Authors:Indira P. Debnath; S. K. Gupta Abstract: Abstract In this article, we have introduced a new class of higher-order \((K\times Q)\) -F-type I functions. Further, we have formulated two higher-order dual models, Wolfe and Schaible type, for a multiobjective fractional programming problem over arbitrary cones and proved appropriate duality relations under the higher-order \((K\times Q)\) -F-type I assumption. Nontrivial examples are also discussed to validate the weak duality results obtained in the paper. PubDate: 2017-09-07 DOI: 10.1007/s40840-017-0542-4

Authors:Aibo Liu; Changchun Liu Abstract: Abstract In this paper, we study the coupling of the non-Newtonian Navier–Stokes equation and the oil–water–surfactant equation which stand for a model of a multi-phase incompressible dipolar viscous non-Newtonian fluid under shear. Based on Galerkin approximation and Simon’s compactness results, we obtain the existence and uniqueness of weak solutions of the system. PubDate: 2017-09-01 DOI: 10.1007/s40840-017-0543-3

Authors:Jingjing Cui; Guohua Peng; Quan Lu; Zhengge Huang Abstract: Abstract In this paper, several new estimates of the minimum H-eigenvalue for weakly irreducible nonsingular \(\mathcal {M}\) -tensors, including the new Brauer-type estimates and the new S-type estimates, are derived. It is proved that the new estimates are tighter than some existing ones and numerical examples are given to verify this fact. The other main result of this paper is to provide a sharper Ky Fan-type theorem which is better than the original Ky Fan theorem for the nonsingular \(\mathcal {M}\) -tensors. PubDate: 2017-08-31 DOI: 10.1007/s40840-017-0544-2

Authors:Qiao Liu Abstract: Abstract In this paper, we consider the regularity of weak solutions to the 3D incompressible micropolar fluid equations. It is proved that if the one directional derivative of the pressure, say \(\partial _{3}P\) , satisfies $$\begin{aligned} \partial _{3}P \in L^{\beta }(0,T;L^{\alpha }(\mathbb {R}^{3})) \quad \text { with } \frac{2}{\beta }+\frac{3}{\alpha }\le 2, \frac{3}{2}\le \alpha <\infty , \end{aligned}$$ then the corresponding weak solution \((u,\omega )\) is regular on [0, T]. PubDate: 2017-08-31 DOI: 10.1007/s40840-017-0545-1

Authors:Peyman Niroomand; Farangis Johari; Mohsen Parvizi; Francesco G. Russo Abstract: Abstract We prove a theorem of splitting for the nonabelian tensor product \(L \otimes N\) of a pair (L, N) of Lie algebras L and N in terms of its diagonal ideal \(L \square N\) and of the nonabelian exterior product \(L \wedge N\) . A similar circumstance was described few years ago in the special case \(N=L\) . The interest is due to the fact that the size of \(L \square N\) influences strongly the structure of \(L \otimes N\) . PubDate: 2017-08-30 DOI: 10.1007/s40840-017-0540-6

Authors:L. M. Camacho; I. A. Karimjanov; M. Ladra; B. A. Omirov Abstract: Abstract In this paper we construct a minimal faithful representation of the \((2m+2)\) -dimensional complex general Diamond Lie algebra, \(\mathfrak {D}_m(\mathbb {C})\) , which is isomorphic to a subalgebra of the special linear Lie algebra \(\mathfrak {sl}(m+2,\mathbb {C})\) . We also construct a faithful representation of the real general Diamond Lie algebra \(\mathfrak {D}_m\) which is isomorphic to a subalgebra of the special symplectic Lie algebra \(\mathfrak {sp}(2m+2,\mathbb {R})\) . Furthermore, we describe Leibniz algebras with corresponding \((2m+2)\) -dimensional real general Diamond Lie algebra \(\mathfrak {D}_m\) and such that the ideal generated by the squares of elements provides a faithful representation of \(\mathfrak {D}_m\) . PubDate: 2017-08-30 DOI: 10.1007/s40840-017-0541-5

Authors:Yong-Hoon Lee; Xianghui Xu Abstract: Abstract We study the homogeneous Dirichlet boundary value problem of a singular \((p_1,p_2)\) -Laplacian system with multiparameters. The global structure of multiparameters for existence, nonexistence and multiplicity of positive solutions can be obtained. Proofs are mainly based on the upper and lower solution method, the fixed point index theory in a cone, generalized Picone identity, global continuum theorem and degree arguments. As an application, we can establish the global result of the positive radial and decaying solutions for a class of quasilinear elliptic systems in exterior domains. PubDate: 2017-08-21 DOI: 10.1007/s40840-017-0539-z

Authors:Cheng Yuan; Cezhong Tong Abstract: Abstract We show that a class of logarithmic Carleson measures is the Carleson measure for the Besov–Sobolev space in the unit ball of \(\mathbb {C}^n\) . PubDate: 2017-08-21 DOI: 10.1007/s40840-017-0538-0

