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This paper focuses on comparing fault detection (FD) conservatism of the set-theoretic unknown input observer (SUIO) based method and the interval observer (IO) based method. The former is implemented by combining both the set theory and the unknown input observer (UIO), where the set theory and the UIO are used to decouple disturbances and noises in passive and active ways, respectively. The latter is based on the set theory and the Luenberger-structure observer, which completely relies on the set-based passive decoupling of disturbances and noises to obtain FD robustness. The objective of this paper is to compare their FD conservatism using systematic mathematical analysis based on zonotopes and a mathematical criterion comparing their FD conservatism is obtained. Moreover, by establishing a general residual framework for conservatism analysis, the proposed method comparing the FD conservatism is also extended to compare the FD conservatism of a wide variety of set-based robust FD methods. At the end of this paper, a two-tank system example is used to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

The main purpose of the article is to show feasibility and efficiency of combining different types of simulating a hypervelocity impact interaction of solids within a single system. It allows effective application of new mathematical apparatus for analysis and comparison of experimental results. The paper considers the features of an integrated system that combines the results of experiments reproducing the high-velocity impact interaction of solids. The experiments included different types of modeling. System structure and the tasks solved within individual functional modulus were discussed. Based on the theory of fuzzy sets, new algorithms were proposed for comparing edges of the images obtained in the physical and computational experiment. Mathematical models were verified by such procedure. Differences in the shape and size of a cloud of particles that appears after penetrating a single barrier were estimated in the framework of designed models, as well as the differences in the sizes of punched holes using fuzzy variables and related membership functions. When analyzing experimental results, fuzzy sets enable switching from data structures to knowledge structures that are necessary to create an intelligent system for analyzing and predicting the effects of the interaction between space debris and spacecraft structures. • Types of simulating a hypervelocity impact interaction of solids can be combined. • This combining is efficient and feasible. • New algorithms were proposed for comparing edges of the images. • Fuzzy sets enable switching from data structures to knowledge structures. [ABSTRACT FROM AUTHOR]

Given the Kekulé structure of a fullerene that gives its Clar structure, the Kekulé edges that do not lie on any benzene ring of the Clar structure lie on open chains that pair up the pentagonal faces and perhaps some closed chains. In this paper, we introduce Fries chains and show that given the Kekulé structure of a fullerene that gives its Fries structure, the Kekulé edges that do not lie on two benzene rings lie on the union of a set of these Fries chains. The edges that lie on exactly one benzene ring belong to exactly one of these chains while edges that lie on no benzene ring belong to exactly two of these chains. We will see that the Fries chains will include the Clar chains in some cases and will be quite distinct from the Clar chains in other cases. Examples of fullerenes with the property that the set of benzene rings that give its Clar number are not a subset of the benzene rings that give its Fries number have been known for a few years. However, in all of these known examples, almost all of the benzene rings of its Clar structure are among benzene rings of its Fries structure. In this paper, we describe a class of fullerenes with the property that the set of benzene rings of its Clar structure and the set of benzene rings of its Fries structure practically disjoint. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to connect R-fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the significance measure allows for an intermediary approach to that of a type-2 fuzzy set. By inspecting the returned significance degree of a particular membership value, one is able to ascertain its true significance in relation, relative to other encapsulated membership values. An R-fuzzy set coupled with the proposed significance measure allows for a type-2 fuzzy equivalence, an intermediary, all the while retaining the underlying sentiment of individual and general perspectives, and with the adage of a significantly reduced computational burden. Several human based perception examples are presented, wherein the significance degree is implemented, from which a higher level of detail can be garnered. The results demonstrate that the proposed research method combines the high capacity in uncertainty representation of type-2 fuzzy sets, together with the simplicity and objectiveness of type-1 fuzzy sets. This in turn provides a practical means for problem domains where a type-2 fuzzy set is preferred but difficult to construct due to the subjective type-2 fuzzy membership. [ABSTRACT FROM AUTHOR]

