



1
Title: Exponential General Sets of Polynomials for Several Complex Variables
Vol.42(6) (2018) page: 791800
Author(s): M. Abdalla and Z. Kishka
Abstract: The main goal of this paper is to describe certain convergence properties of the exponential general basic sets of polynomials of several complex variables {_{\mathbbP}\mathbbE_{m}(z)}={exp(\mathbbP_{m}(z))}; z=(z_{1}, z_{2},...,z_{k}). It is pointed out that under certain conditions on the matrix of coefficients of the original basic set {\mathbbP_{m}(z)}, we prove that the associated basic set {_{\mathbbP}\mathbbE_{m}(z)} has similar convergence properties to those of {\mathbbP_{m}(z)}. The growth order of the exponential general set of polynomials of z is clarified also.
Keywords: Polynomials; Exponential sets; Effectiveness; Hyperelliptical regions. 
2
Title: A New Study on Absolute Matrix Summability Factors of Infinite Series
Vol.42(6) (2018) page: 801808
Author(s): T. Ari
Abstract: In this paper, we prove a generel theorem on A,p_{n}_{k} summability methods, which generalizes the result of Bor [5] dealing with absolute Riesz summability factors of infinite.
Keywords: Riesz mean; Matrix summability; Infinite series; H??lder inequality; Minkowski inequality; Summability factors. 
3
Title: Solvability of a Class of Higher Order Singular Nonlinear Partial Differential Equations
Vol.42(6) (2018) page: 809824
Author(s): D.B. Bacani and J.E.C. Lope
Abstract: This paper studies the singular nonlinear partial differential equation
(t∂_{t})^{m}u = F 
???
??? 
t,x, 
???
???
??? 
(t∂_{t})^{j} ∂_{x}^{α}u 
???
???
??? 
(j,α) ∈ I_{m} 

???
??? 


where I_{m}={(j,α) ∈ \mathbbN×\mathbbN^{n} ; j+α ≤ m, j < m } and F(t,x,Z) is a function continuous in t and holomorphic in (x,Z). We present a unique solvability result for this class of equations under the assumption that F(t,x,0) is of order o(1) (as t→ 0) uniformly in x and (∂F/∂z_{j,α})(0,x,0) ≡ 0 for all (j,α) ∈ I_{m} \{α = 0 }. We then extend the unique solvability result to a wider class of equations.
Keywords: Existence and uniqueness; Fuchs type; Nonlinear partial differentialequations. 
4
Title: Lr Inequalities for Polynomials
Vol.42(6) (2018) page: 825832
Author(s): B. Chanam
Abstract:
Let p(z) = a_{0} +∑_{υ = μ}^{n}a_{υ} z^{υ}, 1 ≤ μ ≤ n, be a polynomial of degree n having no zero in z < k, k ≥ 1 , then Qazi in [16] proved

max
z=1 
p′(z) ≤ n 
1+ 
μ
n 
 \dfraca_{μ}a_{0}  k^{μ+1} 
1+k^{μ+1}+ 
μ
n 
 \dfraca_{μ} a_{0}  (k^{μ+1} +k^{2μ}) 


max
z=1 
p(z). 

