Synthetic studies towards novel terpenic natural products kelsoene and poduran: Construction of the complete 4-5-5-fused tricarbocyclic core

A common synthetic approach to the recently reported sesquiterpene kelsoene 1 and the tetraterpene poduran 5, bearing a novel tricyclo[6.2.0.0(2,6)]decane framework, from commercially available 1,5-COD and leading to the first construction of the carbocyclic core present in these natural products is delineated.

A Complete Characterization of an Optimal Timer Based Selection Scheme

Timer-based mechanisms are often used in several wireless systems to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a function of its local suitability metric. In practice, the best node gets selected successfully only if no other node's timer expires within a `vulnerability' window after its timer expiry. In this paper, we provide a complete closed-form characterization of the optimal metric-to-timer mapping that maximizes the probability of success for any probability distribution function of the metric. The optimal scheme is scalable, distributed, and much better than the popular inverse metric timer mapping. We also develop an asymptotic characterization of the optimal scheme that is elegant and insightful, and accurate even for a small number of nodes.

On the explicit determination of the polar decomposition in n-dimensional vector spaces

A method for the explicit determination of the polar decomposition (and the related problem of finding tensor square roots) when the underlying vector space dimension n is arbitrary (but finite), is proposed. The method uses the spectral resolution, and avoids the determination of eigenvectors when the tensor is invertible. For any given dimension n, an appropriately constructed van der Monde matrix is shown to play a key role in the construction of each of the component matrices (and their inverses) in the polar decomposition.

Complete 'melting' of charge order in hydrothermally grown Pr0.57Ca0.41Ba0.02MnO3 nanowires

Nanowires of Pr0.57Ca0.41Ba0.02MnO3 (PCBM) (diameter similar to 80-90 nm and length similar to 3.5 mu m) were synthesized by a low reaction temperature hydrothermal method. Single-phase nature of the sample was confirmed by XRD experiments. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were used to characterize the morphology and microstructures of the nanowires. While the bulk PCBM is known to exhibit charge order (CO) below 230 K along with a ferromagnetic transition at 110 K, SQUID measurements on the nanowires of PCBM show that the charge order is completely absent and a ferromagnetic transition occurs at 115 K. However, the magnetization in the nanowires is observed to be less compared to that in the bulk. This observation of the complete 'melting' of the charge order in the PCBM nanowires is particularly significant in view of the observation of only a weakening of the CO in the nanowires of Pr0.5Ca0.5MnO3. Electron paramagnetic resonance experiments were also carried out on the PCBM nanowires using an X-band EPR spectrometer. Characteristic differences were observed in the line width of nanowires when compared with that of the bulk.

Study of symmetrical and related components through the theory of linear vector spaces

The paper proposes a study of symmetrical and related components, based on the theory of linear vector spaces. Using the concept of equivalence, the transformation matrixes of Clarke, Kimbark, Concordia, Boyajian and Koga are shown to be column equivalent to Fortescue's symmetrical-component transformation matrix. With a constraint on power, criteria are presented for the choice of bases for voltage and current vector spaces. In particular, it is shown that, for power invariance, either the same orthonormal (self-reciprocal) basis must be chosen for both voltage and current vector spaces, or the basis of one must be chosen to be reciprocal to that of the other. The original �¿, ��, 0 components of Clarke are modified to achieve power invariance. For machine analysis, it is shown that invariant transformations lead to reciprocal mutual inductances between the equivalent circuits. The relative merits of the various components are discussed.

Selective double quantum resolved correlation experiment for the complete separation of entire proton NMR spectra of enantiomers

The present study reports a two dimensional NMR experiment which separates single quantum spectra of enantiomers from that of a racemic mixture. This is a blend of selective double quantum refocusing, for resolving couplings and chemical shift interactions along two dimensions followed by correlation of the selectively excited protons to the entire coupled spin network. The concept is solely based on the presence of distinct intra methyl dipolar couplings of different enantiomers when dissolved in chiral orienting media. The analysis of single enantiomer spectrum obtained from respective F-2 cross sections yield all the spectral information. (C) 2011 Elsevier Inc. All rights reserved.

