Linear time algorithms for Abelian group isomorphism and related problems

We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian. (C) 2007 Elsevier Inc. All rights reserved.

On the Compressibility of non-Abelian-Group Sources in a Distributed Source Coding Setting

We consider the problem of compression of a non-Abelian source.This is motivated by the problem of distributed function computation,where it is known that if one is only interested in computing a function of several sources, then one can often improve upon the compression rate required by the Slepian-Wolf bound. Let G be a non-Abelian group having center Z(G). We show here that it is impossible to compress a source with symbols drawn from G when Z(G) is trivial if one employs a homomorphic encoder and a typical-set decoder.We provide achievable upper bounds on the minimum rate required to compress a non-Abelian group with non-trivial center. Also, in a two source setting, we provide achievable upper bounds for compression of any non-Abelian group, using a non-homomorphic encoder.

On the achievable rates of sources having a group alphabet in a distributed source coding setting

We consider the problem of compression via homomorphic encoding of a source having a group alphabet. This is motivated by the problem of distributed function computation, where it is known that if one is only interested in computing a function of several sources, then one can at times improve upon the compression rate required by the Slepian-Wolf bound. The functions of interest are those which could be represented by the binary operation in the group. We first consider the case when the source alphabet is the cyclic Abelian group, Zpr. In this scenario, we show that the set of achievable rates provided by Krithivasan and Pradhan [1], is indeed the best possible. In addition to that, we provide a simpler proof of their achievability result. In the case of a general Abelian group, an improved achievable rate region is presented than what was obtained by Krithivasan and Pradhan. We then consider the case when the source alphabet is a non-Abelian group. We show that if all the source symbols have non-zero probability and the center of the group is trivial, then it is impossible to compress such a source if one employs a homomorphic encoder. Finally, we present certain non-homomorphic encoders, which also are suitable in the context of function computation over non-Abelian group sources and provide rate regions achieved by these encoders.

On The Topology Of Manifolds With Positive Isotropic Curvature

We show that a closed orientable Riemannian n-manifold, n >= 5, with positive isotropic curvature and free fundamental group is homeomorphic to the connected sum of copies of Sn-1 x S-1.

Amide-Based Glutathione Peroxidase Mimics: Effect of Secondary and Tertiary Amide Substituents on Antioxidant Activity

A series of secondary and tertiary amide-substituted diselenides were synthesized and studied for their GPx-like antioxidant activities using H2O2 Cum-OOH, and tBuOOH as substrates and PhSH as thiol co-substrate.The effect of substitution at the free -NH group of the amide moiety in the sec-amide-based diselenides on GPx activity was analyzed by detailed experimental and theoretical methods. It is observed that substitution at the free -NH group significantly enhances the GPx-like activities of the sec-amide-based diselenides, mainly by reducing the Se center dot center dot center dot O nonbonded interactions. The reduction in strength of the Se center dot center dot center dot O interaction upon introduction of N,N-dialkyl substituents not only prevents the undesired thiol exchange reactions, but also reduces the stability of selenenyl sulfide intermediates. This leads to a facile disproportionation of the selenenyl sulfide to the corresponding diselenide, which enhances the catalytic activity. The mechanistic investigations indicate that the reactivity of diselenides having sec-or tert-amide moieties with PhSH is extremely slow; indicating that the first step of the catalytic cycle involves the reaction between the diselenides and peroxide to produce the corresponding selenenic and seleninic acids.

A Novel Invertase from a Thermophilic FungusThermomyces lanuginosus:Its Requirement of Thiol and Protein for Activation

