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In this paper we consider the Br = Br ′ question for classifying stacks by various group schemes. These are algebraic stacks that do not necessarily admit a finite flat cover by a scheme for which Br = Br ′ holds, hence are not amenable to the usual argument of pushing forward a twisted vector bundle. We provide two classes of examples satisfying Br ≠ Br ′ that do not arise from the scheme case. Communicated by Tony Varilly-Alvarado [ABSTRACT FROM AUTHOR]

In container terminals, the yard area consists of a set of blocks, which consists of a set of bays. Each bay consists of a set of stacks, which consists of a set of tiers. In the container pre-marshalling problem, an initial layout of a bay is converted to a final desired layout. The final layout follows the given loading schedule of this bay. This has a direct impact on the most important container terminal performance measure: the vessel loading time. The deviation between the current layout and the desired layout is expressed by the value of the mis-overlays. The objective of the pre-marshalling problem is to eliminate the mis-overlays with the minimum number of container movements. In this article, a variable chromosome length genetic algorithm was applied to solve the problem. The results of the new solution approach were compared against benchmark instances and the results were remarkably better. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new dynamical system of a pushdown automaton, called automaton with a stack (AS). We prove that every AS has a periodic configuration by construction of it. Next, we define a special case of an AS, called AS with finite memory and we prove that the AS has a finite memory if and only if it is positively expansive. Furthermore, we prove that every AS with finite memory has shadowing property. Having these two properties, we set a finite-to-one map between an AS with finite memory and some vertex subshift, which gives us a semi-conjugacy between these two systems. Additionally, we define an algorithm to decide if a given graphGdescribes some AS with finite memory and to calculate maximal depth of a stack. [ABSTRACT FROM AUTHOR]

The article discusses the continuous analogue of stacking identical bricks in constructing a tower of maximal overhang. It states that the overhang can be arranged to be as large as desired since the harmonic series diverges by using a large number of blocks. It says that the harmonic staircases and all stacks in the interest are simply figures in the xy-plane which are orthogonally extended in the z-direction.

A new bisupporting metal-oxygen cluster with bicapped pseudo-Keggin compound [CuII{Cl0.5Cl(phen)}]2 {[PMoV6MoVI6O40(VIVO)2][CuII(phen)2]2}·2H2O (phen = 1,10-phenathroline) has been synthesized by hydrothermal method and characterized by elemental analysis, IR spectroscopy, TGA, XRPD, and single-crystal X-ray diffraction. The polyoxoanion consists of a bicapped vanadium Keggin polyoxoanion and two {[Cu(phen)]2}2+ subunits producing bisupporting bicapped Keggin-polyoxometalate structure. The isolated dinuclear unit [CuII{Cl0.5Cl(phen)}2]+ acts as the countercation in title compound. In the crystal structure π - π stacking interactions, multiform C-H···O and O-H···O hydrogen bonds lead to a three-dimensional network. [ABSTRACT FROM AUTHOR]

Two new complexes constructed by 1,4-phenylenediacetic acid (H2PDA) and 2,2'-bipyridine (2,2'-bpy), namely [Cu(PDA)(2,2'-bpy)]·5H2O (1) and [Zn2(PDA)(2,2'-bpy)2Cl2] (2), have been synthesized and characterized by single-crystal X-ray diffraction, elemental analysis, IR, and UV-Vis spectrum. Single-crystal X-ray diffraction reveals that they both crystallize in the triclinic space group of P-1. In complex 1, the Cu atom is hexa-coordinated and each asymmetric unit contains five uncoordinated water molecules that form a water cluster (H2O)10 with their symmetric equivalent. Complex 2 is a simple dimer and the Zn atom is penta-coordinated. Both in complex 1 and 2 there are π-π stacking interactions. [ABSTRACT FROM AUTHOR]

A novel copper(II) coordination polymer with the formula [Cu(pmt)(Cl)]n (pmtH=N-(2-pyridylmethylidene)taurine) has been synthesized and characterized by elemental analysis, IR and single-crystal X-ray diffraction. Each CuII atom is six-coordinated with a distorted '4+2' octahedral geometry and a pair of chlorides and sulfonates act as μ2-bridges to head the [Cu(pmt)] subunits together. The two types of rings with sharing apex Cu are alternately created and interconnected to form an interesting 1-D zigzag chain propagating along the a axis. Also, the significant weak C-H...Cl hydrogen bonds and π-π stacking interactions between the adjacent chains expanded the 1-D structure to 2-D network in the ac plane. [ABSTRACT FROM AUTHOR]

This is the second in a series of three papers in which we investigate the rational Chow ring of the stack 0 consisting of nodal curves of genus 0. Here we define the basic classes: the classes of strata and the Mumford classes. [ABSTRACT FROM AUTHOR]

We investigate the modular properties of nodal curves on a low genus K3 surface. We prove that a general genus g curve C is the normalization of a δ-nodal curve X sitting on a primitively polarized K3 surface S of degree 2p - 2, for 2 ≤ g = p - δ < p ≤ 11. The proof is based on a local deformation-theoretic analysis of the map from the stack of pairs (S, X) to the moduli stack of curves Mg that associates to X the isomorphism class [C] of its normalization. [ABSTRACT FROM AUTHOR]

We give a presentation for the stack [image omitted] of rational curves with at most 1 node as the quotient by GL3 of an open set in a 6-dimensional irreducible representation. We then use equivariant intersection theory to calculate the integral Chow ring of this stack. [ABSTRACT FROM AUTHOR]

We study the structure of the stacks of twisted stable maps to the classifying stack of a finite group G-which we call the stack of twisted G-covers, or twisted G-bundles. For a suitable group G we show that the substack corresponding to admissible G-covers is a smooth projective fine moduli space. [ABSTRACT FROM AUTHOR]

Given a separated and locally finitely-presented Deligne-Mumford stack X over an algebraic space S, and a locally finitely-presented O[SUBX]-module F, we prove that the Quot functor Quot(F/X/S ) is represented by a separated and locally finitely-presented algebraic space over S. Under additional hypotheses, we prove that the connected components of Quot(F/X/S ) are quasi-projective over S. [ABSTRACT FROM AUTHOR]

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