The Existence of a Bush-Type Hadamard Matrix of Order 324 and Two New Infinite Classes of Symmetric Designs

A symmetric 2-(324, 153, 72) design is constructed that admits a tactical decomposition into 18 point and block classes of size 18 such that every point is in either 0 or 9 blocks from a given block class, and every block contains either 0 or 9 points from a given point class. This design is self-dual and yields a symmetric Hadamard matrix of order 324 of Bush type, being the first known example of a symmetric Bush-type Hadamard matrix of order 4n ² for n > 1 odd. Equivalently, the design yields a strongly regular graph with parameters v=324, k=153, ==72 that admits a spread of cocliques of size 18. The Bush-type Hadamard matrix of order 324 leads to two new infinite classes of symmetric designs with parameters

Bush‐type Hadamard matrices and symmetric designs

Abstact: A symmetric 2‐(100, 45, 20) design is constructed that admits a tactical decomposition into 10 point and block classes of size 10 such that every point is in either 0 or 5 blocks from a given block class, and every block contains either 0 or 5 points from a given point class. This design yields a Bush‐type Hadamard matrix of order 100 that leads to two new infinite classes of symmetric designs with parameters and where m is an arbitrary positive integer. Similarly, a Bush‐type Hadamard matrix of order 36 is constructed and used for the construction of an infinite family of designs with parameters and a second infinite family of designs with parameters where m is any positive integer. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 72–78, 2001     

Extending the acidity ladder of neutral organic superacids—a DFT-B3LYP study of deprotonation of nonacyanofluorene

It was shown by a carefully selected B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d) model that nonacyanofluorene and its most stable prototropic tautomer represent very powerful neutral organic acids both in the gas phase and in DMSO.     

Dünnschichtchromatographische Trennung kleiner Mengen Gallium von Eisen,Aluminium, Indium und Titan

Ohne Zusammenfassung     

On a free piston problem for potential ideal fluid flow

Our goal was to model and analyze a stationary and evolutionary potential ideal fluid flow through the junction of two pipes in the gravity field. Inside the ‘vertical’ pipe, there is a heavy piston that can freely move along the pipe. In the stationary case, we are interested in the equilibrium position of the piston in dependence on the geometry of junction, and in the evolutionary case, we study motion of the piston also in dependence on geometry. We formulate corresponding initial and boundary value problems and prove the existence results. The problem is nonlinear because the domain is unknown. Furthermore, we study some qualitative properties of the solutions and compare them with the qualitative properties of a free piston problem for Newtonian fluid flow. All theoretical results are illustrated with numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.     

Thermal and flammability behaviour of copolymers of N-(2, 4, 6-tribromophenyl)maleimide with some acrylates

The copolymers of N-(2, 4, 6-tribromophenyl)maleimide (TBPMI) with methyl acrylate, methyl methacrylate and acrylonitrile of different composition were prepared by free radical polymerization at low conversion. Their thermal behaviour was established by TGA measurements in helium atmosphere and flammability properties were determined by limiting oxygen index method. The higher TBPMI content in the copolymer led to a higher thermal stability and lower flammability particularly when Sb₂O₃ was used as a synergist.