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This paper presents an adaptive fuzzy logic controller (FLC) design technique for controlling an induction motor speed drive using backtracking search algorithm (BSA). This technique avoids the exhaustive traditional trial-and-error procedure for obtaining membership functions (MFs). The generated adaptive MFs are implemented in speed controller design for input and output based on the evaluation results of the fitness function formulated by the BSA. In this paper, the mean absolute error (MAE) of the rotor speed response for three phase induction motor (TIM) is used as a fitness function. An optimal BSA-based FLC (BSAF) fitness function is also employed to tune and minimize the MAE to improve the performance of the TIM in terms of changes in speed and torque. Moreover, the measurement of the real TIM parameters via three practical tests is used for simulation the TIM. Results obtained from the BSAF are compared with those obtained through gravitational search algorithm (GSA) and particle swarm optimization (PSO) to validate the developed controller. Design procedure and accuracy of the develop FLC are illustrated and investigated via simulation tests for TIM in a MATLAB/Simulink environment. Results show that the BSAF controller is better than the GSA and PSO controllers in all tested cases in terms of damping capability, and transient response under different mechanical loads and speeds. [ABSTRACT FROM AUTHOR]

Students make sense of mathematical ideas using a variety of representations including physical models, pictures, diagrams, spoken words, and mathematical symbols. As students’ understanding of mathematical ideas becomes more general and abstract, there is a need to express these ideas using mathematical notation. This paper describes students’ movement from model building and personal notations to elegant use of mathematical symbols that show their understanding of advanced counting ideas. Specifically, this paper shows how earlier ideas from investigations of specific combinatorics problems (questions about making pizzas with different toppings and using cubes to build towers) are retrieved and built upon using the formal mathematical register to explain the meaning of Pascal's Identity, the addition rule of Pascal's Triangle. This analysis also shows the power of shared communication in mathematical problem solving. [ABSTRACT FROM AUTHOR]

This paper uses a sociocultural conceptual framework to provide an integrated view of academic literacy in mathematics for English Learners. The proposed definition of academic literacy in mathematics includes three integrated components: mathematical proficiency, mathematical practices, and mathematical discourse. The paper uses an analysis of a classroom discussion to illustrate how the three components of academic literacy in mathematics are intertwined, how academic literacy in mathematics is situated, and how participants engaged in academic literacy in mathematics use hybrid resources. The paper closes by describing the implications of this integrated view of academic literacy in mathematics for mathematics instruction for English Learners, arguing that it is important that the three components not be separated when designing instruction in general, and it is essential that mathematics instruction for English Learners address these three components simultaneously. [ABSTRACT FROM AUTHOR]

Ramsey's Theorem for pairs is a fundamental result in combinatorics which cannot be intuitionistically proved. In this paper we present a new form of Ramsey's Theorem for pairs we call the H -closure Theorem, where H stands for “homogeneous”. The H -closure Theorem is a property of well-founded relations, intuitionistically provable, informative, and simple to use in intuitionistic proofs. Using our intuitionistic version of Ramsey's Theorem we intuitionistically prove the Termination Theorem by Podelski and Rybalchenko [25] . The Termination Theorem concerns an algorithm inferring termination for while-programs, and was originally proved from the classical Ramsey Theorem. Vytiniotis, Coquand, and Wahlstedt provided an intuitionistic proof of the Termination Theorem [29] , using the Almost Full Theorem [11] , an intuitionistic version of Ramsey's Theorem different from the H -closure Theorem. We provide a second intuitionistic proof of the Termination Theorem using the H -closure Theorem. In another paper, we use our proof to extract bounds for the Termination Theorem [5] . [ABSTRACT FROM AUTHOR]

In this paper we study the planar squeeze flow of a Bingham plastic in the lubrication approximation. We assume that the domain occupied by the fluid is closed at one end and open at the other (planar geometry). We consider two cases: (i) planar walls approaching each other in a prescribed way; (ii) parallel walls whose shape depends on both time and longitudinal coordinate. The dynamics of the unyielded region is determined exploiting the integral formulation of the linear momentum balance. We prove that in proximity of the closed end the material is always yielded, so that the rigid part is always detached from it. When dealing with case (ii) , we show that the dynamics of the rigid domain is governed by a very complex integral equation, whose qualitative analysis is beyond the aims of this paper. Conversely, in case (i) we obtain an almost explicit solution. [ABSTRACT FROM AUTHOR]