A Unique Modification of the Eukaryotic Initiation Factor 5A Shows the Presence of the Complete Hypusine Pathway in Leishmania donovani

Deoxyhypusine hydroxylase (DOHH) catalyzes the final step in the post-translational synthesis of an unusual amino acid hypusine (N-(sic)-(4-amino-2-hydroxybutyl) lysine), which is present on only one cellular protein, eukaryotic initiation factor 5A (eIF5A). We present here the molecular and structural basis of the function of DOHH from the protozoan parasite, Leishmania donovani, which causes visceral leishmaniasis. The L. donovani DOHH gene is 981 bp and encodes a putative polypeptide of 326 amino acids. DOHH is a HEAT-repeat protein with eight tandem repeats of alpha-helical pairs. Four conserved histidine-glutamate sequences have been identified that may act as metal coordination sites. A similar to 42 kDa recombinant protein with a His-tag was obtained by heterologous expression of DOHH in Escherichia coli. Purified recombinant DOHH effectively catalyzed the hydroxylation of the intermediate, eIF5A-deoxyhypusine (eIF5A-Dhp), in vitro. L. donovani DOHH (LdDOHH) showed similar to 40.6% sequence identity with its human homolog. The alignment of L. donovani DOHH with the human homolog shows that there are two significant insertions in the former, corresponding to the alignment positions 159-162 (four amino acid residues) and 174-183 (ten amino acid residues) which are present in the variable loop connecting the N- and C-terminal halves of the protein, the latter being present near the substrate binding site. Deletion of the ten-amino-acid-long insertion decreased LdDOHH activity to 14% of the wild type recombinant LdDOHH. Metal chelators like ciclopirox olamine (CPX) and mimosine significantly inhibited the growth of L. donovani and DOHH activity in vitro. These inhibitors were more effective against the parasite enzyme than the human enzyme. This report, for the first time, confirms the presence of a complete hypusine pathway in a kinetoplastid unlike eubacteria and archaea. The structural differences between the L. donovani DOHH and the human homolog may be exploited for structure based design of selective inhibitors against the parasite.

Border basis detection is NP-complete

Border basis detection (BBD) is described as follows: given a set of generators of an ideal, decide whether that set of generators is a border basis of the ideal with respect to some order ideal. The motivation for this problem comes from a similar problem related to Grobner bases termed as Grobner basis detection (GBD) which was proposed by Gritzmann and Sturmfels (1993). GBD was shown to be NP-hard by Sturmfels and Wiegelmann (1996). In this paper, we investigate the computational complexity of BBD and show that it is NP-complete.

Some questions on integral geometry on noncompact symmetric spaces of higher rank

Let be a noncompact symmetric space of higher rank. We consider two types of averages of functions: one, over level sets of the heat kernel on and the other, over geodesic spheres. We prove injectivity results for functions in which extend the results in Pati and Sitaram (Sankya Ser A 62:419-424, 2000).

Light transmission through and its complete stoppage in an ultra slow wave optical medium

Light wave transmission - its compression, amplification, and the optical energy storage in an ultra slow wave medium (USWM) is studied analytically. Our phenomenological treatment is based entirely on the continuity equation for the optical energy flux, and the well-known distribution-product property of Dirac delta-function. The results so obtained provide a clear understanding of some recent experiments on light transmission and its complete stoppage in an USWM.

REPRODUCING KERNEL FOR A CLASS OF WEIGHTED BERGMAN SPACES ON THE SYMMETRIZED POLYDISC

A natural class of weighted Bergman spaces on the symmetrized polydisc is isometrically embedded as a subspace in the corresponding weighted Bergman space on the polydisc. We find an orthonormal basis for this subspace. It enables us to compute the kernel function for the weighted Bergman spaces on the symmetrized polydisc using the explicit nature of our embedding. This family of kernel functions includes the Szego and the Bergman kernel on the symmetrized polydisc.

On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order H-m (H-n), m is an element of N-n, under the heat kernel transform on H-n, using direct sum and direct integral of Bergmann spaces and certain unitary representations of H-n which can be realized on the Hilbert space of Hilbert-Schmidt operators on L-2 (R-n). We also show that the image of Sobolev space of negative order H-s (H-n), s(> 0) is an element of R is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on H-n under the heat kernel transform. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices

Given a metric space with a Borel probability measure, for each integer N, we obtain a probability distribution on N x N distance matrices by considering the distances between pairs of points in a sample consisting of N points chosen independently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.

RIGIDITY OF HOLOMORPHIC MAPS BETWEEN FIBER SPACES

In the study of holomorphic maps, the term ``rigidity'' refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this theme, we begin by studying when, given two compact connected complex manifolds X and Y, a degree-one holomorphic map f :Y -> X is a biholomorphism. Given that the real manifolds underlying X and Y are diffeomorphic, we provide a condition under which f is a biholomorphism. Using this result, we deduce a rigidity result for holomorphic self-maps of the total space of a holomorphic fiber space. Lastly, we consider products X = X-1 x X-2 and Y = Y-1 x Y-2 of compact connected complex manifolds. When X-1 is a Riemann surface of genus >= 2, we show that any non-constant holomorphic map F:Y -> X is of a special form.