Generators for comonoids and universal constructions

We investigate cofree coalgebras, and limits and colimits of coalgebras in some abelian monoidal categories of interest, such as bimodules over a ring, and modules and comodules over a bialgebra or Hopf algebra. We find concrete generators for the categories of coalgebras in these monoidal categories, and explicitly construct cofree coalgebras, products and limits of coalgebras in each case. This answers an open question in Agore (Proc Am Math Soc 139:855–863, 2011) on the existence of a cofree coring, and constructs the cofree (co)module coalgebra on a B-(co)module, for a bialgebra B.     

The use of methylcellulose for the synthesis of Li<Subscript>2</Subscript>FeSiO<Subscript>4</Subscript>/C composites

The key parameters related to cathode materials for commercial use are a high specific capacity, good cycling stability, capacity retention at high current rates, as well as the simplicity of the synthesis process. This study presents a facile synthesis of a composite cathode material, Li₂FeSiO₄ with carbon, under extreme conditions: rapid heating, short dwell at 750 °C and subsequent quenching. The water-soluble polymer methylcellulose was used both as an excellent dispersing agent and a carbon source that pyrolytically degrades to carbon, thereby enabling the homogeneous deployment of the precursor compounds and the control of the Li₂FeSiO₄ particle growth from the earliest stage of processing. X-ray powder diffraction reveals the formation of Li₂FeSiO₄ nanocrystallites with a monoclinic structure in the P2₁/n space group (#14). The composite’s electrochemical performance as a cathode material in Li-ion batteries was examined. The influence of the amount of methylcellulose on the microstructural, morphological, conductive, and electrochemical properties of the obtained powders has been discussed. It has been shown that the overall electrochemical performance is improved with an increase of carbon content, through both the decrease of the mean particle diameter and the increase of electrical conductivity.     

The redox couple avarol/avarone in the fight with malignant gliomas: the case study of U-251 MG cells

This study aimed to screen in vitro antitumour activity of the redox couple avarol/avarone against the human malignant glioma cell line U-251 MG for the first time. Compared both with avarol and positive controls used (temozolomide and doxorubicin), avarone was found to be the most active compound with IC₅₀ value below 1 μM (IC₅₀ 0.68 ± 0.04 μM, 96 h). Considerable less DNA damage in the cells treated with avarol and avarone vs. doxorubicin (105 & 123% vs. 299%, respectively; untreated U-251 MG cells were used as a control, 100%), coupled with no sign of cytotoxicity against the normal human foetal lung fibroblast MRC-5 cells (IC₅₀ > 100 μM), has actually pointed out the importance of this marine sesquiterpenoid quinone structure as a promising lead compound in development of novel brain chemotherapeutics.     

Numerical algorithm for rigid body position estimation using the quaternion approach

This paper deals with rigid body attitude estimation on the basis of the data obtained from an inertial measurement unit mounted on the body. The aim of this work is to present the numerical algorithm, which can be easily applied to the wide class of problems concerning rigid body positioning, arising in aerospace and marine engineering, or in increasingly popular robotic systems and unmanned aerial vehicles. Following the considerations of kinematics of rigid bodies, the relations between accelerations of different points of the body are given. A rotation matrix is formed using the quaternion approach to avoid singularities. We present numerical procedures for determination of the absolute accelerations of the center of mass and of an arbitrary point of the body expressed in the inertial reference frame, as well as its attitude. An application of the algorithm to the example of a heavy symmetrical gyroscope is presented, where input data for the numerical procedure are obtained from the solution of differential equations of motion, instead of using sensor measurements.     

Bounds on trees

We prove a finitary version of the Halpern–Läuchli Theorem. We also prove partition results about strong subtrees. Both results give estimates on the height of trees.     

