Abstract: A graph is 1-planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. A plane graph with near independent crossings (say NIC-planar graph) is a 1-planar graph with the restriction that for any two crossings the four crossed edges are incident with at most one common vertex. The full characterization of NIC-planar complete and complete multipartite graphs is given in this paper.

Abstract: A graph G is supereulerian if G has a spanning eulerian subgraph. Boesch et al. [J. Graph Theory, 1, 79–84 (1977)] proposed the problem of characterizing supereulerian graphs. In this paper, we prove that any 3-edge-connected graph with at most 11 edge-cuts of size 3 is supereulerian if and only if it cannot be contractible to the Petersen graph. This extends a former result of Catlin and Lai [J. Combin. Theory, Ser. B, 66, 123–139 (1996)].

Abstract: We study complex interpolation of weighted Besov and Lizorkin-Triebel spaces. The used weights w 0, w 1 are local Muckenhoupt weights in the sense of Rychkov. As a first step we calculate the Calderon products of associated sequence spaces. Finally, as a corollary of these investigations, we obtain results on complex interpolation of radial subspaces of Besov and Lizorkin-Triebel spaces on ℝ d .

Abstract: In this paper, we study Tingley’s problem on symmetric absolute normalized norms on ℝ2. We construct new methods for Tingley’s problem on two-dimensional spaces by using isosceles orthogonality, which does not make use of the notion of natural extension. Furthermore, using our methods, several sufficient conditions for Tingley’s problem on symmetric absolute normalized norms on ℝ2 are given. As applications, we present various new examples including the two-dimensional Lorentz sequence space d (2)(ω, q) and its dual d (2)(ω, q)* by simple arguments.

Abstract: In this paper, we analyze the problem of constructing a surface pencil from a given spacelike (timelike) line of curvature. Using the Frenet frame of the given line of curvature in Minkowski 3-space, we express the surface pencil as a linear combination of this frame and derive the necessary and sufficient conditions for the coefficients to satisfy the line of curvature requirement. We illustrate this method by presenting some examples.

Abstract: We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-Paley-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as, Calderon-Zygmund operators for all possible values of type parameter λ in this context. This extends results existing in the literature, but being justified only for a restricted range of λ.

Abstract: In this paper, we consider the family of generalized Petersen graphs P(n, 4). We prove that the metric dimension of P(n, 4) is 3 when n ≡ 0 (mod 4), and is 4 when n = 4k + 3 (k is even). For n ≡ 1,2 (mod 4) and n = 4k + 3 (k is odd), we prove that the metric dimension of P(n, 4) is bounded above by 4. This shows that each graph of the family of generalized Petersen graphs P(n, 4) has constant metric dimension.

Abstract: We prove that if D is a domain in ℂ, α > 1 and C > 0, then the family F of functions f meromorphic in D such that $$\frac{{\left| {f'(z)} \right|}} {{1 + \left| {f(z)} \right|^\alpha }} > C for every z \in D$$ is normal in D. For α = 1, the same assumptions imply quasi-normality but not necessarily normality.

Abstract: An antimagic labeling of a graph with q edges is a bijection from the set of edges to the set of positive integers {1, 2, ..., q} such that all vertex weights are pairwise distinct, where the vertex weight of a vertex is the sum of the labels of all edges incident with that vertex. A graph is antimagic if it has an antimagic labeling.

Abstract: To decide when a graph is Gromov hyperbolic is, in general, a very hard problem. In this paper, we solve this problem for the set of short graphs (in an informal way, a graph G is r-short if the shortcuts in the cycles of G have length less than r): an r-short graph G is hyperbolic if and only if S 9r (G) is finite, where S R (G):= sup{L(C): C is an R-isometric cycle in G} and we say that a cycle C is R-isometric if d C (x, y) ≤ d G (x, y) + R for every x, y ∈ C.

Abstract: In this paper, we consider numerical and trigonometric series with a very general monotonicity condition. First, a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting. In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.

Abstract: For real parameters α and β such that 0 ≤ α < 1 < β, we denote by S(α, β) the class of normalized analytic functions which satisfy the following two-sided inequality: $$\alpha < \Re \left( {\frac{{zf'(z)}} {{f(z)}}} \right) < \beta ,z \in \mathbb{U} $$ where \(\mathbb{U}\) denotes the open unit disk. We find a sufficient condition for functions to be in the class S(α, β) and solve several radius problems related to other well-known function classes.

Abstract: Let a, b, k, r be nonnegative integers with 1 ≤ a ≤ b and r ≥ 2. Let G be a graph of order n with $n > \tfrac{{(a + b)(r(a + b) - 2) + ak}} {a} $ . In this paper, we first show a characterization for all fractional (a, b, k)-critical graphs. Then using the result, we prove that G is all fractional (a, b, k)-critical if $\delta (G) \geqslant \tfrac{{(r - 1)b^2 }} {a} + k $ and $|N_G (x_1 ) \cup N_G (x_2 ) \cup \cdots \cup N_G (x_r )| \geqslant \tfrac{{bn + ak}} {{a + b}} $ for any independent subset {x 1, x 2, …, x r } in G. Furthermore, it is shown that the lower bound on the condition $|N_G (x_1 ) \cup N_G (x_2 ) \cup \cdots \cup N_G (x_r )| \geqslant \tfrac{{bn + ak}} {{a + b}} $ is best possible in some sense, and it is an extension of Lu’s previous result.

Abstract: The heat kernel in the setting of classical Fourier-Bessel expansions is defined by an oscillatory series which cannot be computed explicitly. We prove qualitatively sharp estimates of this kernel. Our method relies on establishing a connection with a situation of expansions based on Jacobi polynomials and then transferring known sharp bounds for the related Jacobi heat kernel.