This paper presents a detailed investigation on the post-buckling behaviour of adhesively bonded stiffened panels subjected to in-plane shear loading. An experimental programme was carried to determine the buckling load, buckling shape, collapse load and failure modes of two bonded stiffened panels. A nonlinear finite element based modelling approach, accounting for geometrical and material nonlinearities as well as progressive failure in the adhesively bonded interface between the skin and the stiffener is proposed to predict the structural behaviour of the panels up to failure. This approach consists in modelling the bonded interfaces using a newly developed cohesive zone based constitutive damage model. In order to account for damage in the stiffener and the skin a Von Mises based constitutive damage model is also formulated and presented in the paper. Both constitutive models were implemented into ABAQUS/Explicit finite element code as user-defined material models. A very good agreement between experimental results and numerical predictions is obtained using the proposed modelling approach, with deviations smaller than 8% in buckling load and bonded interface failure load onset. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new class of the generalized mixed equilibrium problems with a new definition of the relaxed monotonicity for bi-functions in topological vector spaces. By employing the KKM technique and under some appropriate assumptions on the considering nonlinear mappings, we obtain the existence of a solution for the generalized mixed equilibrium problems with the new concept of the relaxed monotonicity and coercivity condition(in order to relax the compactness of the domains of the nonlinear mappings) in the setting of topological vector spaces. Moreover, the compactness and convexness of the solution set are investigated. The results in the paper extend and generalize the corresponding results, especially Sintunavarat (2013) [20] in this area by providing mild assumptions in order to guarantee the existence of a solution for the generalized mixed equilibrium problem. [ABSTRACT FROM AUTHOR]

In this paper, to analyze the effect of the cross patch infection between different groups to the spread of gonorrhea in a community, we establish the complete global dynamics of a multi-group SIS epidemic model with varying total population size by a threshold parameter. In the proof, we use special Lyapunov functional techniques, not only one proposed by the paper [Prüss et al., 2006], but also the other one for a varying total population size with some ideas specified to our model and no longer need a grouping technique derived from the graph theory which is commonly used for the global stability analysis of multi-group epidemic models. [ABSTRACT FROM AUTHOR]

In this paper, the underlying general linear methods (GLMs) are adapted to linear neutral multidelay-integro-differential equations (NMIDEs). In order to obtain stability criteria of the extended GLMs, the corresponding results in paper of Zhang and Vandewalle (2008) are generalized. Based on the concepts of A( α )-stability and A-stability of the underlying GLMs, a serial of asymptotic stability criteria of the extended GLMs are obtained. [ABSTRACT FROM AUTHOR]

In this paper I tackle the question What is the mathematics in mathematics education? By providing three different frames for the word mathematics. 1. Frame 1: Mathematics as an abstract body of knowledge/ideas, the organization of that into systems and structures, and a set of methods for reaching conclusions. 2. Frame 2: Mathematics as contextual, ever present, as a lens or language to make sense of the world. 3. Frame 3: Mathematics as a verb (not a noun), a human activity, part of one's identity. After introducing the frames and examining their distinction and their overlap, I discuss their implication with respect to student-centered classroom, context, and culture. • Explicating the definition of mathematics is essential for discussions among educators. • Different definitions of mathematics lead to different implications on education. • Different definitions of mathematics lead to different versions of student-centered mathematics instruction. [ABSTRACT FROM AUTHOR]

This paper uses a new Kudryashov approach to construct various novel exact optical solutions of the time-fractional Fokas system with conformable fractional derivatives. The acquired optical solutions are distributed into several categories of bell shape, singular, exponential, dark, bright, dark–bright, and periodic soliton solutions. The graphical simulations of several graphs are given for a better understanding of the effect of the fractional order derivative and the dynamical behavior of the present optical solutions with various values of time parameter. In order to highlight the significance of the Fokas system, a class of the acquired solutions are given using suitable parameter values on three-dimensional (3D), two-dimensional (2D), and contour graphs. As a result, this technique is productive and practically effective for understanding nonlinear problems in engineering, physics, and mathematics. [ABSTRACT FROM AUTHOR]

