An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas

We show here a 2(Omega(root d.log N)) size lower bound for homogeneous depth four arithmetic formulas. That is, we give an explicit family of polynomials of degree d on N variables (with N = d(3) in our case) with 0, 1-coefficients such that for any representation of a polynomial f in this family of the form f = Sigma(i) Pi(j) Q(ij), where the Q(ij)'s are homogeneous polynomials (recall that a polynomial is said to be homogeneous if all its monomials have the same degree), it must hold that Sigma(i,j) (Number of monomials of Q(ij)) >= 2(Omega(root d.log N)). The above mentioned family, which we refer to as the Nisan-Wigderson design-based family of polynomials, is in the complexity class VNP. Our work builds on the recent lower bound results 1], 2], 3], 4], 5] and yields an improved quantitative bound as compared to the quasi-polynomial lower bound of 6] and the N-Omega(log log (N)) lower bound in the independent work of 7].

Two-Dimensional Noise-Predictive Maximum Likelihood Method for Magnetic Recording Channels

Noise-predictive maximum likelihood (NPML) is a well known signal detection technique used in partial response maximum likelihood (PRML) scheme in 1D magnetic recording channels. The noise samples colored by the partial response (PR) equalizer are predicted/ whitened during the signal detection using a Viterbi detector. In this paper, we propose an extension of the NPML technique for signal detection in 2D ISI channels. The impact of noise prediction during signal detection is studied in PRML scheme for a particular choice of 2D ISI channel and PR targets.

Magnetic properties of nanocrystalline Mn1-xZnxFe2O4

Nanocrystalline Mn1-xZnxFe2O4 (x = 0, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0) were prepared via solution combustion method. Structural and morphology of Mn-Zn ferrites were characterized by X-ray diffraction (XRD) and Transmission Electron Microscopy (TEM). Magnetic properties were carried out using vibrating sample magnetometer (VSM) at room temperature (RT) up to maximum field of 1.5 T. The room temperature real and imaginary part of permeability(mu' and mu'') has been measured in the frequency range of 1MHz to 1GHz. The room temperature XRD patterns exhibits the spinel cubic (Fm-3m) structure and broad XRD patterns shows the presence of nanoparticles. The imaginary part of the permeability (mu'') gradually increased with the frequency and took a broad maximum at a certain frequency, where the real permeability (mu') rapidly decreases, which is known as natural resonance. The coercive filed values are low, hence probability of domain rotation is also lower and the magnetization decreased with zinc substitution. The values of mu' and mu'' increases sharply, attained a maximum and then decreases with zinc content.

Structure and Magnetic Properties of Tb1-xSrxMnO3

Tb1-xSrxMnO3 (x = 0.1, 0.2, 0.3, 0.4 and 0.5) polycrystalline samples are prepared via conventional solid state synthesis route. All samples crystallize in orthorhombic Pnma space group and possess O'-type distortion. Orthorhombic and octahedral distortion is found to decrease with increase in Sr content. At intermediate distortion, (20% and 30% doping level) Curie-Weiss analysis of inverse dc magnetic susceptibility data yields +ve Curies-Weiss constant, characteristic of FM interaction. Isothermal magnetization measurements give the highest magnitude of magnetic moment at these compositions.

Electronic and Magnetic Properties of Yttrium-doped Silicon Carbide Nanotubes: Density Functional Theory Investigations

The electronic structure of yttrium-doped Silicon Carbide Nanotubes has been theoretically investigated using first principles density functional theory (DFT). Yttrium atom is bonded strongly on the surface of the nanotube with a binding energy of 2.37 eV and prefers to stay on the hollow site at a distance of around 2.25 angstrom from the tube. The semi-conducting nanotube with chirality (4, 4) becomes half mettalic with a magnetic moment of 1.0 mu(B) due to influence of Y atom on the surface. There is strong hybridization between d orbital of Y with p orbital of Si and C causing a charge transfer from d orbital of the Y atom to the tube. The Fermi level is shifted towards higher energy with finite Density of States for only upspin channel making the system half metallic and magnetic which may have application in spintronic devices.

Effect of Super-exchange Interaction on Ground state Magnetic Properties of Spin-dependent Falicov-Kimball Model on a Triangular Lattice

Ground state magnetic properties are studied by incorporating the super-exchange interaction (J(se)) in the spin-dependent Falicov-Kimball model (FKM) between localized (f-) electrons on a triangular lattice for half filled case. Numerical diagonalization and Monte-Carlo simulation are used to study the ground state magnetic properties. We have found that the magnetic moment of (d-) and (f-) electrons strongly depend on the value of Hund's exchange (J), super-exchange interaction (J(se)) and also depends on the number of (d-) electrons (N-d). The ground state changes from antiferromagnetic (AFM) to ferromagnetic (FM) state as we decrease (N-d). Also the density of d electrons at each site depends on the value of J and J(se).

