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In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ*-algebras for the following Cauchy-Jensen additive mapping: The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias’ stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297–300. This is applied to investigate isometric isomorphisms between proper CQ*-algebras. [ABSTRACT FROM AUTHOR]

Let Π = B/ B/ ··· / B be any set partition of [ n] = {1, 2,..., n} satisfying that entries are increasing in each block and blocks are arranged in increasing order of their first entries. Then Callan defined the flattened Π to be the permutation of [ n] obtained by erasing the divers between its blocks, and Callan also enumerated the number of set partitions of [ n] whose flattening avoids a single 3-letter pattern. Mansour posed the question of counting set partitions of [ n] whose flattening avoids a pattern of length 4. In this paper, we present the number of set partitions of [ n] whose flattening avoids one of the patterns: 1234, 1243, 1324, 1342, 1423, 1432, 3142 and 4132. [ABSTRACT FROM AUTHOR]

In this paper, we construct a new class of finite groups whose common divisor graphs are complete graphs, while there is no prime dividing all the nontrivial degrees. [ABSTRACT FROM AUTHOR]

In this paper, we prove that some volume-preserving almost Anosov systems are ergodic if they are essentially accessible. The key idea is that there are stable and unstable manifolds with uniform size on the orbits of the hyperbolic points for these systems. [ABSTRACT FROM AUTHOR]

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

The center of a graph is the set of vertices with minimum eccentricity. Graphs in which all vertices are central are called self-centered graphs. In this paper almost self-centered (ASC) graphs are introduced as the graphs with exactly two non-central vertices. The block structure of these graphs is described and constructions for generating such graphs are proposed. Embeddings of arbitrary graphs into ASC graphs are studied. In particular it is shown that any graph can be embedded into an ASC graph of prescribed radius. Embeddings into ASC graphs of radius two are studied in more detail. ASC index of a graph G is introduced as the smallest number of vertices needed to add to G such that G is an induced subgraph of an ASC graph. [ABSTRACT FROM AUTHOR]

A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. In this paper, we propose the Cayley-Bacharach theorem for continuous piecewise algebraic curves over cross-cut triangulations. We show that, if two continuous piecewise algebraic curves of degrees m and n respectively meet at mnT distinct points over a cross-cut triangulation, where T denotes the number of cells of the triangulation, then any continuous piecewise algebraic curve of degree m + n − 2 containing all but one point of them also contains the last point. [ABSTRACT FROM AUTHOR]

In this paper, the existence and multiplicity of a class of double resonant semilinear elliptic equations with the Dirichlet boundary value are studied. [ABSTRACT FROM AUTHOR]

The existence conditions of globally proper efficient points and a useful property of iccone-convexlike set-valued maps are obtained. Under the assumption of the ic-cone-convexlikeness, the optimality conditions for globally proper efficient solutions are established in terms of Lagrange multipliers. The new concept of globally proper saddle-point for an appropriate set-valued Lagrange map is introduced and used to characterize the globally proper efficient solutions. The results which are obtained in this paper are proven under the conditions that the ordering cone need not to have a nonempty interior. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the following implicit iteration scheme recently introduced by Xu and Ori [ Numer. Funct. Anal. Optim., 22, (2001) 767–773]: and to prove several strongly and weakly convergent theorems of the iteration for a finite family of pseudocontractive mappings under condition α n ∈ (0, b] ⊂ (0, 1). [ABSTRACT FROM AUTHOR]

M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin( απ/2) on the whole complex plane $$ \bar {\Bbb C} $$ which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k ≤ α to the whole plane $$ \bar {\Bbb C} .$$ In this paper we will give a negative approach to the question. [ABSTRACT FROM AUTHOR]

Let { X, X; n ≥ 0} be a sequence of independent and identically distributed random variables with E X = 0, and assume that E X I(| X| ≤ x) is slowly varying as x→∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series $$\sum\nolimits_{n = 0}^\infty {{\beta ^n}{X_n}\left( {0 < \beta < 1} \right)} $$ is obtained, under some minimal conditions. [ABSTRACT FROM AUTHOR]

Let G ( n, k, t) be a set of graphs with n vertices, k cut edges and t cut vertices. In this paper, we classify these graphs in G ( n, k, t) according to cut vertices, and characterize the extremal graphs with the largest spectral radius in G ( n, k, t). [ABSTRACT FROM AUTHOR]