The chromatic edge-stability number e s χ (G) of a graph G is the minimum number of edges whose removal results in a spanning subgraph with the chromatic number smaller than that of G. A graph G is called (3 , 2) -critical if χ (G) = 3 , e s χ (G) = 2 and for any edge e ∈ E (G) , e s χ (G − e) < e s χ (G). In this paper, we characterize (3 , 2) -critical graphs which contain at least five odd cycles. This answers a question proposed by Brešar, Klavžar and Movarraei in [Critical graphs for the chromatic edge-stability number, Discrete Math. 343 (2020) 111845]. [ABSTRACT FROM AUTHOR]

Anyone involved in mathematics education will at some point encounter a classroom situation in which a student's statement provides an opportunity for the teacher to enhance students' mathematical understanding. This paper aims to characterize such classroom situations, known as critical events, as noticed by pre-service mathematics teachers during classroom observations and teaching. Analysis of 80 critical events reported by 20 pre-service mathematics teachers during a field-based teaching preparation program yielded a model that enables teacher-educators and researchers to characterize critical events while reflecting on the wide variations within these events. The model comprises three axes: the participants in the event, the focus of the event, and the dimensions in learning and teaching mathematics (i.e., cognitive, affective and social). The paper discusses the theoretical and empirical construction of the model and demonstrates its potential contribution using examples taken from our research. • Pre-service teachers identified critical events during classroom observations. • A model for characterizing critical events was constructed theoretically and empirically. • The model affords eliciting the multidimensional nature and complexity of critical events. • The model's potential contribution is presented using examples from our research. [ABSTRACT FROM AUTHOR]

This is a survey or exposition of a particular collection of results and open problems involving snarks — simple “cubic” (3-valent) graphs for which, for nontrivial reasons, the edges cannot be 3-colored. The results and problems here are rooted in a series of papers by László Kászonyi that were published in the early 1970s. The problems posed in this survey paper can be tackled without too much specialized mathematical preparation, and in particular seem well suited for interested undergraduate mathematics students to pursue as independent research projects. This survey paper is intended to facilitate research on these problems. [ABSTRACT FROM AUTHOR]

The paper critically overviews the recent developments of the theory of spatially dispersive spin fluctuations (SF) in itinerant electron magnetism with particular emphasis on spin-fluctuation coupling or spin anharmonicity. It is argued that the conventional self-consistent renormalized (SCR) theory of spin fluctuations is usually used aside of the range of its applicability actually defined by the constraint of weak spin anharmonicity based on the random phase approximation (RPA) arguments. An essential step in understanding SF in itinerant magnets beyond RPA-like arguments was made recently within the soft-mode theory of SF accounting for strong spin anharmonicity caused by zero-point SF. In the present paper we generalize it to apply for a wider range of temperatures and regimes of SF and show it to lead to qualitatively new results caused by zero-point effects. [ABSTRACT FROM AUTHOR]

Research in mathematics and science education reveals a disconnect for students as they attempt to apply their mathematical knowledge to science and engineering. With this conclusion in mind, this paper investigates a particular calculus topic that is used frequently in science and engineering: the definite integral. The results of this study demonstrate that certain conceptualizations of the definite integral, including the area under a curve and the values of an anti-derivative, are limited in their ability to help students make sense of contextualized integrals. In contrast, the Riemann sum-based “adding up pieces” conception of the definite integral (renamed in this paper as the “multiplicatively-based summation” conception) is helpful and useful in making sense of a variety of applied integral expressions and equations. Implications for curriculum and instruction are discussed. [ABSTRACT FROM AUTHOR]

