Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Zip Property on Malcev-Neumann Series Modules
Get PDFLet R be a ring, MR a right R-module, G a totally ordered group, σ a map from G into the group of automorphisms of R which assigns to each x ∈ G an automorphism σ_x ∈ Aut(R), τ a map from G × G to U(R) (the group of unit elements of R) and M((G; σ ; τ)) the Malcev-Neumann series module. Then, under some certain conditions, we show that MR is a right zip R-module if and only if M((G; σ ; τ))_{R((G;σ ;τ))} is a right zip R((G; σ ; τ))-module, where R((G; σ ; τ)) is the Malcev-Neumann series ring
Salagean-type harmonic univalent functions with fixed finitely many coefficients
Get PDFIn the present paper, authors introduce and study a new class of Salagean-type harmonic univalent functions that have fixed finitely many coefficients. We obtain coefficient conditions, extreme points, convolution condition, convex combinations for the above class of harmonic univalent functions
Edge ideals and DG algebra resolutions
Get PDFLet R = S/I where S = k[T_1, . . . , T_n] and I is a homogeneous ideal in S. The acyclic closure R<Y> of k over R is a DG algebra resolution obtained by means of Tate’s process of adjoining variables to kill cycles. In a similar way one can obtain the minimal model S[X], a DG algebra resolution of R over S. By a theorem of Avramov there is a tight connection between these two resolutions. In this paper we study these two resolutions when I is the edge ideal of a path or a cycle. We determine the behavior of the deviations ε_i (R), which are the number of variables in R<Y> in homological degree i. We apply our results to the study of the k-algebra structure of the Koszul homology of R
Some results of p-valent analytic functions defined by integral operator
Get PDFIn this paper we study different applications of the inclusion relationships, radius problems and some other interesting properties of p-valent functions which are defined by integral operator
Normal filters in residuated lattices
Get PDFResiduated lattices play an important role in the study of fuzzy logic. In the present paper, we introduce the notion of a normal filter in a residuated lattice and give some characterizations of them. We state and prove some theorems and examples which determine the relationship between this notion and the other types of filters of a residuated lattice. Finally we investigate the relation between the set of dense elements and normal filters of a residuated lattice
An algorithm for constructing certain differential operators in positive characteristic
Get PDFGiven a non-zero polynomial f in a polynomial ring R with coefficients in a finite field of prime characteristic p, we present an algorithm to compute a differential operator δ which raises 1/ f to its pth power. For some specific families of polynomials, we also study the level of such a differential operator δ , i.e., the least integer e such that δ is R^{p^e} -linear. In particular, we obtain a characterization of supersingular elliptic curves in terms of the level of the associated differential operator
Some fractional calculus results associated with the I-function
Get PDFThe effect of Marichev-Saigo-Maeda (MSM) fractional operators involving third Appell function on the function is studied. It is shown that the order of the -function increases on application of these operators to the power multiple of the -function. The Caputo-type MSM fractional derivatives are introduced and studied for the -function. As special cases, the corresponding assertions for Saigo and Erd\\u27elyi-Kober fractional operators are also presented. The results obtained in this paper generalize several known results obtained recently in the literature
Distance two labeling on special family of graphs
Get PDFAn L(2,1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of non-negative integers such that |f(x)-f(y)|\ge 2 if x and y are adjacent and |f(x)-f(y)|\ge 1 if x and y are at distance 2, for all x and y in V(G). A k-L(2,1)-labeling is an L(2,1)-labeling f:V(G) to {0,...,k}, and we are interested to find the minimum k among all possible assignments. This invariant, the minimum k, is known as the L(2,1)-labeling number or λ-number and is denoted by λ(G). In this paper, we determine the λ-number for the coronas P_m \circ P_n, P_m\circ C_n, P_m \circ K_{1,n} and P_m\circ W_n and find an upper bound of the λ-number for the corona G_1 \circ G_2 where G_1 and G_2 are any two graphs such that G_2 has an injective L(2,1)-labeling and also we prove that the bound is attainable when G_1 and G_2 are complete. Also we present an upper bound of the -number for the corona G_1 \circ G_2 where G_1 and G_2 are any two graphs
Nilradicals of skew Hurwitz series of rings
No full textFor a ring endomorphism α of a ring R, Krempa called α a rigid endomorphism if aα(a)=0 implies a = 0 for a in R. A ring R is called rigid if there exists a rigid endomorphism of R. In this paper, we extend the α-rigid property of a ring R to the upper nilradical N_r(R) of R. For an endomorphism α and the upper nilradical N_r(R) of a ring R, we introduce the condition (*): N_r(R) is a α-ideal of R and aα(a) in N_r(R) implies a in N_r(R) for a in R. We study characterizations of a ring R with an endomorphism α satisfying the condition (*), and we investigate their related properties. The connections between the upper nilradical of R and the upper nilradical of the skew Hurwitz series ring (HR,α) of R are also investigated
Quadruple fixed point theorem for hybrid pair of mappings under generalized nonlinear contraction
Get PDFWe establish a quadruple coincidence and common quadruple fixed point theorem for hybrid pair of mappings under generalized nonlinear contraction on a noncomplete metric space which is not partially ordered. It is to be noted that to find quadruple coincidence point, we do not employ the condition of continuity of any mapping involved therein. We also give an example to validate our result. We improve, extend and generalize various known results