Error bounds of a quadrature formula with multiple nodes for the Fourier-Chebyshev coefficients for analytic functions

Three kinds of effective error bounds of the quadrature formulas with multiple nodes that are generalizations of the well-known Micchelli-Rivlin quadrature formula, when the integrand is a function analytic in the regions bounded by confocal ellipses, are given. A numerical example which illustrates the calculation of these error bounds is included.     

DNA Intercalating Near-Infrared Luminescent Lanthanide Complexes Containing Dipyrido[3,2-a:2′,3′-c]phenazine (dppz) Ligands: Synthesis,Crystal Structures,Stability, Luminescence Properties and CT-DNA Interaction

In order to create near-infrared (NIR) luminescent lanthanide complexes suitable for DNA-interaction, novel lanthanide dppz complexes with general formula [Ln(NO₃)₃(dppz)₂] (Ln = Nd³⁺, Er³⁺ and Yb³⁺; dppz = dipyrido[3,2-a:2′,3′-c]phenazine) were synthesized, characterized and their luminescence properties were investigated. In addition, analogous compounds with other lanthanide ions (Ln = Ce³⁺, Pr³⁺, Sm³⁺, Eu³⁺, Tb³⁺, Dy³⁺, Ho³⁺, Tm³⁺, Lu³⁺) were prepared. All complexes were characterized by IR spectroscopy and elemental analysis. Single-crystal X-ray diffraction analysis of the complexes (Ln = La³⁺, Ce³⁺, Pr³⁺, Nd³⁺, Eu³⁺, Er³⁺, Yb³⁺, Lu³⁺) showed that the lanthanide’s first coordination sphere can be described as a bicapped dodecahedron, made up of two bidentate dppz ligands and three bidentate-coordinating nitrate anions. Efficient energy transfer was observed from the dppz ligand to the lanthanide ion (Nd³⁺, Er³⁺ and Yb³⁺), while relatively high luminescence lifetimes were detected for these complexes. In their excitation spectra, the maximum of the strong broad band is located at around 385 nm and this wavelength was further used for excitation of the chosen complexes. In their emission spectra, the following characteristic NIR emission peaks were observed: for a) Nd³⁺: ⁴F_3/2 → ⁴I_9/2 (870.8 nm), ⁴F_3/2 → ⁴I_11/2 (1052.7 nm) and ⁴F_3/2 → ⁴I_13/2 (1334.5 nm); b) Er³⁺: ⁴I_13/2 → ⁴I_15/2 (1529.0 nm) c) Yb³⁺: ²F_5/2 → ²F_7/2 (977.6 nm). While its low triplet energy level is ideally suited for efficient sensitization of Nd³⁺ and Er³⁺, the dppz ligand is considered not favorable as a sensitizer for most of the visible emitting lanthanide ions, due to its low-lying triplet level, which is too low for the accepting levels of most visible emitting lanthanides. Furthermore, the DNA intercalation ability of the [Nd(NO₃)₃(dppz)₂] complex with calf thymus DNA (CT-DNA) was confirmed using fluorescence spectroscopy.     

Graphs with Exactly Two Negative Eigenvalues

In this paper we determine all finite connected graphs whose spectrum contains exactly two negative eigenvalues. The main theorem says that a graph has exactly two negative eigenvalues if and only if its “canonical graph” (defined below) is one of nine particular graphs on 3, 4, 5 and 6 vertices.     

Highly porous LiMnPO4 in combination with an ionic liquid-based polymer gel electrolyte for lithium batteries

A porous well defined LiMnPO₄ cathode material is synthesized by a sol-gel method. The electrochemical performance of the cathode material is evaluated in a cell with an ionic liquid-based polymer electrolyte (0.5 M LITFSI in EMImTFSI) and a lithium metal electrode. The results are compared to a cell with a traditional organic carbonate-based electrolyte (1 M LiPF₆ in EC/DMC). The cell with the ionic liquid-based polymer electrolyte presents an enhanced electrochemical intercalation performance of lithium ions, a high electrochemical stability window of 5 V, and an excellent cycling ability as compared with the organic based counterpart. Furthermore, the ionic liquid-based polymer gel electrolyte effectively prevents the dissolution of manganese — otherwise a common problem.     

The protective effects of silymarin against doxorubicin-induced cardiotoxicity and hepatotoxicity in rats

Silymarin is a complex of five major compounds, and silibinin is the most biologically active component of the complex. The aim of this study was to investigate, evaluate and confirm the potential cardioprotective and hepatoprotective effects of administration of silymarin, rich in silibinin, at a dose of 60 mg/kg orally for a time-span of 12 days on doxorubicin induced toxicity in male Wistar rats. The in vivo model was used to explore whether silymarin could prevent damage of liver and heart tissue induced by doxorubicin administered every other day at dose of 1.66 mg/kg intraperitoneally for twelve days. In the study the change of body weight, ECG changes, biochemical parameters of oxidative stress, serum activity of alanine and aspartate transaminase, lactate dehydrogenase, creatine kinase and histological preparations of heart and liver samples of treated animals were examined. According to physiological, pharmacological, microscopic and biochemical results, we confirmed that at the examined dose, silymarin exhibits a protective influence on the heart and liver tissue against toxicity induced by doxorubicin.     

