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In order to deal with uncertainty, Molodtsov propoed soft set theory as a mathematical tool in 1999. Since that time, numerous forms of soft set operations have been defined and employed. By establishing the soft binary piecewise operations' distributions over complementary soft binary piecewise intersection and union operations, this study aims to contribute to the literature on soft set theory by giving inspiration to researchers as regards examining and obtaining some algebraic structures using these new soft set operations. [ABSTRACT FROM AUTHOR]

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This paper deals with fundamental arithmetic operations on fuzzy numbers and use of these operations for carrying out various fuzzy processes. When modelling specific problems in the field of sciences as well as engineering, it's common to notice that the problem's characteristics aren't known precisely and instead fall into a range. Interval arithmetic, which permits mathematical evaluations (operations) to be conducted on intervals in order to produce significant estimations of required values in terms of intervals, has already been used to deal with similar problems. Fuzzy arithmetic can be thought of as an extension of arithmetic interval, in which numerous levels in [0,1] are considered instead of only one (constant) level. [ABSTRACT FROM AUTHOR]

Let h be a real-analytic function on the neighborhood of some compact set K on the plane, and let f(y) be the Fourier--Stieltjes transform of a complex measure of a finite total variation without singular components on the Euclidean space. Then there exists another measure of a finite total variation with the Fourier--Stieltjes transform g(y) such that g(y) = h(f(y)) whenever the value f(y) belongs to K. [ABSTRACT FROM AUTHOR]

When Loday and Ronco studied ternary planar trees, they introduced types of algebras, called trioids and trialgebras. A trioid is a nonempty set equipped with three binary associative operations satisfying additional eight axioms relating these operations, while a trialgebra is just a linear analog of a trioid. If all operations of a trioid (trialgebra) coincide, we obtain the notion of a semigroup (associative algebra), and if two concrete operations of a trioid (trialgebra) coincide, we obtain the notion of a dimonoid (dialgebra) and so, trioids (trialgebras) are a generalization of semigroups (associative algebras) and dimonoids (dialgebras). Trioids and trialgebras have close relationships with the Hopf algebras, the Leibniz 3-algebras, the Rota-Baxter operators, and the post-Jordan algebras. Originally, these structures arose in algebraic topology. One of the most useful concepts in algebra is the free object. Every variety contains free algebras and free objects in any variety of algebras are important in the study of that variety. Loday and Ronco constructed the free trioid of rank 1 and the free trialgebra. Recently, the free trioid of an arbitrary rank, the free commutative trioid, the free n-nilpotent trioid, the free rectangular triband, the free left n-trinilpotent trioid and the free abelian trioid were constructed and the least dimonoid congruences as well as the least semigroup congruence on the first four free algebras were characterized. However, just mentioned congruences on free left (right) n-trinilpotent trioids and free abelian trioids were not considered. In this paper, we characterize the least dimonoid congruences and the least semigroup congruence on free left (right) n-trinilpotent trioids and free abelian trioids. [ABSTRACT FROM AUTHOR]

Hesitant fuzzy linguistic term set (HFLTS) provides a new and useful tool for expressing decision makers (DMs)'s qualitative views and ideas since it allows DMs to hesitate about several possible linguistic terms. Consistency is the fundamental research in decision-making process under hesitant fuzzy linguistic preference relations (HFLPRs) decision-making environment and the distance measure is utilized as a technology to measure the consistency level of HFLPRs. However, traditional distance measures were developed based on an assumption that the number of linguistic terms in the corresponding HFLTSs is the same. Some optimization models to improve consistency level of HFLPRs did not give DMs strong sense of participation and a sense of respect for their preferences. To solve the above issues, in this paper, a new distance measure of HFLTSs is defined, and some desirable properties are discussed. After that, in line with the distance measure, we propose a consistency index of HFLPRs by computing the deviation between the normalized hesitant fuzzy linguistic preference relation (N-HFLPR) and its expected hesitant fuzzy linguistic preference relation (E-HFLPR). Furthermore, for unacceptable consistent HFLPRs, some local revised strategies provided by an automatic iterative algorithm are used to modify original HFLPRs until it satisfies acceptable consistency. Finally, some comparisons between the existing methods and our proposed approaches are to demonstrate the feasibility of the proposed approaches by utilizing several illustrative examples. [ABSTRACT FROM AUTHOR]