This paper provides evidence that helps understand the digital divide in education. It does so by comparing the effect of economic, social and cultural status (ESCS) on the digital skills of Chilean students compared with mathematics and language. This comparison is made using national standardized tests. The marginal effect of a group of variables measuring student ESCS was compared both as a whole and separately using multivariate linear regression analysis. The results show that the marginal effect of ESCS as a whole on students' digital skills was equal to the effect on mathematics and greater than the effect on language. Furthermore, the results show that the parents' level of education was the most relevant factor of ESCS for explaining student performance on the digital test, more so than for mathematics and language. These findings challenge the belief that the Internet would reduce economic, social and cultural inequalities in new generations. Instead, they reveal that the gap among Chilean students tends to perpetuate or widen when comparing performance in mathematics and language with performance in the digital domain. At the same time, by comparing national test results, this paper offers empirical evidence for the existence of a second digital divide in the field of education, a concept which is widely discussed at a theoretical level but with little empirical support to date. [ABSTRACT FROM AUTHOR]

This paper considers the study of the optimality of the extended design generated by adding few runs to an existing E ( χ 2 ) -optimal mixed-level supersaturated design. This paper covers the work of Gupta et al. (2010, 2012) on extended two-level and s -level supersaturated designs as two special cases. A lower bound to E ( χ 2 ) has been obtained for the proposed designs. A small example is presented here attaining the lower bound. [ABSTRACT FROM AUTHOR]

After publishing his recent paper in SIAM J. Appl. Math. 74, 392-410, 2014 the author has realized that actually he has addressed in that paper, for the first time, a long standing open question being unaware about this. This question is about the uniqueness of a 3-d inverse scattering problem without the phase information. Thus, it makes sense in the current paper to explicitly make the latter statement and to formulate corresponding uniqueness theorems. [ABSTRACT FROM AUTHOR]

Given a linear equation L , a set A of integers is L -free if A does not contain any ‘non-trivial’ solutions to L . This notion incorporates many central topics in combinatorial number theory such as sum-free and progression-free sets. In this paper we initiate the study of (parameterised) complexity questions involving L -free sets of integers. The main questions we consider involve deciding whether a finite set of integers A has an L -free subset of a given size, and counting all such L -free subsets. We also raise a number of open problems. [ABSTRACT FROM AUTHOR]

Linear feedback shift registers (LFSRs) play a significant role in communications security and we investigate design of a selected class of word-based LFSRs known as σ -LFSRs. Both the search algorithm and the construction algorithm generate efficient primitive σ -LFSRs. The search algorithm first constructs the σ -polynomial and then checks the primitiveness of the σ -polynomial, whereas the construction algorithm for the σ -LFSR, first finds a primitive polynomial f ( x ) and then constructs the primitive σ -LFSR from f ( x ) . In this paper, we present some novel results pertaining to the search algorithm for primitive σ -LFSR along with the exhaustive search space complexity of the search algorithm for σ -LFSRs. Then we investigate and compare the performance of the construction algorithm with the search algorithm for the primitive σ -LFSR. Finally, the number of σ -LFSRs similar to the σ -LFSRs generated by the construction algorithm is provided. [ABSTRACT FROM AUTHOR]

The generalized Wiener polarity index of a graph G , denoted by W k ( G ) , is the number of unordered pairs of vertices that are at distance k in G. In this paper, we characterize the extremal trees with respect to the index among all trees of order n and diameter d , which partially answers a question of Bollobás and Tyomkyn (2012) and also generalizes some results of Deng et al. (2010). [ABSTRACT FROM AUTHOR]

For positive integers k and r , a ( k , r )-coloring of a graph G is a proper k -coloring of the vertices such that every vertex of degree d is adjacent to vertices with at least min { d , r } different colors. The r -hued chromatic number of a graph G , denoted by χ r ( G ) , is the smallest integer k such that G has a ( k , r ) -coloring. In Song et al. (2014), it is conjectured that if r ≥ 8 , then every planar graph G satisfies χ r ( G ) ≤ ⌈ 3 r 2 ⌉ + 1 . Wegner in 1977 conjectured that the above-mentioned conjecture holds when r = Δ ( G ) . This conjecture, if valid, would be best possible in some sense. In this paper, we prove that, if G is a planar graph and r ≥ 8 , then χ r ( G ) ≤ 2 r + 16 . [ABSTRACT FROM AUTHOR]