Unlike the invertases from the mesophilic fungi and yeasts, invertase from a thermophilic fungus,Thermomyces lanuginosus,was unusually unstable bothin vivoandin vitro.The following observations suggested that the unstable nature of the enzyme activity in the cell-free extracts was due to the oxidation of the cysteine residue(s) in the enzyme molecule: (a) the addition of dithiothreitol or reduced glutathione stabilized invertase activity during storage of the extracts and also revived enzyme activity in the extracts which had become inactive with time; (b)N-ethylmaleimide, iodoacetamide, oxidized glutathione, cystine, or oxidized coenzyme A-inactivated invertase; (c) invertase activity was low when the ratio reduced/oxidized glutathione was lower and high when this ratio was higher, suggesting regulation of the enzyme by thiol/disulfide exchange reaction. In contrast to the activation of invertase by the thiol compounds and its inactivation by the disulfides in the cell-free extracts, the purified enzyme did not respond to these compounds. Following its inactivation, the purified enzyme required a helper protein in addition to dithiothreitol for maximal activation. A cellular protein was identified that promoted activation of invertase by dithiothreitol and it was called “PRIA” for theprotein which helps inrestoringinvertaseactivity. The revival of enzyme activity was due to the conversion of the inactive invertase molecules into an active form. A model is presented to explain the modulation of invertase activity by the thiol compounds and the disulfides, both in the crude cell-free extracts and in the purified preparations. The requirement of free sulfhydryl group(s) for the enzyme activity and, furthermore, the reciprocal effects of the thiols and the disulfides on invertase activity have not been reported for invertase from any other source. The finding of a novel invertase which shows a distinct mode of regulation demonstrates the diversity in an enzyme that has figured prominently in the development of biochemistry.

Tribology of soot suspension in hexadecane as distinguished by the physical structure and chemistry of soot particles

Ethylene gas is burnt to generate soot which is collected thermophoretically from different locations of the flame. Tribological performance of the collected soot in hexadecane suspension is compared with that of carbon black and diesel soot. The soots are analysed to yield a range of mechanical properties, physical structures and chemistry. The paper correlates these property variations with the corresponding variations in friction and wear when the soot suspended in hexadecane is used to lubricate a steel on steel sliding interaction. The particles are dispersed in hexadecane by a non-ionic surfactant, poly-isobutylene succinimide (PIBS), which is mono-functional with no free amine group. The grafting of the surfactant on the soot particles is found to have a profound effect on the dispersion of the soot, in general, while, between the different soot types, the tribology is differentiated by the physical structure and chemistry.

Grafting of Dispersants on MoS2 Nanoparticles in Base Oil Lubrication of Steel

Solid lubricant nanoparticles in suspension in oil are good lubricating options for practical machinery. In this article, we select a range of dispersants, based on their polar moieties, to suspend 50-nm molybdenum disulfide particles in an industrial base oil. The suspension is used to lubricate a steel on steel sliding contact. A nitrogen-based polymeric dispersant (aminopropyl trimethoxy silane) with a free amine group and an oxygen-based polymeric dispersant (sorbital monooleate) when grafted on the particle charge the particle negatively and yield an agglomerate size which is almost the same as that of the original particle. Lubrication of the contact by these suspensions gives a coefficient of friction in the similar to 0.03 range. The grafting of these surfactants on the particle is shown here to be of a chemical nature and strong as the grafts survive mechanical shear stress in tribology. Such grafts are superior to those of other silane-based test surfactants which have weak functional groups. In the latter case, the particles bereft of strong grafts agglomerate easily in the lubricant and give a coefficient of friction in the 0.08-0.12 range. This article investigates the mechanism of frictional energy dissipation as influenced by the chemistry of the surfactant molecule.

Secure Computation in a Bidirectional Relay

Bidirectional relaying, where a relay helps two user nodes to exchange equal length binary messages, has been an active area of recent research. A popular strategy involves a modified Gaussian MAC, where the relay decodes the XOR of the two messages using the naturally-occurring sum of symbols simultaneously transmitted by user nodes. In this work, we consider the Gaussian MAC in bidirectional relaying with an additional secrecy constraint for protection against a honest but curious relay. The constraint is that, while the relay should decode the XOR, it should be fully ignorant of the individual messages of the users. We exploit the symbol addition that occurs in a Gaussian MAC to design explicit strategies that achieve perfect independence between the received symbols and individual transmitted messages. Our results actually hold for a more general scenario where the messages at the two user nodes come from a finite Abelian group G, and the relay must decode the sum within G of the two messages. We provide a lattice coding strategy and study optimal rate versus average power trade-offs for asymptotically large dimensions.