Abstract We show that all strongly non-degenerate trigonometric solutions of the associative Yang–Baxter equation (AYBE) can be obtained from triple Massey products in the Fukaya categories of square-tiled surfaces. Along the way, we give a classification result for cyclic A ∞ -algebra structures on a certain Frobenius algebra associated with a pair of 1-spherical objects in terms of the equivalence classes of the corresponding solutions of the AYBE. As an application, combining our results with homological mirror symmetry for punctured tori (cf. [17]), we prove that any two simple vector bundles on a cycle of projective lines are related by a sequence of 1-spherical twists and their inverses. [ABSTRACT FROM AUTHOR]

Inter-modulo arithmetic operations, such as reverse conversion and scaling, are important but difficult operations in the RNS domain. This paper proposes efficient arithmetic units to perform this hard class of RNS operations for a new family of augmented three-moduli sets { 2 n + k, 2 n − 1, 2 n + 1 − 1 } (0 ≤ k ≤ n) ⁠. Experimental results for 65 nm CMOS technology show that the proposed reverse converter reduces the delay by about (17.6 − 33.4) % in comparison with the state of the art. Moreover, this work presents the first architecture of a scaler dedicated for this augmented three-moduli sets. [ABSTRACT FROM AUTHOR]

In this paper we extend the notion of classical (pre-)semiadditive category to (pre-)semihyperadditive category. Algebraic hyperstructures are algebraic systems whose objects possessing the hyperoperations or multi-valued operation. We introduce categories in which for objects A and B, the class of all morphisms from A to B denoted by Mor(A,B), admits an algebraic hyperstructures, such as semihyper-group or hypergroup. In this regards we introduce the various types of pre-semihyperadditive categories. Also, we construct some (pre-)semi-hyperadditive categories by introducing a class of hypermodules named general Krasner hypermodules. Finally, we investigate some properties of these categories. [ABSTRACT FROM AUTHOR]

In this paper, we will show that based on the concept of multialgebras and relying on the power structures of these algebras, which we could also consider as relational structures, and adding the set of operations ... we get a Boolean algebra with operator. The power structure of relational structure = (A,) is an algebra with the set (A) and the set of all basic operations defined. [ABSTRACT FROM AUTHOR]

Abstract The theory of biset functors, introduced by Serge Bouc, gives a unified treatment of operations in representation theory that are induced by permutation bimodules. In this paper, by considering fibered bisets, we introduce and describe the basic theory of fibered biset functors which is a natural framework for operations induced by monomial bimodules. The main result of this paper is the classification of simple fibered biset functors. [ABSTRACT FROM AUTHOR]

Abstract This paper studies two approaches to formalize helping in wait-free implementations of shared objects. The first approach is based on operation valency , and it allows us to make an important distinction between trivial and nontrivial helping. We show that any wait-free implementation of a queue from Test&Set requires nontrivial helping. We also define a weaker type of nontrivial helping and show that any wait-free queue implementation from a set of arbitrary base objects requires it. In contrast, there is a wait-free implementation of a stack from Test&Set with only trivial helping. These results shed light on the well-known open question of whether there exists a wait-free implementation of a queue in Common2 , and indicate why it seems to be more difficult than implementing a stack. The other approach formalizes the helping mechanism employed by Herlihy's universal wait-free construction and is based on having an operation by one process restrict the possible linearizations of operations by other processes. We show that queue and stack implementations possessing such universal helping can be used to solve consensus. This result can be used to show that a strongly linearizable (Golab et al., 2011) implementation of a queue or a stack for n processes must use objects that allow to solve consensus among n or more processes. Highlights • Two formalizations of helping are presented: nontrivial and universal. • Nontrivial helping separates queues and stacks from Test&Set primitives. • A weaker version of nontrivial helping is introduced and shown necessary in queue implementations. • Universal helping for queues and stacks is universal: it solves consensus. • Strongly linearizable queue or stack for n processes requires primitives with consensus number at least n. [ABSTRACT FROM AUTHOR]

