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TitleExponential General Sets of Polynomials for Several Complex Variables
Vol.42(6) (2018) page: 791-800
Author(s): M. Abdalla and Z. Kishka  

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\mathbbEm(z)}={exp(\mathbbPm(z))};   z=(z1, z2,...,zk). It is pointed out that under certain conditions on the matrix of coefficients of the original basic set {\mathbbPm(z)}, we prove that the associated basic set {\mathbbP\mathbbEm(z)} has similar convergence properties to those of {\mathbbPm(z)}. The growth order of the exponential general set of polynomials of z is clarified also.

Keywords: Polynomials; Exponential sets; Effectiveness; Hyperelliptical regions.
Size:129KB   download
TitleA New Study on Absolute Matrix Summability Factors of Infinite Series
Vol.42(6) (2018) page: 801-808
Author(s): T. Ari  

In this paper, we prove a generel theorem on |A,pn|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.
Size:88KB   download
TitleSolvability of a Class of Higher Order Singular Nonlinear Partial Differential Equations
Vol.42(6) (2018) page: 809-824
Author(s): D.B. Bacani and J.E.C. Lope  

This paper studies the singular nonlinear partial differential equation

(t∂t)mu = F ???
t,x, ???
(t∂t)jxαu ???

(j,α) ∈ Im 

where Im={(j,α) ∈ \mathbbN×\mathbbNn  ;  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/∂zj,α)(0,x,0) ≡ 0 for all (j,α) ∈ Im \{α = 0 }. We then extend the unique solvability result to a wider class of equations.

Keywords: Existence and uniqueness; Fuchs type; Nonlinear partial differentialequations.
Size:176KB   download
TitleLr Inequalities for Polynomials
Vol.42(6) (2018) page: 825-832
Author(s): B. Chanam  


Let p(z) = a0 +∑υ = μnaυ zυ, 1 ≤ μ ≤ n, be a polynomial of degree n having no zero in |z| < k, k ≥ 1 , then Qazi in [16] proved

|p′(z)| ≤ n
1+ μ

| \dfracaμa0 | kμ+1

1+kμ+1+ μ

| \dfracaμ a0 | (kμ+1 +k)

In this paper, we obtain the Lr 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 Lr analogues for r > 0.

Keywords: Lr norm; Inequality; Polynomial; Zero.
Size:104KB   download
TitleNormalized Laplacian Spectrum of Some R-Coronas of Two Regular Graphs
Vol.42(6) (2018) page: 833-844
Author(s): A. Das and P. Panigrahi  

In this paper we determine the full normalized Laplacian spectrum of the R-vertex corona, R-edge corona, R-vertex neighborhood corona, and R-edge 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 non-regular normalized Laplacian co-spectral graphs.

Keywords: Normalized Laplacian matrix; R-vertex corona; R-edge corona; R-vertex neighborhood corona; R-edge neighborhood corona; Kronecker product; Hadamard product.
Size:169KB   download
TitleSymmetric Sker n-Derivations in Prime and Semiprime Rings
Vol.42(6) (2018) page: 845-852
Author(s): B. Dhara and F. Shujat   

For a ring R with an automorphism α an n-additive mapping D:Rn→ R is called a skew n-derivation w.r.t. α if it is an α-derivation of R for each argument. Namely it is always an α-derivation 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 n-derivation 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 n-derivation; Centralizing mapping; Commuting mapping.
Size:106KB   download
TitleTwisted Partial Skew Generalized Power Series over Zip and Weak Zip Rings
Vol.42(6) (2018) page: 853-864
Author(s): M. Fahmy, A. Ageeb and R. Abdel-Khalek  

In this article, the twisted partial skew generalized power series ring A=[[RG, ≤ ; 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.
Size:143KB   download
TitleOn the Number of Cyclic Subgroups in a Finite Group
Vol.42(6) (2018) page: 865-873
Author(s): E. Haghil and A.R. Ashrafi  

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 ≅ A5, the alternating group on five symbols.

Keywords: Number of cyclic subgroups; Simple group; Element order.
Size:122KB   download
TitleSpectrum and L-Spectrum of the Cyclic Graph
Vol.42(6) (2018) page: 875-884
Author(s): A. Hamzeh  

Let G be a finite group. The cyclic graph ΓG 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, semi-dihedral, cyclic and dicyclic groups.

Keywords: Cyclic graph; Characteristic polynomial; Spectrum; Laplacian spectrum.
Size:160KB   download
TitleRecursive Formula of Enumeration on Forbidden Words
Vol.42(6) (2018) page: 885-898
Author(s): C.X. Huang and J.P. Li  

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 {Lk} and {Etk} (t=1,2,…, m) is constructed;
(ii) By utilizing this recursive relation, we design a polynomial-time 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 Thue-Morse sequence and the Rudin-Shapiro sequence [1,9].



Keywords: Alphabet; Strings; Minimal set B of forbidden words; Enumeration; Recurrence.
Size:141KB   download
TitleOn the Characteristic Polynomial of t-Tuple and b-Bridge Coalescence Graphs
Vol.42(6) (2018) page: 899-906
Author(s): N.B. Ibrahim and A.A. Jund  

In this paper, we determine the characteristic polynomial of t-tuple and b-bridge coalescence graphs. Finally, we obtain a new formula of the characteristic polynomial of a path graph of order n.


Keywords: Characteristic polynomial; t-tuple graph; b-bridge coalescence graph.
Size:97KB   download
TitlePermuting Tri-Derivations and Generalized d-Derivations on Almost Distributive Lattices
Vol.42(6) (2018) page: 907-919
Author(s): G.C. Rao, K. Ravi Babu and K.P. Shum  

In this paper, we introduce the concept of a permuting tri-derivation on an Almost Distributive Lattice (ADL) and derive important properties of permuting tri-derivation in ADLs. Also, we define the concept of a generalized d-derivation where d is the trace of a permuting tri-derivation on an ADL and derive its properties.

Keywords: Almost distributive lattice (ADL); Prime ADL; Permuting tri-derivation; Isotone permuting tri-derivation and weak ideal.
Size:115KB   download
TitleSome Properties of Double Sequences and the P-Convergence of Doubly-Sequence Iterations with Error Terms in CAT(0) Spaces
Vol.42(6) (2018) page: 921-936
Author(s): A. SahIn, M. BaSarir and R.F. Patterson  

In this paper, we obtain some properties related to double sequences. Moreover, we prove some P-convergence theorems of some Halpern-type double-sequence 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.
Size:148KB   download
Titlek-Type Bi-null Cartan Slant Helices in $R_3^6$
Vol.42(6) (2018) page: 937-946
Author(s): A. Ucum, K. Ilarslan and M. Sakaki  

In the present paper, we give the notion of k-type bi-null Cartan slant helices in \mathbbR36, where k ∈ { 1,2,3,4,5,6} . We give the necessary and sufficient conditions for bi-null Cartan curves to be k-type slant helices in terms of their curvature functions.

Keywords: k-slant helix; Bi-null Cartan curves; semi-Euclidean space; Cartan curvatures; Frenet equations.
Size:113KB   download
TitleContents for Volume 42
Vol.42(6) (2018) page: 947-952

Contents for Volume 42

Size:51KB   download
15 Records!


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