Abstract In this paper the spherical quasi-convexity of quadratic functions on spherically convex sets is studied. Several conditions characterizing the spherical quasi-convexity of quadratic functions are presented. In particular, conditions implying spherical quasi-convexity of quadratic functions on the spherical positive orthant are given. Some examples are provided as applications of the obtained results. [ABSTRACT FROM AUTHOR]

A graph G = ( V , E ) is a word-representable graph if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if ( x , y ) ∈ E for each x ≠ y . In this paper we give an effective characterization of word-representable graphs in terms of orientations. Namely, we show that a graph is word-representable if and only if it admits a semi-transitive orientation defined in the paper. This allows us to prove a number of results about word-representable graphs, in particular showing that the recognition problem is in NP, and that word-representable graphs include all 3-colorable graphs. We also explore bounds on the size of the word representing the graph. The representation number of G is the minimum k such that G is a representable by a word, where each letter occurs k times; such a k exists for any word-representable graph. We show that the representation number of a word-representable graph on n vertices is at most 2 n , while there exist graphs for which it is n / 2 . [ABSTRACT FROM AUTHOR]

This short article is in fact an erratum to Theorem 2.5 in Ghirati and Taherifar (2014) [6] . In this paper, we prove that J ( C ( X ) / C F ( X ) ) = 0 or equivalently, the socle C F ( X ) of C ( X ) coincides with the intersection of all essential maximal ideals of C ( X ) if and only if every infinite subset of I ( X ) contains a closed infinite subset, if and only if every pseudocompact subset of X has at most a finite number of isolated points. This fact shows that part (2) of aforementioned Theorem 2.5 is not correct. Our results in this paper also amend Theorem 5.6 in Azarpanah et al. (2008) [2] . Examples are provided to illustrate and delimit our results. [ABSTRACT FROM AUTHOR]

In the present paper we will give some properties of the subclass of harmonic mappings which is related to m -fold starlike functions in the open unit disc D = { z | | z | < 1 } . Throughout this paper we restrict ourselves to the study of sense-preserving harmonic mappings. We also note that an elegant and complete treatment theory of the harmonic mapping is given in Durens monograph (Duren, 1983). The main aim of us to investigate some properties of the new class of us which represented as in the following form, S ∗ H ( m ) = f = h ( z ) + g ( z ) ‾ | f ∈ SH ( m ) , g ′ ( z ) h ′ ( z ) ≺ b 1 p ( z ) , h ( z ) ∈ S ∗ ( m ) , p ( z ) ∈ P ( m ) , where h ( z ) = z + ∑ n = 1 ∞ a mn + 1 z mn + 1 , g ( z ) = ∑ n = 0 ∞ b mn + 1 z mn + 1 , | b 1 | < 1 . [ABSTRACT FROM AUTHOR]

Abstract: The aim of the paper is to construct some Godbillon–Vey classes of a family of regular foliations, defined in the paper. These classes are cohomology classes on the manifold or on suitable open subsets. Some examples are also considered. [Copyright &y& Elsevier]

Abstract: In this paper, we obtain some Lyapunov-type inequalities for a class of higher-order linear differential equations. The results of this paper generalize and improve some earlier results on this topic. [Copyright &y& Elsevier]

A half-space over a distance space is a generalization of a half-space in a vector space. An important advantage of a distance space over a metric space is that the triangle inequality need not be satisfied, which makes our results potentially very useful in practice. Given two points in a set, a half-space is defined by them, as the set of all points closer to the first point than to the second. In this paper we consider the problem of learning half-spaces in any finite distance space, that is, any finite set equipped with a distance function. We make use of a notion of ‘width’ of a half-space at a given point: this is defined as the difference between the distances of the point to the two points that define the half-space. We obtain probabilistic bounds on the generalization error when learning half-spaces from samples. These bounds depend on the empirical error (the fraction of sample points on which the half-space does not achieve a large width) and on the VC-dimension of the effective class of half-spaces that have a large sample width. Unlike some previous work on learning classification over metric spaces, the bound does not involve the covering number of the space, and can therefore be tighter. [ABSTRACT FROM AUTHOR]

In this paper we compute the critical group of the Kneser graph K G ( n , 2 ) . This is equivalent to computing the Smith normal form of a Laplacian matrix of this graph. [ABSTRACT FROM AUTHOR]

