Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

On abstract differential equations with nonlocal conditions involving the temporal derivative of the solution

In this paper we discuss the existence of solutions for a class of abstract differential equations with nonlocal conditions for which the nonlocal term involves the temporal derivative of the solution. Some concrete applications to parabolic differential equations with nonlocal conditions are considered. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

Evaluation of Solid-Phase Microextraction using a Polythiophene Film and Liquid Chromatography with Spectrophotometric Detection for the Determination of Antidepressants in Plasma Samples

Polythiophene (PTh) phase electropolymerized on the stainless steel wire was evaluated as solid-phase microextraction (SPME), and analysis by liquid chromatography with spectrophotometric detection (LC-UV) for determination of new-generation antidepressants, selective serotonin reuptake inhibitors (SSRIs) (citalopram, paroxetine, fluoxetine and sertraline), in plasma samples. The influence of electropolymerization variables (scan rate, potential range and scan cycles) was evaluated on SPME performance. The SPME variables (extraction time, temperature, matrix pH, ionic strength and desorption procedure), as well as the influence of plasma proteins on sorption mechanisms were also evaluated. The SPME/LC-UV method developed for determination of antidepressants in plasma sample presented a linear range between the limit of quantification (LOQ, 200-250 ng mL(-1)) to 4000 ng mL(-1), and interday precision with coefficient of variation (CV) ranged from 11 to 15%. The proposed method can be a useful tool for the determination of antidepressants in human plasma samples in urgent toxicological analysis after the accidental or suicidal intake of higher doses of medications.

Flow-injection spectrophotometric determination of captopril in pharmaceutical formulations using a new solid-phase reactor containing AgSCN immobilized in a polyurethane resin

A simple flow-injection analysis procedure was developed for determining captopril in pharmaceutical formulations employing a novel solid-phase reactor containing silver thiocyanate immobilized in a castor oil derivative polyurethane resin. The method was based on silver mercaptide formation between the captopril and Ag(I) in the solid-phase reactor. During such a reaction, the SCN- anion was released and reacted with Fe3+, which generated the FeSCN2+ complex that was continuously monitored at 480 nm. The analytical curve was linear in the captopril concentration range from 3.0 x 10(-4) mol L-1 to 1.1 x 10(-3) mol L-1 with a detection limit of 8.0 x 10(-5) mol L-1. Recoveries between 97.5% and 103% and a relative standard deviation of 2% for a solution containing 6.0 x 10(-4) mol L-1 captopril (n = 12) were obtained. The sample throughput was 40 h(-1) and the results obtained for captopril in pharmaceutical formulations using this procedure and those obtained using a pharmacopoeia procedure were in agreement at a 95% confidence level.

Measure functional differential equations and functional dynamic equations on time scales

We study measure functional differential equations and clarify their relation to generalized ordinary differential equations. We show that functional dynamic equations on time scales represent a special case of measure functional differential equations. For both types of equations, we obtain results on the existence and uniqueness of solutions, continuous dependence, and periodic averaging.

Boundedness of solutions of retarded functional differential equations with variable impulses via generalized ordinary differential equations

In this paper, we give sufficient conditions for the uniform boundedness and uniform ultimate boundedness of solutions of a class of retarded functional differential equations with impulse effects acting on variable times. We employ the theory of generalized ordinary differential equations to obtain our results. As an example, we investigate the boundedness of the solution of a circulating fuel nuclear reactor model.

DERIVATIVE SPECTROPHOTOMETRIC METHOD FOR DEYERMINATION OF ACYCLOVIR IN POLYMERIC NANOPARTICLES

A derivative spectrophotometric method was validated for quzintification of acyclovir in poly (n-butylcyanoacrylate) (PBCA) nanoparticles. Specificity, linearity. precision, accuracy, recovery. detection (LOD) and quantification (LOQ) Inuits were established for method validation. First-derivative it 295.2 nm eliminated interferences from nanoparticle ingredients and presented linearity for acyclovir concentrations ranging front 1.25 to 40.0 mu g/mL. (r = 0.9999). Precision and accuracy data demonstrated good reproducibility. Recovery ranged from 99.3 to 101.2. LOD) was 0.08 mu g/mL and LOQ. 0.25 mu g/mL. Thus. the proposed method proved to be easy. low cost. and accurate, and therefore, an useful alternative to quantify acyclovir in nanoparticles.

