Traces and Sobolev extension domains

Assume that is a bounded domain and its boundary is -regular, . We show that if there exists a bounded trace operator , and , and -Hölder continuous functions are dense in , , then the domain is a -extension domain.

     

Enumeration of 2-(9, 3, λ) Designs and Their Resolutions

We consider 2-(9, 3, ) designs, which are known to exist for all 1, andenumerate such designs for = 5 and their resolutions for 3 5, the smallestopen cases. The number of nonisomorphic such structures obtained is 5 862 121 434, 426, 149 041, and 203 047732, respectively. The designs are obtained by an orderly algorithm, and the resolutions by two approaches:either by starting from the enumerated designs and applying a clique-finding algorithm on two levels or by anorderly algorithm.     

Formation and evolution of scroll waves in photosensitive excitable media

Experimental and computational studies of the formation and evolution of scroll waves in three-dimensional excitable media are presented. Scroll waves are initiated in the photosensitive Belousov-Zhabotinsky reaction by perturbing traveling waves transverse to their direction of propagation. Scroll rings are generated by perturbing circular waves, which expand or contract depending on the strength of an imposed excitability gradient and its direction relative to the rotational direction of the scroll wave. (c) 1998 American Institute of Physics.     

Classification of resolvable balanced incomplete block designs — the unitals on 28 points

Approaches for classifying resolvable balanced incomplete block designs (RBIBDs) are surveyed. The main approaches can roughly be divided into two types: those building up a design parallel class by parallel class and those proceeding point by point. With an algorithm of the latter type — and by refining ideas dating back to 1917 and the doctoral thesis by Pieter Mulder — it is shown that the list of seven known resolutions of 2-(28, 4, 1) designs is complete; these objects are also known as the resolutions of unitals on 28 points. This research was supported in part by the Academy of Finland, Grants No. 107493, 110196, and 117499.     

Shifting Chemical Equilibria in Flow—Efficient Decarbonylation Driven by Annular Flow Regimes

To efficiently drive chemical reactions, it is often necessary to influence an equilibrium by removing one or more components from the reaction space. Such manipulation is straightforward in open systems, for example, by distillation of a volatile product from the reaction mixture. Herein we describe a unique high‐temperature/high‐pressure gas/liquid continuous‐flow process for the rhodium‐catalyzed decarbonylation of aldehydes. The carbon monoxide released during the reaction is carried with a stream of an inert gas through the center of the tubing, whereas the liquid feed travels as an annular film along the wall of the channel. As a consequence, carbon monoxide is effectively vaporized from the liquid phase into the gas phase and stripped from the reaction mixture, thus driving the equilibrium to the product and preventing poisoning of the catalyst. This approach enables the catalytic decarbonylation of a variety of aldehydes with unprecedented efficiency with a standard coil‐based flow device.     

An enumeration of graphical designs

Let Ψ(t,k) denote the set of pairs (v,λ) for which there exists a graphical t‐(v,k,λ) design. Most results on graphical designs have gone to show the finiteness of Ψ(t,k) when t and k satisfy certain conditions. The exact determination of Ψ(t,k) for specified t and k is a hard problem and only Ψ(2,3), Ψ(2,4), Ψ(3,4), Ψ(4,5), and Ψ(5,6) have been determined. In this article, we determine completely the sets Ψ(2,5) and Ψ(3,5). As a result, we find more than 270,000 inequivalent graphical designs, and more than 8,000 new parameter sets for which there exists a graphical design. Prior to this, graphical designs are known for only 574 parameter sets. © 2006 Wiley Periodicals, Inc. J Combin Designs 16: 70–85, 2008     

The Cycle Switching Graph of the Steiner Triple Systems of Order 19 is Connected

Switching is a local transformation that when applied to a combinatorial object gives another object with the same parameters. It is here shown that the cycle switching graph of the 11 084 874 829 isomorphism classes of Steiner triple systems of order 19 as well as the cycle switching graph of the 1 348 410 350 618 155 344 199 680 000 labeled such designs are connected. In addition to giving an understanding of the multitude of Steiner triple systems—at least for order 19 but perhaps also generally—this work also presents an algorithm for testing connectedness of large implicit graphs and brings forward a benchmark instance for such algorithms.     

Steiner triple systems satisfying the 4-vertex condition

Higman asked which block graphs of Steiner triple systems of order v satisfy the 4-vertex condition and left the cases v = 9, 13, 25 unsettled.We give a complete answer to this question by showing that the affine plane of order 3 and the binary projective spaces are the only such systems. The major part of the proof is to show that no block graph of a Steiner triple system of order 25 satisfies the 4-vertex condition.     

Mechanical fabrication of high-strength and redispersible wood nanofibers from unbleached groundwood pulp

In the past, the direct production of lignin-containing nanofibers from wood materials has been very limited, and nanoscale fibers (nanocelluloses) have been mainly isolated from chemically delignified, bleached cellulose pulp. In this study, we have introduced a newly adapted, heat-intensified disc nanogrinding process for the enhanced nanofibrillation of wood nanofibers (WNF) with a high lignin content (27.4 wt%). The WNF produced this way have many unique and intriguing properties in their naturally occurring form, for example, being able to be dispersed in ethanol and having ethanol solution viscosities higher than water solution viscosities. When WNF nanopapers were formed with ethanol, the properties of the nanofibers were recoverable without a notable decrease in the viscosity or mechanical strength after redispersing them in water. The preservation of lignin in the WNF was noticed as an increase in the water contact angles (89°), the rapid removal of water in the fabrication of the nanopapers, and the enhanced strength of the nanopapers when subjected to high pressure and heat. The nanopapers fabricated from the WNF were mechanically stable, having an elastic modulus of 6.2 GPa, a maximum stress of 103.4 MPa, and a maximum strain of 3.5%. Throughout the study, characteristics of the WNF were compared to those of the delignified and bleached reference cellulose nanofibers. We envision that the exciting characteristics of the WNF and their lower cost of production compared to that of bleached cellulose nanofibers may offer new opportunities for nanocellulose and biocomposite research.