Saturation of Berge hypergraphs

Given a graph $F$, a hypergraph is a Berge- $F$ if it can be obtained by expanding each edge in $F$ to a hyperedge containing it. A hypergraph $H$ is Berge-$F$-saturated if $H$ does not contain a subhypergraph that is a Berge-$F$, but for any edge $e\in E\left(\overline{H}\right)$, $H+e$ does. The $k$-uniform saturation number of Berge-$F$ is the minimum number of edges in a $k$-uniform Berge-$F$-saturated hypergraph on $n$ vertices. For $k=2$ this definition coincides with the classical definition of saturation for graphs. In this paper we study the saturation numbers for Berge triangles, paths, cycles, stars and matchings in $k$-uniform hypergraphs.     

Spectroscopic investigations of 1.06 μm emission in Nd-doped alkali niobium zinc tellurite glasses

Thermal, structural and optical properties of Nd³⁺ ions in tellurite glass (TeO₂-ZnO-Na₂O-Li₂O-Nb₂O₅) have been investigated. Differential thermal analysis revealed reasonably good forming tendency of the glass composition. FTIR spectra were used to analyze the functional groups present in the glass. Judd-Ofelt intensity parameters were derived from the absorption spectrum and used to calculate the radiative lifetime, branching ratio and stimulated emission cross-section of the ⁴F_3/2→⁴I_9/2, _{11/2, 13/2} transitions. The quantum efficiency of the ⁴F_3/2 level is comparable as well as higher than the typical value of the other tellurite based glasses. The decay from the ⁴F_3/2 level is found to be single exponential for different concentrations of Nd³⁺ ions with a shortening of lifetime with increasing concentration. The experimental values of branching ratio and saturation intensity of ⁴F_3/2→⁴I_11/2 transition indicate the favourable lasing action with low threshold power.     

Magnetic characterization of dual phase FeZrB soft magnetic alloy

The magnetic properties and the annealing process of Fe₇₈Zr₇B₁₅ amorphous ribbons are investigated by X-ray diffraction (XRD), differential scanning calorimetry, and vibrating sample magnetometer. The fully amorphous structure of the as-quenched ribbons is confirmed by the XRD pattern. The Curie temperature and the saturation magnetization M_s of the ribbons are 305 °C and 124.3 emu/g, respectively. Annealing at 550 °C can result in an increase in M_s with annealing time due to the increasing crystallized volume fraction of α-Fe phase. The optimized annealing process is established at 550 °C for 20-30 min with maximum M_s of 146.6 emu/g. The morphology of the ribbons annealed at 550 °C is observed by scanning electron microscopy, showing that nanocrystalline α-Fe grains are dispersed in an amorphous matrix.     

Improvement in magnetic properties of La substituted BaFe12O19 particles prepared with an unusually low Fe/Ba molar ratio

In this study, effect of lanthanum substitution on the phase composition, lattice parameters and magnetic properties of barium hexaferrite has been studied in samples synthesized in ammonium nitrate melt. Samples, prepared with different lanthanum amount and having various initial Fe/(Ba+La) ratios in between 12 and 2 {(Ba_1−xLa_x)·n Fe₂O₃, where 0≤x≤1 and 1≤n≤6)}, are sintered at temperatures from 800 to 1200 °C. The lattice parameters, both a and c, decreases with increasing La amount which results in a decrease of the unit cell volume. The scanning electron microscope micrographs show that the pure and La-substituted sample with x=0.3, both calcinated at 1000 °C, have grain sizes smaller than 1 μm. The coercivities of the La-substituted samples increase with increasing La amount and reaches to a maximum value of 5.73 kOe, when x=0.3. Sintering at higher temperatures (above 1000 °C) decreases the coercivity, resembling a transition from single to multi-domain behavior of the particles, while saturation magnetization of the samples continues to increase due to the increasing grain size. Magnetization measurements of the samples prepared with different Fe/(Ba+La) molar ratios, n's, revealed that the specific saturation magnetization slightly increases with decreasing n, while coercivities fluctuates around 5.5 kOe. However, a sharp increase in the saturation magnetization has been observed in the sample having n=1 and washed in HCl. It was measured as 59.2 emu/g at 15 kOe, which is higher than that of the pure sample (57.5 emu/g). Thus, the magnetic parameters are optimized in the sample Ba_0.7La_0.3Fe₁₂O₁₉ so as to maximize both coercivity and specific saturation magnetization in the HCl-washed sample synthesized by starting with an unusually low Fe/(Ba+La) molar ratio of 2 (or n=1).     