A space X is selectively absolutely star-Lindelöf [1,3] if for each open cover U of X and any sequence ( D n : n ∈ ω ) of dense subsets of X , there are finite sets F n ⊆ D n ( n ∈ ω ) such that S t ( ⋃ n ∈ ω F n , U ) = X . In this paper, we continue to investigate topological properties of selectively absolute star-Lindelöf spaces, and show the following statements: (1) There exists a Tychonoff selectively a-star-Lindelöf, pseudocompact space X having a regular closed G δ subset which is not star-Lindelöf (hence not selectively a-star-Lindelöf); (2) Assuming 2 ℵ 0 = 2 ℵ 1 , there exists a normal selectively a-star-Lindelöf space X having a regular closed G δ subset which is not star-Lindelöf (hence not selectively a-star-Lindelöf); (3) An open F σ -subset of a selectively a-star-Lindelöf space is selectively a-star-Lindelöf; (4) For any cardinal κ , there exists a Tychonoff selectively a-star-Lindelöf, pseudocompact space X such that e ( X ) ≥ κ . [ABSTRACT FROM AUTHOR]

The class of hyper-CR Einstein–Weyl structures on R 3 can be described in terms of the solutions to the dispersionless Hirota equation. In the present paper we show that simple geometric constructions on the associated twistor space lead to deformations of the Hirota equation that have been introduced recently by B. Kruglikov and A. Panasyuk. Our method produces also the hyper-CR equation and can be applied to other geometric structures related to different twistor constructions. [ABSTRACT FROM AUTHOR]

In this paper we prove the linear instability for the Boussinesq equations experiencing a diabatic forcing. To do so, we first prove the local well-posedness of the governing set of equations. An example of an unstable solution to the linearized set of equations is then constructed. Finally, we show that the unstable solution to the linearized problem is also unstable in the nonlinear sense. [ABSTRACT FROM AUTHOR]

A connected graph G with at least 2 m + 2 n + 2 vertices is said to satisfy the property E ( m , n ) if G contains a perfect matching and for any two sets of independent edges M and N with | M | = m and | N | = n with M ∩ N = ∅ , there is a perfect matching F in G such that M ⊂ F and N ∩ F = ∅ . In particular, if G is E ( m , 0 ) , we say that G is m -extendable. One of the authors has proved that every m -tough graph of even order at least 2 m + 2 is m -extendable (Plummer, 1988). Chen (1995) and Robertshaw and Woodall (2002) gave sufficient conditions on binding number for m -extendability. In this paper, we extend these results and give lower bounds on toughness and binding number which guarantee E ( m , n ) . [ABSTRACT FROM AUTHOR]

The Szeged index of a graph G is defined as S z ( G ) = ∑ e = u v ∈ E n u ( e ) n v ( e ) , where n u ( e ) and n v ( e ) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u . A cactus is a graph in which any two cycles have at most one common vertex. Let C ( n , k ) denote the class of all cacti with order n and k cycles, and C n t denote the class of all cacti with order n and t pendant vertices. In this paper, a lower bound of the Szeged index for cacti of order n with k cycles is determined, and all the graphs that achieve the lower bound are identified. As well, the unique graph in C n t with minimum Szeged index is characterized. [ABSTRACT FROM AUTHOR]

In this paper we enumerate and give bijections for the following four sets of vertices among rooted ordered trees of a fixed size: (i) first-children of degree k at level ℓ , (ii) non-first-children of degree k at level ℓ − 1 , (iii) leaves having k − 1 elder siblings at level ℓ , and (iv) non-leaves of outdegree k at level ℓ − 1 . Our results unite and generalize several previous works in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study four games, they are all restrictions of ( s , t ) -Wythoff’s game which was introduced by A.S. Fraenkel. The first one is a modular type restriction of ( s , t ) -Wythoff’s game, where a player is restricted to remove a multiple of K tokens in each move ( K is a fixed positive integer). The others we called rook type restrictions of ( s , t ) -Wythoff’s game, including Odd-Arbitrary-Nim ( s , t ) -Wythoff’s Game, Odd–Odd-Nim ( s , t ) -Wythoff’s Game and Odd–Even-Nim ( s , t ) -Wythoff’s Game. In these three games, the restrictions are only made on horizontal and vertical moves, but not on the extended diagonal moves. For any K , s , t ≥ 1 , the sets of P -positions of our games are given in both normal and misère play. [ABSTRACT FROM AUTHOR]