Abstract: In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the sufficient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is effective.

Abstract: In this paper, the perturbations of the Moore-Penrose metric generalized inverses of linear operators in Banach spaces are described. The Moore-Penrose metric generalized inverse is homogeneous and nonlinear in general, and the proofs of our results are different from linear generalized inverses. By using the quasi-additivity of Moore-Penrose metric generalized inverse and the theorem of generalized orthogonal decomposition, we show some error estimates of perturbations for the single-valued Moore-Penrose metric generalized inverses of bounded linear operators. Furthermore, by means of the continuity of the metric projection operator and the quasi-additivity of Moore-Penrose metric generalized inverse, an expression for Moore-Penrose metric generalized inverse is given.

Abstract: In this paper, by introducing the space with weak mixed norms, weak type estimates of two kinds of multilinear fractional Hausdorff operators {ie1407-1} and {ie1407-2} on Lebesgue spaces are shown. By virtue of Marcinkiewicz interpolation, strong type estimates of these two operators on Lebesgue spaces are also obtained. Our methods shed some new light on dealing with the case of non-radial function Φ.

Abstract: In this paper, we give a relationship between projective generators (resp., injective cogenerators) in the category of R-modules and the counterparts in the category of complexes of R-modules. As a consequence, we get that complexes of W-Gorenstein modules are actually Open image in new window-Gorenstein complexes whenever W is a subcategory of R-modules satisfying W ⊥ W, where Open image in new window is the subcategory of exact complexes with all cycles in W. We also study when all cycles of a Open image in new window-Gorenstein complexes are W-Gorenstein modules.

Abstract: It is established that all even positive integers up to N but at most O(N15/16+ɛ) exceptions can be expressed in the form p12 + p23 + p34 + p45, where p1, p2, p3 and p4 are prime numbers.

Abstract: 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 $$bind(G) = min\left\{ {\frac{{\left| {N_G (X)} \right|}} {{\left| X \right|}}: ot 0 e X \subseteq V(G),N_G (X) e V(G)} \right\}.$$ In this paper, it is proved that a graph G is fractional ID-k-factor-critical if n ≥ 6k − 9 and bind(G) \(> \frac{{(3k - 1)(n - 1)}} {{kn - 2k + 2}}\).

Abstract: In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literatures on this topic.

Abstract: A pseudo-real Riemann surface admits anticonformal automorphisms but no anticonformal involution We obtain the classification of actions and groups of automorphisms of pseudo-real Riemann surfaces of genera 2, 3 and 4 For instance the automorphism group of a pseudo-real Riemann surface of genus 4 is either C 4 or C 8 or the Frobenius group of order 20, and in the case of C 4 there are exactly two possible topological actions Let M be the set of surfaces in the moduli space M corresponding to pseudo-real Riemann surfaces We obtain the equisymmetric stratification of M for genera g = 2, 3, 4, and as a consequence we have that M is connected for g = 2, 3 but M has three connected components

Abstract: Let X be a space of homogenous type and φ: X × [0,∞) → [0,∞) be a growth function such that φ (·, t) is a Muckenhoupt weight uniformly in t and φ(x, ·) an Orlicz function of uniformly upper type 1 and lower type p ∈ (0, 1]. In this article, the authors introduce a new Musielak-Orlicz BMO-type space BMO φ (χ) associated with the generalized approximation to the identity, give out its basic properties and establish its two equivalent characterizations, respectively, in terms of the spaces BMO ,max φ (χ) and $\widetilde{BMO}_A^\phi (\chi )$ . Moreover, two variants of the John-Nirenberg inequality on BMO φ (χ) are obtained. As an application, the authors further prove that the space $BMO_{\sqrt \Delta }^\phi (\mathbb{R}^n )$ , associated with the Poisson semigroup of the Laplace operator Δ on ℝ n , coincides with the space $BMO^\phi (\mathbb{R}^n )$ introduced by Ky.

Abstract: In this article, we prove some strong and weak convergence theorems for quasi-nonexpansive multivalued mappings in Banach spaces. The iterative process used is independent of Ishikawa iterative process and converges faster. Some examples are provided to validate our results. Our results extend and unify some results in the contemporary literature.

Abstract: In this paper, we investigate the general solution and the Hyers-Ulam stability of the following mixed functional equation $$f(2x + y) + f(2x - y) = 2f(2x) + 2f(x + y) + 2f(x - y) - 4f(x) - f(y) - f( - y)$$ deriving from additive, quadratic and cubic mappings on Banach spaces.

Abstract: This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called “Acquistapace-Terreni” conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.

Abstract: The augmented Lagrangian method is a classical method for solving constrained optimization. Recently, the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive sensing and low rank matrix optimization problems. However, most Lagrangian methods use first order information to update the Lagrange multipliers, which lead to only linear convergence. In this paper, we study an update technique based on second order information and prove that superlinear convergence can be obtained. Theoretical properties of the update formula are given and some implementation issues regarding the new update are also discussed.

Abstract: We study blow-up, global existence and ground state solutions for the N-coupled focusing nonlinear Schrodinger equations. Firstly, using the Nehari manifold approach and some variational techniques, the existence of ground state solutions to the equations (CNLS) is established. Secondly, under certain conditions, finite time blow-up phenomena of the solutions is derived. Finally, by introducing a refined version of compactness lemma, the L 2 concentration for the blow-up solutions is obtained.

Abstract: In this work, we give a complete classification of spherical dihedral f-tilings when the prototiles are two noncongruent isosceles triangles with certain adjacency pattern. As it will be shown, this class is composed by two discrete families denoted by {ieɛ} m , m ≥ 2, m ∈ ℕ, F k , k ≥ 4, k ∈ ℕ and two sporadic tilings denoted by G and H.