Increasingly, mathematical, scientific and technical information is being distributed by electronic means, but having a high-quality paper printout remains important. We show here examples of techniques that are available for having both high-quality typesetting, in particular of mathematics, as well as useful navigation features and text extraction within electronic documents. For HTML, we sho...

Louis Nirenberg is one of the most outstanding analysts of the twentieth century. For more than half a century, he has been a world leader in partial differential equations – a master of inequalities and regularity theory – with fundamental contribution in geometry, complex analysis, and fluid dynamics. Nirenberg is a household name in these fields. In addition to the depth and its basic import...

A triangle is a lower triangular matrix with all principal diagonal entriesbeing nonzero. Given an almost increasing sequence {Xn} and a sequence {λn} satisfying certain conditions, we obtain sufficient conditions for the series ∑ anλn to be absolutely summable of order k ≥ 1 by a triangle T . As a corollary we obtain the corresponding result when T is a weighted mean matrix. Theorem 1 of this ...

In this paper we investigate generalized ordered (GO) spaces that have a flexible diagonal in the sense of Arhangel’skii [2]. Spaces with a flexible diagonal are generalizations of topological groups and include spaces that are continuously homogeneous, Choban spaces, and rotoid spaces. We prove some some paracompactness and metrization theorems for such spaces and construct examples of general...

There is an increasing interest in the evaluation of prognostic and predictive biomarkers for personalizing cancer care. The literature on the trial designs for evaluation of these markers is diverse and there is no consensus in the classification or nomenclature. We set this study to review the literature systematically, to identify the proposed trial designs, and to develop a classification s...

This is a corrected version of my paper published in Journal of Geometry and Physics 25(1998), 205-226. I added missing cases to the classification theorem 1.1, namely the SO(n + 1)-manifold SO(n + 2)/(SO(n) × SO(2)), the SO(3)-manifold CP 2 and the SU(3)-manifold CP 1 × CP . Preface Christopher T. Woodward, in his review MR1619843 in MathSciNet, pointed out a gap in the classification of compa...

A solid and distinctive online record of a scientist’s research achievements is nowadays a must, in particular for a researcher at an early career stage looking for a better university position, applying for a grant or a promotion, or trying to establish new contacts and build partnerships and projects. In the global world of science there are already numerous services offering research profile...

We prove existence of variational solutions for a class doubly nonlinear nonlocal evolution equations whose prototype is the double phase equation $$\begin{aligned}&\partial _t u^m + P.V.\int _{\mathbb {R}^N} \frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+ps}}\\&\qquad \quad +a(x,y)\frac{|u(x,t)-u(y,t)|^{q-2}(u(x,t)-u(y,t))}{|x-y|^{N+qr}} \,\mathrm{d}y = 0,\,m>0,\,p>1,\,s,r\in (0,1). \end...

In 1988 S. Mori, D. Morrison, and I. Morrison published a paper [4] in which they gave a computer-based conjectural classification of four-dimensional terminal cyclic quotient singularities of prime index. This classification was partially proven in 1990 by G. Sankaran (cf. [7]). Basically, the conjecture of [4] says that these singularities form a finite number of series (cf. definition in sec...

is an extensively studied nonlinear equation. It first appeared as an abstract biHamiltonian partial differential equation in an article of Fuchssteiner and Fokas [39] but did not receive much attention until Camassa and Holm [15] (see also [16]) derived it as a nonlinear wave equation that models unidirectional wave propagation on shallow water and discovered its rich mathematical structure. I...