Search results for "Mink"
showing 10 items of 115 documents
Introduction to Part IV
2018
When looking at the early development of relativity theory, one finds an astonishing number of contributions by mathematicians, some of which deeply influenced the work of leading theoretical physicists. Within the context of special relativity, Hermann Minkowski’s writings come immediately to mind (Walter 2008). Klein and Hilbert followed Minkowski’s ideas from their infancy, and both pursued some of their consequences after the latter’s premature death in January 1909. Two other figures with close ties to Gottingen, Max Born and Arnold Sommerfeld, were both instrumental in elaborating Minkowski’s 4-dimensional approach for physicists (Walter 2007). Born had been Minkowski’s assistant for …
Diphyllobothriids (Cestoda: Pseudophyllidea) from the long-finned pilot whale Globicephala melas (Traill, 1809) off the Faroe Islands, with comments …
1993
The taxonomy of marine species of the genus Diphyllobothrium, particularly those parasitic in cetaceans, is rather confused. During parasitological investigations of long-finned pilot whales Globicephala melas from waters off the Faroe Islands, five diphyllobothriid species were detected: Diphyllobothrium sp. (possibly D. polyrugosum), D. stemmacephalum, Diphyllobothrium sp. A, Diphyllobothrium sp. B and Diphyllobothriidae sp. D. stemmacephalum is reported for the first time from G. melas. The stituation regarding the taxonomy of Diphylobothrium species from cetaceans is briefly reviewed. It is concluded that the recent development of genetic techniques may be of great value in relation to …
Robustness of the Gaussian concentration inequality and the Brunn–Minkowski inequality
2016
We provide a sharp quantitative version of the Gaussian concentration inequality: for every $r>0$, the difference between the measure of the $r$-enlargement of a given set and the $r$-enlargement of a half-space controls the square of the measure of the symmetric difference between the set and a suitable half-space. We also prove a similar estimate in the Euclidean setting for the enlargement with a general convex set. This is equivalent to the stability of the Brunn-Minkowski inequality for the Minkowski sum between a convex set and a generic one.
Singularities of lightlike hypersurfaces in Minkowski four-space
2006
We classify singularities of lightlike hypersurfaces in Minkowski 4-space via the contact invariants for the corresponding spacelike surfaces and lightcones.
Flat lightlike hypersurfaces in Lorentz–Minkowski 4-space
2009
Abstract The lightlike hypersurfaces in Lorentz–Minkowski space are of special interest in Relativity Theory. In particular, the singularities of these hypersurfaces provide good models for the study of different horizon types. We introduce the notion of flatness for these hypersurfaces and study their singularities. The classification result asserts that a generic classification of flat lightlike hypersurfaces is quite different from that of generic lightlike hypersurfaces.
Global properties of codimension two spacelike submanifolds in Minkowski space
2009
Abstract We consider codimension two spacelike submanifolds with a parallel normal field (i.e. vanishing normal curvature) in Minkowski space. We use the analysis of their contacts with hyperplanes and hyperquadrics in order to get some global information on them. As a consequence we obtain new versions of Carathéodory's and Loewner's conjectures on spacelike surfaces in 4-dimensional Minkowski space and 4-flattenings theorems for closed spacelike curves in 3-dimensional Minkowski space.
A soft-quadrumer model for diblock copolymers
2010
We present a new soft-particle type model for diblock copolymers and compare its phase diagram to experimental data as well as to results of other models. To determine the phase diagram we suggest studying geometrical characteristics of the mesophases. Diblock copolymer mesophases differ by the number and geometrical form of clusters of the two components formed in the mesophase. The form of these clusters can be characterized by values of the principle components of their gyration tensor and shape invariants determined from them. Alternatively, it has been suggested to use Minkowski functionals to characterize the global morphology of the different mesophases. We will also discuss the prac…
The role of the Euclidean signature in lattice calculations of quasi-distributions and other non-local matrix elements
2017
Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as lightfront parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic …
A quasiconformal composition problem for the Q-spaces
2017
Given a quasiconformal mapping $f:\mathbb R^n\to\mathbb R^n$ with $n\ge2$, we show that (un-)boundedness of the composition operator ${\bf C}_f$ on the spaces $Q_{\alpha}(\mathbb R^n)$ depends on the index $\alpha$ and the degeneracy set of the Jacobian $J_f$. We establish sharp results in terms of the index $\alpha$ and the local/global self-similar Minkowski dimension of the degeneracy set of $J_f$. This gives a solution to [Problem 8.4, 3] and also reveals a completely new phenomenon, which is totally different from the known results for Sobolev, BMO, Triebel-Lizorkin and Besov spaces. Consequently, Tukia-V\"ais\"al\"a's quasiconformal extension $f:\mathbb R^n\to\mathbb R^n$ of an arbitr…
L p-Spaces and the Radon–Nikodym Theorem
2020
In this chapter, we study the spaces of functions whose pth power is integrable. In Section 7.2, we first derive some of the important inequalities (Holder, Minkowski, Jensen) and then in Section 7.3 investigate the case p=2 in more detail.