An elementary approach to gap theorems

Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension >= 3. Suppose that the sectional curvature K satisfies -1-s(r) <= K <= -1, where r denotes distance to a fixed point in M. If lim(r ->infinity) e(2r) s(r) = 0, then (M, g) has to be isometric to H-n.The same proof also yields that if K satisfies -s(r) <= K <= 0 where lim(r ->infinity) r(2) s(r) = 0, then (M, g) is isometric to R-n, a result due to Greene and Wu.Our second result is a local one: Let (M, g) be any Riemannian manifold. For a E R, if K < a on a geodesic ball Bp (R) in M and K = a on partial derivative B-p (R), then K = a on B-p (R).

Low-Complexity Detection and Performance in Multi-Gigabit High Spectral Efficiency Wireless Systems

Recently, we reported a low-complexity likelihood ascent search (LAS) detection algorithm for large MIMO systems with several tens of antennas that can achieve high spectral efficiencies of the order of tens to hundreds of bps/Hz. Through simulations, we showed that this algorithm achieves increasingly near SISO AWGN performance for increasing number of antennas in Lid. Rayleigh fading. However, no bit error performance analysis of the algorithm was reported. In this paper, we extend our work on this low-complexity large MIMO detector in two directions: i) We report an asymptotic bit error probability analysis of the LAS algorithm in the large system limit, where N-t, N-r -> infinity keeping N-t = N-r, where N-t and N-r are the number of transmit and receive antennas, respectively. Specifically, we prove that the error performance of the LAS detector for V-BLAST with 4-QAM in i.i.d. Rayleigh fading converges to that of the maximum-likelihood (ML) detector as N-t, N-r -> infinity keeping N-t = N-r ii) We present simulated BER and nearness to capacity results for V-BLAST as well as high-rate non-orthogonal STBC from Division Algebras (DA), in a more realistic spatially correlated MIMO channel model. Our simulation results show that a) at an uncoded BER of 10(-3), the performance of the LAS detector in decoding 16 x 16 STBC from DA with N-t = = 16 and 16-QAM degrades in spatially correlated fading by about 7 dB compared to that in i.i.d. fading, and 19) with a rate-3/4 outer turbo code and 48 bps/Hz spectral efficiency, the performance degrades by about 6 dB at a coded BER of 10(-4). Our results further show that providing asymmetry in number of antennas such that N-r > N-t keeping the total receiver array length same as that for N-r = N-t, the detector is able to pick up the extra receive diversity thereby significantly improving the BER performance.

Coherence of the real symmetric Hardy algebra

Let D denote the open unit disk in C centered at 0. Let H-R(infinity) denote the set of all bounded and holomorphic functions defined in D that also satisfy f(z) = <(f <(z)over bar>)over bar> for all z is an element of D. It is shown that H-R(infinity) is a coherent ring.

Exchange spring behaviour in SrFe12O19-CoFe2O4 nanocomposites

Nanocomposites of hard (SrFe12O19) and soft ferrite (CoFe2O4) are prepared by mixing individual ferrite components at appropriate weight ratio and subsequent heat treatment. The magnetization of the composites showed hysteresis loop that is characteristic of the exchange spring system. The variation of J(r)/J(r)(infinity) vs. J(d)/J(r)(infinity) for these nanocomposites are investigated to understand the presence of both the interacting field and the disorder in the system. This is further corroborated with the First Order Reversal Curve analysis (FORC) on the nanocomposites of 1:4 (Cobalt Ferrite: Strontium Ferrite) and 1:16 (Cobalt Ferrite: Strontium Ferrite). The FORC distribution reveals that the pinning mechanism is stronger in the nanocomposite of 1:4 compared to 1:16. However, the nanocomposite of 1:16 exhibit superior exchange coupling strength in contrast to 1:4. The asymmetric nature of the FORC distribution at H-c = 0 Oe for both the nanocomposites validates the intercoupling between the reversible and irreversible magnetization. (C) 2015 Author(s).

Acetylation of Transition Protein 2 (TP2) by KAT3B (p300) Alters Its DNA Condensation Property and Interaction with Putative Histone Chaperone NPM3

The hallmark of mammalian spermiogenesis is the dramatic chromatin remodeling process wherein the nucleosomal histones are replaced by the transition proteins TP1, TP2, and TP4. Subsequently these transition proteins are replaced by the protamines P1 and P2. Hyperacetylation of histone H4 is linked to their replacement by transition proteins. Here we report that TP2 is acetylated in vivo as detected by anti-acetylated lysine antibody and mass spectrometric analysis. Further, recombinant TP2 is acetylated in vitro by acetyltransferase KAT3B (p300) more efficiently than by KAT2B (PCAF). In vivo p300 was demonstrated to acetylate TP2. p300 acetylates TP2 in its C-terminal domain, which is highly basic in nature and possesses chromatin-condensing properties. Mass spectrometric analysis showed that p300 acetylates four lysine residues in the C-terminal domain of TP2. Acetylation of TP2 by p300 leads to significant reduction in its DNA condensation property as studied by circular dichroism and atomic force microscopy analysis. TP2 also interacts with a putative histone chaperone, NPM3, wherein expression is elevated in haploid spermatids.Interestingly, acetylation of TP2 impedes its interaction with NPM3. Thus, acetylation of TP2 adds a new dimension to its role in the dynamic reorganization of chromatin during mammalian spermiogenesis.

