DSpace collection: 第47卷第3期
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TWIN SIGNED ROMAN DOMINATION NUMBERS IN DIRECTED GRAPHS
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109357
title: TWIN SIGNED ROMAN DOMINATION NUMBERS IN DIRECTED GRAPHS abstract: Let DD be a finite simple digraph with vertex set V(D)V(D) and arc set A(D)A(D). A twin signed Roman dominating function (TSRDF) on the digraph DD is a function f:V(D)→{−1,1,2}f:V(D)→{−1,1,2} satisfying the conditions that (i) ∑x∈N−[v]f(x)≥1∑x∈N−[v]f(x)≥1 and ∑x∈N+[v]f(x)≥1∑x∈N+[v]f(x)≥1 for each v∈V(D)v∈V(D), where N−[v]N−[v] (resp. N+[v]N+[v]) consists of vv and all in-neighbors (resp. out-neighbors) of vv, and (ii) every vertex uu for which f(u)=−1f(u)=−1 has an in-neighbor vv and an out-neighbor ww for which f(v)=f(w)=2f(v)=f(w)=2. The weight of an TSRDF ff is ω(f)=∑v∈V(D)f(v)ω(f)=∑v∈V(D)f(v). The twin signed Roman domination number γ∗sR(D)γsR∗(D) of DD is the minimum weight of an TSRDF on DD. In this paper, we initiate the study of twin signed Roman domination in digraphs and we present some sharp bounds on γ∗sR(D)γsR∗(D). In addition, we determine the twin signed Roman domination number of some classes of digraphs.
<br>Tue, 17 Jan 2017 01:46:51 GMTINEQUALITIES FOR SOME CLASSICAL INTEGRAL TRANSFORMS
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109356
title: INEQUALITIES FOR SOME CLASSICAL INTEGRAL TRANSFORMS abstract: By using a form of the Cauchy-Bunyakovsky-Schwarz inequality, we establish new inequalities for some classical integral transforms such as Laplace transform,Fourier transform, Fourier cosine transform, Fourier sine transform, Mellin transform and Hankel transform.
<br>Tue, 17 Jan 2017 01:44:58 GMTON CERTAIN INTEGRAL FORMULAS INVOLVING THE PRODUCT OF BESSEL FUNCTION AND JACOBI POLYNOMIAL
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109355
title: ON CERTAIN INTEGRAL FORMULAS INVOLVING THE PRODUCT OF BESSEL FUNCTION AND JACOBI POLYNOMIAL abstract: In the present paper, we establish some interesting integrals involving the product of Bessel function of the first kind with Jacobi polynomial, which are expressed in terms of Kampe de Feriet and Srivastava and Daoust functions. Some other integrals involving the product of Bessel (sine and cosine) function with ultraspherical polynomial, Gegenbauer polynomial, Tchebicheff polynomial, and Legendre polynomial are also established as special cases of our main results. Further, we derive an interesting connection between Kampe de Feriet and Srivastava and Daoust functions.
<br>Tue, 17 Jan 2017 01:43:13 GMTQUENCHING PROBLEMS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM WITH SINGULAR BOUNDARY OUTFLUX
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109354
title: QUENCHING PROBLEMS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM WITH SINGULAR BOUNDARY OUTFLUX abstract: In this paper, we study two quenching problems for the following semilinear reaction-diffusion system:
ut=uxx+(1−v)−p1,0<x<1, 0<t<T,ut=uxx+(1−v)−p1,0<x<1, 0<t<T,
vt=vxx+(1−u)−p2,0<x<1, 0<t<T,vt=vxx+(1−u)−p2,0<x<1, 0<t<T,
ux(0,t)=0, ux(1,t)=−v−q1(1,t), 0<t<T,ux(0,t)=0, ux(1,t)=−v−q1(1,t), 0<t<T,
vx(0,t)=0, vx(1,t)=−u−q2(1,t), 0<t<T,vx(0,t)=0, vx(1,t)=−u−q2(1,t), 0<t<T,
u(x,0)=u0(x)<1,v(x,0)=v0(x)<1, 0≤x≤1,u(x,0)=u0(x)<1,v(x,0)=v0(x)<1, 0≤x≤1,
where p1,p2,q1,q2p1,p2,q1,q2 are positive constants and u0(x),v0(x)u0(x),v0(x) are positive smooth functions. We firstly get a local exisence result for this system. In the first problem, we show that quenching occurs in finite time, the only quenching point is x=0x=0 and (ut,vt)(ut,vt) blows up at the quenching time under the certain conditions. In the second problem, we show that quenching occurs in finite time, the only quenching point is x=1x=1 and (ut,vt)(ut,vt)blows up at the quenching time under the certain conditions.