In this paper, we obtain the L^{r} version of the above inequality for r > 0 which extends a result obtained by Dewan et al. in [6] from r ≥ 1 to r > 0. Further, as applications of our result, we extend results of Chan and Malik in [5] and of Dewan et al. in [7] into L^{r} analogues for r > 0.
Keywords: Lr norm; Inequality; Polynomial; Zero. 
5
Title: Normalized Laplacian Spectrum of Some RCoronas of Two Regular Graphs
Vol.42(6) (2018) page: 833844
Author(s): A. Das and P. Panigrahi
Abstract: In this paper we determine the full normalized Laplacian spectrum of the Rvertex corona, Redge corona, Rvertex neighborhood corona, and Redge neighborhood corona of a connected regular graph with an arbitrary regular graph in terms of their normalized Laplacian eigenvalues. Moreover, applying these results we find nonregular normalized Laplacian cospectral graphs.
Keywords: Normalized Laplacian matrix; Rvertex corona; Redge corona; Rvertex neighborhood corona; Redge neighborhood corona; Kronecker product; Hadamard product. 
6
Title: Symmetric Sker nDerivations in Prime and Semiprime Rings
Vol.42(6) (2018) page: 845852
Author(s): B. Dhara and F. Shujat
Abstract: For a ring R with an automorphism α an nadditive mapping D:R^{n}→ R is called a skew nderivation w.r.t. α if it is an αderivation of R for each argument. Namely it is always an αderivation of R for the argument being left once (n−1) arguments are fixed by (n−1) elements in R. In the present note, begin with a result of Park [9], we prove that if a skew nderivation D associated with an automorphism α with trace τ of a noncommutative n! torsion free semiprime ring R satisfying [τ(x), α(x)] ∈ Z(R) for all x ∈ I, then [τ(x), α(x)]=0 for all x ∈ I, a nonzero ideal of R. Moreover, we investigate the commutativity in case of prime rings.
Keywords: Prime ring; Semiprime ring; Symmetric skew nderivation; Centralizing mapping; Commuting mapping. 
7
Title: Twisted Partial Skew Generalized Power Series over Zip and Weak Zip Rings
Vol.42(6) (2018) page: 853864
Author(s): M. Fahmy, A. Ageeb and R. AbdelKhalek
Abstract: In this article, the twisted partial skew generalized power series ring A=[[R^{G, ≤ }; Θ]] is introduced and considered. We also study the transfer of zip and weak zip properties between A and its ground ring R, more precisely, under some circumstances we show that A is right zip (weak zip) if and only if R is.
Keywords: Partial action; Zip ring; Weak zip ring; Partial skew generalized power series ring. 
8
Title: On the Number of Cyclic Subgroups in a Finite Group
Vol.42(6) (2018) page: 865873
Author(s): E. Haghil and A.R. Ashrafi
Abstract: Let c(G) denote the number of cyclic subgroups of a finite group G. In this article, the classification of finite groups with at most eight cyclic subgroups are given. It is also proved that a group with ≤ 31 cyclic subgroups is solvable. Finally, a finite simple group has exactly 32 cyclic subgroups if and only if G ≅ A_{5}, the alternating group on five symbols.
Keywords: Number of cyclic subgroups; Simple group; Element order. 
9
Title: Spectrum and LSpectrum of the Cyclic Graph
Vol.42(6) (2018) page: 875884
Author(s): A. Hamzeh
Abstract: Let G be a finite group. The cyclic graph Γ_{G} is a simple graph with the vertex set G. Two elements x,y ∈ G are adjacent in the cyclic graph if and only if ⟨x, y⟩ is cyclic. The aim of this paper is to compute the characteristic polynomial and Laplacian spectrum of this graph. As an application, the algebraic connectivity, the number of spanning trees and Laplacian energy of this graph are computed for the dihedral, semidihedral, cyclic and dicyclic groups.
Keywords: Cyclic graph; Characteristic polynomial; Spectrum; Laplacian spectrum. 
10
Title: Recursive Formula of Enumeration on Forbidden Words
Vol.42(6) (2018) page: 885898
Author(s): C.X. Huang and J.P. Li
Abstract: Hao et al. [4, 11] proposed an enumeration problem in the life science, where the strings of a given length containing no element of B as substrings were enumerated. In this paper, completely different from Hao's method, we utilize a combinatorial method to resolve the enumeration problem where the set B may permit to contain more than one forbidden words. In details, we obtain the following results:
(i) A recursive relation between the m+1 ( ≥ 2) integer sequences {L_{k}} and {E^{t}_{k}} (t=1,2,…, m) is constructed; (ii) By utilizing this recursive relation, we design a polynomialtime algorithm to the enumeration problem, which decreases both complexity of computing time and complexity of space time; (iii) The experiment results of our algorithm executed on some examples are provided, such as the forbidden words in the ThueMorse sequence and the RudinShapiro sequence [1,9].
Keywords: Alphabet; Strings; Minimal set B of forbidden words; Enumeration; Recurrence. 
11
Title: On the Characteristic Polynomial of tTuple and bBridge Coalescence Graphs
Vol.42(6) (2018) page: 899906
Author(s): N.B. Ibrahim and A.A. Jund
Abstract: In this paper, we determine the characteristic polynomial of ttuple and bbridge coalescence graphs. Finally, we obtain a new formula of the characteristic polynomial of a path graph of order n.
Keywords: Characteristic polynomial; ttuple graph; bbridge coalescence graph. 
12
Title: Permuting TriDerivations and Generalized dDerivations on Almost Distributive Lattices
Vol.42(6) (2018) page: 907919
Author(s): G.C. Rao, K. Ravi Babu and K.P. Shum
Abstract: In this paper, we introduce the concept of a permuting triderivation on an Almost Distributive Lattice (ADL) and derive important properties of permuting triderivation in ADLs. Also, we define the concept of a generalized dderivation where d is the trace of a permuting triderivation on an ADL and derive its properties.
Keywords: Almost distributive lattice (ADL); Prime ADL; Permuting triderivation; Isotone permuting triderivation and weak ideal. 
13
Title: Some Properties of Double Sequences and the PConvergence of DoublySequence Iterations with Error Terms in CAT(0) Spaces
Vol.42(6) (2018) page: 921936
Author(s): A. SahIn, M. BaSarir and R.F. Patterson
Abstract: In this paper, we obtain some properties related to double sequences. Moreover, we prove some Pconvergence theorems of some Halperntype doublesequence iterations with error terms in a CAT(0) space and present an example to support these results. Our results extend and improve some recent results announced in the current literature.
Keywords: Double sequence; Iteration process; Fixed point; Nonexpansive mapping; P convergence; CAT(0) space. 
14
Title: kType Binull Cartan Slant Helices in $R_3^6$
Vol.42(6) (2018) page: 937946
Author(s): A. Ucum, K. Ilarslan and M. Sakaki
Abstract: In the present paper, we give the notion of ktype binull Cartan slant helices in \mathbbR_{3}^{6}, where k ∈ { 1,2,3,4,5,6} . We give the necessary and sufficient conditions for binull Cartan curves to be ktype slant helices in terms of their curvature functions.
Keywords: kslant helix; Binull Cartan curves; semiEuclidean space; Cartan curvatures; Frenet equations. 
15
Title: Contents for Volume 42
Vol.42(6) (2018) page: 947952
Author(s):
Abstract: Contents for Volume 42
Keywords: 
15 Records!