The fractal and self-similarity are important properties in complex networks. Information dimension is a useful dimension for complex networks to reveal these properties. In this paper, an information dimension is proposed for weighted complex networks. Based on the box-covering algorithm for weighted complex networks (BCANw), the proposed method can deal with the weighted complex networks which appear frequently in the real-world, and it can get the influence of the number of nodes in each box on the information dimension. To show the wide scope of information dimension, some applications are illustrated, indicating that the proposed method is effective and feasible. [ABSTRACT FROM AUTHOR]

The bicategory LG of Landau–Ginzburg models has polynomials as objects and matrix factorisations as 1-morphisms. The composition of these 1-morphisms produces infinite rank matrix factorisations, which is a nuisance. In this paper we define a bicategory C which is equivalent to LG in which composition of 1-morphisms produces finite rank matrix factorisations equipped with the action of a Clifford algebra. This amounts to a finite model of composition in LG . [ABSTRACT FROM AUTHOR]

Let C be a projective nonsingular curve of genus g and let B r , d k be the locus of stable rank r degree d vector bundles with at least k linearly independent sections on C . It is known that when C is general and under certain conditions on g , d , r , and k , there exists a component B of B r , d k of the expected dimension. In this paper we show that for a general vector bundle E of B , the Petri map is injective. [ABSTRACT FROM AUTHOR]

In this paper we study the homogeneity of radicals defined by nilpotence or primality conditions, in rings graded by a semigroup S . When S is a unique product semigroup, we show that the right (and left) strongly prime and uniformly strongly prime radicals are homogeneous, and an even stronger result holds for the generalized nilradical. We further prove that rings graded by torsion-free, nilpotent groups have homogeneous upper nilradical. We conclude by showing that non-semiprime rings graded by a large class of semigroups must always contain nonzero homogeneous nilpotent ideals. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that induction is derivable in a type-assignment formulation of the second-order dependent type theory λ P 2 , extended with the implicit product type of Miquel, dependent intersection type of Kopylov, and a built-in equality type. The crucial idea is to use dependent intersections to internalize a result of Leivant's showing that Church-encoded data may be seen as realizing their own type correctness statements, under the Curry–Howard isomorphism. [ABSTRACT FROM AUTHOR]

This paper assesses how the integration of ICT in education has affected the mathematics test scores for Italian students measured by the Programme for International Student Assessment 2012 data. The problem of endogeneity that affects survey data in this area, is addressed by applying the Bayesian Additive Regression Trees (BART) methodology as in Cabras & Tena Horrillo (2016). The BART methodology needs a prior and likelihood functions using the Markov Chain Monte Carlo (MCMC) algorithm to obtain the posterior distribution. Controlling for socio-economic, demographic and school factors, the predicted posterior distribution implies an increase, on average, of 16 points in the test scores. The result indicates that the use of ICT at school has a positive and strong impact on mathematic test scores. [ABSTRACT FROM AUTHOR]

There is a public perception that relatively low doses of mercury found in seafood are harmful to the fetal brain but little consistent evidence to support this. In earlier publications we have shown no adverse associations between maternal total blood mercury levels and child behaviour, early development or cognitive function as measured by IQ. However, for IQ the lack of adverse association was conditional upon the mother being a fish eater. In this paper we analyse further data from the Avon Longitudinal Study of Parents and Children (ALSPAC), this time examining whether prenatal exposure to total mercury is associated with the child's scholastic abilities in reading, spelling, phoneme awareness, mathematics and science; the number of participants with prenatal mercury and relevant test results varied from 1500 to 2200. Multiple regression was used to assess relationships between prenatal total blood mercury concentrations and 16 different test results, after taking account of a variety of potential confounders; in parallel, logistic regression was used to determine associations with the risk of the child being in the lowest 15% of each score. Analyses were repeated stratifying for fish consumption and sex of the child. There was no evidence of harm associated with the level of total mercury, provided the mother ate fish during pregnancy. This was particularly true for tests of mathematics and science. We conclude that women should be confident that eating fish in pregnancy is beneficial for their unborn child. [ABSTRACT FROM AUTHOR]