Authors:Dongdong Qin; Fangfang Liao; Yubo He; Xianhua Tang Abstract: Abstract Employing the minimax method incorporated with invariant sets of descending flow, we prove some results about the existence of sign-changing solutions for a class of Kirchhoff-type equation. In particular, a sequence of high-energy sign-changing solutions is obtained. PubDate: 2017-08-17 DOI: 10.1007/s40840-017-0534-4

Authors:Sokhobiddin Akhatkulov; Mohd. Salmi Md. Noorani Abstract: Abstract Let \(f_1\) and \(f_2\) be two orientation-preserving circle homeomorphisms with the same irrational rotation number \(\rho \) and each with a single break point \(b_1\) and \(b_2\) , respectively. Suppose that the derivatives \(Df_1\) and \(Df_2\) satisfy a certain Zygmund condition except break points and the jumps \(\sigma (b_1)=\frac{Df_1(b_1-0)}{Df_1(b_1+0)}\) , \(\sigma (b_2)=\frac{Df_2(b_2-0)}{Df_1(b_2+0)}\) do not coincide. Then the map \(\psi \) conjugating \(f_1\) and \(f_2\) is singular. PubDate: 2017-08-09 DOI: 10.1007/s40840-017-0535-3

Authors:Jihong Zhao Abstract: Abstract In this paper, we study the three-dimensional dissipative fluid-dynamical model, which is a strongly coupled nonlinear nonlocal system characterized by the Navier–Stokes/Poisson–Nernst–Planck system. It is proved that the local smooth solution can be continued beyond the time T provided that the vorticity \(\omega \) satisfies $$\begin{aligned} \int _{0}^{T}\frac{\Vert \omega (\cdot ,t)\Vert _{\dot{B}^{-\alpha }_{\infty ,\infty }}^{\frac{2}{2-\alpha }}}{1+\ln \left( e+\Vert \omega (\cdot ,t)\Vert _{\dot{B}^{-\alpha }_{\infty ,\infty }}\right) }\mathrm{d}t<\infty \quad \text {for} \,\, 0<\alpha <2. \end{aligned}$$ Moreover, two regularity criteria for the marginal cases \(\alpha =0\) and \(\alpha =2\) are also established, respectively. PubDate: 2017-08-07 DOI: 10.1007/s40840-017-0537-1

Authors:Fengwei Li; Qingfang Ye; Juan Rada Abstract: Abstract The augmented Zagreb index (AZI index) of a graph \(G=(V,E)\) , which is a valuable predictive index in the study of the heat of formation in octanes and heptanes, is defined as $$\begin{aligned} \hbox {AZI}(G)=\sum _{uv\in E(G)}\left( \frac{d_{u}d_{v}}{d_{u}+d_{v}-2}\right) ^{3}{,} \end{aligned}$$ where \(d_{u}\) and \(d_{v}\) are the degrees of the terminal vertices u and v of edge uv, respectively. In this paper, we give the expressions for computing the augmented Zagreb indices of fluoranthene-type benzenoid systems, and we determine the extremal values of augmented Zagreb index in f-benzenoid systems with h hexagons. Especially, we give the extremal values of augmented Zagreb index in cata-catacondensed fluoranthene-type benzenoid systems with h hexagons. PubDate: 2017-08-06 DOI: 10.1007/s40840-017-0536-2

Authors:Ivy Carol B. Lomerio; Editha C. Jose Abstract: Abstract In this paper, we consider a time-dependent semilinear parabolic problem modeling the heat diffusion in a two-component composite. The domain has an \(\varepsilon \) -periodic interface, where the flux of the temperature is proportional to the jump of the temperature field by a factor of order \(\varepsilon ^\gamma \) . We determine the existence and uniqueness of the weak solution of the problem and use the periodic unfolding method to find the homogenization results. PubDate: 2017-08-05 DOI: 10.1007/s40840-017-0532-6

Authors:Hua Wang; Cai Wu; Junjie Huang Abstract: Abstract In this note, we investigate the existence of the Drazin inverse for the anti-triangular operator matrix \(M= \left( {\begin{matrix} A &{} B \\ C &{} 0 \end{matrix}}\right) \) with \(A^2=A\) and \( CAB=0\) , and the explicit representation of \(M^D\) is given in term of \(A, A^D, B,C \) and \((CB)^D\) . In addition, it is shown that \(\mathrm {ind} (M)\le 2 \ \mathrm {ind} (CB)+2\) , which is important to prove the existence and representation of the Drazin inverse for M. PubDate: 2017-08-02 DOI: 10.1007/s40840-017-0533-5

