The size of random fragmentation trees

We consider the random fragmentation process introduced by Kolmogorov, where a particle having some mass is broken into pieces and the mass is distributed among the pieces at random in such a way that the proportions of the mass shared among different daughters are specified by some given probability distribution (the dislocation law); this is repeated recursively for all pieces. More precisely, we consider a version where the fragmentation stops when the mass of a fragment is below some given threshold, and we study the associated random tree. Dean and Majumdar found a phase transition for this process: the number of fragmentations is asymptotically normal for some dislocation laws but not for others, depending on the position of roots of a certain characteristic equation. This parallels the behavior of discrete analogues with various random trees that have been studied in computer science. We give rigorous proofs of this phase transition, and add further details. The proof uses the contraction method. We extend some previous results for recursive sequences of random variables to families of random variables with a continuous parameter; we believe that this extension has independent interest.     

Novel ferroelectric liquid crystals based on optically active Preliminary communication propargylic alcohols

Some new calamitic chiral mesogens (2,5-diphenyl-1,3,4-thiadiazoles, 2,5-diphenylpyrimidines and a biphenylyl benzoate) incorporating the 1-alkylpropynyl moiety have been synthesized as enantiomerically enriched materials (ee c. 87%) and/or as racemates. Their liquid crystalline properties were studied by polarizing microscopy, differential scanning calorimetry and electro-optical investigation. Thereby it was found that most of the new compounds exhibit smectic C phases. The spontaneous polarization (Ps) of the optically active materials was measured to be around 10 nCcm-2.     

Phosphorylated serine and threonine residues promote site‐specific fragmentation of singly charged,arginine‐containing peptide ions

In order to investigate gas‐phase fragmentation reactions of phosphorylated peptide ions, matrix‐assisted laser desorption/ionization (MALDI) and electrospray ionization (ESI) tandem mass (MS/MS) spectra were recorded from synthetic phosphopeptides and from phosphopeptides isolated from natural sources. MALDI‐TOF/TOF (TOF: time‐of‐flight) spectra of synthetic arginine‐containing phosphopeptides revealed a significant increase of y ions resulting from bond cleavages on the C‐terminal side of phosphothreonine or phosphoserine. The same effect was found in ESI‐MS/MS spectra recorded from the singly charged but not from the doubly charged ions of these phosphopeptides. ESI‐MS/MS spectra of doubly charged phosphopeptides containing two arginine residues support the following general fragmentation rule: Increased amide bond cleavage on the C‐terminal side of phosphorylated serines or threonines mainly occurs in peptide ions which do not contain mobile protons. In MALDI‐TOF/TOF spectra of phosphopeptides displaying N‐terminal fragment ions, abundant b–H₃PO₄ ions resulting from the enhanced dissociation of the pSer/pThr–X bond were detected (X denotes amino acids). Cleavages at phosphoamino acids were found to be particularly predominant in spectra of phosphopeptides containing pSer/pThr–Pro bonds. A quantitative evaluation of a larger set of MALDI‐TOF/TOF spectra recorded from phosphopeptides indicated that phosphoserine residues in arginine‐containing peptides increase the signal intensities of the respective y ions by almost a factor of 3. A less pronounced cleavage‐enhancing effect was observed in some lysine‐containing phosphopeptides without arginine. The proposed peptide fragmentation pathways involve a nucleophilic attack by phosphate oxygen on the carbon center of the peptide backbone amide, which eventually leads to cleavage of the amide bond. Copyright © 2009 John Wiley & Sons, Ltd.     

Semiconductor Research Needs in the Nanoscale Physical Sciences: A Semiconductor Research Corporation Working Paper

The purpose of this paper is to identify areas in the basic physical sciences where additional research is needed to sustain the extraordinary progress in electronics that has now extended for several decades. Also, it is argued that basic research will provide the foundation for the discovery of new generations of nanoelectronic devices that will continue the experimental rate of reduction in cost per function. Some of the fundamental areas requiring further research are the chemistry and physics of material interfaces, conductivity at small dimensions, deterministic doping effects, and nanomagnetics. Discovery research also is needed in the functional synergy of nanoelectronic materials and non-traditional fabrication methods.     

Group theoretic properties of Rijndael-like ciphers

We provide conditions for which the round functions of an ?-bit Rijndael-like block cipher generate the alternating group on the set {0,1}^?. These conditions show that the class of Rijndael-like ciphers whose round functions generate the alternating group on their message space is large, and includes both the actual Rijndael and the block cipher used by the compression function of the Whirlpool hash function. The result indicates that there is no trapdoor design for a Rijndael-like cipher based on the imprimitivity of the group action of its proper round functions which is difficult to detect.     

The synthesis and reactivity of polysilylacetylenes: Diels—Alder reactions to give bis (silyl) benzenes

Six bis(silyl)acetylenes (XMe²Si? C?C? SiMe₂X) with the following varied silicon substituents X were prepared: 1 (Me, Me); 2 (H, H); 3 (C1, H); 4 (CI, CI); 5 (MeO, H); 6 (MeO, MeO). While 1 and 2 may be prepared by the reaction of dilithio- or bis(bromomagnesium)-acetylide with the appropriate chlorosilane, similar reactions designed to give 3–6 yielded oligomers, XMe₂Si? (? C?C? SiMe₂)_n? X, 7, X=CI, MeO, as the major products, indicating that the acetylenic functionality on silicon activates the chlorosilane towards nucleophilic substitution. Compounds 3 and 4 were prepared by free radical chlorination of 2. Methanolysis of 3 and 4 gave quantitative yields of 5 and 6 respectively. Compounds 1–6 undergo a Diels–Alder reaction with α-pyrone to produce, after loss of carbon dioxide, bis(silyl)-substituted benzene derivatives. The order of reactivity has been determined to be: 4=6>3=5>1>2, indicating that chloro or alkoxy substituents favor the cycloaddition with 2- pyrone. The adducts formed by compounds 3–6 undergo an unusually facile hydrolysis or elimination to give 1,1,3,3-tetramethyl-1,3-disila-2-oxaindane.