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Several formulas for translation-invariant operator ideals overLp-spaces of compact groups are proved by tensor product methods.

The aim of this short note is to improve some recent results of B. Grunbaum by some remarks. We use Grunbaum's notations.

In the first section of this note we recall the generalized Hodge conjecture (G.H.C.) and its correction as stated by Grothendieck (G.G.H.C.).

The dynamic response of an infinite, elastic plate to a steadily moving transverse force is studied under the so-called improved plate theory. Analytic solutions for the subsonic and the intersonic cases are obtained using the method of integral transforms. The usual difficulty of the nonuniqueness of the steady-state solutions is circumvented by formulating the problems as initial value problems and then seeking the large time limits of the solutions of such initial value problems. The subsonic and intersonic solutions obtained here are similar to that obtained previously for the supersonic case. However, in contrast with the supersonic solution, which contains two families of Mach lines, the subsonic solution contains no Mach lines and the intersonic solution contains only one family of Mach lines.

It is proved (without the assumption of the continuum hypothesis) that under the condition there exist on the Marcinkiewicz space M(ψ) abnormal functionals which are not localizable.

Results of A. Feldzamen on semi-similarity of operators are proved here using matrix methods. The use of these methods yields simpler proofs, the formulations of the theorems assume a more transparent form.

Two lower bounds of Sperb for the first eigenvalue of an elastically attached membrane are proved in an elementary way.

For every separable Banach spaceX there is a Banach spaceY with a separable dual such thatY ⊕X* ≈Y**. There is also a separable spaceZ so thatZ**/JZ is isomorphic toX.

Let H be a real or complex Hilbert space and let L p(1≦p

This is a short exposition and slight reorgnization of Hahn’s work concerning discrete real time flows with quasi-discrete spectra.

In sections 2 and 3 two methods for proving the non existence of certain universal Banach spaces, are presented. In section 4 it is proved that every infinite-dimensional conjugate Banach space has a two-dimensional subspace whose unit cell is not a polygon.

The main goal of this short paper is to prove the existence of rank 2 simple and special Ulrich bundles on a wide class of elliptic surfaces: namely, on regular Weierstrass fibrations \(\pi : S\rightarrow \mathbb {P}^1\). Alongside we also show the existence of rank 2 weakly Ulrich sheaves on arbitrary Weierstrass fibrations \(S\rightarrow C_0\) and we deal with the (non-)existence of rank one Ulrich bundles on them.

In this paper the following generalization of a theorem by B.R. Gelbaum is proved: Let (K, d) be a compact, connected metric space. Let B denote the Borel sets of (K, d), and P be a probability measure on B with P(G)≠O for any nonempty open G, f, geC(K,d) independent random variables on (K,B,P) and let g satisfy the following assumption: There is an y o∃ℝ such that g −1(y0) is a finite nonempty set. Then f is a constant function. Examples show that the assumptions of this theorem are essential.

Within the class of offspring distributions with given meanm>1 and probability of no offspringp o, the probabilityq of ultimate extinction in a Galton-Watson branching process starting from one individual satisfiesp 0

In this short paper, we consider the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of two squares of primes and a k-th power of prime for any integer $$k \ge 3$$ . Our results improve the recent results due to Brudern (in: Sander, Steuding, Steuding (eds) From arithmetic to zeta-functions, Springer, Cham 2016). The similar method can be also applied to some related questions in this direction, and this can improve the previous results.

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.

The aim of this short note is to discuss Szisz's paper [1] on rings with almost nil adjoint semigroups and to make some remarks about it. His results should be read as a characterization of rings with almost nit, rather than almost nil adjoint semigroups as stated. All his propositions could be simplified considerably once the word adjoint is dropped. Towards this we state the following result appearing in JACOBSO~ [2].

The result indicated in the title of this paper (Ref. Zh. Mat. 1976, 7A225) is false. The error is corrected.

B. R. Srinivasan has defined a weakly inverse semigroup in his paper "Weakly Inverse Semigroups" El], using the following terminology. An idempotent e in a semigroup S is called a principal idempotent of S if f e f = f e for all idempotents f in S. An element a in S is called a principal element of S if there exists an inverse a' of a such that aa' is a principal idempotent. Let Ea denote the set of principal inverses of the element a (the inverses of a which are principal elements of S). Then a semigroup S is called weakly inverse if for each element a in S, the set Ea is not null, and for an), elements a, b in S

In a recent paper on subreflexive normed linear spaces (see Arch. Math. 8, 444--450 (1957)) and its correction (see Arch. Math. 9,439--440, (1958)) R. R. PHELPS proved the following theorem.

We propose a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these run-time bounds are independent of the number of optimization variables and, in particular, are valid for optimization problems with infinitely many optimization variables, we prove that the algorithm converges to an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}ε-suboptimal global solution within finite run-time for any given termination tolerance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon > 0$$\end{document}ε>0. Finally, we illustrate these results for a problem of calculus of variations.