Abstract We study the following problem: for given integers d , k and graph G , can we reduce some fixed graph parameter π of G by at least d via at most k graph operations from some fixed set S ? As parameters we take the chromatic number χ , clique number ω and independence number α , and as operations we choose edge contraction ec and vertex deletion vd. We determine the complexity of this problem for S = { ec } and S = { vd } and π ∈ { χ , ω , α } for a number of subclasses of perfect graphs. We use these results to determine the complexity of the problem for S = { ec } and S = { vd } and π ∈ { χ , ω , α } restricted to H -free graphs. [ABSTRACT FROM AUTHOR]

We show that the Nine Lemma holds for special Schreier extensions of monoids with operations. This fact is used to obtain a push forward construction for special Schreier extensions with abelian kernel. This construction permits to give a functorial description of the Baer sum of such extensions. [ABSTRACT FROM AUTHOR]

It is known that the pass move is not an unknotting operation in classical knot theory. In this paper, we prove that the pass move is an unknotting operation in welded knot theory. [ABSTRACT FROM AUTHOR]

It is aimed to determine the strategies used by the fourth-grade elementary students during the operational estimations in this research which is designed by using basic qualitative analysis. The study group consists of 26 fourth-grade students selected through convenience sampling method and attending at a state school which was located in the centre of Kütahya province during the 2016/2017 academic year. In order to determine the strategies used by the students while estimating the results of the basic mathematical operations, a 20-question scale consisting of 5 questions from each of the addition, subtraction, multiplication and division operations was developed. The research data were collected via semi-structured interview method. In the process of the data collection, students were asked to solve each question through using a method of thinking aloud and the interviews were recorded by a camera. The obtained records were sorted out as a part of elementary school program developed by the Ministry of National Education (MEB, 2005) by three specialists in elementary mathematics teaching according to strategies such as suggested rounding, grouping, using the front-end orders, using matched numbers, distribution, adjusting-rearranging and using algorithmic calculation. As a result of the research, it has been seen that the fourth-grade students mostly prefer the strategy of algorithmic calculation when making estimations in four basic operations. It has been also seen that fewer students used rounding, matched numbers, adjusting-rearranging in addition; rounding, adjusting-rearranging strategies in subtraction, multiplication and division mentioned by MEB (2005). It has been seen that students who obtained solutions using the strategies determined by MEB (2005), were realistic and estimated the result of the operation in a very short time, whereas students who preferred algorithmic calculation strategy, often had unrealistic results and long estimation spans. [ABSTRACT FROM AUTHOR]

We lift Grothendieck-Verdier-Spaltenstein’s six functor formalism for derived categories of sheaves on ringed spaces over a field to differential graded enhancements. Our main tools come from enriched model category theory. [ABSTRACT FROM AUTHOR]

Graph minors play an important role in graph theory. The focus of this paper is on immersion minors and their relationship to planarity. In general, planar graphs can have non-planar immersion minors. This paper shows that by placing a simple restriction on the immersion-minor operations, all immersion minors of a planar graph are planar. This then allows one to easily obtain a characterization of planar graphs using immersion minors. A dual form of this characterization, as well as an extension to binary matroids, are also considered. [ABSTRACT FROM AUTHOR]

Spiking neural P systems (SN P systems, for short) are a class of distributed and parallel computing devices inspired from the way neurons communicate by means of spikes. In most of the SN P systems investigated so far, the system communicates on command, and the application of evolution rules depends on the contents of a neuron. However, inspired from the parallel-cooperating grammar systems, it is natural to consider the opposite strategy: the system communicates on request, which means spikes are requested from neighboring neurons, depending on the contents of the neuron. Therefore, SN P systems with communication on request were proposed, where the spikes should be moved from a neuron to another one when the receiving neuron requests that. In this paper, we consider implementing arithmetical operations by means of SN P systems with communication on request. Specifically, adder, subtracter and multiplier are constructed by using SN P systems with communication on request. [ABSTRACT FROM AUTHOR]