Authors:Zaihong Jiang; Mingxuan Zhu Abstract: Abstract This paper deals with the asymptotic behavior, regularity criterion and global existence for the generalized Navier–Stokes equations. Firstly, an upper bound for the difference between the solution of our equation and the generalized heat equation in \(L^2\) space is proved. We optimize the upper bound of decay for the solutions and obtain the algebraic lower bound by using Fourier splitting method. Then, a new scaling invariant regularity criterion on the fractional derivative is established. Finally, global existence is obtained provided that the initial data are small enough. PubDate: 2017-08-01 DOI: 10.1007/s40840-017-0531-7

Authors:M. Afkhami; S. Bahrami; K. Khashyarmanesh Abstract: Abstract Let \((P,\le )\) be a partially ordered set with a least element 0. The regular digraph of ideals of P, denoted by \(\overrightarrow{\Gamma }(P)\) , is a digraph whose vertex-set is the set of all nontrivial ideals of P and, for every two distinct vertices I and J, there is an arc from I to J whenever I contains a nonzero zero-divisor on J. Also, the undirected regular graph of ideals of P, denoted by \(\Gamma (P)\) , is a graph with all nontrivial ideals of P being the vertex-set, and for two distinct vertices I and J, I is adjacent to J if and only if I contains a nonzero zero-divisor on J or J contains a nonzero zero-divisor on I. In this paper, we study some basic properties of \(\overrightarrow{\Gamma }(P)\) . Also we completely characterize all posets P with planar regular graph. PubDate: 2017-07-31 DOI: 10.1007/s40840-017-0530-8

Authors:László Horváth; Đilda Pečarić; Josip Pečarić Abstract: Abstract The Jensen’s inequality plays a crucial role to obtain inequalities for divergences between probability distributions. In this paper, we introduce a new functional, based on the f-divergence functional, and then, we obtain some estimates for the new functional, the f-divergence and the Rényi divergence by applying a cyclic refinement of the Jensen’s inequality. Some inequalities for Rényi and Shannon entropies are obtained too. Zipf–Mandelbrot law is used to illustrate the results. PubDate: 2017-07-28 DOI: 10.1007/s40840-017-0526-4

Authors:Leilei Wei Abstract: Abstract In this paper, the numerical approximation of the distributed-order time-fractional reaction–diffusion equation is proposed and analyzed. Based on the finite difference method in time and local discontinuous Galerkin method in space, we develop a fully discrete scheme and prove that the scheme is unconditionally stable and convergent with order \(O\left( h^{k+\frac{1}{2}}+(\Delta t)^2+\Delta \alpha ^4\right) \) , where \(h,k,\Delta t\) and \(\Delta \alpha \) are the space-step size, piecewise polynomial degree, time-step size, step size in distributed-order variable, respectively. Numerical examples are presented to show the effectiveness and the accuracy of the numerical scheme. PubDate: 2017-07-27 DOI: 10.1007/s40840-017-0525-5

Authors:Hongbo Hua; Zhengke Miao Abstract: Abstract Classical topological indices, such as Zagreb indices ( \(M_{1}\) and \(M_2\) ) and the well-studied eccentric connectivity index ( \(\xi ^{c}\) ) directly or indirectly consider the total contribution of all edges in a graph. By considering the total degree sum of all non-adjacent vertex pairs in a graph, Ashrafi et al. (Discrete Appl Math 158:1571–1578, 2010) proposed two new Zagreb-type indices, namely the first Zagreb coindex ( \(\overline{M}_{1}\) ) and second Zagreb coindex ( \(\overline{M}_{2}\) ), respectively. Motivated by Ashrafi et al., we consider the total eccentricity sum of all non-adjacent vertex pairs, which we call the eccentric connectivity coindex ( \(\overline{\xi }^{c}\) ), of a connected graph. In this paper, we study the extremal problems of \(\overline{\xi }^{c}\) for connected graphs of given order, connected graphs of given order and size, and the trees, unicyclic graphs, bipartite graphs containing cycles and triangle-free graphs of given order, respectively. Additionally, we establish various lower bounds for \(\overline{\xi }^{c}\) in terms of several other graph parameters. PubDate: 2017-07-27 DOI: 10.1007/s40840-017-0528-2

Authors:Leyla Bugay; Melek Yağcı; Hayrullah Ayık Abstract: Abstract For \(n\in \mathbb {N}\) , let \(O_{n}\) be the semigroup of all order-preserving transformations on the finite chain \(X_{n}=\{1,\ldots ,n\}\) , under its natural order. For any non-empty subset A of \(X_{n}\) , let \(O_{n}(A)\) and \(O_{n}^+(A)\) be the subsemigroups of all order-preserving and A-decreasing, and of all order-preserving and A-increasing transformations on \(X_{n}\) , respectively. In this paper we obtain formulae for the number of elements and for the number of idempotents in \(O_{n}(A)\) . Moreover, we show that \(O_{n}(A)\) contains a zero element if and only if \(1\in A\) , and then we obtain the number of nilpotents in \(O_{n}(A)\) when \(1\in A\) . PubDate: 2017-07-26 DOI: 10.1007/s40840-017-0529-1