Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses

In this article on quasidifferential equation with non-fixed time of impulses we consider the continuous dependence of the solutions on the initial conditions as well as the mappings defined by these equations. We prove general theorems for quasidifferential equations from which follows corresponding results for differential equations, differential inclusion and equations with Hukuhara derivative.

Viability Kernels of Higher Order

AMS subject classification: Primary 34A60, Secondary 49K24.

Passivity analysis of memristor-based complex-valued neural networks with time-varying delays

In this paper, the model of memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is established and the problem of passivity analysis for MCVNNs is considered and extensively investigated. The analysis in this paper employs results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. By employing the appropriate Lyapunov–Krasovskii functional, differential inclusion theory and linear matrix inequality (LMI) approach, some new sufficient conditions for the passivity of the given MCVNNs are obtained in terms of both complex-valued and real-value LMIs, which can be easily solved by using standard numerical algorithms. Numerical examples are provided to illustrate the effectiveness of our theoretical results.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Increasing ionic conductivity and mechanical strength of a plastic electrolyte by inclusion of a polymer

in this contribution we present a soft matter solid electrolyte which was obtained by inclusion of a polymer (polyacrylonitrile, PAN) in LiClO4/LiTFSI-succinonitrile (SN), a semi-solid organic plastic electrolyte. Addition of the polymer resulted in considerable enhancement in ionic conductivity as well as mechanical strength of LiX-SN (X=ClO4, TFSI) plastic electrolyte. Ionic conductivity of 92.5%-[1 M LiClO4-SN]:7.5%-PAN (PAN amount as per SN weight) composite at 25 degrees C recorded a remarkably high value of 7 x 10(-3) Omega(-1) cm(-1), higher by few tens of order in magnitude compared to 1 M LiClO4-SN. Composite conductivity at sub-ambient temperature is also quite high. At -20 degrees C, the ionic conductivity of (100 -x)%-[1 M LiClO4-SN]:x%-PAN composites are in the range 3 x 10(-5)-4.5 x 10(-4) Omega(-1) cm(-1), approximately one to two orders of magnitude higher with respect to 1 M LiClO4-SN electrolyte conductivity. Addition of PAN resulted in an increase of the Young's modulus (Y) from Y -> 0 for LiClO4-SN to a maximum of 0.4MPa for the composites. Microstructural studies based on X-ray diffraction, differential scanning calorimetry and Fourier transform infrared spectroscopy suggest that enhancement in composite ionic conductivity is a combined effect of decrease in crystallinity and enhanced trans conformer concentration. (c) 2008 Elsevier Ltd. All rights reserved.

Detailed investigation of a gamma-cyclodextrin inclusion complex with L-thyroxine for improved pharmaceutical formulations

Thyroxine is a naturally occurring human hormone produced by the thyroid gland. Clinical applications of thyroxine to treat several chronic disorders are limited by poor water solubility and instability under physiological conditions. An inclusion complex of levo-thyroxine (l-thyroxine), the active form of the hormone with gamma cyclodextrin (gamma-CD) has been obtained and studied with the aim of improving oral delivery rather than the injection formulation of the sodium salt. In addition to greater patient acceptability, inclusion complexes often improve aqueous solubility and bioavailability, stability, and reduce toxicity of drugs, thus providing enhanced pharmaceutical formulations. Physicochemical characterization of the inclusion complex was carried out using Fourier transform infrared spectroscopy, X-ray diffractometry, differential scanning calorimetry, scanning electron microscopy and proton nuclear magnetic resonance spectroscopy. Intermolecular dipolar interactions for the inclusion complex were also studied using 2 dimensional ROESY experiments. Formation of the inclusion complex between the protons H3 and H5 of cyclodextrin with aromatic protons of thyroxine was confirmed by their dipolar interaction. Molecular modelling was used to understand the basis for the complex formation and predict the formation of other complexes. Interestingly, we found that l-thyroxine forms an inclusion complex only with the larger gamma-CD and not with other available alpha and beta forms.

