Graph pegging numbers

In graph pegging, we view each vertex of a graph as a hole into which a peg can be placed, with checker-like “pegging moves” allowed. Motivated by well-studied questions in graph pebbling, we introduce two pegging quantities. The pegging number (respectively, the optimal pegging number) of a graph is the minimum number of pegs such that for every (respectively, some) distribution of that many pegs on the graph, any vertex can be reached by a sequence of pegging moves. We prove several basic properties of pegging and analyze the pegging number and optimal pegging number of several classes of graphs, including paths, cycles, products with complete graphs, hypercubes, and graphs of small diameter.     

Irreducibility of the punctual quotient scheme of a surface

It is shown that the punctual quotient schemeQ _l ^r parametrizing all zero-dimensional quotients of lengthl and supported at some fixed point O∈A ² in the plane is irreducible.     

Novel diapocarotenoid dications with VIS/NIR absorption

Isoprenoid acyclic polyene carbodications with 6, 14 and 18 π electrons have been synthesized and characterized in comparison with previously prepared dicyclic C₄₀-carotenoid dications. An equation correlating λ_max (400-1100 nm region) and the number of sp² hybridized carbon atoms in the dication is presented.     

On the effects of irregular boundaries in finite difference models

Propagation of periodic waves in the vicinity of irregular saw-tooth shaped boundary in finite difference models is investigated. The reflection of an incoming wave from a single saw-tooth boundary is found to be accompanied by a phase shift. It is shown that any wave mode propagating along such a boundary is trapped and decays in the direction normal to the boundary. A wave propagating along a channel with saw-tooth shaped lateral boundaries is influenced by the trapped waves, which leads to a reduction of the phase velocity. Phase velocities obtained from the present normal mode analysis are compared to velocities in numerical experiments. The agreement is excellent.     

Tempered distributions in infinitely many dimensions

The space of testing functions for tempered distributions is characterized in an abstract way as the maximal space in a certain class of locally convex topological vector-spaces. The main characteristic of this class is stability under the differentiation and multiplication operators.The ensuing characterization of tempered distributions may readily be generalized to the case of infinitely many dimensions, and a certain class of such generalizations is studied. The spaces of testing elements are required to be stable under the action of the canonical field operators of the quantum theory of free fields, and it is shown that extreme spaces of testing elements exist and have simple properties. In fact, the maximal space is a Montel space, and the minimal complete space is a direct sum of such spaces.The formalism is applied to the problem of extending the canonical field operators, and a number of extension theorems are derived. In a forthcoming paper the theory of tempered distributions in infinitely many variables will be applied to a structurally simple linear operator equation.     

Activated carbon obtained from sapelli wood sawdust by microwave heating for o-cresol adsorption

Research on Chemical Intermediates - Activated carbon (AC) was prepared from sapelli wood sawdust using a microwave heating process. The biomass was mixed with inorganic components...     

Depth‐averaged non‐hydrostatic extension for shallow water equations with quadratic vertical pressure profile: equivalence to Boussinesq‐type equations

We reformulate the depth‐averaged non‐hydrostatic extension for shallow water equations to show equivalence with well‐known Boussinesq‐type equations. For this purpose, we introduce two scalars representing the vertical profile of the non‐hydrostatic pressure. A specific quadratic vertical profile yields equivalence to the Serre equations, for which only one scalar in the traditional equation system needs to be modified. Equivalence can also be demonstrated with other Boussinesq‐type equations from the literature when considering variable depth, but then the non‐hydrostatic extension involves mixed space–time derivatives. In case of constant bathymetries, the non‐hydrostatic extension is another way to circumvent mixed space–time derivatives arising in Boussinesq‐type equations. On the other hand, we show that there is no equivalence when using the traditionally assumed linear vertical pressure profile. Linear dispersion and asymptotic analysis as well as numerical test cases show the advantages of the quadratic compared with the linear vertical non‐hydrostatic pressure profile in the depth‐averaged non‐hydrostatic extension for shallow water equations. Copyright © 2017 John Wiley & Sons, Ltd.     

Preparation of a Bridged Verbenindenyl Ligand for Metallocenes

The preparation of an annulated verbenyl indene is described. Reduction of the verbenone oxo group and water elimination provided a verbenylindene with an embedded fulvene unit, which was reduced to an annulated verbenylindene, a fluorene derivative. The ansa‐bridge was constructed between the fluorene 9‐position and 6,6‐dimethylfulvene by way of the lithiated indene. Dilithiation of the ligand and treatment with ZrCl₄ yielded the corresponding zirconocene.     

QUANTIFIED MODAL LOGIC WITH NEIGHBORHOOD SEMANTICS

The paper presents a semantics for quantified modal logic which has a weaker axiomatization than the usual Kripke semantics. In particular, the Barcan Formula (BF) and its converse are not valid with the proposed semantics. Subclasses of models which validate BF and other interesting formulas are presented. A completeness theorem is proved, and the relation between this result and completeness with respect to Kripke models is investigated.