The problem of modeling and operating spatiotemporal data has received a great deal of interest, due to its various applications in the real world such as GIS and sensor database. A wide range of work covering spatial data, temporal data and spatiotemporal data assumes that the data is known, accurate and complete. But in reality, information is often imprecise and imperfect. In addition, traditional data models which are investigating in the context of traditional database suffer from some inadequacy of necessary semantics such as inability to handle imprecise and uncertain information. Consequently, the advent of XML, which has the advantages of simplicity, readability and extensibility, seems to provide an opportunity for modeling and operating uncertain spatiotemporal data. Hence, the new problem that emerges is how to model and operate uncertain spatiotemporal data in XML. Therefore, in this paper, we establish an uncertain spatiotemporal data model based on XML. Then, on the basis of the model we provide a set of algebraic operations for capturing and handling uncertain spatiotemporal data. By employing algebraic operations, we demonstrate how to translate queries expressed in XQuery to our algebra. A translation example shows that our algebraic operations are full of expressive power and illustrates that our algebra can be applied to general data. Apart from this, we also propose a set of equivalence rules to optimize the process of query and give an example to show how the optimization approach works. [ABSTRACT FROM AUTHOR]

In this paper, we deal with nilpotency of atomic Steenrod squares. We prove that the nilpotence height of atomic square Sq2(2b-1) for all integers b ≥ 2 is b+2. Finally, we give a nilpotency table, a remark and an important conjecture related to the nilpotence height of atomic squares. [ABSTRACT FROM AUTHOR]

We consider clones on countable sets. If such a clone has quasigroup operations, is locally closed and countable, then there is a function $${f : \mathbb{N} \rightarrow \mathbb{N}}$$ such that the n-ary part of C is equal to the n-ary part of Pol $${{\rm Inv}^{[f(n)]} C}$$ , where $${{\rm Inv}^{[f(n)]} C}$$ denotes the set of f( n)-ary invariant relations of C. [ABSTRACT FROM AUTHOR]

The paper deals with monounary algebras and their first and second centralizers. First we show that operations are equivalent with respect to the first centralizer if and only if they are equivalent with respect to the second centralizer. We find necessary and sufficient conditions for an operation when the operation is uniquely determined by its centralizer. In this case, a sequence of steps for a description of the operation is presented. [ABSTRACT FROM PUBLISHER]

In this paper, we define the sequence space BV ⌢θ (f, p, q, s) on a seminormed complex linear space, by using a Modulus function. We give various properties and some inclusion relations on this space. [ABSTRACT FROM AUTHOR]

Constructing large biomodels de-novo is a computationally expensive process, requiring large sets of high-quality data. An alternative approach is to construct them from smaller existing models through various operations such as union, intersection, difference, and refinement. We introduce in this paper a foundational framework for biomodel construction capturing these operations, and we discuss some of their properties. [ABSTRACT FROM AUTHOR]

A d-hypercube of order n is an n × ··· × nd (d times) array with nd elements from a set Q of cardinality n. We recall several connections between d-hypercubes of order n and d-ary operations of order n. We give constructions of orthogonal d-ary operations that generalize a result of Belyavskaya and Mullen. Our main result is a general construction of d-orthogonal d-ary operations from d-ary quasigroups. [ABSTRACT FROM AUTHOR]

An efficient method for the characterization of some important classes of matrices, using the rank, is the method of elementary operations in the partitioned matrices. We will use this method for idempotent matrices, involutory matrices, tripotent matrices and other classes of matrices with annihilator polynomials of the form f (x) = xk - xp. [ABSTRACT FROM AUTHOR]

We provide a uniform definition of higher order Toda brackets in a general setting, covering the known cases of long Toda brackets for topological spaces and Massey products for differential graded algebras, among others. [ABSTRACT FROM AUTHOR]

We show that the absolute Galois group of any field has the vanishing triple Massey product property. Several corollaries for the structure of maximal pro-p-quotient of absolute Galois groups are deduced. Furthermore, the vanishing of some higher Massey products is proved. [ABSTRACT FROM AUTHOR]