Preparation and magnetic properties of barium ferrites substituted with manganese, cobalt, and tin

Barium ferrites substituted by Mn-Sn, Co-Sn, and Mn-Co-Sn with general formulae BaFe_12−2xMn_xSn_xO₁₉ (x=0.2-1.0), BaFe_12−2xCo_xSn_xO₁₉ (x=0.2-0.8), and BaFe_12−2xCo_x/2Mn_x/2Sn_xO₁₉ (x=0.1-0.6), respectively, have been prepared by a previously reported co-precipitation method. The efficiency of the method was refined by lowering the reaction temperature and shortening the required reaction time, due to which crystallinity improved and the value of saturated magnetization increased as well. Low coercivity temperature coefficients, which are adjustable by doping, were achieved by Mn-Sn and Mn-Co-Sn doping. Synthesis efficiency and the effect of doping are discussed taking into account accumulated data concerning the synthesis and crystal structure of ferrites.     

Novel hybrid nanostructured materials of magnetite nanoparticles and pectin

A novel hybrid nanostructured material comprising superparamagnetic magnetite nanoparticles (MNPs) and pectin was synthesized by crosslinking with Ca²⁺ ions to form spherical calcium pectinate nanostructures, referred as MCPs, which were typically found to be 100-150 nm in size in dried condition, confirmed from transmission electron microscopy and scanning electron microscopy. The uniform size distribution was revealed from dynamic light scattering measurement. In aqueous medium the MCPs showed swelling behavior with an average size of 400 nm. A mechanism of formation of spherical MCPs is outlined constituting a MNP-pectin interface encapsulated by calcium pectinate at the periphery, by using an array of characterization techniques like zeta potential, thermogravimetry, Fourier transformed infrared and X-ray photoelectron spectroscopy. The MCPs were stable in simulated gastrointestinal fluid and ensured minimal loss of magnetic material. They exhibited superparamagnetic behavior, confirmed from zero field cooled and field cooled profiles and showed high saturation magnetization (M_s) of 46.21 emu/g at 2.5 T and 300 K. M_s decreased with increasing precursor pectin concentrations, attributed to quenching of magnetic moments by formation of a magnetic dead layer on the MNPs.     

Structure and magnetic properties of Nb-doped FeZrB soft magnetic alloys

Structure and magnetic properties of Nb-doped (FeZrB)_100−xNb_x alloy are investigated by X-ray diffraction (XRD), differential scanning calorimetry and vibrating sample magnetometer. The fully amorphous structure of the as-quenched ribbons is confirmed by the XRD pattern. With increasing Nb, the glass transition temperature and the onset crystallization temperature are increased, indicating increased stability of the amorphous structure. For x=1, the saturation magnetization of the ribbons is 125.7 emu/g and the optimized annealing temperature increases from 550 to 630 °C. The morphology of the crystallized phases is observed by scanning electron microscopy. The results show that nanocrystalline α-Fe grains are dispersed in the amorphous matrix.     

Pattern memory analysis of second-order neural networks with time-delay

In this paper, the pattern memory of the second-order neural networks with time-delay are investigated based on the stability theory. Several sufficient conditions are obtained such that the equilibrium point is locally exponential stable when the equilibrium point located in the saturation region. These conditions can be directly derived from the synaptic connection weights and the external input of the second-order neural networks, and be verified easily. In addition, four examples are given to show the effectiveness of the results.     

Stabilization of unbounded bilinear control systems in Hilbert space

We consider bilinear control systems of the form y^′(t)=Ay(t)+u(t)By(t) where A generates a strongly continuous semigroup of contraction (etA)_t?0 on an infinite-dimensional Hilbert space Y whose scalar product is denoted by 〈.,.〉. We suppose that this system is unbounded in the sense that the linear operator B is unbounded from the state Y into itself. Tacking into account eventual control saturation, we study the problem of stabilization by (possibly nonquadratic) feedback of the form u(t)=−f(〈By(t),y(t)〉). Applications to the heat equation is considered.