Novel inclusion complex of ibuprofen tromethamine with cyclodextrins: Physico-chemical characterization

Guest-host interactions of ibuprofen tromethamine salt (Ibu.T) with native and modified cyclodextrins (CyDs) have been investigated using several techniques, namely phase solubility diagrams (PSDs), proton nuclear magnetic resonance (H-1 NMR), differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FT-IR), X-ray powder diffractometry (XRPD). scanning-electron microscopy (SEM) and molecular mechanics (MM). From the analysis of PSD data (A(L)-type) it is concluded that the anionic tromethamine salt of ibuprofen (pK(a) = 4.55) forms 1: 1 soluble complexes with all CyDs investigated in buffered water at pH 7.0, while the neutral form of Ibu forms an insoluble complex with beta-CyD (B-S-type) in buffered water at pH 2.0. Ibu.T has a lower tendency to complex with beta-CyD (K-11 = 58 M-1 at pH 7.0) compared with the neutral Ibu (K-11 = 4200 M (1)) in water. Complex formation of Ibu.T with beta-CyD (Delta G degrees = -20.4 kJ/mol) is enthalpy driven (Delta H degrees = -22.9 kJ/mol) and is accompanied by a small unfavorable entropy (Delta S degrees = -8.4 J/mol K) change. H-1 NMR studies and MM computations revealed that, on complexation, the hydrophobic central benzene ring of lbu.T and part of the isobutyl group reside within the beta-CyD cavity leaving the peripheral groups (carboxylate, tromethamine and methyl groups) located near the hydroxyl group networks at either rim of beta-CyD. PSD, H-1 NMR, DSC, FT-IR, XRPD, SEM and MM studies confirmed the formation of Ibu.T/beta-CyD inclusion complex in solution and the solid state. (C) 2009 Elsevier B.V. All rights reserved.

Inclusion of poorly soluble drugs in highly ordered mesoporous silica nanoparticles

Silica nanoparticles (MSNs) with a highly ordered mesoporous structures (103A) with cubic Im3 m have been synthesized using triblock copolymers with high poly(alkylene oxide) (EO) segments in acid media. The produced nanoparticles displayed large specific surface area (approximately 765 cm(2)/g) with an average particles size of 120 nm. The loading efficiency was assessed by incorporating three major antiepileptic active substances via passive loading and it was found to varying from 17 to 25%. The state of the adsorbed active agents was further analyzed using differential scanning calorimetry (DSC) and X-ray powder diffraction (XRPD). Dissolution studies revealed rapid release profiles within the first 3 h. The viability of 3T3 endothelial cells was not affected in the presence of MSNs indicating negligible cytotoxicity. 2009 Elsevier B.V. All rights reserved.

Quadratic Predictor based Differential Encoding and Decoding of Speech Signals

Modeling nonlinear systems using Volterra series is a century old method but practical realizations were hampered by inadequate hardware to handle the increased computational complexity stemming from its use. But interest is renewed recently, in designing and implementing filters which can model much of the polynomial nonlinearities inherent in practical systems. The key advantage in resorting to Volterra power series for this purpose is that nonlinear filters so designed can be made to work in parallel with the existing LTI systems, yielding improved performance. This paper describes the inclusion of a quadratic predictor (with nonlinearity order 2) with a linear predictor in an analog source coding system. Analog coding schemes generally ignore the source generation mechanisms but focuses on high fidelity reconstruction at the receiver. The widely used method of differential pnlse code modulation (DPCM) for speech transmission uses a linear predictor to estimate the next possible value of the input speech signal. But this linear system do not account for the inherent nonlinearities in speech signals arising out of multiple reflections in the vocal tract. So a quadratic predictor is designed and implemented in parallel with the linear predictor to yield improved mean square error performance. The augmented speech coder is tested on speech signals transmitted over an additive white gaussian noise (AWGN) channel.

Surprising effect of nanoparticle inclusion on ion conductivity in a lithium doped organic ionic plastic crystal

Doping lithium bis(trifluoromethanesulfonyl)amide (Li[NTf₂]) into the N-ethyl,N′-methylpyrrolidinium bis(trifluoromethanesulfonyl)amide ([C₂mpyr][NTf₂]) plastic crystal material has previously indicated order of magnitude enhancements in ion transport and conductivity over pure [C₂mpyr][NTf₂]. Recently, conductivity enhancements in this ionic plastic crystal induced by SiO₂ nanoparticles have also been reported. In this work the inclusion of SiO₂ nanoparticles in Li ion doped [C₂mpyr][NTf₂] has been investigated over a wide temperature range by differential scanning calorimetry (DSC), impedance spectroscopy, positron annihilation lifetime spectroscopy (PALS), Raman spectroscopy, NMR spectroscopy and scanning electron microscopy (SEM). Solid state ¹H NMR indicates that the addition of the nanoparticles increases the mobility of the [C₂mpyr] cation and positron lifetime spectroscopy (PALS) measurements indicate an increase in mean defect size and defect concentration as a result of nanoparticle inclusion, especially with 10 wt% SiO₂. Thus, the substantial drop in ion conductivity observed for this doped nanocomposite material was surprising. This decrease is most likely due to the decrease in mobility of the [NTf₂] anion, possibly by its adsorption at the SiO₂/grain boundary interface and concomitant decrease in mobility of the Li ion.