Polyak showed that any Milnor's -invariant of length 3 can be represented as a combination of the Conway polynomials of knots obtained by certain band sum of the link components. On the other hand, Habegger and Lin showed that Milnor invariants are also invariants for string links, called -invariants. We show that any Milnor's -invariant of length can be represented as a combination of the HOMFLYPT polynomials of knots obtained from the string link by some operation, if all -invariants of length vanish. Moreover, -invariants of length are given by a combination of the Conway polynomials and linking numbers without any vanishing assumption. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concept of soft uniform spaces and the relationships between soft uniform spaces and uniform spaces. The notions of soft uniform structure, soft uniform continious function, and operations on soft uniform space are introduced and their basic properties are investigated. [ABSTRACT FROM AUTHOR]

A new algorithm is proposed to project, exactly and in finite time, a vector of arbitrary size onto a simplex or an $$l_1$$ -norm ball. It can be viewed as a Gauss-Seidel-like variant of Michelot's variable fixing algorithm; that is, the threshold used to fix the variables is updated after each element is read, instead of waiting for a full reading pass over the list of non-fixed elements. This algorithm is empirically demonstrated to be faster than existing methods. [ABSTRACT FROM AUTHOR]

In this article we construct symmetric operations for all primes (previously known only for p = 2). These unstable operations are more subtle than the Landweber-Novikov operations, and encode all p-primary divisibilities of characteristic numbers. Thus, taken together (for all primes) they plug the gap left by the Hurewitz map L → Z[b1, b2, ...], providing an important structure on algebraic cobordism. Applications include questions of rationality of Chow group elements, and the structure of the algebraic cobordism. We also construct Steenrod operations of tom Dieck style in algebraic cobordism. These unstable multiplicative operations are more canonical and subtle than Quillen-style operations, and complement the latter. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a subclass of interval valued neutrosophic graphs called strong interval valued neutrosophic graphs, which were introduced by Broumi et al. [41]. The operations of Cartesian product, composition, union and join of two strong interval valued neutrosophic graphs are defined. Some propositions involving strong interval valued neutrosophic graphs are stated and proved. [ABSTRACT FROM AUTHOR]

We prove a conjecture of J. P. May concerning the nilpotence of elements in ring spectra with power operations, that is, H∞-ring spectra. Using an explicit nilpotence bound on the torsion elements in K(n)-local H∞-algebras over En, we reduce the conjecture to the nilpotence theorem of Devinatz, Hopkins, and Smith. As corollaries, we obtain nilpotence results in various bordism rings including MSpin* and MString*, results about the behavior of the Adams spectral sequence for E∞-ring spectra, and the non-existence of E∞-ring structures on certain complex-oriented ring spectra. [ABSTRACT FROM AUTHOR]

We prove the K- and L-theoretic Farrell-Jones conjecture (with coefficients in additive categories) for virtually solvable groups. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study a geometric spectral sequence on ℤ2 Khovanov homology. [ABSTRACT FROM AUTHOR]

In this note, we prove that the Swiss-cheese operad is not formal. We also give a criterion in terms of Massey operadic product for the non-formality of a topological operad. [ABSTRACT FROM AUTHOR]

A simplified approach for calculating the equivalent isotropic displacement parameter is presented and the transformation property of the tensor representation U to point-group operations is analysed. Complete tables have been compiled for the restrictions imposed upon the tensor owing to the site symmetry associated with all special positions as listed in Hahn [(2011), International Tables for Crystallography, Vol. A, Space-group Symmetry, 5th revised ed. Chichester: John Wiley and Sons, Ltd]. [ABSTRACT FROM AUTHOR]

Since the introduction of extended Canetti-Krawczyk (eCK) security model for two-party key exchange, many protocols have been proposed to provide eCK security. However, most of those protocols are provably secure in the random oracle model or rely on special design technique, which is well known as the NAXOS trick. In contrast to previous schemes, we present an eCK secure protocol in the standard model, without NAXOS trick and without knowledge of secret key assumption for public key registration. The security proof of our scheme is based on standard pairing assumption, collision-resistant hash functions, Bilinear Decision Diffie-Hellman and Decision Linear Diffie-Hellman assumptions, and pseudo-random functions with pairwise independent random source. Although our proposed protocol is based on bilinear groups, it does not require any pairing operation during key exchange procedure. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]