In this paper, we propose a theory for linear time fractional PDEs on L 2 ( R d ) , with two time parameters. The order of the time derivatives under consideration is less than 1. We study well-posedness, regularizing effects and dissipative properties. Regarding regularizing effects, we describe quite precisely the equations that have this effect or not. We highlight that, in purely fractional settings, the regularizing effect acts always only up to finite order; unlike to the standard case. Also, we investigate the properties of the three time variables solution operator generated by these PDEs. [ABSTRACT FROM AUTHOR]

Nuclear concrete containment structures serve as the main line of defense to prevent escape of radioactive material during catastrophic events including the loss of coolant accident (LOCA), explosions and earthquake. In the case that such an event occurred, the containment would need to resist high internal pressure and temperature loads. This paper studies the dome-cylinder interface of concrete containments subjected to significant internal pressure and temperature load. In particular, the compatibility at geometry discontinuity and internal forces as a result of displacement discrepancy is investigated using nonlinear mechanics based formulas. A practical example of concrete containment is presented as a case study. The study reveals that the current practice in nuclear concrete containment design may significantly underestimate the stress at the dome-cylinder interface, which would lead to insufficient design. The presented approach provides an easy to use tool to assess the dome-cylinder interface of a concrete containment. [ABSTRACT FROM AUTHOR]

Given a computable ordinal Λ, the transfinite provability logic GLP Λ has for each ξ < Λ a modality [ ξ ] intended to represent a provability predicate within a chain of increasing strength. One possibility is to read [ ξ ] ϕ as ϕ is provable in T using ω-rules of depth at most ξ, where T is a second-order theory extending ACA 0 . In this paper we will formalize such iterations of ω -rules in second-order arithmetic and show how it is a special case of what we call uniform provability predicates. Uniform provability predicates are similar to Ignatiev's strong provability predicates except that they can be iterated transfinitely. Finally, we show that GLP Λ is sound and complete for any uniform provability predicate. [ABSTRACT FROM AUTHOR]

In-depth knowledge about the gas sorption within hydrogen (H 2 ) selective nanocomposite membranes at various conditions is crucial, particularly in petrochemical and separation processes. Hence, various artificial intelligence (AI) methods such as multilayer perceptron artificial neural network (MLP-ANN), adaptive neuro-fuzzy inference system (ANFIS), the adaptive neuro-fuzzy inference system optimized by genetic algorithm (GA-ANFIS), Genetic Programming (GP) and Committee Machine Intelligent System (CMIS) were applied to predict the sorption of gases in H 2 -selective nanocomposite membranes consist of porous nanoparticles as the dispersed phase and polymer matrix as continuous phase. The momentous purpose of this paper was to estimate the sorption of C 3 H 8 , H 2 , CH 4 and CO 2 within H 2 -selective nanocomposite membranes considering the effect of nanoparticles loading, critical temperature (gas type characteristics) and upstream pressure. Obtained data were categorized into two parts including training and testing data set. The CMIS method showed more precise results rather than other intelligent models. Having developed different intelligent approaches rely on algorithms, a powerful successor for labor-intensive experimental processes of solubility was revealed. The prediction results and experimental data were significantly consistent in approach with a correlation coefficient (R 2 ) of 0.9999, 0.9987, 0.9998, 0.9995, and 0.9997 for CMIS, GP, GA-ANFIS, ANFIS and ANN models respectively. [ABSTRACT FROM AUTHOR]

In this paper, we employ contraction theory to solve cluster synchronization problem under directed topology. According to the cluster structure, we develop an invariant subspace. Then we take the advantage of the complementary space to prove that the whole systems will synchronize to this invariant subspace, leading to cluster synchronization. We first deal with the linear systems which are linearly coupled under the framework of directed topology. Some sufficient conditions are given to guarantee that the coupled linear systems can achieve cluster synchronization. Moreover, the case of linearly coupled non-linear systems is also considered. Two simulation examples are given to verify our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we mainly prove the following: Let G be a connected almost bridgeless simple graph of order n sufficiently large such that σ ¯ 2 ( G ) =min { d ( u ) + d ( v ) : u v ∈ E ( G ) } ≥ 2 ( ⌊ n / 11 ⌋ − 1 ) . Then either L ( G ) is traceable or Catlin’s reduction of the core of G is one of eight graphs of order 10 or 11, where the core of G is obtained from G by deleting the vertices of degree 1 of G and replacing each path of length 2 whose internal vertex has degree 2 in G by an edge. We also give a new proof for the similar theorem in Niu et al. (2012) which has flaws in their proof. [ABSTRACT FROM AUTHOR]