<br>Tue, 17 Jan 2017 01:40:56 GMTHERMITE-HADAMARD TYPE INEQUALITIES FOR (P1,H1)-(P2,H2)-CONVEX FUNCTIONS ON THE CO-ORDINATES
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109353
title: HERMITE-HADAMARD TYPE INEQUALITIES FOR (P1,H1)-(P2,H2)-CONVEX FUNCTIONS ON THE CO-ORDINATES abstract: In this paper, we establish some Hermite-Hadamard type inequalities for (p1,h1)(p1,h1)-(p2,h2)(p2,h2)-convex function on the co-ordinates. Furthermore, some inequalities of Hermite-Hadamard type involving product of two convex functions on the co-ordinates are also considered. The results presented here would provide extensions of those given in earlier works.
<br>Tue, 17 Jan 2017 01:38:36 GMTON SOLVABILITY OF COUPLED HYBRID SYSTEM OF QUADRATIC FRACTIONAL INTEGRAL EQUATIONS
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109352
title: ON SOLVABILITY OF COUPLED HYBRID SYSTEM OF QUADRATIC FRACTIONAL INTEGRAL EQUATIONS abstract: Of concern is studying solvability of the hybrid systems of quadratic fractional integral equations. To this aim applying hybrid fixed point theory due to DhageDhage, existence of at least one positive solution for mentioned systems via so called D-Lipschitzian mappings will be concluded . We illustrate the obtained results by presenting an example.
<br>Tue, 17 Jan 2017 01:35:42 GMTA NOTE ON THE LEAST (NORMALIZED) LAPLACIAN EIGHVA;UE OF SIGNED GRAPHS
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109351
title: A NOTE ON THE LEAST (NORMALIZED) LAPLACIAN EIGHVA;UE OF SIGNED GRAPHS abstract: Let Γ=(G,σ)Γ=(G,σ) be a connected signed graph, and L(Γ)L(Γ) be its Laplacian and L(Γ)L(Γ) its normalized Laplacian with eigenvalues λ1≥λ2≥⋯≥λnλ1≥λ2≥⋯≥λn and μ1≥μ2≥⋯≥μnμ1≥μ2≥⋯≥μn, respectively. It is known that a signed graph ΓΓ is balanced if and only if λn=0λn=0 (or μn=0μn=0). We show that λnλn and μnμn measure how much ΓΓ is far from being balanced by proving that
μn(Γ)λn(Γ)≤min{2ϵ(Γ)m,ν(Γ)ν(Γ)+ν1(Γ)},≤min{λ1(Γ′):Γ−Γ′isbalanced},
μn(Γ)≤min{2ϵ(Γ)m,ν(Γ)ν(Γ)+ν1(Γ)},λn(Γ)≤min{λ1(Γ′):Γ−Γ′isbalanced},
where ν(Γ)ν(Γ) (resp. ϵ(Γ)ϵ(Γ)) denotes the frustration number (resp. the frustration index) of ΓΓ, that is the minimum number of vertices (resp. edges) to be deleted such that the signed graph is balanced.
<br>Tue, 17 Jan 2017 01:33:54 GMTA GCD AND LCM-LIKE INEQUALITY FOR MULTIPLICATIVE LATTICES
https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109350
title: A GCD AND LCM-LIKE INEQUALITY FOR MULTIPLICATIVE LATTICES abstract: Let A1,…,AnA1,…,An (n≥2)(n≥2) be elements of an commutative multiplicative lattice. Let G(k)G(k) (resp., L(k)L(k)) denote the product of all the joins (resp., meets) of kk of the elements. Then we show that
L(n)G(2)G(4)⋯G(2⌊n/2⌋)≤G(1)G(3)⋯G(2⌈n/2⌉−1).
L(n)G(2)G(4)⋯G(2⌊n/2⌋)≤G(1)G(3)⋯G(2⌈n/2⌉−1).
In particular this holds for the lattice of ideals of a commutative ring. We also consider the relationship between
G(n)L(2)L(4)⋯L(2⌊n/2⌋) and L(1)L(3)⋯L(2⌈n/2⌉−1)
G(n)L(2)L(4)⋯L(2⌊n/2⌋) and L(1)L(3)⋯L(2⌈n/2⌉−1)
and show that any inequality relationships are possible.
<br>Tue, 17 Jan 2017 01:31:13 GMT