Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces Hk,p(G), where k ∈ ℕ*, 1 ⩽ p ⩽ ∞ and G is either the open unit disk ⅅ or the annular domain Gs, 0 < s < 1 of the complex space ℂ. More precisely, we study the behavior on the interior of G of any function f belonging to the unit ball of the Hardy-Sobolev spaces Hk,p(G) from its behavior on any open connected subset I of the boundary ∂G of G with respect to the L1-norm. Our results can be viewed as an improvement and generalization of those established in S. Chaabane, I. Feki (2009), I. Feki, H. Nfata, F. Wielonsky (2012), I. Feki (2013), I. Feki, H. Nfata (2014). As an application, we establish a logarithmic stability results for the Cauchy problem of the identification of Robin’s coefficient by boundary measurements. PubDate: 2024-07-22
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let G be a finite simple graph with the vertex set V and let IG be its edge ideal in the polynomial ring \(S=\mathbb{K}[V]\) . We compute the depth and the Castelnuovo-Mumford regularity of S/IG when G = G1 ◦ G2 or G = G1 * G2 is a graph obtained from Cohen-Macaulay bipartite graphs G1, G2 by the ◦ operation or * operation, respectively. PubDate: 2024-07-21
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We prove the boundedness of the generalized fractional maximal operator Mα and the generalized fractional integral operator Iα on weak Choquet spaces with respect to Hausdorff content over quasi-metric measure spaces. PubDate: 2024-07-18
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let S be a numerical semigroup. We say that h ∈ ℕ S is an isolated gap of S if {h − 1, h + 1} ⊆ S. A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by m(S) the multiplicity of a numerical semigroup S. A covariety is a nonempty family \(\mathscr{C}\) of numerical semigroups that fulfills the following conditions: there exists the minimum of \(\mathscr{C}\) , the intersection of two elements of \(\mathscr{C}\) is again an element of \(\mathscr{C}\) , and \(S\backslash\{{\rm m}(S)\}\in\mathscr{C}\) for all \(S\in\mathscr{C}\) such that \(S\neq\min(\mathscr{C})\) . We prove that the set \({\mathscr{P}}(F)=\{S\colon\ S\ \text{is}\ \text{a}\ \text{perfect}\ \text{numerical}\ \text{semigroup}\ \text{with}\ \text{Frobenius}\ \text{number}\ F\}\) is a covariety. Also, we describe three algorithms which compute: the set \({\mathscr{P}}(F)\) , the maximal elements of \({\mathscr{P}}(F)\) , and the elements of \({\mathscr{P}}(F)\) with a given genus. A Parf-semigroup (or Psat-semigroup) is a perfect numerical semigroup that in addition is an Arf numerical semigroup (or saturated numerical semigroup), respectively. We prove that the sets Parf(F) = {S: S is a Parf-numerical semigroup with Frobenius number F} and Psat(F) = {S: S is a Psat-numerical semigroup with Frobenius number F} are covarieties. As a consequence we present some algorithms to compute Parf(F) and Psat(F). PubDate: 2024-07-15
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract At first we prove some results on a general polynomial derivation using few results of linear derivation. Then we study the ring of constants of a linear derivation for some rings. We know that any linear derivation is a nonsimple derivation. In the last section we find the smallest integer w > 1 such that the polynomial ring in n variables is w-differentially simple, all w derivations are nonsimple and the w derivations set contains a linear derivation. PubDate: 2024-07-15
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let R[x] be the polynomial ring over a ring R with unity. A polynomial f(x) ∈ R[x] is referred to as a left annihilating content polynomial (left ACP) if there exist an element r ∈ R and a polynomial g(x) ∈ R[x] such that f(x) = rg(x) and g(x) is not a right zero-divisor polynomial in R[x]. A ring R is referred to as left EM if each polynomial f(x) ∈ R[x] is a left ACP. We observe the structure of left EM rings with various properties, and study the relationships between the one-sided EM condition and other standard ring theoretic conditions. Moreover, several extensions of EM rings are investigated, including polynomial rings, matrix rings, and Ore localizations. PubDate: 2024-07-15
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let [t] be the integral part of a real number t, and let f be the arithmetic function satisfying some simple condition. We establish a new asymptotical formula for the sum \(S_f (x)=\sum_{n\leqslant x}f([ x/ n ])\) , which improves the recent result of J. Stucky (2022). PubDate: 2024-07-01
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let D be a nonempty open set in a metric space (X, d) with ∂D ≠ Ø. Define $$h_{D,c}(x,y)=\log\left(1+c{{{d(x,y)}}\over{{\sqrt{d_{D}(x)d_{D}(y)}}}}\right).$$ where dD(x) = d(x, ∂D) is the distance from x to the boundary of D. For every c ⩾ 2, hD,c is a metric. We study the sharp Lipschitz constants for the metric hD,c under Möbius transformations of the unit ball, the upper half space, and the punctured unit ball. PubDate: 2024-07-01
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We introduce a type of n-dimensional bilinear fractional Hardy-type operators with rough kernels and prove the boundedness of these operators and their commutators on central Morrey spaces with variable exponents. Furthermore, the similar definitions and results of multilinear fractional Hardy-type operators with rough kernels are obtained. PubDate: 2024-07-01