Ionic liquids and oligomer electrolytes based on the B(CN)4(-) anion; ion association, physical and electrochemical properties

The role of B(CN)(4)(-) (Bison) as a component of battery electrolytes is addressed by investigating the ionic conductivity and phase behaviour of ionic liquids (ILs), ion association mechanisms, and the electrochemical stability and cycling properties of LiBison based electrochemical cells. For C(4)mpyrBison and C(2)mimBison ILs, and mixtures thereof, high ionic conductivities (3.4 ≤σ(ion)≤ 18 mS cm(-1)) are measured, which together with the glass transition temperatures (-80 ≤T(g)≤-76 °C) are found to shift systematically for most compositions. Unfortunately, poor solubility of LiBison in these ILs hinders their use as solvents for lithium salts, although good NaBison solubility offers an alternative application in Na(+) conducting electrolytes. The poor IL solubility of LiBison is predicted to be a result of a preferred monodentate ion association, according to first principles modelling, supported by Raman spectroscopy. The solubility is much improved in strongly Li(+) coordinating oligomers, for example polyethylene glycol dimethyl ether (PEGDME), with the practical performance tested in electrochemical cells. The electrolyte is found to be stable in Li/LiFePO(4) coin cells up to 4 V vs. Li and shows promising cycling performance, with a capacity retention of 99% over 22 cycles.     

Determination of molecular configuration by debye length modulation

Silicon nanowire field effect transistors (FETs) have emerged as ultrasensitive, label-free biodetectors that operate by sensing bound surface charge. However, the ionic strength of the environment (i.e., the Debye length of the solution) dictates the effective magnitude of the surface charge. Here, we show that control of the Debye length determines the spatial extent of sensed bound surface charge on the sensor. We apply this technique to different methods of antibody immobilization, demonstrating different effective distances of induced charge from the sensor surface.     

A new potentiometric sensor for the determination of α-amylase activity

A platinum redox sensor for the direct potentiometric determination of α-amylase concentration has been described. The sensor measured the amount of triiodide released from a starch-triiodide complex, which was correlated with the α-amylase activity after biocatalytic starch degradation. The composition and stability of the potassium triiodide solution was optimized. The starch-triiodide complex was characterized potentiometrically at variable starch and triiodide concentrations. The response mechanism of the platinum redox sensor towards α-amylase was proposed and the appropriate theoretical model was elaborated. The results obtained using the redox sensor exhibited satisfactory accuracy and precision and good agreement with a standard spectrophotometric method and high-sensitive fully automated descret analyser method. The sensor was tested on pure α-amylase (EC 3.2.1.1, Fluka, Switzerland), industrial granulated α-amylase Duramyl 120 T and an industrial cogranulate of protease and α-amylase Everlase/Duramyl 8.0 T/60 T. The detection limit was found to be 1.944 mU for α-amylase in the range of 0-0.54 U (0-15 μg), 0.030 mKNU for Duramyl 120 T in the range of 0-9.6 mKNU (0-80 μg) and 0.032 mKNU for Everlase/Duramyl 8.0 T/60 T in the range of 0-9.24 mKNU (0-140 μg).     

New results on the energy of integral circulant graphs

Circulant graphs are an important class of interconnection networks in parallel and distributed computing. Integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer as well. The integral circulant graph ICG_n(D) has the vertex set Z_n = {0, 1, 2, … , n − 1} and vertices a and b are adjacent if gcd(a − b, n) ∈ D, where D ⊆ {d : d∣n, 1 ? d < n}. These graphs are highly symmetric, have integral spectra and some remarkable properties connecting chemical graph theory and number theory. The energy of a graph was first defined by Gutman, as the sum of the absolute values of the eigenvalues of the adjacency matrix. Recently, there was a vast research for the pairs and families of non-cospectral graphs having equal energies. Following Bapat and Pati [R.B. Bapat, S. Pati, Energy of a graph is never an odd integer, Bull. Kerala Math. Assoc. 1 (2004) 129-132], we characterize the energy of integral circulant graph modulo 4. Furthermore, we establish some general closed form expressions for the energy of integral circulant graphs and generalize some results from Ili? [A. Ili?, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009), 1881-1889]. We close the paper by proposing some open problems and characterizing extremal graphs with minimal energy among integral circulant graphs with n vertices, provided n is even.     

Free vibration control of smart composite beams using particle swarm optimized self-tuning fuzzy logic controller

This paper deals with active free vibrations control of smart composite beams using particle-swarm optimized self-tuning fuzzy logic controller. In order to improve the performance and robustness of the fuzzy logic controller, this paper proposes integration of self-tuning method, where scaling factors of the input variables in the fuzzy logic controller are adjusted via peak observer, with optimization of membership functions using the particle swarm optimization algorithm. The Mamdani and zero-order Takagi–Sugeno–Kang fuzzy inference methods are employed. In order to overcome stability problem, at the same time keeping advantages of the proposed self-tuning fuzzy logic controller, this controller is combined with the LQR making composite controller. Several numerical studies are provided for the cantilever composite beam for both single mode and multimodal cases. In the multimodal case, a large-scale system is decomposed into smaller subsystems in a parallel structure. In order to represent the efficiency of the proposed controller, obtained results are compared with the corresponding results in the cases of the optimized fuzzy logic controllers with constant scaling factors and linear quadratic regulator.