Archiv der Mathematik最新文献

Recently the Brill–Noether theory of curves C of both fixed genus and gonality was established. In particular, in this theory (now called the Hurwitz–Brill–Noether theory), all irreducible components of the variety of complete linear series of a fixed degree and dimension on C are obtained from the closures of certain so-called “Brill–Noether splitting loci” (loci which have a rather succinct description). In this paper, a method previously invented for the construction of some of these irreducible components is applied to get simply designed varieties inside the difference between these splitting loci and their closures, i.e., inside the boundary of the splitting loci.

We explore general intrinsic and extrinsic conditions that allow the transitivity of the relation of being an ideal in Lie algebras. We also prove that perfect Lie algebras of arbitrary dimension and over any field are intrinsically characterized by transitivity of this type. In particular, we show that a Lie algebra (mathfrak {h}) is perfect (i.e., (mathfrak {h}=[mathfrak {h}, mathfrak {h}])) if and only if for all Lie algebras (mathfrak {k}, mathfrak {g}) such that (mathfrak {h}) is an ideal of (mathfrak {k}) and (mathfrak {k}) is an ideal of (mathfrak {g}), it follows that (mathfrak {h}) is an ideal of (mathfrak {g}).

In this article, we have considered the problem of effective determination of modular forms of half-integral weight in the weight aspect. The result is a generalization of a result of Munshi to the case of modular forms of half-integral weight.

This article concerns a connection between the fractional Schrödinger equation and the logarithmic fractional Schrödinger equation. By rescaling and the constrained minimization method, we prove the asymptotic behaviors of normalized ground states for two equations.

In this paper, we delve into a singular periodic predator-prey system, a model that aptly captures the intricate dynamics of human population evolution on Easter Island. Based on the coincidence degree theory for first-order high-dimensional differential systems, we derive a novel result regarding the existence of positive periodic solution for this system. Additionally, we offer numerical simulations to visualize and substantiate our theoretical result.

Let G be a finite group and (N_{Omega }(G)) be the intersection of the normalizers of all subgroups belonging to the set (Omega (G),) where (Omega (G)) is a set of all subgroups of G which have some theoretical group property. In this paper, we show that (N_{Omega }(G)= Z_{infty }(G)) if (Omega (G)) is one of the following: (i) the set of all self-normalizing subgroups of G; (ii) the set of all subgroups of G satisfying the subnormalizer condition in G; (iii) the set of all pronormal subgroups of G; (iv) the set of all weakly normal subgroups of G; (v) the set of all NE-subgroups of G.

A bounded Hilbert space operator T for which the closure of the annulus

is a spectral set is called an (mathbb {A}_r)-contraction. A celebrated theorem due to Douglas, Muhly, and Pearcy gives a necessary and sufficient condition such that a (2 times 2) block matrix of operators ( begin{bmatrix} T_1 & X 0 & T_2 end{bmatrix} ) is a contraction. We seek an answer to the same question in the setting of an annulus, i.e., under what conditions does (widetilde{T}_Y=begin{bmatrix} T_1 & Y 0 & T_2 end{bmatrix} ) become an (mathbb {A}_r)-contraction? For (mathbb {A}_r)-contractions (T, T_1,T_2) and an operator X that commutes with (T, T_1,T_2), here we find a necessary and sufficient condition such that each of the block matrices

becomes an (mathbb {A}_r)-contraction.

In this paper, we obtain the ({L^p}) boundedness of Fourier integral operators with rough amplitude (a in {L^infty }S_rho ^m) and phase (varphi ) that satisfies some generalized derivative estimation and some measure condition. Our main conclusions extend and improve some known results about ({L^p}) boundedness of Fourier integral operators.

We study the effect of non-negative potentials on the spectral gap of one-dimensional Schrödinger operators in the limit of large intervals. We derive upper bounds on the gap for different classes of potentials and show, as a main result, that the spectral gap of a Schrödinger operator with a non-zero and sufficiently fast decaying potential closes strictly faster than the gap of the free Laplacian. We show optimality of this result in some sense and establish a conjecture towards the actual decay rate of the spectral gap.

The Wiman–Valiron inequality relates the maximum modulus of an analytic function to its Taylor coefficients via the maximum term. After a short overview of the known results, we obtain a general version of this inequality that seems to have been overlooked in the literature so far. We end the paper with an open problem.