Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Posets of h-vectors of standard determinantal schemes
Full text linkWe study the combinatorial structure of the poset H consisting of h-vectors of length s of codimension c standard determinantal schemes, defined by the maximal minors of a t × (t + c − 1) homogeneous, polynomial matrix. We show that H obtains a natural stratification, where each strata contains a maximum h-vector. Moreover, we prove that any h-vector in H is bounded from above by a h-vector of the same length and which corresponds to a codimension c level standard determinantal scheme. Furthermore, we show that the only strata in which there exists also a minimum h-vector is the one consisting of h-vectors of level standard determinantal schemes
Fibonacci difference sequence spaces for modulus functions
Full text linkIn the present paper we introduce Fibonacci difference sequence spaces l(F, Ƒ, p, u) and l_∞(F, Ƒ, p, u) by using a sequence of modulus functions and a new band matrix F. We also make an effort to study some inclusion relations, topological and geometric properties of these spaces. Furthermore, the alpha, beta, gamma duals and matrix transformation of the space l(F, Ƒ, p, u) are determined
Hadamard Product Concerning Certain Meromorphic Functions
Full text linkIn this paper the authors introduced a new generalized differintegral operator for meromorphic univalent functions in U* = {z : z ∈ C, 0 < |z| < 1}. The objective of this paper is to establish certain results concerning the Hadamard product of functions in the classes ∑^{∗,m}_{μ,λ} (α, β , γ, k) and ∑^h_{μ,λ} (α, β , γ, k)
Multivalence of bivariate functions of bounded index
Full text linkThis paper examines the relationship between the concept of bounded index and the radius of equivalence, respectively p-valence, of entire bivariate functions and their partial derivatives at arbitrary points in C^2
Some notes on bornological and nonbornological locally convex cones
Full text linkBornological and b-bornological locally convex cones have studied in [D. Ayaseh and A. Ranjbari, Bornological Locally Convex Cones, Le Matematiche, Vol. LXIX (2014) Fasc. II, pp. 267-284]. In this paper, we obtain new results on bornological locally convex cones and present an example of nonbornological locally convex cone. We show that the projectivelimit of bornological cones is not bornological in general. Also, we present a bornological locally convex cone which is not b-bornological
The symmetric Mellin transform in quantum calculus
Full text linkIn this paper, we define the q-analogue of Mellin Transform symmetric under interchange of q and 1/q, and present some of its main properties and explore the possibility of using the integral transform to solve a class of differential equations q-differences
Fixed points of contractive dominated mappings on a closed ball in an ordered quasi partial metric space
No full textIn this paper, we obtain some fixed point theorems for dominated mappings satisfying locally contractive conditions on a closed ball in a left K-sequentially O-complete ordered quasi-partial metric space and in a right K-sequentially O-complete ordered quasi-partial metric space, respectively. Our results improve several well known results.
Cohomological dimension and arithmetical rank of some determinantal ideals
Full text linkLet M be a (2 × n) non-generic matrix of linear forms in a polynomial ring. For large classes of such matrices, we compute the cohomological dimension (cd) and the arithmetical rank (ara) of the ideal I_2(M) generated by the 2-minors of M. Over an algebraically closed field, any (2×n)-matrix of linear forms can be written in the Kronecker-Weierstrass normal form, as a concatenation of scroll, Jordan and nilpotent blocks. Badescu and Valla computed ara(I_2 (M)) when M is a concatenation of scroll blocks. In this case we compute cd(I2 (M)) and extend these results to concatenations of Jordan blocks. Eventually we compute ara(I_2(M)) and cd(I_2 (M)) in an interesting mixed case, when M contains both Jordan and scroll blocks. In all cases we show that ara(I_2(M)) is less than the arithmetical rank of the determinantal ideal of a generic matrix
Regularity of Tor for weakly stable ideals
Full text linkIt is proved that if I and J are weakly stable ideals in a polynomial ring R = k[x_1, . . ., x_n], with k a field, then the regularity of Tor^R_i (R/I, R/J) has the expected upper bound. We also give a bound for the regularity of Ext^i_R (R/I, R) for I a weakly stable ideal
A new class of generalized polynomials associated with Hermite and Bernoulli polynomials
Full text linkIn this paper, we introduce a new class of generalized polynomials associated with the modified Milne-Thomson\u27s polynomials Φ_{n}^{(α)}(x,ν) of degree n and order α introduced by Derre and Simsek.The concepts of Bernoulli numbers B_n, Bernoulli polynomials B_n(x), generalized Bernoulli numbers B_n(a,b), generalized Bernoulli polynomials B_n(x;a,b,c) of Luo et al, Hermite-Bernoulli polynomials {_HB}_n(x,y) of Dattoli et al and {_HB}_n^{(α)} (x,y) of Pathan are generalized to the one {_HB}_n^{(α)}(x,y,a,b,c) which is called the generalized polynomial depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B_n, B_n(x), B_n(a,b), B_n(x;a,b,c) and {}_HB_n^{(α)}(x,y;a,b,c) are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Bernoulli numbers and polynomial