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let A be a bounded linear operator in a complex separable Hilbert space ℌ, and S be a selfadjoint operator in ℌ. Assuming that A − S belongs to the Schattenvon Neumann ideal \(\cal{S}_{p}\ (p>1)\) , we derive a bound for \(\sum_k\vert\rm{R}\ \lambda_{k}(A)-\lambda_{k}(S)\vert^{p}\) , where λk(A) (k = 1, 2, …) are the eigenvalues of A. Our results are formulated in terms of the “extended” eigenvalue sets in the sense introduced by T. Kato. In addition, in the case p = 2 we refine the Weyl inequality between the real parts of the eigenvalues of A and the eigenvalues of its Hermitian component. PubDate: 2024-06-06 DOI: 10.21136/CMJ.2024.0468-23
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let R be any noncommutative prime ring of char(R) ≠ 2, 3, L a noncentral Lie ideal of R and F, G two nonzero b-generalized skew derivations of R. Suppose that $$[F(u),\,u]G(u) = 0$$ for all u ∈ L. Then at least one of the following conclusions holds: F(x) = λx for all x ∈ R and for some λ ∈ C, where C is the extended centroid of R R ⊆ M2(K), the algebra of 2 × 2 matrices over a field K. PubDate: 2024-06-06 DOI: 10.21136/CMJ.2024.0507-23
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let R ⊂ S be an extension of domains. Then R is called a maximal non-pseudovaluation subring of S if R is not a pseudovaluation subring of S, and for any ring T such that R ⊂ T ⊂ S, T is a pseudovaluation subring of S. We show that if S is not local, then there no such T exists between R and S. We also characterize maximal non-pseudovaluation subrings of a local integral domain. PubDate: 2024-06-05 DOI: 10.21136/CMJ.2024.0122-23
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract It was known that the vertex set of every planar graph can be partitioned into three forests. We prove that the vertex set of a planar graph without chordal 5-cycles can be partitioned into two forests. This extends a result obtained by Raspaud and Wang in 2008. PubDate: 2024-06-03 DOI: 10.21136/CMJ.2024.0065-23
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract It is known that if f is holomorphic in the open unit disc \(\mathbb{D}\) of the complex plane and if, for some c > 0, ∣f(z)∣ ⩽ 1/(1−∣z∣2)c, \(z \in \mathbb{D}\) , then ∣f′(z)∣ ⩽ 2(c+1)/(1−∣z∣2)c+1. We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in D. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class. PubDate: 2024-05-31 DOI: 10.21136/CMJ.2024.0332-23
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Given a graph G = (V, E), if we can partition the vertex set V into two nonempty subsets V1 and V2 which satisfy Δ(G[V1]) ⩽ d1 and Δ(G[V2]) ⩽ d2, then we say G has a ( \({{\rm{\Delta }}_{{d_1}}}\,,{{\rm{\Delta }}_{{d_2}}}\) )-partition. And we say G admits an ( \({F_{d_{1}}}, {F_{d_{2}}}\) )-partition if G[V1] and G[V2] are both forests whose maximum degree is at most d1 and d2, respectively. We show that every planar graph with girth at least 5 has an (F4, F4)-partition. PubDate: 2024-05-30 DOI: 10.21136/CMJ.2024.0394-21
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract For finite groups X, G and the right G-action on X by group automorphisms, the non-balanced quantum double D(X; G) is defined as the crossed product (ℂXop)* ⋊ ℂG. We firstly prove that D(X; G) is a finite-dimensional Hopf C*-algebra. For any subgroup H of G, D(X; H) can be defined as a Hopf C*-subalgebra of D(X; G) in the natural way. Then there is a conditonal expectation from D(X; G) onto D(X; H) and the index is [G; H]. Moreover, we prove that an associated natural inclusion of non-balanced quantum doubles is the crossed product by the group algebra. PubDate: 2024-05-17 DOI: 10.21136/CMJ.2024.0022-24
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let \({\cal P}_{2}\) denote a positive integer with at most 2 prime factors, counted according to multiplicity. For integers a, q such that (a, q) = 1, let \({\cal P}_{2}(q, \ a)\) denote the least \({\cal P}_{2}\) in the arithmetic progression \({\{nq+a\}_{n=1}^{\infty}}\) . It is proved that for sufficiently large q, we have $${\cal P}_{2}(q, \ a) \ll q^{1.825}.$$ This result constitutes an improvement upon that of J. Li, M. Zhang and Y. Cai (2023), who obtained \({\cal P}_{2}(q, \ a) \ll q^{1.8345}\) . PubDate: 2024-05-16 DOI: 10.21136/CMJ.2024.0459-23
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract We study the LND conjecture concerning the images of locally nilpotent derivations, which arose from the Jacobian conjecture. Let R be a domain containing a field of characteristic zero. We prove that, when R is a one-dimensional unique factorization domain, the image of any locally nilpotent R-derivation of the bivariate polynomial algebra R[x, y] is a Mathieu-Zhao subspace. Moreover, we prove that, when R is a Dedekind domain, the image of a locally nilpotent R-derivation of R[x, y] with some additional conditions is a Mathieu-Zhao subspace. PubDate: 2024-05-06 DOI: 10.21136/CMJ.2024.0008-24
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract Let G be a finite group and construct a graph Δ(G) by taking G {1} as the vertex set of Δ(G) and by drawing an edge between two vertices x and y if 〈x, y〉 is cyclic. Let K(G) be the set consisting of the universal vertices of Δ(G) along the identity element. For a solvable group G, we present a necessary and sufficient condition for K(G) to be nontrivial. We also develop a connection between Δ(G) and K(G) when ∣G∣ is divisible by two distinct primes and the diameter of Δ(G) is 2. PubDate: 2024-04-29 DOI: 10.21136/CMJ.2024.0065-24
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract For any integer n > 1, we provide a parametric family of biquadratic fields with class groups having n-rank at least 2. Moreover, in some cases, the n-rank is bigger than 4. PubDate: 2024-04-15 DOI: 10.21136/CMJ.2024.0356-23