It is obtained a selection theorem for paraconvex-valued mappings possessing two natural properties. Several known results follow easily from this theorem. Moreover, it implies the affirmative solution to a question stated in a paper of N.R. Loufouma Makala. [ABSTRACT FROM AUTHOR]

Entropy-based measures have been used to characterize the structure of complex networks. Various graph entropies based on different graph parameters have been proposed and studied. So, it has been intricate to decide which measure is the right one for solving a particular problem. In this paper, we introduce graph entropy measures based on independent sets and matchings of graphs. The values of entropies of some special graphs are calculated and we draw several conclusions regrading the usability of the measures. Based on our findings, we conclude that it should be demanding studying extremal values of the novel entropies. [ABSTRACT FROM AUTHOR]

The paper contains new results on the impact of harvesting times and intensities on the stability properties of Seno population models. It is proved that sufficiently high harvest intensities are stabilizing for any harvesting time in the sense that they create a positive equilibrium that attracts all positive solutions. Moreover, in the special case that the nonlinearity in the Seno model is a Ricker function, we derive a global stability result independent of timing and valid for low to medium harvesting efforts. The proof is based on a characterization of those harvesting intensities which guarantee a negative Schwarzian derivative for all harvesting times. Finally, we rigorously show that timing can be stabilizing as well as destabilizing by itself. In particular, a recent conjecture formulated by Cid et al. (2014) [1] is shown to be false. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the basic homogeneous -machine scheduling problem where weakly dependent unit-time jobs have to be scheduled within the time windows between their release dates and due dates so that, for any subset of machines, the set of the time units at which at least one machine is busy, is in interval. We first introduce the notions of pyramidal structure, -hole, -matching, preschedule, -schedule and schedule for this problem. Then we provide a feasibility criteria for a preschedule. The key result of the paper is then to provide a structural necessary and sufficient condition for an instance of the problem to be feasible. We conclude by giving the directions of ongoing works and by bringing open questions related to different variants of the basic non-idling -machine scheduling problem. [Copyright &y& Elsevier]

Abstract: There is an abundant literature on inequalities for the (Euler’s) Gamma function Γ and its various related functions. Yet, only very recently, several authors began to study inequalities for the (Barnes’) double Gamma function . Here, in this paper, we aim at presenting several two-sided inequalities for the multiple Gamma functions . In our investigation of these two-sided inequalities for the multiple Gamma functions , we employ and extend a method based upon Taylor’s formula and express as series involving the Zeta functions. We also give a more convenient explicit form of the multiple Gamma functions being the set of positive integers. The main two-sided inequalities for the multiple Gamma functions (which we have presented in this paper) are presumably new and their derivations provide a fruitful insight into the corresponding problem for the multiple Gamma functions when . [Copyright &y& Elsevier]

Abstract: Let be a family of subsets of an -element set. Sperner’s theorem says that if there is no inclusion among the members of then the largest family under this condition is the one containing all -element subsets. The present paper surveys certain generalizations of this theorem. The maximum size of is to be found under the condition that a certain configuration is excluded. The configuration here is always described by inclusions. More formally, let be a poset. The maximum size of a family which does not contain as a (not-necessarily induced) subposet is denoted by . The paper is based on a lecture of the author at the Jubilee Conference on Discrete Mathematics [Banasthali University, January 11–13, 2009], but it was somewhat updated in December 2010. [Copyright &y& Elsevier]