Spectral Invariance of SG Pseudo-Differential Operators on L-P(R-n)

We prove the spectral invariance of SG pseudo-differential operators on L-P(R-n), 1 < p < infinity, by using the equivalence of ellipticity and Fredholmness of SG pseudo-differential operators on L-p(R-n), 1 < p < infinity. A key ingredient in the proof is the spectral invariance of SC pseudo-differential operators on L-2(R-n).

Study of the CP property of the Higgs boson at a photon collider using gamma gamma -> t(t)over-bar -> lX

We study the possible effects of CP violation in the Higgs sector on t (t) over bar production at a gammagamma collider. These studies are performed in a model-independent way in terms of six form factors {R(S-gamma), J(S-gamma), R(P-gamma), J(P-gamma), S-t, P-t} which parametrize the CP mixing in the Higgs sector, and a strategy for their determination is developed. We observe that the angular distribution of the decay lepton from t/(t) over bar produced in this process is independent of any CP violation in the tbW vertex and hence best suited for studying CP mixing in the Higgs sector. Analytical expressions are obtained for the angular distribution of leptons in the c.m. frame of the two colliding photons for a general polarization state of the incoming photons. We construct combined asymmetries in the initial state lepton (photon) polarization and the final state lepton charge. They involve CP even (x's) and odd (y's) combinations of the mixing parameters. We study limits up to which the values of x and y, with only two of them allowed to vary at a time, can be probed by measurements of these asymmetries, using circularly polarized photons. We use the numerical values of the asymmetries predicted by various models to discriminate among them. We show that this method can be sensitive to the loop-induced CP violation in the Higgs sector in the minimal supersymmetric standard model.

Synthesis, Structure, Negative Thermal Expansion, and Photocatalytic Property of Mo Doped ZrV(2)O(7)

A new series of compounds identified in the phase diagram of ZrO(2)-V(2)O(8)-MoO(3) have been synthesized via the solution combustion method. Single crystals of one of the compounds in the series, ZrV(1.50)Mo(0.50)O(7.25), were grown by the melt-cool technique from the starting materials with double the MoO(3) quantity. The room temperature average crystal structure of the grown crystals was solved using the single crystal X-ray diffraction technique. The crystals belong to the cubic crystal system, space group Pa (3) over bar (No. 205) with a = 8.8969 (4) angstrom, V = 704.24 (6) angstrom(3), and Z = 4. The final R(1) value of 0.0213 was achieved for 288 independent reflections during the structure refinement. The Zr(4+) occupies the special position (4a) whereas V(5+) and Mo(6+) occupy two unique (8c) Wyckoff positions. Two fully occupied O atoms, (24d) and (4b), one partially occupied 0 atom (8c) have been identified for this molybdovanadate, which is a unique feature for these crystals. The structure is related to both ZrV(2)O(7) and cubic ZrMo(2)O(8). The temperature dependent single crystal studies show negative thermal expansion above 370 K. The compounds have been characterized by powder X-ray diffraction, solid-state UV-vis diffuse reflectance spectra, scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The photocatalytic activity of these compounds has been investigated for the degradation of various dyes, and these compounds show specificity toward the degradation of non-azoic dyes.

Snakes with Ellipse-Reproducing Property

We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortestpossible support subject to some design constraints to maximize efficiency. While the resulting snakes are versatile enough to provide a good approximation of any closed curve in the plane, their most important feature is the fact that they admit ellipses within their span. Thus, they can perfectly generate circular and elliptical shapes. These features are appropriate to delineate cross sections of cylindrical-like conduits and to outline blob-like objects. We address the implementation details and illustrate the capabilities of our snake with synthetic and real data.

A Zero-Crossing Rate Property of Power Complementary Analysis Filterbank Outputs

We establish zero-crossing rate (ZCR) relations between the input and the subbands of a maximally decimated M-channel power complementary analysis filterbank when the input is a stationary Gaussian process. The ZCR at lag is defined as the number of sign changes between the samples of a sequence and its 1-sample shifted version, normalized by the sequence length. We derive the relationship between the ZCR of the Gaussian process at lags that are integer multiples of Al and the subband ZCRs. Based on this result, we propose a robust iterative autocorrelation estimator for a signal consisting of a sum of sinusoids of fixed amplitudes and uniformly distributed random phases. Simulation results show that the performance of the proposed estimator is better than the sample autocorrelation over the SNR range of -6 to 15 dB. Validation on a segment of a trumpet signal showed similar performance gains.