On the generalized canonical equations of Hamilton for a time-dependent mass particle

Fundamental principles of mechanics were primarily conceived for constant mass systems. Since the pioneering works of Meshcherskii (see historical review in Mikhailov (Mech. Solids 10(5):32-40, 1975), efforts have been made in order to elaborate an adequate mathematical formalism for variable mass systems. This is a current research field in theoretical mechanics. In this paper, attention is focused on the derivation of the so-called 'generalized canonical equations of Hamilton' for a variable mass particle. The applied technique consists in the consideration of the mass variation process as a dissipative phenomenon. Kozlov's (Stek. Inst. Math 223:178-184, 1998) method, originally devoted to the derivation of the generalized canonical equations of Hamilton for dissipative systems, is accordingly extended to the scenario of variable mass systems. This is done by conveniently writing the flux of kinetic energy from or into the variable mass particle as a 'Rayleigh-like dissipation function'. Cayley (Proc. R Soc. Lond. 8:506-511, 1857) was the first scholar to propose such an analogy. A deeper discussion on this particular subject will be left for a future paper.

Hyperbolic-like estimates for higher order equations

The main goal of this paper is to derive long time estimates of the energy for the higher order hyperbolic equations with time-dependent coefficients. in particular, we estimate the energy in the hyperbolic zone of the extended phase space by means of a function f (t) which depends on the principal part and on the coefficients of the terms of order m - 1. Then we look for sufficient conditions that guarantee the same energy estimate from above in all the extended phase space. We call this class of estimates hyperbolic-like since the energy behavior is deeply depending on the hyperbolic structure of the equation. In some cases, these estimates produce a dissipative effect on the energy. (C) 2012 Elsevier Inc. All rights reserved.

Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' threshold theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

Existence and concentration of solutions for a class of biharmonic equations

Some superlinear fourth order elliptic equations are considered. A family of solutions is proved to exist and to concentrate at a point in the limit. The proof relies on variational methods and makes use of a weak version of the Ambrosetti-Rabinowitz condition. The existence and concentration of solutions are related to a suitable truncated equation. (C) 2012 Elsevier Inc. All rights reserved.

Periodic averaging theorems for various types of equations

We prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem. We also present a periodic averaging theorem for a large class of retarded equations.

Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier Inc. All rights reserved.

Modified CUPRAC spectrophotometric quantification of total polyphenol content in beer samples using Cu(II)/neocuproine complexes

Cu(II)/neocuproine (2,9-dimethyl-1,10-phenanthroline) complexes were utilized for spectrophotometric determination of total polyphenol content in beers. This procedure is based on the reduction of Cu(II) by polyphenols in hydroethanolic medium (pH 7.0) in the presence of neocuproine, yielding Cu(I)/complexes with maximum absorption at 454 nm. The sensitivity of the proposed method was compared with the AOAC method using tannic and gallic acid as standards. The average apparent molar absorptivity, in L cm(-1) mol(-1), of tannic acid (3.50 +/- 0.20) x 10(5) and gallic acid (5.12 +/- 0.21) x 10(4), was twice as high for the proposed method. A lower limit of detection (LOD) (2.9 x 10(-1) mg L-1) was found when tannic acid was used in the proposed method. Additionally, less interference from the most common additives in beers was noticed. Total content of polyphenols was analyzed in 17 Brazilian samples. Results ranged from 35.5 to 556 mg L-1 of tannic acid, with higher values for recovery rates (45.4-118%, mean 85.0%) than for gallic acid. Although tannic acid is a mixture of polygalloyl glucoses, the total polyphenol content found in the samples suggests that tannic acid should be used as a standard. This is the first attempt to use this particular copper complex to quantify total polyphenol content in beer samples. (C) 2012 Elsevier Inc. All rights reserved.

MULTIPLICITY OF NONRADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON ANNULUS WITH EXPONENTIAL CRITICAL GROWTH

In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems (p) {-Delta(N)u = lambda f(vertical bar x vertical bar, u) x is an element of Omega(r), u > 0 x is an element of Omega(r), u = 0 x is an element of Omega(r), where Omega(r) = {x is an element of R-N : r < vertical bar x vertical bar < r + 1}, N >= 2, N not equal 3, r >0, lambda > 0, Delta(N)u = div(vertical bar del u vertical bar(N-2)del u) is the N-Laplacian operator and f is a continuous function with exponential critical growth.