Abstract: Gong et al. (2010) and Xiao et al. (2010) have proposed the notion of bijective soft set and exclusive disjunctive soft set, respectively, which is a subtype of soft set. On the basis of their work, this paper extends these notions to fuzzy environments, and formulates the concept of bijective fuzzy soft set, which can deal with more uncertain problems. Moreover, this paper proposes two parameters reduction algorithms: one (Algorithm 1) is based on bijective fuzzy soft system, and the other (Algorithm 2) takes weight of an element into consideration. Since the threshold plays an important role in these algorithms, we proposed an algorithm (Algorithm 3) to decide the optimal value of threshold specially. Afterwards, an example analysis of the two parameters reduction algorithms is given and the result shows that the two algorithms lead to the same parameters reduction of a bijective fuzzy soft system. Since Algorithm 2 considers the detail weights of elements, thus it can be used in more uncertain problems, such as time series analysis problems, than Algorithm 1. [Copyright &y& Elsevier]

Abstract: In the present paper, the authors derive several sharp coefficient estimates for the function class consisting of the inverses of functions in a certain class of spirallike functions in the open unit disk , which was introduced by Libera. They also obtain a number of sharp coefficient bounds of functions in the more general classes and , each of which is introduced here. Some of the results derived in this paper would generalize those in a recent work of Kapoor and Mishra. [Copyright &y& Elsevier]

Bierbrauer (2012) developed the theory of q -linear cyclic codes over ( F q ) m and he obtained a parametric description of such codes by cyclotomic cosets. Recently, Cao et al. (2015) obtained the structure of cyclic additive codes over the Galois ring GR ( p ℓ , m ) , where m is a prime integer. Let R be a finite commutative ring and R n = R [ x ] ∕ 〈 x n − 1 〉 . In this paper, we generalize the theory of F q -linear codes over vector spaces to R -linear codes over free R -algebras (free as R -module). We call these codes, R -additive codes. We introduce a one-to-one correspondence between the classes of cyclic R -additive code and the classes of R n -linear code. Using the structure of R n -linear codes, we present the structure of cyclic R -additive codes, where R is a chain ring. Among other results, q -linear cyclic codes over ( F q ) m are described by ring-theoretic facts, and the structure of cyclic additive codes over the Galois ring GR ( p ℓ , m ) is given for an arbitrary integer m , not necessarily a prime number. [ABSTRACT FROM AUTHOR]

A Hamilton ℓ -cycle in a k -uniform hypergraph of n -vertex is an ordering of all vertices, combined with an ordered subset C of edges, such that any two consecutive edges share exactly ℓ vertices and each edge in C contains k consecutive vertices. A classic result of O. Ore in 1960 is that if the degree sum of any two independent vertices in an n -vertex graph is at least n , then the graph contains a Hamiltonian cycle. Naturally, we consider to generalize it to hypergraphs situation. In this paper, we prove the following theorems. (i) For any n ≥ 4 k 2 , there is an n -vertex k -uniform hypergraph, with degree sum of any two strongly independent sets of k − 1 vertices bigger than 2 n − 4 ( k − 1 ) , contains no Hamilton l -cycle, 1 ≤ ℓ ≤ k − 1 . (ii) If the degree sum of two weakly independent sets of k − 1 vertices in an n -vertex k -uniform hypergraph is ( 1 + o ( 1 ) ) n , then the hypergraph contains a Hamilton ( k − 1 ) -cycle, where two distinct sets of k − 1 vertices are weakly (strongly) independent if there exist no edge containing the union of them (intersecting both of them). [ABSTRACT FROM AUTHOR]

The (bi)simulation relation has recently been attracting growing interest in the study of nonlinear control systems, in the hope that through such a relation, the behaviors and properties of a nonlinear system can be inferred from those of another system which is easier to handle. In this paper, we consider the propagation of the property of nonlinear norm-observability through a simulation relation. Given two control systems that are related by a graph simulation relation, we derive conditions under which the norm-observability of the simulating system implies the norm-observability of the simulated system. The obtained results are given in terms of set-valued functions. Several examples are included to illustrate various applications of our results. [ABSTRACT FROM AUTHOR]

