Archiv der Mathematik最新文献

The Chermak–Delgado measure of a finite group is a function which assigns to each subgroup a positive integer. In this paper, we give necessary and sufficient conditions for when the Chermak–Delgado measure of a group is actually a map of posets, i.e., a monotone function from the subgroup lattice to the positive integers. We also investigate when the Chermak–Delgado measure, restricted to the centralizers, is increasing.

Let (uge -1) be a solution to the semilinear elliptic equation (-Delta u = f(u)) in (mathbb {R}^N) such that (lim _{x_Nrightarrow -infty } u(x',x_N) = -1) uniformly in (x'in mathbb {R}^{N-1}), (lim _{trightarrow +infty } inf _{x_N>t} u(x) > -1), and u is bounded in each half-space ({x_N<lambda }), (lambda in mathbb {R}). Here (f:[-1,+infty )rightarrow mathbb {R}) is a locally Lipschitz continuous function which satisfies some mild assumptions. We show that u is strictly monotonically increasing in the (x_N)-direction. Under some further assumptions on f, we deduce that u depends only on (x_N) and it is unique up to a translation. In particular, such a solution u to the problem (Delta u = u + 1) in (mathbb {R}^N) must have the form (u(x)equiv e^{x_N+alpha }-1) for some (alpha in mathbb {R}).

It is shown that if (a!:!b) is the parallel sum of the two positive definite elements a and b of a (C^*)-algebra, then for any (s, tin [0, 1]),

This inequality, which is sharper than the inequality (big Vert a!:!bbig Vert le Vert aVert !:!Vert bVert ), generalizes an earlier related inequality.

In this short note, we prove that the one-dimensional Kronecker sequence (ialpha bmod 1, i=0,1,2,ldots ,) is quasi-uniform over the unit interval [0, 1] if and only if (alpha ) is a badly approximable number. Our elementary proof relies on a result on the three-gap theorem for Kronecker sequences due to Halton (Proc Camb Philos Soc, 61:665–670, 1965).

Denote by (S_n(x,y)) the length of the longest common substring of x and y with shifts in their first n digits of the b-ary expansions. We show that the sets of pairs (x, y), for which the growth rate of (S_n(x,y)) is (alpha log n) with (0le alpha le infty ), have full Hausdorff dimension. Our method relies upon some estimation of the spectral radius of matrices.

We use an intrinsic Klotz–Osserman type result for surfaces in terms of Codazzi operators to study surfaces with parallel mean curvature and non-positive Gaussian curvature in product spaces.

This short note deals with compact and complete and non-compact gradient Yamabe solitons (M, g, f) such that it has metric of constant scalar curvature. Firstly, we give a new proof of triviality for gradient compact Yamabe solitons. Also, under some integral conditions, we are able to improve a result due to Ma and Miquel (Ann Global Anal Geom 42:195–205, 2012). Finally, we obtain that the Yamabe metric becomes rotationally symmetric. Results for k-Yamabe solitons are also obtained here.

In this paper, we give a generalization of Zhang’s recent work about a sharp Li–Yau gradient bound on compact manifolds by extending Hamilton’s gradient estimates. In particular, we take a special auxiliary function to indicate that our estimate is a slight improvement of Zhang’s result.

In this paper, we obtain some of the partial Dedekind zeta values for ideal classes of the real quadratic field ({mathbb {Q}})((sqrt{D})), where (D = 9m^{2}+2m) is a square-free positive integer and (m equiv 2) (mod 3) is an odd positive integer.

A repairable threshold scheme is a threshold scheme in which a player can securely reconstruct a lost share with the help from a subset of players. In 2018, Stinson and Wei proposed distribution designs to construct repairable threshold schemes. In this paper, we use packing quadruples as distribution designs to distribute subshares of a ramp scheme. The resulting repairable threshold scheme has lower computational complexity and repairing degree.