Czechoslovak Mathematical Journal最新文献

Let A be a CM-finite Artin algebra with a Gorenstein-Auslander generator E, M be a Gorenstein projective A-module and B = End_AM. We give an upper bound for the finitistic dimension of B in terms of homological data of M. Furthermore, if A is n-Gorenstein for 2 ⩽ n < ∞, then we show the global dimension of B is less than or equal to n plus the B-projective dimension of Hom_A(M, E). As an application, the global dimension of End_AE is less than or equal to n.

We construct a family of non-weight modules which are free (U(frak{h}))-modules of rank 2 over the N = 1 super Schrödinger algebra in (1+1)-dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free (U(frak{h}))-modules of rank 2 over (frak{osp}(1mid 2)) are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.

I. Gutman (2022) constructed six new graph invariants based on geometric parameters, and named them Sombor-index-like graph invariants, denoted by (cal{SO}_1, cal{SO}_2, dots, cal{SO}_6). Z. Tang, H. Deng (2022) and Z. Tang, Q. Li, H. Deng (2023) investigated the chemical applicability and extremal values of these Sombor-index-like graph invariants, and raised some open problems, see Z. Tang, Q. Li, H. Deng (2023). We consider the first open problem formulated at the end of Z. Tang, Q. Li, H. Deng (2023). We obtain the extremal values of the graph invariants (cal{SO}_5) and (cal{SO}_6) among all trees and molecular trees of order n, and characterize the trees and molecular trees that achieve the extremal values, respectively. Thus, the problem is completely solved.

Let (cal{A}) and (cal{B}) be abelian categories with enough projective and injective objects, and (T coloncal{A}rightarrowcal{B}) a left exact additive functor. Then one has a comma category ((mathopen{cal{B} downarrow T})). It is shown that if (T coloncal{A}rightarrowcal{B}) is (cal{X})-exact, then is a (hereditary) cotorsion pair in (cal{A}) and is a (hereditary) cotorsion pair in (cal{B}) if and only if is a (hereditary) cotorsion pair in ((mathopen{cal{B}downarrow T})) and (cal{X}) and (cal{Y}) are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories (cal{A}) and (cal{B}) can induce special preenveloping classes in ((mathopen{cal{B}downarrow T})).

We are interested in regularizing effect of the interplay between the coefficient of zero order term and the datum in some noncoercive integral functionals of the type

where Ω ⊂ ℝ^N, j is a Carathéodory function such that ξ ↦ j(x, s, ξ) is convex, and there exist constants 0 ⩽ τ < 1 and M > 0 such that

for almost all x ∈ Ω, all s ∈ ℝ and all ξ ∈ ℝ^N. We show that, even if 0 < a(x) and f(x) only belong to L¹(Ω), the interplay

implies the existence of a minimizer u ∈ W^1,2₀ (Ω) which belongs to L^∞(Ω).

The objective of this manuscript is to investigate the structure of linear maps on the space of real symmetric matrices (cal{S}^{n}) that leave invariant the closed convex cones of copositive and completely positive matrices (COP_n and CP_n). A description of an invertible linear map on (cal{S}^{n}) such that L(CP_n) ⊂ CP_n is obtained in terms of semipositive maps over the positive semidefinite cone (cal{S}_{+}^{n}) and the cone of symmetric nonnegative matrices (cal{N}_{+}^{n}) for n ⩽ 4, with specific calculations for n = 2. Preserver properties of the Lyapunov map X ↦ AX + XA^t, the generalized Lyapunov map X ↦ AXB + B^tXA^t, and the structure of the dual of the cone π(CP_n) (for n ⩽ 4) are brought out. We also highlight a different way to determine the structure of an invertible linear map on (cal{S}^{2}) that leaves invariant the closed convex cone (cal{S}_{+}^{2}).

Let G be a finite simple graph with the vertex set V and let I_G be its edge ideal in the polynomial ring (S=mathbb{K}[V]). We compute the depth and the Castelnuovo-Mumford regularity of S/I_G 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.

We prove the boundedness of the generalized fractional maximal operator M_α and the generalized fractional integral operator I_α on weak Choquet spaces with respect to Hausdorff content over quasi-metric measure spaces.

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 (Sbackslash{{rm m}(S)}inmathscr{C}) for all (Sinmathscr{C}) such that (Sneqmin(mathscr{C})). We prove that the set ({mathscr{P}}(F)={Scolon 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).

Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping h and that of zh, we study various L² norms for T_ϕ(h), where T_ϕ is the Toeplitz operator with symbol ϕ. In Theorem 2.1, given polynomials p and q we find a symbol ϕ such that T_ϕ(p) = q. We extend some of our results to the polydisc.