Let G be a graph, and k ≥ 2 be a positive integer. A graph G is fractional independentset-deletable k-factor-critical (in short, fractional ID- k-factor-critical), if G-I has a fractional k-factor for every independent set I of G. The binding number bind( G) of a graph G is defined as $$bind(G) = min\left\{ {\frac{{\left| {N_G (X)} \right|}} {{\left| X \right|}}:\not 0 \ne X \subseteq V(G),N_G (X) \ne V(G)} \right\}.$$ In this paper, it is proved that a graph G is fractional ID- k-factor-critical if n ≥ 6 k − 9 and bind( G) $$> \frac{{(3k - 1)(n - 1)}} {{kn - 2k + 2}}$$ . [ABSTRACT FROM AUTHOR]

In this paper, we give some decompositions of triples of $\mathbb{Z}_{p^n } $ or $\mathbb{Z}_{3p^n } $ into cyclic triple systems. New constructions of difference families are given. Some infinite classes of simple cyclic triple systems are obtained from these decompositions. [ABSTRACT FROM AUTHOR]

In this paper, we prove a quantitative version of the statement that every nonempty finite subset of ℕ is a set of quadratic residues for infinitely many primes of the form [ n] with 1 ≤ c ≤ 243/205. Correspondingly, we can obtain a similar result for the case of quadratic non-residues under reasonable assumptions. These results generalize the previous ones obtained by Wright in certain aspects. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the definition of ( m, n)-regularity in Γ-semigroups. We investigate and characterize the 2-regular class of Γ-semigroups using Green's relations. Extending and generalizing the Croisot's Theory of Decomposition for Γ-semigroups, we introduce and study the absorbent and regular absorbent Γ-semigroups. We approach this problem by examining quasi-ideals using Green's relations. [ABSTRACT FROM AUTHOR]

Let M be a closed smooth manifold M, and let f: M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f. We show that if f has the C-stably average shadowing property on Λ, then Λ admits a dominated splitting. [ABSTRACT FROM AUTHOR]

For a simple digraph G, let β( G) be the size of the smallest subset X ⊆ E( G) such that G−X has no directed cycles, and let γ( G) be the number of unordered pairs of nonadjacent vertices in G. A digraph G is called k-free if G has no directed cycles of length at most k. This paper proves that β( G) ≤ 0.3819 γ( G) if G is a 4-free digraph, and β( G) ≤ 0.2679 γ( G) if G is a 5-free digraph. These improve the results of Sullivan in 2008. [ABSTRACT FROM AUTHOR]

The induced path number ρ( G) of a graph G is defined as the minimum number of subsets into which the vertex set of G can be partitioned so that each subset induces a path. Broere et al. proved that if G is a graph of order n, then $$\sqrt n \leqslant \rho \left( G \right) + \rho \left( {\bar G} \right) \leqslant \left\lceil {\tfrac{{3n}} {2}} \right\rceil$$. In this paper, we characterize the graphs G for which $$\rho \left( G \right) + \rho \left( {\bar G} \right) = \left\lceil {\tfrac{{3n}} {2}} \right\rceil$$, improve the lower bound on $$\rho \left( G \right) + \rho \left( {\bar G} \right)$$ by one when n is the square of an odd integer, and determine a best possible upper bound for $$\rho \left( G \right) + \rho \left( {\bar G} \right)$$ when neither G nor $$\bar G$$ has isolated vertices. [ABSTRACT FROM AUTHOR]

Kôpka's D-poset is a very important notion in quantum structures. In this paper the conditional probability on the Kôpka's D-posets is studied. The notion of conditional probability is introduced and the basic properties of conditional probability are proved. [ABSTRACT FROM AUTHOR]

A family ( X, B), ( X, B), ..., ( X, B) of q STS( υ)s is a λ-fold large set of STS( υ) and denoted by LSTS( υ) if every 3-subset of X is contained in exactly λ STS( υ)s of the collection. It is indecomposable and denoted by IDLSTS( υ) if there does not exist an LSTS( υ) contained in the collection for any λ′ < λ. In this paper, we show that for λ = 5, 6, there is an IDLSTS( υ) for υ ≡ 1 or 3 (mod 6) with the exception IDLSTS(7). [ABSTRACT FROM AUTHOR]