The class of Boolean functions, which can never occur as output of a faulty combinational circuit, is known as Impossible Class of Faulty Functions (ICFF). Despite years of research, the characterization of ICFF for a complex logic network is yet a significantly open problem. In a recent work (Das et al., 2014), a partial characterization of ICFF was done by completely enumerating a subclass of ICFFs, also called the root functions . For 2 -level AND-OR logic networks for up to 6 -variable the root functions were completely enumerated. This paper significantly extends this line of research by providing a more general framework for handling this class of functions. Both the upper and lower bounds are derived and the maximum cardinality of the weight of non-affine root functions is established. A constructive method for obtaining non-affine root functions of maximum possible weight is provided and it is shown that there are no other such functions than those obtained by our method. The direct correspondence of these functions to the independent dominating sets in the n -dimensional hypercube G n is used for establishing new results concerning the minimum weight of these functions. In particular, we give the exact value of the minimum cardinality of independent dominating set in G n for any n = 2 r − 1 , where r ≥ 2 . Since our approach is also constructive, we essentially efficiently solve this problem for any n = 2 r − 1 , where r ≥ 2 , and our results conform to the observation of Harary and Livingston (2010). Finally, the problem of classifying and enumerating root functions is addressed leading to some non-trivial lower bounds on their number, though the problem appears to be hard and further research in this direction is needed. [ABSTRACT FROM AUTHOR]

Let E be a set of points in F q d . Bennett et al. (2016) proved that if | E | ≫ q d − d − 1 k + 1 then E determines a positive proportion of all k -simplices. In this paper, we give an improvement of this result in the case when E is the Cartesian product of sets. Namely, we show that if E is the Cartesian product of sets and q k d k + 1 − 1 ∕ d = o ( | E | ) , the number of congruence classes of k -simplices determined by E is at least ( 1 − o ( 1 ) ) q k + 1 2 , and in some cases our result is sharp. [ABSTRACT FROM AUTHOR]

A space X is selectively absolutely star-Lindelöf if for any open cover U of X and any sequence ( D n : n ∈ ω ) of dense subsets of X , there are finite sets F n ⊂ D n ( n ∈ ω ) such that S t ( ⋃ n ∈ ω F n , U ) = X . This notion was introduced by S. Bhowmik [3] , and it lies between absolute countable compactness in Matveev [9] and absolute star-Lindelöfness in Bonanzinga [4] . In this paper, we distinguish absolute star-Lindelöfness from selective absolute star-Lindelöfness, and study the general properties of selectively absolutely star-Lindelöf spaces. [ABSTRACT FROM AUTHOR]

The purpose in this paper is to prove the existence of a canonical-pre-quasi-uniform extension ( X , U ) ˆ of a pre-quasi-uniform space ( X , U ) . Most of the concepts used in quasi-uniform spaces may be applied to pre-quasi-uniform spaces. These spaces were introduced by the first author and developed by the second in his doctoral thesis. We shall study the main properties of this class of spaces which contains the class of quasi-uniform spaces. [ABSTRACT FROM AUTHOR]

A dihedral SQS is an SQS admitting a point-regular dihedral automorphism group. Some constructions of dihedral SQSs are established in this paper. We also prove that for v ≡ 2 , 4 ( m o d 6 ) , there is a dihedral SQS ( v ) if there is a dihedral H ( p , 2 , 4 , 3 ) design or an S -cyclic SQS ( 2 p ) for each odd prime divisor p of v . As a corollary, we enlarge the set of known values of v for which there exists a dihedral SQS ( v ) . [ABSTRACT FROM AUTHOR]

Recently, linear codes with a few weights have been constructed and extensively studied. In this paper, for an odd prime p , we determine the complete weight enumerator of two classes of p -ary linear codes constructed from defining set. Our results show that the codes have at most seven weights and may have applications in secret sharing schemes. [ABSTRACT FROM AUTHOR]

Let G be a connected graph with vertex set V , minimum degree δ and edge-connectivity λ . If α is a real number, then the zeroth-order general Randić index is defined by ∑ x ∈ V deg α ( x ) , where deg ( x ) denotes the degree of the vertex x . A graph is maximally edge-connected if λ = δ . In this paper, we present sufficient conditions for connected graphs (resp. connected triangle-free graphs) to be maximally edge-connected in terms of the zeroth-order general Randić index, the order and the minimum degree when α ∈ ( − ∞ , 0 ) or α ∈ ( 1 , 2 ] (resp. α ∈ [ − 1 , 0 ) ∪ ( 1 , 2 ] ). [ABSTRACT FROM AUTHOR]

