Configuration-like spaces and coincidences of maps on orbits

In this paper we study the spaces of $q$-tuples of points in a Euclidean space, without $k$-wise coincidences (configuration-like spaces). A transitive group action by permuting these points is considered, and some new upper bounds on the genus (in the sense of Krasnosel'skii--Schwarz and Clapp--Puppe) for this action are given. Some theorems of Cohen--Lusk type for coincidence points of continuous maps to Euclidean spaces are deduced

Optimal approximate fixed point results in locally convex spaces

Let $C$ be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps $f\colon C\to\bar{C}$. First we prove that if $f(C)$ is totally bounded, then it has an approximate fixed point net. Next, it is shown that if $C$ is bounded but not totally bounded, then there is a uniformly continuous map $f\colon C\to C$ without approximate fixed point nets. We also exhibit an example of a sequentially continuous map defined on a compact convex set with no approximate fixed point sequence. In contrast, it is observed that every affine (not-necessarily continuous) self-mapping a bounded convex subset of a topological vector space has an approximate fixed point sequence. Moreover, it is constructed a affine sequentially continuous map from a compact convex set into itself without fixed points.Comment: 12 page

Vacuum Calculations for the LHC Experimental Beam Chambers

The vacuum stability is studied for the LHC experimental beam vacuum chambers of ALICE, ATLAS, and CMS. The present baseline design includes sputtered Non-Evaporable Getter (NEG) coating over the whole chamber inner surface providing distributed pumping and an antimultipactor coating. The data are presented for the dominant gas species (H2, CH4, CO and CO2) in a baked system. It results that the distributed pumping is necessary for vacuum stability of CO. Lumped pumping with Sputter Ion Pumps (SIP) is also indispensable for the stability of CH4. The operational constraints with NEG technology are described

A note on Makeev's conjectures

A counterexample is given for the Knaster-like conjecture of Makeev for functions on $S^2$. Some particular cases of another conjecture of Makeev, on inscribing a quadrangle into a smooth simple closed curve, are solved positively

Design Aspects of the RF Contacts for the LHC Beam Vacuum Interconnects

The LHC requires a very low longitudinal and transverse beam coupling impedance, in particular at low frequencies. This implies an admissible DC contact resistance of less than 0.1 m$\Omega$ for the RF contacts inside the vacuum bellows which must carry the image current (up to 50 A peak) of the beam at each vacuum chamber interconnect. Technological aspects, measurement methods and test results are presented for the contacts which will be used in the LHC. The modified mechanical design and the justifications for specific choices will be discusse

Knaster's problem for (Z2)k(Z_2)^k-symmetric subsets of the sphere S2k−1S^{2^k-1}

We prove a Knaster-type result for orbits of the group $(Z_2)^k$ in $S^{2^k-1}$, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$ by $(Z_2)^{k+1}$-symmetric convex fans

Artstream of Utsjoki: A student’s perspective on creative collaboration and ethical challenges in community art

This thesis examines the collaborative dynamics and ethical challenges within an artist student team during the community art project, ArtStream of Utsjoki. The project aimed to increase access to art and artistic activities in Utsjoki villages. The project was a collaboration between three students from the Arctic Art & Design master program at the University of Lapland and locals of Utsjoki municipality. The aim of this thesis is to illuminate the challenges artists face when working within a community art project where they must combine artistic identities, approaches, visions, and goals within the broader framework of creative collaboration. The perspective is that of less experienced community artists, combining both student and artist viewpoints. This thesis is a case study of the project adopting an art-based research approach. Data includes project materials, researcher-created artworks, and an interview. This study found that the collaboration was shaped by local, institutional, team, and individual level dynamics. These influence six interconnected themes: direction, benefits, motivation, participation, engagement, and boundaries. This study proposes the idea of fairness at the heart of ethical collaboration to ensure more meaningful experience for all involved. This study contributes practical insights for students and practitioners working in participatory art through an open description of events from the perspective of the artist-students

Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

Resolving Conflicts Over Climate Change Solutions: Making the Case for Mediation

This article explores the role that mediation can play in resolving the conflicts that are emerging in the climate change arena. Case studies describing mediation of disputes over air quality standards, timber harvesting, species protection, and ecosystems restoration, which resulted in consensus agreements among multiple, diverse stakeholder groups, demonstrate its applicability to the climate change arena. Mediation is not suited to every dispute or set of disputants. However, an analysis of the opportunities and constraints for addressing climate change disputes at the state, regional, and local levels suggests that mediated negotiations is well suited for resolving a number of the conflicts that are emerging over the siting of alternative energy projects, stringency of new regulations, and allocation of responsibility and costs among jurisdictions for reducing green house gas emissions