Revistas académicas de la Universidad Católica del Norte
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New bounds on the distance Laplacian and distance signless Laplacian spectral radii
No full textLet G be a simple undirected connected graph. In this paper, new upper bounds on the distance Laplacian spectral radius of G are obtained. Moreover, new lower and upper bounds for the distance signless Laplacian spectral radius of G are derived. Some of the above mentioned bounds are sharp and the graphs attaining the corresponding bound are characterized. Several illustrative examples are included.
 
Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays
No full textHermite processes are self-similar processes with stationary increments, the Hermite process of order 1 is fractional Brownian motion and the Hermite process of order 2 is the Rosenblatt process. In this paper we consider a class of time-dependent neutral stochastic functional differential equations with finite delay driven by Rosenblatt process with index H ∈ (1/2, 1) which is a special case of a self-similar process with long-range dependence. More precisely, we prove the existence and uniqueness of mild solutions by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is provided to demonstrate the effectiveness of the theoretical result
On rough convergence of triple sequence spaces of Bernstein-Stancu operators of fuzzy numbers defined by a metric function
No full textWe define the concept of rough limit set of a triple sequence space of Bernstein-Stancu polynomials of fuzzy numbers and obtain the relation between the set of rough limit and the extreme limit points of a triple sequence space of Bernstein-Stancu polynomials of fuzzy numbers. Finally, we investigate some properties of the rough limit set of Bernstein-Stancu polynomials
On approximation of signals in the generalized Zygmund class via (E, 1) (N̅, p n ) summability means of conjugate Fourier series
No full textApproximation of functions of different classes have been considered by various researchers under different summability means. In the present paper, presumably a new theorem has been established under (E, 1)(N̅ pn) -product summability mean of conjugate Fourier series of a function of Zr (⍵) r (r ≥ 1) -class (generalized Zygmund class). Moreover, the result obtained here is a generalization of several known theorems
Asymptotic behavior of linear advanced dynamic equations on time scales
No full textLet T be a time scale which is unbounded above and below and such that t0 ∈ T. Let id + h, id + r: [t0,∞) ∩ T → T be such that (id + h)([t0,∞) ∩ T) and (id + r)([t0,∞) ∩ T) are time scales. We use the contraction mapping theorem to obtain convergence to zero about the solution for the following linear advanced dynamic equation
x∆ (t) + a (t) xσ (t + h (t)) + b (t) xσ (t + r (t)) = 0, t ∈ [t0, ∞) ∩ T
where f∆ is the ∆-derivative on T. A convergence theorem with a necessary and sufficient condition is proved. The results obtained here extend the work of Dung [11]. In addition, the case of the equation with several terms is studied
Further results on 3-product cordial labeling
No full textA mapping f : V (G) → {0, 1, 2} is called 3-product cordial labeling if |vf(i) − vf(j)| ≤ 1 and |ef(i) − ef(j)| ≤ 1 for any i, j ∈ {0, 1, 2}, where vf(i) denotes the number of vertices labeled with i, ef(i) denotes the number of edges xy with f(x)f(y) ≡ i(mod 3). A graph with 3-product cordial labeing is called 3-product cordial graph. In this paper we establish that switching of an apex vertex in closed helm, double fan, book graph K1,n × K2 and permutation graph P (K2 + mK1, I) are 3-product cordial graphs
Odd harmonious labeling of grid graphs
No full textA graph G(p, q) is said to be odd harmonious if there exists an injection f : V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function f* : E(G) → {1, 3, · · · , 2q − 1} defined by f∗ (uv) = f (u) + f (v) is a bijection. In this paper we prove that path union of t copies of Pm×Pn, path union of t different copies of Pmᵢ×Pnᵢ where 1 ≤ i ≤ t, vertex union of t copies of Pm×Pn, vertex union of t different copies of Pmᵢ×Pnᵢ where 1 ≤ i ≤ t, one point union of path of Ptn (t.n.Pm×Pm), t super subdivision of grid graph Pm×Pn are odd harmonious graphs
Near ω-continuous multifunctions on bitopological spaces
No full textIn this paper, we introduce and study basic characterizations, several properties of upper (lower) nearly (i, j)-ω-continuous multifunctions on bitopological space
Equitable total chromatic number of splitting graph
No full textAmong the varius coloring of graphs, the concept of equitable total coloring of graph G is the coloring of all its vertices and edges in which the number of elements in any two color classes differ by atmost one. The minimum number of colors required is called its equitable total chromatic number. In this paper, we determine an equitable total chromatic number of splitting graph of Pn, Cn and K1,n
On graded 2-classical prime submodules of graded modules over graded commutative rings
No full textLet G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded 2-classical prime submodules. Various properties of graded 2-classical prime submodules are considered