Let G = ( V , E ) be a graph with no isolated vertex. A subset of vertices S is a total dominating set if every vertex of G is adjacent to some vertex of S . For some α with 0 < α ≤ 1 , a total dominating set S in G is an α -total dominating set if for every vertex v ∈ V ∖ S , | N ( v ) ⋂ S | ⩾ α | N ( v ) | . The α -total domination number of G , denoted by γ α t ( G ) , is the minimum cardinality of an α -total dominating set of G . In Henning and Rad (2012), Henning and Rad posed the following question: Let G be a connected cubic graph with order n . Is it true that γ α t ( G ) ≤ 3 n 4 for 2 3 < α ≤ 1 ? In this paper, we give a positive answer toward this question. Furthermore, we give a characterization on cubic graphs attaining the bound for the α -total domination number. [ABSTRACT FROM AUTHOR]

In their celebrated paper, Erdos et al. (1961) posed the following question. Let F be a family of k -element subsets of an n -element set satisfying the condition that | F ∩ G | ≥ ℓ holds for any two members of F where ℓ ≤ k are fixed positive integers. What is the maximum size | F | of such a family? They gave a complete solution for the case ℓ = 1 : the largest family is the one consisting of all k -element subsets containing a fixed element of the underlying set. (One has to suppose 2 k ≤ n , otherwise the problem is trivial.) They also proved that the best construction for arbitrary ℓ is the family consisting of all k - element subsets containing a fixed ℓ -element subset, but only for large n ’s. They also gave an example showing that this statement is not true for small n ’s. Later Frankl gave a construction for the general case that he believed to be the best. Frankl, Wilson and Füredi made serious progress towards the proof of this conjecture, but the complete solution was not achieved until 1996 when the surprising news came: Rudolf Ahlswede and Levon Khachatrian have found the proof. They invented the expressive name: Complete Intersection Theorem. We will show some of the consequences of this deep and important theorem. [ABSTRACT FROM AUTHOR]

Abstract: Net subdivision schemes recursively refine nets of univariate continuous functions defined on the lines of planar grids, and generate as limits bivariate continuous functions. In this paper a family of interpolatory net subdivision schemes related to the family of Dubuc–Deslauriers interpolatory subdivision schemes is constructed and analyzed. The construction is based on Gordon blending interpolants to nets of univariate functions, and on a particular class of blending functions with properties related to the Dubuc–Deslauriers schemes. The general analysis tools for net subdivision schemes, developed in a previous paper by the authors, together with the properties of the blending functions, lead to the proof of the convergence of these schemes to limit functions having the same integer smoothness as the limits of the corresponding Dubuc–Deslauriers schemes. These results are proved for net subdivision schemes corresponding to the first 84 members of the Dubuc–Deslauriers family, and conjectured for the rest. A concrete example of a family of piecewise polynomial blending functions is considered, together with the corresponding family of net subdivision schemes. The performance of the first two net subdivision schemes in this family is demonstrated by two examples. [Copyright &y& Elsevier]

Abstract: In this paper a new discrepancy measure of uniformity for uniform designs (UDs) in a unit cube is presented. Alternative measures of uniformity based on distance criteria which can be applied to higher dimensions are also discussed. The good lattice point (glp) method was used to construct the uniform designs. Two approaches (generator equivalence and projection) of reducing the computational cost of the glp method are proposed and discussed. Two examples are presented in this paper. [Copyright &y& Elsevier]

