Massively winning configurations in the convex grabbing game on the plane

The convex grabbing game is a game where two players, Alice and Bob, alternate taking extremal points from the convex hull of a point set on the plane. Rational weights are given to the points. The goal of each player is to maximize the total weight over all points that they obtain. We restrict the setting to the case of binary weights. We show a construction of an arbitrarily large odd-sized point set that allows Bob to obtain almost 3/4 of the total weight. This construction answers a question asked by Matsumoto, Nakamigawa, and Sakuma in [Graphs and Combinatorics, 36/1 (2020)]. We also present an arbitrarily large even-sized point set where Bob can obtain the entirety of the total weight. Finally, we discuss conjectures about optimum moves in the convex grabbing game for both players in general

Generalized minimum 0-extension problem and discrete convexity

Given a fixed finite metric space (V,μ), the {\em minimum 0-extension problem}, denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai: if metric μ is {\em orientable modular} then 0-Ext[μ] can be solved in polynomial time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed a theory of discrete convex functions on orientable modular graphs generalizing several known classes of functions in discrete convex analysis, such as L♮-convex functions. We consider a more general version of the problem in which unary functions fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where set F⊆(V2) is fixed. We extend the complexity classification above by providing an explicit condition on (μ,F) for the problem to be tractable. In order to prove the tractability part, we generalize Hirai's theory and define a larger class of discrete convex functions. It covers, in particular, another well-known class of functions, namely submodular functions on an integer lattice. Finally, we improve the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs

Fiber composites for car seats

Currently there is an effort to replace conventional construction materials – steel, by new modern materials. Ones of the new modern material we can include fiber composites materials. Basic fiber composite materials are composite with fibers of glass, carbon or linen. These types of composites are used in construction of car by their useful properties. Linen composites are used in interior of car for upholstery. Glass or carbon composites are used in the body part of car as bumper, mudguards, and door sections. Next possibility is used carbon fiber composites in construction of car seat. In the case of material replacement, it is necessary to compare the basic mechanical properties between the conventional material and the new material. Due to the anisotropic properties of fibrous composites, it is necessary to compare mechanical properties by experimental method on shape-like samples with real car seat parts. This article describes comparison mechanical properties of steel and carbon fibers composites on the specimen of the tube with circle and rectangle profil

Generation and performance of localised surface plasmons utilising nano-scale structured multi-layered thin films deposited upon D-shaped optical fiber

A new generation of surface plasmonic optical fibre sensors is fabricated using multiple coatings deposited on a lapped section of a single mode fibre. Post-deposition UV laser irradiation using a phase mask produces a nano-scaled surface relief grating structure, resembling nano-wires. The overall length of the individual corrugations is approximately 14 μm with an average full width half maximum of 100 nm. Evidence is presented to show that these surface structures result from material compaction created by the silicon dioxide and germanium layers in the multi-layered coating and the surface topology is capable of supporting localised surface plasmons. The coating compaction induces a strain gradient into the D-shaped optical fibre that generates an asymmetric periodic refractive index profile which enhances the coupling of the light from the core of the fibre to plasmons on the surface of the coating. Experimental data are presented that show changes in spectral characteristics after UV processing and that the performance of the sensors increases from that of their pre-UV irradiation state. The enhanced performance is illustrated with regards to change in external refractive index and demonstrates high spectral sensitivities in gaseous and aqueous index regimes ranging up to 4000 nm/RIU for wavelength and 800 dB/RIU for intensity. The devices generate surface plasmons over a very large wavelength range, (visible to 2 μm) depending on the polarization state of the illuminating light

BK Lyncis: The Oldest Old Nova?... And a Bellwether for Cataclysmic-Variable Evolution

We summarize the results of a 20-year campaign to study the light curves of BK Lyncis, a nova-like star strangely located below the 2-3 hour orbital period gap in the family of cataclysmic variables. Two apparent "superhumps" dominate the nightly light curves - with periods 4.6% longer, and 3.0% shorter, than P_orb. The first appears to be associated with the star's brighter states (V~14), while the second appears to be present throughout and becomes very dominant in the low state (V~15.7). Starting in the year 2005, the star's light curve became indistinguishable from that of a dwarf nova - in particular, that of the ER UMa subclass. Reviewing all the star's oddities, we speculate: (a) BK Lyn is the remnant of the probable nova on 30 December 101, and (b) it has been fading ever since, but has taken ~2000 years for the accretion rate to drop sufficiently to permit dwarf-nova eruptions. If such behavior is common, it can explain other puzzles of CV evolution. One: why the ER UMa class even exists (because all members can be remnants of recent novae). Two: why ER UMa stars and short-period novalikes are rare (because their lifetimes, which are essentially cooling times, are short). Three: why short-period novae all decline to luminosity states far above their true quiescence (because they're just getting started in their postnova cooling). Four: why the orbital periods, accretion rates, and white-dwarf temperatures of short-period CVs are somewhat too large to arise purely from the effects of gravitational radiation (because the unexpectedly long interval of enhanced postnova brightness boosts the mean mass-transfer rate). These are substantial rewards in return for one investment of hypothesis: that the second parameter in CV evolution, besides P_orb, is time since the last classical-nova eruption.Comment: PDF, 46 pages, 4 tables, 10 figures; in preparation; more info at http://cbastro.org