In this paper, we give a class of C*-algebras with non-stable K-group property which include the example non-simple tracial topological rank zero and stable rank two C*-algebra given by Lin and Osaka. [ABSTRACT FROM AUTHOR]

A vertex labeling f: V → ℤ of a simple graph G = ( V, E) induces two edge labelings f, f*: E → ℤ defined by f( uυ) = f( u) + f( υ) and f*( uυ) = f( u) f( υ). For each i ∈ ℤ, let υ( i) = |{ υ ∈ V: f( υ) = i}|, e( i) = |{ e ∈ E: f( e) = i}| and e*( i) = |{ e ∈ E: f*( e) = i}|. We call f friendly if | υ(0) − υ(1)| ≤ 1. The friendly index set and the product-cordial index set of G are defined as the sets {| e f(0) − e(1)|: f is friendly} and {| e*(0) − e*(1)|: f is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs. [ABSTRACT FROM AUTHOR]

Let r ≥ 1, k ≥ 2 and $$F_{m_1 , \ldots m_k ;r}$$ denote the most general definition of a friendship graph, that is, the graph of $$K_{r + m_1 } , \ldots ,K_{r + m_k }$$ meeting in a common r set, where $$K_{r + m_1 }$$ is the complete graph on r + m vertices. Clearly, $$\left| {F_{m_1 , \ldots m_k ;r} } \right| = m_1 + \cdots + m_k + r$$. Let $$\sigma \left( {F_{m_1 , \ldots m_k ;r} ,n} \right)$$ be the smallest even integer such that every n-term graphic sequence π = ( d, d, ..., d) with term sum $$\sigma \left( \pi \right) = d_1 + d_2 + \cdots + d_n \geqslant \sigma \left( {F_{m_1 , \ldots m_k ;r} ,n} \right)$$, has a realization G containing $$F_{m_1 , \ldots m_k ;r}$$ as a subgraph. In this paper, we determine $$\sigma \left( {F_{m_1 , \ldots m_k ;r} ,n} \right)$$ for n sufficiently large. [ABSTRACT FROM AUTHOR]

Let k be a positive integer. A Roman k-dominating function on a graph G is a labeling f: V ( G) → {0, 1, 2} such that every vertex with label 0 has at least k neighbors with label 2. A set { f, f, ..., f} of distinct Roman k-dominating functions on G with the property that Σ f( v) ≤ 2 for each v ∈ V (G), is called a Roman k-dominating family (of functions) on G. The maximum number of functions in a Roman k-dominating family on G is the Roman k-domatic number of G, denoted by d( G). Note that the Roman 1-domatic number d( G) is the usual Roman domatic number d( G). In this paper we initiate the study of the Roman k-domatic number in graphs and we present sharp bounds for d( G). In addition, we determine the Roman k-domatic number of some graphs. Some of our results extend those given by Sheikholeslami and Volkmann in 2010 for the Roman domatic number. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of mild solutions of a class of impulsive neutral stochastic evolution inclusions in Hilbert space in the case where the right hand side is convex or nonconvex-valued. The results are obtained by using two fixed point theorems for multivalued mappings and evolution system theory. [ABSTRACT FROM AUTHOR]

This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent. [ABSTRACT FROM AUTHOR]

defensive ( offensive) k- alliance in Γ = ( V,E) is a set S ⊆ V such that every υ in S (in the boundary of S) has at least k more neighbors in S than it has in V / S. A set X ⊆ V is defensive ( offensive) k-alliance free, if for all defensive (offensive) k-alliance S, S/ X ≠ ∅, i.e., X does not contain any defensive (offensive) k-alliance as a subset. A set Y ⊆ V is a defensive ( offensive) k-alliance cover, if for all defensive (offensive) k-alliance S, S ∩ Y ≠ ∅, i.e., Y contains at least one vertex from each defensive (offensive) k-alliance of Γ. In this paper we show several mathematical properties of defensive (offensive) k-alliance free sets and defensive (offensive) k-alliance cover sets, including tight bounds on their cardinality. [ABSTRACT FROM AUTHOR]