Abstract: There exist a number of definitions of the concept of risk. Very few of them directly express how “exposure” and “risk exposure” are connected to the risk. Clearly there is a connection, but it is not evident how these concepts are related. In this paper we provide an in-depth study of this issue. A model is presented which links risk sources, hazards/threats and exposed systems. Using this model, it is shown how the concepts of exposure and risk exposure can be given plausible explanations for some common risk perspectives. The model provides new insights on some main perspectives on risk used for risk assessment and risk management. A set of adjusted risk definitions, all reflecting the exposure dimension, is considered. The principal aim of this paper is to contribute to a clarification of the issue in order to strengthen the foundations of the meaning and characterisation of risk, and in this way provide a basis for improved risk management. [Copyright &y& Elsevier]

Abstract: This paper studies to what extent the Logsum-measure of user benefits relates to travelers’ perceptions of choice set-desirability and choice-satisfaction. Knowing these relations is important since researchers have recently started to analyze and interpret user benefits in general – and Logsums in specific – in terms of these more behaviorally oriented notions, rather than in terms of expected utility. Participants to a stated route choice experiment were asked to indicate, after each choice made, to what extent they considered the choice set to be desirable, or to what extent they were satisfied with the chosen alternative. These measurements were correlated with Logsums that were computed for each choice situation. In addition, the paper derives a regret-based Logsum (which gives the expected regret of a choice situation) and presents a comparison with its utilitarian counterpart. Also for this regret-based Logsum, correlations with desirability- and satisfaction-ratings are computed. As a general finding, it appears that all computed correlations are rather weak. This suggests that, at least in the context of our data, the utility-based Logsum and its regret-based counterpart appear to have only a fairly weak connection with the behavioral notions of choice set-desirability and choice-satisfaction. [Copyright &y& Elsevier]

Let d 1 , d 2 , … , d k be k non-negative integers. A graph G is ( d 1 , d 2 , … , d k ) -colorable, if the vertex set of G can be partitioned into subsets V 1 , V 2 , … , V k such that the subgraph G [ V i ] induced by V i has maximum degree at most d i for i = 1 , 2 , … , k . Borodin, Montassier and Raspaud asked: Is every planar graph without adjacent cycles of length at most five 3-colorable, i.e., ( 0 , 0 , 0 ) -colorable? This problem has now been answered negatively by Cohen-Addad et al. who successfully constructed a non-3-colorable planar graph with neither 4-cycles nor 5-cycles. Is every planar graph without adjacent cycles of length at most five ( 1 , 0 , 0 ) -colorable? To this new problem, this paper proves that every planar graph without adjacent cycles of length at most five is ( 1 , 1 , 0 ) -colorable. [ABSTRACT FROM AUTHOR]

A 3-way ( v , k , t ) trade of volume m consists of three disjoint collections T 1 , T 2 and T 3 , each of m blocks of size k , such that for every t -subset of v -set V , the number of blocks containing this t -subset is the same in each T i ( 1 ≤ i ≤ 3 ) . If any t -subset of found(T) occurs at most once in T 1 ( T j , j ≥ 2 ) , then T is called 3-way ( v , k , t ) Steiner trade. In this paper the spectrum (that is, the set of allowable volumes) of 3-way ( v , k , t ) Steiner trades is discussed. Here it is shown that the volume of a 3-way ( v , k , 2 ) Steiner trade is at least 3 ( k − 1 ) for k ≠ 4 . Also we show how to construct a 3-way ( v , k , 2 ) Steiner trade of volume m when m ≥ 12 ( k − 1 ) for k ≥ 15 , or m is multiple of three and 3 ( k − 1 ) ≤ m ≤ 12 ( k − 1 ) . [ABSTRACT FROM AUTHOR]

In this paper, continuity properties of set multifunctions, such as regularity and continuity from above and below (as well as others), are introduced by way of a Wijsman topology. Some of the relationships between them are established. Different examples, counterexamples and applications are provided. [ABSTRACT FROM AUTHOR]

Two paths are equivalent modulo a given string τ , whenever they have the same length and the positions of the occurrences of τ are the same in both paths. This equivalence relation was introduced for Dyck paths in Baril and Petrossian (2015), where the number of equivalence classes was evaluated for any string of length 2. In this paper, we evaluate the number of equivalence classes in the set of ballot paths for any string of length 2 and 3, as well as in the set of Dyck paths for any string of length 3. [ABSTRACT FROM AUTHOR]