Probabilistic evolution theory for explicit autonomous ordinary differential equations: recursion of squarified telescope matrices and optimal space extension

Probabilistic evolution theory facilitates the solution of initial value problem of explicit autonomous ordinary differential equations with second degree multinomial right hand side functions. Its formulation has components we call telescope matrices. The matrices grow in size very rapidly and has many zeroes and repeating structures. In order to avoid the computational complexity coming from telescope matrices, squarified telescope matrices are utilized. Their calculation is through a recursion. This recursion has been used in several works by the authors and their colleagues but its proof was not given. This work gives the proof of the recursion and all the surrounding details. A second purpose of this work is to provide a method for most facilitative (optimal) space extension. Space extension is needed for using probabilistic evolution theory when degree of multinomiality of the right hand side functions is more than two. For this purpose, an approach using method of exhaustion (brute-force) is proposed.     

Crystal structure of bis-N,N′-p-chlorosalicylideneamine-1,2-diaminobenzene

The crystal structure of the title compound, C₂₀H₁₄N₂O₂Cl₂, has been determined by single crystal X-ray diffraction techniques. It crystallizes in the orthorhombic system witha=7.532(3)Å,b=18.563(2)Å,c=25.089(3)Å, space groupPbca,V=3507.9(3)ų,Z=8,F(000)=1584.D _x =1.459 g cm^–3,M=385.3 a. m. u., (MoK)=0.7107 Å, =3.35 cm^–1,T=297°K,R=0.086,R _w =0.049 for 2119 unique diffractometer data. The molecules are linked by van der Waals forces.     

Synthesis and structure elucidation of bromination products from dibromohomobenzonorbornadienes: high temperature bromination--part 17

The electrophilic addition of bromine to dibromohomobenzonorbornadiene derivatives at -45 +/- 5 degrees C led to the formation of the rearranged and non-rearranged tetrabromides in a ratio of 6:4. However, high-temperature bromination of the same system in CCl4 at 77 degrees C produced only non-rearranged products. The formation mechanism of the isomers and the role of the substituent on the rearrangement is discussed. The structure elucidation of the isomeric tetrabromides was achieved from NMR spectral data. The agreement between the calculated dihedral angles and the measured coupling constants is especially excellent. The gamma-gauche effect is discussed.     

Manganese(III)-mediated oxidative free-radical additions of 1,3-dicarbonyl compounds to homobenzonorbornadiene and benzobarrelene: mechanistic studies

Homobenzonorbornadiene and benzobarrelene were reacted with dimedone/acetylacetone and Mn(OAc)₃ in the presence of Cu(OAc)₂ in acetic acid. Mainly rearranged products having a [2.2.2]skeleton and the nonrearranged dihydrofuran derivatives were obtained. These observations clearly indicated that the second oxidation takes place before the cyclization reaction. Furthermore, intramolecular tandem oxidations were observed where unusually oxyl radicals attack the double bond to form the products. The mechanism of the formation of the products is discussed.     

Electric Multipole Moments for Some First—Row Diatomic Hydride Molecules

As an example of the use of the analytical formulas derived for electric multipole moment integrals over STOs in our previous work(I.I.Guseinov,et al.,J.Mol.Struct(Theochem)465(1999)5),the 2ν-pole electric moments have been calculated for the ground electronic states of LiH,BH and FH of the first-row diatomic hydride molecules,Calculated electric multipole moment values are in agteement with literatures.By the use of these analytical formulas the 2^ν-pole moments for multiatomic molecules can be evaluated most efficiently and accurately by employing STOs as basis sets.     

A Modified Gravity Theory: Null Aether

General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the "aether". In this paper, we put forward the idea of a null aether field and introduce, for the first time, the Null Aether Theory(NAT) — a vector-tensor theory. We first study the Newtonian limit of this theory and then construct exact spherically symmetric black hole solutions in the theory in four dimensions, which contain Vaidya-type non-static solutions and static Schwarzschild-(A)dS type solutions, Reissner-Nordstr?m-(A)dS type solutions and solutions of conformal gravity as special cases. Afterwards, we study the cosmological solutions in NAT:We find some exact solutions with perfect fluid distribution for spatially flat FLRW metric and null aether propagating along the x direction. We observe that there are solutions in which the universe has big-bang singularity and null field diminishes asymptotically. We also study exact gravitational wave solutions — AdS-plane waves and pp-waves — in this theory in any dimension D ≥ 3. Assuming the Kerr-Schild-Kundt class of metrics for such solutions, we show that the full field equations of the theory are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. The main conclusion of these computations is that the spin-0 aether field acquires a "mass" determined by the cosmological constant of the background spacetime and the Lagrange multiplier given in the theory.     

The structure of the water–propane interface investigated by x‐ray reflectivity measurements

We present an x‐ray reflectivity study of the water–propane interface. The vertical structure of the interface is analyzed and the adsorption of thin layers of propane on the water surface is observed. An increase of layer thickness with rising pressure is found. The electron density of the thin films is identical with the corresponding value of bulk liquid propane. From the adsorption isotherm we determine the Hamaker constant of the system, which shows a considerably higher value compared to calculations based on the Lifshitz theory. The surface tension of the molecularly thin layer is reduced in comparison to the bulk value. The measured surface roughness is in good agreement with a modified model based on capillary wave fluctuations of the water‐propane–gas interfaces. Copyright © 2008 John Wiley & Sons, Ltd.     

The effect of opacifier properties on thermal conductivity of vacuum insulation panel with fumed silica

Journal of Thermal Analysis and Calorimetry - The reduction of radiation heat transfer in VIPs is an important issue. In VIPs, the radiation heat transfer is reduced by the use of opacifier....