This paper introduces a system for measuring the elegance of a graph based on the steps needed to build the graph and on its symmetry structure. The measure is designed to capture the essence of the notion of elegance in mathematics, namely, simplicity and clarity. The term “elegance” is used instead of “aesthetics” to distinguish the measure from those dependent on visual representation of a graph. Elegance is based solely on the abstract properties of a graph. A framework for measurement is defined and applied in a special case. [ABSTRACT FROM AUTHOR]

An edge-coloured path is rainbow if its edges have distinct colours. For a connected graph G , the rainbow connection number (resp. strong rainbow connection number ) of G is the minimum number of colours required to colour the edges of G so that any two vertices of G are connected by a rainbow path (resp. rainbow geodesic). These two graph parameters were introduced by Chartrand, Johns, McKeon, and Zhang in 2008. Krivelevich and Yuster generalised this concept to the vertex-coloured setting. Similarly, Liu, Mestre, and Sousa introduced the version which involves total-colourings. Dorbec, Schiermeyer, Sidorowicz, and Sopena extended the concept of the rainbow connection to digraphs. In this paper, we consider the (strong) total rainbow connection number of digraphs. Results on the (strong) total rainbow connection number of biorientations of graphs, tournaments, and cactus digraphs are presented. [ABSTRACT FROM AUTHOR]

An arc-coloured digraph D is alternating if whenever ( u , v ) and ( v , w ) are arcs in D they are of different colours. In an arc coloured digraph D , a subset K ⊂ V ( D ) of vertices of D is a kernel by alternating paths (or alternating kernel ) if it is absorbent and independent by directed alternating paths. In this paper we prove sufficient conditions for the existence of alternating kernels in arc-coloured tournaments, quasi-transitive digraphs, and k -partite digraphs. [ABSTRACT FROM AUTHOR]

In this paper we continue studying the independent transversal domination number in a graph, i.e., the cardinality of a smallest dominating set which intersects each maximum independent set. As our main result, we prove two upper bounds on the independent transversal domination number in terms of the order and minimum degree of a graph. [ABSTRACT FROM AUTHOR]

A matching in a hypergraph H is a set of pairwise disjoint hyperedges. The matching number ν ( H ) of H is the size of a maximum matching in H . A subset D of vertices of H is a dominating set of H if for every v ∈ V ∖ D there exists u ∈ D such that u and v lie in an hyperedge of H . The cardinality of a minimum dominating set of H is the domination number of H , denoted by γ ( H ) . It was proved that γ ( H ) ≤ ( r − 1 ) ν ( H ) for r -uniform hypergraphs and the 2-uniform hypergraphs (graphs) achieving equality γ ( H ) = ν ( H ) have been characterized. In this paper we generalize the inequality γ ( H ) ≤ ( r − 1 ) ν ( H ) to arbitrary hypergraph of rank r and we completely characterize the extremal hypergraphs H of rank 3 achieving equality γ ( H ) = ( r − 1 ) ν ( H ) . [ABSTRACT FROM AUTHOR]

The spectrum of a first order sentence is the set of all α such that G ( n , n − α ) does not obey zero–one law with respect to this sentence. In this paper, we prove that the minimal number of quantifier alternations of a first order sentence with infinite spectrum equals 3. We have also proved that the spectrum of a first-order sentence with quantifier depth 4 has no limit points except possibly the points 1 ∕ 2 and 3 ∕ 5 . [ABSTRACT FROM AUTHOR]

