In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...
Neuromodulation of neocortical microcircuits is one of the most fascinating
and mysterious aspects of brain physiology. Despite over a century of research,
the neuroscientific community has yet to uncover the fundamental
biological organizing principles un ...
Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...
The valorisation of the plant biopolymer lignin is now recognised as essential to enabling the economic viability of the lignocellulosic biorefining industry. In this context, the "lignin-first" biorefining approach, in which lignin valorisation is conside ...
Theoretical and computational approaches to the study of materials and molecules have, over the last few decades, progressed at an exponential rate. Yet, the possibility of producing numerical predictions that are on par with experimental measurements is t ...
Soft pneumatic actuators (SPAs) are highly desirable for interactive robotics applications owing to their unconventional properties like high compliance, safe human-machine interaction and adaptable design space. The SPA dynamic behaviour is governed by pn ...
We investigate the regularity of the free boundary for the Signorini problem in Rn+1. It is known that regular points are (n−1)-dimensional and C∞. However, even for C∞ obstacles φ, the set of non-regular (or degenerate) points could be very large—e.g. wit ...
New methods are required for sustainable and economical management of bridges. Efficient management can be achieved by a detailed understanding of bridge behavior through monitoring and model-based data interpretation. This paper presents a methodology to ...
On ten loose handwritten folios dating back from April 1679, Leibniz gradually devised, in the course of three days, a full-blown theory of thought that nonetheless remained unpublished and still has received little attention from scholars. Conceiving of a ...
The Boolean lattice (2[n],subset of) is the family of all subsets of [n]={1,MIDLINE HORIZONTAL ELLIPSIS,n}, ordered by inclusion. Let P be a partially ordered set. We prove that if n is sufficiently large, then there exists a packing P of copies of P in (2 ...
Many decision problems in science, engineering, and economics are affected by uncertainty, which is typically modeled by a random variable governed by an unknown probability distribution. For many practical applications, the probability distribution is onl ...
We consider sets L = {l(1),..., l(n)} of n labeled lines in general position in R-3, and study the order types of point sets {p(1),..., p(n)} that stem from the intersections of the lines in L with (directed) planes Pi, not parallel to any line of L, that ...
This paper discusses the design of load-bearing systems for buildings with regard to their current lack of open-ended reusability. The reason for dismantling load-bearing systems today tends to be less related to material degradation than to a loss of func ...
Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...
It is proved that the total length of any set of countably many rectifiable curves whose union meets all straight lines that intersect the unit square U is at least 2.00002. This is the first improvement on the lower bound of 2 known since 1964. A similar ...
A subfamily {F-1, F-2, ..., F-vertical bar P vertical bar} subset of F is a copy of the poset P if there exists a bijection i : P -> {F-1, F-2, ..., F-vertical bar P vertical bar}, such that p
Consider the problem of constructing a polar code of block length N for a given transmission channel W. Previous approaches require one to compute the reliability of the N synthetic channels and then use only those that are sufficiently reliable. However, ...
The need for predictive capabilities greater than 95% with very limited false alarms are demanding requirements for reliable disruption prediction systems in tokamaks such as JET or, in the near future, ITER. The prediction of an upcoming disruption must b ...
We show that the Chow covectors of a linkage matching field define a bijection of lattice points and we demonstrate how one can recover the linkage matching field from this bijection. This resolves two open questions from Sturmfels & Zelevinsky (1993) on l ...
An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...