Covalent Postassembly Modification and Water Adsorption of Pd3 Self-Assembled Trinuclear Barrels

Three new ditopic imidazole ligands (2-4) were synthesized in high yields and characterized by various spectroscopic techniques. These ligands resulted in the formation of 3 + 6] self-assembled trinuclear barrels (5-7) in quantitative yields by stoichiometric combination of individual ligands and Pd(NO3)(2) in DMSO. All the three assemblies (5-7) were characterized by `H NMR and ESI-MS analysis, and subsequently, structures of the complexes 5 and 6 were confirmed by single-crystal X-ray diffraction studies. Structure analysis reveals the presence of NO3- counter anions in the intermolecular channels/pockets, which could potentially act as H-bonding sites between adsorbed water molecules within the channels. In fact, both the assemblies (5 and 6) showed water uptake (136.58, and 123.78 cm(3) g(-1), respectively) at ambient temperature under maximum allowable humidity. In addition, free aldehyde group present in the bridging ligand in complex 7 provides reactive site for postassembly modification. Herein, Knoevenagel condensation with Meldrum's acid was utilized under mild conditions by targeting aldehyde group appended in prefabricated complex 7 and transformed into a different complex (8) with altered functional group. Such postassembly functionalization enables incorporation of a new functional group without disrupting the integrity of the trifacial structure.

1- and 2-Chloromorphine. Halogenation of Morphine meta to the Free Phenolic Hydroxyl Group

Treatment of morphine in aqueous HCl at 70° with KIO3 yields a monochloromorphine, identified as 1-chloromorphine by spectroscopic means and by the fact that it, and its methyl ether 1-chlorocodeine, are different from 2-chloromorphine and 2-chlorocodeine prepared from 2-aminomorphine of unequivocally established structure. Formation of 1-chloromorphine and the previously known 1-bromomorphine involves entry of the halogen into the position meta to the free phenolic hydroxyl. Possible mechanistic interpretations of this unusual orientation are discussed.

Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity

Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.

Enantioselective and Protecting Group-Free Synthesis of 1-Deoxythionojirimycin, 1-Deoxythiomannojirimycin, and 1-Deoxythiotalonojirimycin

1-Deoxythioglyconojirimycins were synthesized by using a protecting group-free strategy, starting from readily available carbohydrates, in good overall yield. Use of benzyl-triethylammonium tetrathiomolybdate, BnEt3N](2)MoS4, as a sulfur transfer reagent and borohydride exchange resin (BER) reduction of a lactone enabled the efficient synthesis of the title compounds.

Model domains in C-3 with abelian automorphism group

It is shown that every hyperbolic rigid polynomial domain in C-3 of finite-type, with abelian automorphism group is equivalent to a domain that is balanced with respect to some weight.

Dynamics of the reaction between the free end of a tethered self-avoiding polymer and a flat penetrable surface: A renormalization group study

The average time tau(r) for one end of a long, self-avoiding polymer to interact for the first time with a flat penetrable surface to which it is attached at the other end is shown here to scale essentially as the square of the chain's contour length N. This result is obtained within the framework of the Wilemski-Fixman approximation to diffusion-limited reactions, in which the reaction time is expressed as a time correlation function of a ``sink'' term. In the present work, this sink-sink correlation function is calculated using perturbation expansions in the excluded volume and the polymer-surface interactions, with renormalization group methods being used to resum the expansion into a power law form. The quadratic dependence of tau(r) on N mirrors the behavior of the average time tau(c) of a free random walk to cyclize, but contrasts with the cyclization time of a free self-avoiding walk (SAW), for which tau(r) similar to N-2.2. A simulation study by Cheng and Makarov J. Phys. Chem. B 114, 3321 (2010)] of the chain-end reaction time of an SAW on a flat impenetrable surface leads to the same N-2.2 behavior, which is surprising given the reduced conformational space a tethered polymer has to explore in order to react. (C) 2014 AIP Publishing LLC.