In this paper, parabolic Marcinkiewicz integral operators along surfaces on the product domain ℝ × ℝ ( n,m ⩾ 2) are introduced. L bounds of such operators are obtained under weak conditions on the kernels. [ABSTRACT FROM AUTHOR]

In the present paper we propose a new hierarchical management scheme within suitable extensions of 2-adic numbers, in which the subfields are treated as classes, and the communications are realized by computation on elliptic curves. The security of our system is much stronger than that of the traditional public key cryptographic systems. [ABSTRACT FROM AUTHOR]

Let G0 and G1 be two graphs with the same vertices. The new graph G( G0, G1; M) is a graph with the vertex set V ( G0)∪ V( G1) and the edge set E( G0)∪ E( G1)∪ M, where M is an arbitrary perfect matching between the vertices of G0 and G1, i.e., a set of cross edges with one endvertex in G0 and the other endvertex in G1. In this paper, we will show that if G0 and G1 are f-fault q-panconnected, then for any f ≥ 2, G( G0, G1; M) is ( f + 1)-fault ( q + 2)-panconnected. [ABSTRACT FROM AUTHOR]

Each Tribonacci sequence starting with an arbitrary triple of integers is periodic modulo m for any modulus m > 1. For a given m, the mapping between the set S of all m3 triples of initial values and the set of their coresponding periods define a partition of the set S. In this paper we shall investigate some basic questions related to these partitions from the point of view of enumerative combinatorics. [ABSTRACT FROM AUTHOR]

In this paper, some topological concepts and definitions are generalized to cone metric spaces. It is proved that every cone metric space is first countable topological space and that sequentially compact subsets are compact. Also, we define diametrically contractive mappings and asymptotically diametrically contractive mappings on cone metric spaces to obtain some fixed point theorems by assuming that our cone is strongly minihedral. [ABSTRACT FROM AUTHOR]

Let P be a finite group and denote by ω( P) the set of its element orders. P is called κ-recognizable by the set of its element orders if for any finte group G with ω( G) = ω( P) there are, up to isomorphism, κ finite groups G such that G ≃ P. In this paper we will prove that the group L p(3), where p > 3 is a prime number, is at most 2-recognizable. [ABSTRACT FROM AUTHOR]

In this paper, we prove several results concerning meromorphic functions f and g of hyperorder less than one such that f ( j) and g ( j) have the same zeros and poles for j = 0, 1, 2. We provide some examples to show that our results are sharp. [ABSTRACT FROM AUTHOR]

The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the centered L-discrepancy to assess the optimal foldover plans was studied for four-level design. A new analytical expression and a new lower bound of the centered L-discrepancy for fourlevel combined design under a general foldover plan are respectively obtained. A necessary condition for the existence of an optimal foldover plan meeting this lower bound was described. An algorithm for searching the optimal four-level foldover plans is also developed. Illustrative examples are provided, where numerical studies lend further support to our theoretical results. These results may help to provide some powerful and efficient algorithms for searching the optimal four-level foldover plans. [ABSTRACT FROM AUTHOR]

In this paper, we present some modules over the rank–three quantized Weyl algebra, which are closely related to modules over some vertex algebras. The isomorphism classes among these modules are also determined. [ABSTRACT FROM AUTHOR]

The relation among transitivity, indecomposability and ℤ-transitivity is discussed. It is shown that for a non-wandering system (each point is non-wandering), indecomposability is equivalent to transitivity, and for the dynamical systems without isolated points, ℤ-transitivity and transitivity are equivalent. Besides, a new transitive level as weak transitivity is introduced and some equivalent conditions of Devaney's chaos are given by weak transitivity. Moreover, it is proved that both d-shadowing property and d-shadowing property imply weak transitivity. [ABSTRACT FROM AUTHOR]

Let $\mathbb{F}_p $ be the finite field of p elements with p prime. If A is a subset of $\mathbb{F}_p $ and g is an element of $\mathbb{F}_p^* $ with order ν, then . [ABSTRACT FROM AUTHOR]

We show that the Aubry sets, the Mañé sets and the barrier functions are the same for two commuting time-periodic Tonelli Hamiltonians. [ABSTRACT FROM AUTHOR]

We show that many Kadison-Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified. [ABSTRACT FROM AUTHOR]

Let T be a triangulated category and ξ a proper class of triangles. Some basics properties and diagram lemmas are proved directly from the definition of ξ. [ABSTRACT FROM AUTHOR]