Air Stable Iron/Iron Carbide Magnetic Nanoparticles Embedded in Amorphous Carbon Globules

We have synthesized Fe/Fe3C magnetic nanoparticles embedded in an amorphous carbon globule by pyrolysing of benzene, ferrocene and hydroboric acid. The diameter of the globules is similar to 1 mu m and that of Fe/Fe3C magnetic nanoparticles is similar to 40 nm. The globules exhibit ferromagnetic like behavior and the magnetization as well as the coercivity is found to increases with decreasing temperature.

Thermal, magnetic and electrical properties of Tb1-xDyxMnO3 multiferroics

A series of multiferroic materials with the compositional formula, Tb1 - xDyxMnO3 (where x=0, 0.1, 0.2, 0.3 and 0.4) were prepared by the sol gel method. After characterizing the samples structurally, a systematic investigation of specific heat, magnetization and dielectric properties over the temperature range, 4-300 K, was undertaken. Based on these studies, it was found that all the samples exhibit a transition at 40 K and the observed behavior may be attributed to the ordering of Mn3+ ions. Further, all the five samples are found to exhibit a ferroelectric transition in the temperature range 20-24 K. Finally, yet another transition was also exhibited by all the samples at temperatures below 10 K and is attributed to the antiferromagnetic (AF) ordering of rare-earth ionic moments. The magnetic entropy of all the samples was also computed with the help of their heat capacity data. (C) 2015 Elsevier B.V. All rights reserved.

Incorporation of Cr3+ ions in tuning the magnetic and transport properties of nano zinc ferrite

Cost effective and low temperature synthesis methods namely solution combustion and hydrothermal methods were used to prepare chromium incorporated nanocrystalline zinc ferrites. The effect of incorporation of low concentration Cr3+ ions on the structural, morphological, magnetic and transport properties of the zinc ferrite compounds were investigated. The crystalline nature and size variation with chromium content were valid from powder x-ray diffraction. Particles size and crystallite size variation were valid from scanning electron microscopy and transmission electron microscopy respectively. With the increase in chromium incorporation, the crystallite and particles sizes were decreased. Fourier transform infrared spectroscopy (FTIR) studies confirmed the presence of strong metal-oxygen bonds. The elastic properties of the materials in both the methods were estimated by FTIR studies. Magnetic properties namely saturation magentization, remanent magnetization and coercivity values were decreased with increase in Cr3+ ions concentration. The dielectric properties of the samples decreased with increase in the Cr3+ ions. The dielectric constant was observed to be of the order of 10(6) at low frequency and almost 1 at higher frequency range. The activation energy estimated using Arrhenius plots was of the order of 0.182 eV and 0.368 eV respectively for the compounds prepared by solution combustion and hydrothermal methods. The emission spectra of the samples excited at 344 nm were reported using photoluminescence (PL) spectroscopy. Further, the approximate energy band gap(E-g) was estimated from PL studies. The E-g of the materials were lie in the range of 2.11-1.98 eV. (C) 2015 Elsevier B.V. All rights reserved.

On the Structural Stability of Melt Spun Ribbons of Fe95-x Zr (x) B4Cu1 (x=7 and 9) Alloys and Correlation with Their Magnetic Properties

Melt spun ribbons of Fe95-x Zr (x) B4Cu1 with x = 7 (Z7B4) and 9 (Z9B4) alloys have been prepared, and their structure and magnetic properties have been evaluated using XRD, DSC, TEM, VSM, and Mossbauer spectroscopy. The glass forming ability (GFA) of both alloys has been calculated theoretically using thermodynamical parameters, and Z9B4 alloy is found to possess higher GFA than that of Z7B4 alloy which is validated by XRD results. On annealing, the amorphous Z7B4 ribbon crystallizes into nanocrystalline alpha-Fe, whereas amorphous Z9B4 ribbon shows two-stage crystallization process, first partially to bcc solid solution which is then transformed to nanocrystalline alpha-Fe and Fe2Zr phases exhibiting bimodal distribution. A detailed phase analysis using Mossbauer spectroscopy through hyperfine field distribution of phases has been carried out to understand the crystallization behavior of Z7B4 and Z9B4 alloy ribbons. In order to understand the phase transformation behavior of Z7B4 and Z9B4 ribbons, molar Gibbs free energies of amorphous, alpha-Fe, and Fe2Zr phases have been evaluated. It is found that in case of Z7B4, alpha-Fe is always a stable phase, whereas Fe2Zr is stable at higher temperature for Z9B4. (C) The Minerals, Metals & Materials Society and ASM International 2015

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

Prior image based temporally constrained reconstruction algorithm for magnetic resonance guided high intensity focused ultrasound

Purpose: A prior image based temporally constrained reconstruction ( PITCR) algorithm was developed for obtaining accurate temperature maps having better volume coverage, and spatial, and temporal resolution than other algorithms for highly undersampled data in magnetic resonance (MR) thermometry. Methods: The proposed PITCR approach is an algorithm that gives weight to the prior image and performs accurate reconstruction in a dynamic imaging environment. The PITCR method is compared with the temporally constrained reconstruction (TCR) algorithm using pork muscle data. Results: The PITCR method provides superior performance compared to the TCR approach with highly undersampled data. The proposed approach is computationally expensive compared to the TCR approach, but this could be overcome by the advantage of reconstructing with fewer measurements. In the case of reconstruction of temperature maps from 16% of fully sampled data, the PITCR approach was 1.57x slower compared to the TCR approach, while the root mean square error using PITCR is 0.784 compared to 2.815 with the TCR scheme. Conclusions: The PITCR approach is able to perform more accurate reconstructions of temperature maps compared to the TCR approach with highly undersampled data in MR guided high intensity focused ultrasound. (C) 2015 American Association of Physicists in Medicine.