Development and pharmacological evaluation of ropivacaine-2-hydroxypropyl-beta-cyclodextrin inclusion complex

Ropivacaine (RVC) is an enantiomerically pure local anesthetic (LA) largely used in surgical procedures, which presents physico-chemical and therapeutic properties similar to those of bupivacaine (BPV), but associated to less systemic toxicity This study focuses on the development and pharmacological evaluation of a RVC in 2-hydroxypropyl-beta-cyclodextrin (HP-P-CD) inclusion complex. Phase-solubility diagrams allowed the determination of the association constant between RVC and HP-beta-CD (9.46 M-1) and showed an increase on RVC solubility upon complexation. Release kinetics revealed a decrease on RVC release rate and reduced hemolytic effects after complexation. (onset at 3.7 mM and 11.2 mM for RVC and RVCHP-beta-CD, respectively) were observed. Differential scanning calorimetry (DSC), scanning electron microscopy (SEM) and X-ray analysis (X-ray) showed the formation and the morphology of the complex. Nuclear magnetic resonance (NMR) and job-plot experiments afforded data regarding inclusion complex stoichiometry (1:1) and topology. Sciatic nerve blockade studies showed that RVCHP-beta-CD was able to reduce the latency without increasing the duration of motor blockade, but prolonging the duration and intensity of the sensory blockade (p < 0.001) induced by the LA in mice. These results identify the RVCHP-beta-CD complex as an effective novel approach to enhance the pharmacological effects of RVC, presenting it as a promising new anesthetic formulation. (c) 2007 Elsevier B.V All rights reserved.

Non-inclusion complexes between riboflavin and cyclodextrins

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Computational analysis and physico-chemical characterization of an inclusion compound between praziquantel and methyl-beta-cyclodextrin for use as an alternative in the treatment of schistosomiasis

Schistosomiasis is still an endemic disease in many regions, with 250 million people infected with Schistosoma and about 500,000 deaths per year. Praziquantel (PZQ) is the drug of choice for schistosomiasis treatment, however it is classified as Class II in the Biopharmaceutics Classification System, as its low solubility hinders its performance in biological systems. The use of cyclodextrins is a useful tool to increase the solubility and bioavailability of drugs. The aim of this work was to prepare an inclusion compound of PZQ and methyl-beta-cyclodextrin (MeCD), perform its physico-chemical characterization, and explore its in vitro cytotoxicity. SEM showed a change of the morphological characteristics of PZQ:MeCD crystals, and IR data supported this finding, with changes after interaction with MeCD including effects on the C-H of the aromatic ring, observed at 758 cm(-1). Differential scanning calorimetry measurements revealed that complexation occurred in a 1:1 molar ratio, as evidenced by the lack of a PZQ transition temperature after inclusion into the MeCD cavity. In solution, the PZQ UV spectrum profile in the presence of MeCD was comparable to the PZQ spectrum in a hydrophobic solvent. Phase solubility diagrams showed that there was a 5.5-fold increase in PZQ solubility, and were indicative of a type A(L) isotherm, that was used to determine an association constant (K(a)) of 140.8 M(-1). No cytotoxicity of the PZQ:MeCD inclusion compound was observed in tests using 3T3 cells. The results suggest that the association of PZQ with MeCD could be a good alternative for the treatment of schistosomiasis.

Sufentanil-2-hydroxypropyl-beta-cyclodextrin inclusion complex for pain treatment: Physicochemical, cytotoxicity, and pharmacological evaluation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Inclusion complex of S(-) bupivacaine and 2-hydroxypropyl- β-cyclodextrin: Study of morphology and cytotoxicity

Local anesthetics (LA) belong to a class of pharmacological compounds that attenuate or eliminate pain by binding to the sodium channel of excitable membranes, blocking the influx of sodium ions and the propagation of the nerve impulse. S (-) bupivacaine (S(-) bvc) is a local anesthetic of amino-amide type, widely used in surgery and obstetrics for sustained peripheral and central nerve blockade. This article focuses on the characterization of an inclusion complex of S(-) bvc in 2-hydroxypropyl-β-cyclodextrin (HP-β-CD). Differential scanning calorimetry, scanning electron microscopy and X-Ray diffraction analysis showed structural changes in the complex. In preliminary toxicity studies, the cell viability tests revealed that the inclusion complex decreased the toxic effect (p<0.001) produced by S(-) bvc. These results suggest that the S(-) bvc:HP-β-CD inclusion complex represents a promising agent for the treatment of regional pain.