considering the camera parameters related to any image moments is derived in this paper. As a servoing controller, an optimal visual PD controller is presented to improve the performance of the visual servoing system instead of the P controller, which is the method extensively used in visual servoing. A genetic algorithm-based PD parameters tuning method is applied to obtain the optimal parameters. The method proposed is used to align the micropeg and hole, and the simulation results show that the object can reach its desired position faster and more smoothly. [ABSTRACT FROM AUTHOR]

This paper presents a proposal for an expert system for inspection and diagnosis of epoxy resin on industrial floor coatings (PIRE). The system proposed intends to contribute to normalize the inspections and related reports and make the in situ inspector activities more objective and standardized. A classification system for epoxy resin floor defects and their most probable causes are proposed. With these data, anomaly files were prepared, in which the designation, a brief description, possible causes and consequences, the main aspects to be checked, inspection parameters, and a classification of the anomaly according to its importance/urgency, are presented. In parallel, the floor coatings’ diagnosis and repair techniques were also identified and classified. With these data, correlation matrices between anomalies and causes, anomalies between themselves, anomalies and diagnostic techniques, and finally, anomalies and repair floor techniques, were built. The validation of the classification system was made via a number of cases of standardized inspections. The paper presents indispensable data for industrial floor designers, builders, and users in terms of maximizing the service life of epoxy resin coatings. [ABSTRACT FROM AUTHOR]

For about two decades, numerous methods have been developed to blindly identify overdetermined (P ≤ N) mixtures of P statistically independent narrowband (NB) sources received by an array of N sensors. These methods exploit the information contained in the second-order (SO), the fourth-order (FO) or both the SO and FO statistics of the data. However, in practical situations, the probability of receiving more sources than sensors increases with the reception bandwidth and the use of blind identification (BI) methods able to process underdetermined mixtures of sources, for which P > N may be required. Although such methods have been developed over the past few years, they all present serious limitations in practical situations related to the radiocommunications context. For this reason, the purpose of this paper is to propose a new attractive BI method, exploiting the information contained in the FO data statistics only, that is able to process underdetermined mixtures of sources without the main limitations of the existing methods, provided that the sources have different trispectrum and nonzero kurtosis with the same sign. A new performance criterion that is able to quantify the identification quality of a given source and allowing the quantitative comparison of two BI methods for each source, is also proposed in the paper. Finally, an application of the proposed method is presented through the introduction of a powerful direction-finding method built from the blindly identified mixture matrix. [ABSTRACT FROM AUTHOR]