Let 0 ≤ α < n, Ω be a rough kernel, and let A have derivatives of order m−1 in $$C\dot BMO^{q,\mu _2 }$$ with m ≥ 2. We consider a class of generalized commutators TΩ,αA of Cohen-Gosselin type, and obtain the boundedness of TΩ,αA from the central Morrey spaces $$\dot E^{p,\mu _1 }$$ to $$\dot E^{r,\lambda }$$ for λ = µ 1 + µ 2 + α/n and 1/ r = 1/ p + 1/ q − α/n. [ABSTRACT FROM AUTHOR]

A homeomorphism w = f( z) of a domain D is called a locally quasiconformal mapping, if for each subdomain D′ of D with $$\overline {D'} \subset D$$, the restriction of f( z) on D′ is a quasiconformal mapping. We give some conditions for a measurable function µ( z) on the unit disc to be the complex dilatation of a locally quasiconformal mapping f which can be homeomorphically extended to the closed unit disc. [ABSTRACT FROM AUTHOR]

A vertex x in a graph G strongly resolves a pair of vertices v,w if there exists a shortest x − w path containing v or a shortest x − v path containing w in G. A set of vertices S ⊆ V ( G) is a strong resolving set of G if every pair of distinct vertices of G is strongly resolved by some vertex in S. The strong metric dimension of G, denoted by sdim( G), is the minimum cardinality over all strong resolving sets of G. For a connected graph G of order n ≥ 2, we characterize G such that sdim( G) equals 1, n − 1, or n − 2, respectively. We give a Nordhaus-Gaddum-type result for the strong metric dimension of a graph and its complement: for a graph G and its complement $$\bar G$$, each of order n ≥ 4 and connected, we show that $$2 \leqslant sdim\left( G \right) + sdim\left( {\bar G} \right) \leqslant 2\left( {n - 2} \right)$$. It is readily seen that $$sdim\left( G \right) + sdim\left( {\bar G} \right) = 2$$ if and only if n = 4; we show that, when G is a tree or a unicyclic graph, $$sdim\left( G \right) + sdim\left( {\bar G} \right) = 2\left( {n - 2} \right)$$ if and only if n = 5 and $$G \cong \bar G \cong C_5$$, the cycle on five vertices. For connected graphs G and $$\bar G$$ of order n ≥ 5, we show that $$3 \leqslant sdim\left( G \right) + sdim\left( {\bar G} \right) \leqslant 2\left( {n - 3} \right)$$ if G is a tree; we also show that $$4 \leqslant sdim\left( G \right) + sdim\left( {\bar G} \right) \leqslant 2\left( {n - 3} \right)$$ if G is a unicyclic graph of order n ≥ 6. Furthermore, we characterize graphs G satisfying $$sdim\left( G \right) + sdim\left( {\bar G} \right) = 2\left( {n - 3} \right)$$ when G is a tree or a unicyclic graph. [ABSTRACT FROM AUTHOR]

By means of Mawhin's continuation theorem and some analysis methods, the existence of 2 kT-periodic solutions is studied for a class of neutral functional differential equations, and then a homoclinic solution is obtained as a limit of a certain subsequence of the above periodic solutions set. [ABSTRACT FROM AUTHOR]

Denote by SFin( v) the set of all integer pairs ( t, s) for which there exist three symmetric Latin squares of order v on the same set having fine structure ( t, s). We completely determine the set SFin(2 n) for any integer n ≥ 5. [ABSTRACT FROM AUTHOR]

By constructing certain maps, this note completes the answer of the question: For which closed orientable 3-manifold N, is the set of mapping degrees D( M,N) finite for any closed orientable 3-manifold M? [ABSTRACT FROM AUTHOR]

set S of vertices in a graph G = ( V, E) without isolated vertices is a total outer-connected dominating set (TCDS) of G if S is a total dominating set of G and G[ V − S] is connected. The total outer-connected domination number of G, denoted by γ( G), is the minimum cardinality of a TCDS of G. For an arbitrary graph without isolated vertices, we obtain the upper and lower bounds on γ( G) + γ( $$ \bar G $$), and characterize the extremal graphs achieving these bounds. [ABSTRACT FROM AUTHOR]