Measuring the magnetic-field-dependent chemical potential of a low-density three-dimensional electron gas in n-GaAs and extracting its magnetic susceptibility

We report the magnetic-field-dependent shift of the electron chemical potential in bulk, n-type GaAs at room temperature. A transient voltage of similar to 100 mu V was measured across a Au-Al2O3-GaAs metal-oxide-semiconductor capacitor in a pulsed magnetic field of similar to 6 T. Several spurious voltages larger than the signal that had plagued earlier researchers performing similar experiments were carefully eliminated. The itinerant magnetic susceptibility of GaAs is extracted from the experimentally measured data for four different doping densities, including one as low as 5 x 10(15) cm(-3). Though the susceptibility in GaAs is dominated by Landau-Peierls diamagnetism, the experimental technique demonstrated can be a powerful tool for extracting the total free carrier magnetization of any electron system. The method is also virtually independent of the carrier concentration and is expected to work better in the nondegenerate limit. Such experiments had been successfully performed in two-dimensional electron gases at cryogenic temperatures. However, an unambiguous report on having observed this effect in any three-dimensional electron gas has been lacking. We highlight the 50 year old literature of various trials and discuss the key details of our experiment that were essential for its success. The technique can be used to unambiguously yield only the itinerant part of the magnetic susceptibility of complex materials such as magnetic semiconductors and hexaborides, and thus shed light on the origin of ferromagnetism in such systems.

Role of (La, Gd) co-doping on the enhanced dielectric and magnetic properties of BiFeO3 ceramics

The effect of the La3+ and Gd3+ co-doping on the structure, electric and magnetic properties of BiFeO3 (BFO) ceramics are investigated. For the compositions (x=0 and 0 <= y <= 0.15) in the perovskite structured LaxGdyBi1-xFeO3 system, a tiny residual phase of Bi2Fe4O9 is noticed. Such a secondary phase is suppressed with the incorporation of `La' content (x). The magnitude of dielectric constant (epsilon(r) increases progressively by increasing the `La' content from x=0 to 0.15 with a remarkable decrease of dielectric loss. For x=0.15, the system LaxGdyBi1-x(x+y)FeO3 exhibits highest remanent magnetization (M-r) of 0.18 emu/g and coercive magnetic field (H-c) of similar to 1 Tin the presence of external magnetic field of 9 T at 300 K. The origin of enhanced dielectric and magnetic properties of LaxGdyBil (x+y)Fe03 and the role of doping elements, La3+, Gd3+ has been discussed. (C) 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Magnetic structures and magnetic phase transitions in the Mn-doped orthoferrite TbFeO3 studied by neutron powder diffraction

The magnetic structures and the magnetic phase transitions in the Mn-doped orthoferrite TbFeO3 studied using neutron powder diffraction are reported. Magnetic phase transitions are identified at T-N(Fe/Mn) approximate to 295K where a paramagnetic-to-antiferromagnetic transition occurs in the Fe/Mn sublattice, T-SR(Fe/Mn) approximate to 26K where a spin-reorientation transition occurs in the Fe/Mn sublattice and T-N(R) approximate to 2K where Tb-ordering starts to manifest. At 295 K, the magnetic structure of the Fe/Mn sublattice in TbFe0.5Mn0.5O3 belongs to the irreducible representation Gamma(4) (G(x)A(y)F(z) or Pb'n'm). A mixed-domain structure of (Gamma(1) + Gamma(4)) is found at 250K which remains stable down to the spin re-orientation transition at T-SR(Fe/Mn) approximate to 26K. Below 26K and above 250 K, the majority phase (>80%) is that of Gamma(4). Below 10K the high-temperature phase Gamma(4) remains stable till 2K. At 2 K, Tb develops a magnetic moment value of 0.6(2) mu(B)/f.u. and orders long-range in F-z compatible with the Gamma(4) representation. Our study confirms the magnetic phase transitions reported already in a single crystal of TbFe0.5Mn0.5O3 and, in addition, reveals the presence of mixed magnetic domains. The ratio of these magnetic domains as a function of temperature is estimated from Rietveld refinement of neutron diffraction data. Indications of short-range magnetic correlations are present in the low-Q region of the neutron diffraction patterns at T < T-SR(Fe/Mn). These results should motivate further experimental work devoted to measure electric polarization and magnetocapacitance of TbFe0.5Mn0.5O3. (C) 2016 AIP Publishing LLC.