For a graph G , we denote by σ 2 ( G ) the minimum degree sum of two non-adjacent vertices if G is non-complete; otherwise, σ 2 ( G ) = + ∞ . In this paper, we prove the following two results: (i) If s 1 , s 2 ≥ 2 are integers and G is a non-complete graph with σ 2 ( G ) ≥ 2 ( s 1 + s 2 + 1 ) − 1 , then G contains two vertex-disjoint subgraphs H 1 and H 2 such that each H i is a graph of order at least s i + 1 with σ 2 ( H i ) ≥ 2 s i − 1 . (ii) If s 1 , s 2 ≥ 2 are integers and G is a triangle-free graph of order at least 3 with σ 2 ( G ) ≥ 2 ( s 1 + s 2 ) − 1 , then G contains two vertex-disjoint subgraphs H 1 and H 2 such that each H i is a graph of order at least 2 s i with σ 2 ( H i ) ≥ 2 s i − 1 . By using this result, we also give some corollaries concerning degree conditions for the existence of k vertex-disjoint cycles. [ABSTRACT FROM AUTHOR]

The multiplication of a semitopological (quasitopological) group G is called sequentially continuous if the product map of G × G into G is sequentially continuous. In this paper, we mainly consider the properties of semitopological (quasitopological) groups with sequentially continuous multiplications and three-space problems in quasitopological groups. It is showed that (1) every snf -countable semitopological group G with the sequentially continuous multiplication is sof -countable; (2) if G is a sequential quasitopological group with the sequentially continuous multiplication, then G contains a closed copy of S ω if and only if it contains a closed copy of S 2 , which give a partial answer to a problem posed by R.-X. Shen; (3) let G be a quasitopological group with the sequentially continuous multiplication, then the following are equivalent: (i) G is a sequential α 4 -space; (ii) G is Fréchet; (iii) G is strongly Fréchet; (4) (MA+¬CH) there exists a non-metrizable, separable, normal and Moore quasitopological group; (5) some examples are constructed to show that metrizability, first-countability and second-countability are not three-space properties in the class of quasitopological groups. [ABSTRACT FROM AUTHOR]

In recent work, Hess and Shipley [18] defined a theory of topological coHochschild homology (coTHH) for coalgebras. In this paper we develop computational tools to study this new theory. In particular, we prove a Hochschild–Kostant–Rosenberg type theorem in the cofree case for differential graded coalgebras. We also develop a coBökstedt spectral sequence to compute the homology of coTHH for coalgebra spectra. We use a coalgebra structure on this spectral sequence to produce several computations. [ABSTRACT FROM AUTHOR]

In Gordon (1998), Gordon presented alternate proofs of several well known results in elementary real analysis using tagged partitions. In this paper, we provide a set of alternative proofs based on the dyadic partitions. An important difference between tagged and dyadic partitions is that the results based on the dyadic partition can be obtained constructively, i.e. an algorithm is supplied to reach the conclusion of each proof. In addition, the construction involves only concepts and results presented in a first course real analysis, which is the reason why, comparing tagged partition and its theory, the proofs based on dyadic partition are more straightforward and accessible to a wide range of audience. [ABSTRACT FROM AUTHOR]

In this paper, we establish some scaling invariant regularity criteria for the Navier–Stokes–Maxwell system. [ABSTRACT FROM AUTHOR]

Given a metric continuum X , we define the hyperspace of regular subcontinua of X as the collection of all regular closed subcontinua of X . This is a new hyperspace for X . In this paper we study the connectedness, compactness, arcwise connectedness and contractibility of this hyperspace. Also we raise some open questions. [ABSTRACT FROM AUTHOR]

This paper is devoted to an elementary new construction of 1-singular Gelfand–Tsetlin modules using complex geometry. We introduce a universal ring D v together with the vector space S = S ( D v ) with basis B v = B ( D v ) consisted of some local distributions such that S is a natural D v -module. For any homomorphism of rings U ( h ) → D v , where h is a Lie algebra, it follows that S is also an h -module. We observe that the homomorphism of rings constructed in [8] is a homomorphism of type U ( gl n ( C ) ) → D v . Using this observation we obtain a construction of the universal 1-singular Gelfand–Tsetlin gl n ( C ) -module from [7] . [ABSTRACT FROM AUTHOR]