Study of the aggregation of human insulin Langmuir monolayer

The human insulin (HI) Langmuir monolayer at the air-water interface was systematically investigated in the presence and absence of Zn(II) ions in the subphase. HI samples were dissolved in acidic (pH 2) and basic (pH 9) aqueous solutions and then spread at the air-water interface. Spectroscopic data of aqueous solutions of HI show a difference in HI conformation at different pH values. Moreover, the dynamics of the insulin protein showed a dependence on the concentration of Zn(II) ions. In the absence of Zn(II) ions in the subphase, the acidic and basic solutions showed similar behavior at the air-water interface. In the presence of Zn(II) ions in the subphase, the surface pressure-area and surface potential-area isotherms suggest that HI may aggregate at the air-water interface. It was observed that increasing the concentration of Zn(II) ions in the acidic (pH 2) aqueous solution of HI led to an increase of the area at a specific surface pressure. It was also seen that the conformation of HI in the basic (pH 9) medium had a reverse effect (decrease in the surface area) with the increase of the concentration of Zn(II) ions in solution. From the compression-decompression cycles we can conclude that the aggregated HI film at air-water interface is not stable and tends to restore a monolayer of monomers. These results were confirmed from UV-vis and fluorescence spectroscopy analysis. Infrared reflection-absorption and circular dichroism spectroscopy techniques were used to determine the secondary structure and orientation changes of HI by zinc ions. Generally, the aggregation process leads to a conformation change from α-helix to β-strand and β-turn, and at the air-water interface, the aggregation process was likewise seen to induce specific orientations for HI in the acidic and basic media. A proposed surface orientation model is presented here as an explanation to the experimental data, shedding light for further research on the behavior of insulin as a Langmuir monolayer.     

Electrochemical behaviour of V2O5 xerogel in aqueous LiNO3 solution

By dissolving crystalline V₂O₅ in hydrogen peroxide and drying at elevated temperature, the V₂O₅ xerogel was obtained. Its electrochemical behaviour was examined in aqueous solution of LiNO₃ by both cyclic voltammetry and galvanostatic charging/discharging cycling. Peak-to-peak potential separation observed at the cyclovoltammograms indicated fast Li⁺ intercalation/deintercalation reactions. Initial discharge capacity amounted to 69 mAhg^?1, and after 100 charging/discharging cycles, capacity fade amounted to 11% only. This presents a remarkable improvement in comparison with the behaviour of crystalline, vanadium oxide based, lithium intercalates in aqueous electrolytes.     

Error estimates of anti-Gaussian quadrature formulae

Anti-Gauss quadrature formulae associated with four classical Chebyshev weight functions are considered. Complex-variable methods are used to obtain expansions of the error in anti-Gaussian quadrature formulae over the interval [−1,1]$[-1,1]$. The kernel of the remainder term in anti-Gaussian quadrature formulae is analyzed. The location on the elliptic contours where the modulus of the kernel attains its maximum value is investigated. This leads to effective L^∞$L^{\infty }$-error bounds of anti-Gauss quadratures. Moreover, the effective L¹$L^1$-error estimates are also derived. The results obtained here are an analogue of some results of Gautschi and Varga (1983) [11], Gautschi et al. (1990) [9] and Hunter (1995) [10] concerning Gaussian quadratures.     

Gain compensated symmetric loaded transmission line exhibiting bidirectional negative group delay

A one-dimensional medium capable of bidirectional lossless negative group delay electromagnetic wave propagation is described. The medium is implemented as a microwave circuit comprising two symmetric resonator-loaded transmission lines, with active gain compensation and coupled through power combiners. We experimentally demonstrate the circuit is conditionally stable and is capable of lossless transmission of a finite bandwidth pulse in both directions. A measured group delay of ?600?ps with a gain of 1.12?dB in both directions is achieved for a Gaussian pulse with a bandwidth of 14?MHz modulated at a frequency of 280?MHz (NGD-bandwidth-product of 0.0084). This circuit demonstrates the possibility of constructing a one-dimensional spatial void.     

Row Space Cardinalities

Let be the set of all Boolean matrices. Let R(A) denote the row space of , let , and let . By extensive computation we found that