Effect of Te Addition into As2Se3 Thin Film: Optical Property Study by FTIR and XPS.

In the present work, we report the effect of Te deposition onto As2Se3 film which affects the optical properties. The Te/As2Se3 film was illuminated with 532 nm laser to study the photo induced diffusion. The prepared As2Se3, Te/As2Se3 films were characterized by X-ray diffraction which show a completely amorphous nature. On the basis of optical transmission data carried out by Fourier Transform infrared Spectroscopy, a non direct transition was found for these films. The optical bandgap is found to be decreased with Te deposition and photo darkening phenomena is observed for the diffused film. The change in the optical constants are also supported by the corresponding change in different types of bonds which are being analyzed by X-ray photoelectron spectroscopy.

Human genome studies and intellectual property rights: Whither national interests?

India has been acknowledged as a large reservoir of nature's random mutation, an original 'rich' source of knowledge in the context of international genome studies. Human genome knowledge and the possible understanding of the basis of uniqueness of each individual in chemical terms has presented a number of inescapable challenges to our own jurisprudence philosophies and our ethical sensibilities.

Synthesis and vesicle formation from hybrid bolaphile/amphiphile ion-pairs. Evidence of membrane property modulation by molecular design

Four new hybrid (bolaphile/amphiphile) ion-pairs were synthesized. Electron microscopy indicated that each of these forms bilayer membranes upon dispersion in aqueous media. Membrane properties have also been examined by differential scanning calorimetry, microcalorimetry, temperature-dependent fluorescence anisotropy measurements, and UV-vis spectroscopy. The T-m values for the vesicular 1, 2, 3, 4, and 5 were 38, 12, 85, 31.3, and 41.6 degrees C, respectively. Interestingly the T-m values for 1 and 3 were found to depend on their concentration. The entrapment of small solute and the release capability have also been examined to demonstrate that these bilayers form enclosed vesicles. X-ray diffraction of the cast films has been performed to understand the nature and the thickness of these membrane organizations. The membrane widths ranged from 33 to 47 Angstrom. Finally, the above observations have been analyzed in light of the results obtained from molecular modeling studies. Thus we have demonstrated that membrane properties can be modulated by simple structural changes at the amphiphile level. It was shown that by judicious incorporation of central, isomeric, disubstituted aromatic units as structural anchors into different bolaphiles, one can modulate the properties of the resulting vesicles.

A combined experimental and theoretical study of the charge-transfer compound between C60Br8 and tetrathiafulvalene

C60Br8, unlike C60Br6 and C60Cl6, forms a solid charge-transfer compound with tetrathiafulvalene (TTF), the composition being C60Br8(TTF)(8). The unique complex-forming property of C60Br8 can be understood on the basis of the electronic structures of the halogenated derivatives of C-60. Molecular orbital calculations show that the low LUMO energy of C60Br8 compared with the other halogen derivatives renders the formation of the complex with TTF favourable, the four virtual LUMOs being able to accept 8 electrons. The Raman spectrum of C60Br8(TTF)(8) shows a marked softening of the bands (-46 cm(-1) on average) with respect to C60Br8 suggesting that indeed 8 electrons are transferred per C60Br8 molecule, one from each TTF molecule. The complex is weakly paramagnetic and shows a magnetic transition around 80 K.

Structure and magnetotransport properties of the layered manganites REl.2Srl.8Mn,07(R E = La, Pr, Nd)

We have examined the magnetotransport properties and the structure, by Rietveld refinement of powder X-ray data, of the phases RE(1.2)Sr(1.8)Mn(2)O(7) (RE = La, Pr, Nd). We find that on cooling, La1.2Sr1.8Mn2O7 undergoes a transition to a nearly perfect ferromagnet with 90% magnetization at 1.45 T, as reported by earlier workers, but the Pr and Nd phases show only a small magnetization that grows gradually as the temperature is decreased. There seems to be significant correlation between electrical transport and the Jahn-Teller elongation of the apical Mn-O bonds in these systems. The elongation of the apical Mn-O bonds forces the nine-coordinate rock-salt site to be occupied preferentially by the smaller rare-earth-metal cations. This preferential occupation is reliably obtained from the X-ray refinement. All three title phases show a magnetoresistance ratio of about 4(corresponding to a magnetoresistance, [R(0)-R(H)]/R(0), of about 75%) at a field of 7 T and temperatures around 100 K.