Discounted dynamic programming with unbounded returns: Application to economic models

In this paper, we study discounted Markov decision processes on an uncountable state space. We allow a utility (reward) function to be unbounded both from above and below. A new feature in our approach is an easily verifiable rate of growth condition introduced for a positive part of the utility function. This assumption, in turn, enables us to prove the convergence of a value iteration algorithm to a solution to the Bellman equation. Moreover, by virtue of the optimality equation we show the existence of an optimal stationary policy.     

Three critical points theorem and its application to quasilinear elliptic equations

In this paper, we prove a Pucci-Serrin type three critical points theorem for continuous functionals and study its application to quasilinear elliptic equations with natural growth.     

Zero distribution of solutions of complex linear differential equations determines growth of coefficients

It is shown that the exponent of convergence λ(f) of any solution f of with entire coefficients A₀(z), …, A_k?2(z), satisfies λ(f) ? λ ∈ [1, ∞) if and only if the coefficients A₀(z), …, A_k?2(z) are polynomials such that for j = 0, …, k ? 2. In the unit disc analogue of this result certain intersections of weighted Bergman spaces take the role of polynomials. The key idea in the proofs is W. J. Kim’s 1969 representation of coefficients in terms of ratios of linearly independent solutions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.     

A three-dimensional steady-state tumor system

The growth of tumors can be modeled as a free boundary problem involving partial differential equations. We consider one such model and compute steady-state solutions for this model. These solutions include radially symmetric solutions where the free boundary is a sphere and nonradially symmetric solutions. Linear and nonlinear stability for these solutions are determined numerically.     

Bending and vibration of an electrostatically actuated circular microplate in presence of Casimir force

The pull-in instability and the vibration for a prestressed circular electrostatically actuated microplate are investigated in consideration of the Casimir force. Based on von Kármán’s nonlinear bending theory of thin plates, the governing equations for the whole analysis are decomposed into two two-point boundary value problems. For static deformation of the plate, the geometric nonlinearity is involved and the pull-in parameters are obtained by using the shooting method through taking the applied voltage or Casimir parameter as an unknown. This algorithm is also used to study the small amplitude free vibration about the predeformed bending configuration following an assumed harmonic time mode, and the variation of the prestress and Casimir parameters dependent fundamental natural frequency with the applied voltage is presented. Several case studies are compared with available published simulations to confirm the proposed method. The influences of various parameters, such as the initial gap-thickness ratio, Casimir effect, prestress on the pull-in instability behavior and the natural frequency are examined.     

Solitary waves for the Klein-Gordon-Maxwell system with critical exponent

In this paper we study the existence of solutions for nonlinear Klein-Gordon-Maxwell equations coupled with Maxwell’s equations when the nonlinearity exhibits critical growth. We improve some previous existence results in Azzollini et al. (2009) [5], Carrião et al. (2009) [4] and Cassani (2004) [3].     

Characterization of silver nanoparticles using flow-field flow fractionation interfaced to inductively coupled plasma mass spectrometry

The ability to detect and identify the physiochemical form of contaminants in the environment is important for degradation, fate and transport, and toxicity studies. This is particularly true of nanomaterials that exist as discrete particles rather than dissolved or sorbed contaminant molecules in the environment. Nanoparticles will tend to agglomerate or dissolve, based on solution chemistry, which will drastically affect their environmental properties. The current study investigates the use of field flow fractionation (FFF) interfaced to inductively coupled plasma-mass spectrometry (ICP-MS) as a sensitive and selective method for detection and characterization of silver nanoparticles. Transmission electron microscopy (TEM) is used to verify the morphology and primary particle size and size distribution of precisely engineered silver nanoparticles. Subsequently, the hydrodynamic size measurements by FFF are compared to dynamic light scattering (DLS) to verify the accuracy of the size determination. Additionally, the sensitivity of the ICP-MS detector is demonstrated by fractionation of μg/L concentrations of mixed silver nanoparticle standards. The technique has been applied to nanoparticle suspensions prior to use in toxicity studies, and post-exposure biological tissue analysis. Silver nanoparticles extracted from tissues of the sediment-dwelling, freshwater oligochaete Lumbriculus variegatus increased in size from approximately 31-46nm, indicating a significant change in the nanoparticle characteristics during exposure.     

One target, different effects: a comparison of distinct therapeutic antibodies against the same targets

To date, more than 30 antibodies have been approved worldwide for therapeutic use. While the monoclonal antibody market is rapidly growing, the clinical use of therapeutic antibodies is mostly limited to treatment of cancers and immunological disorders. Moreover, antibodies against only five targets (TNF-α, HER2, CD20, EGFR, and VEGF) account for more than 80 percent of the worldwide market of therapeutic antibodies. The shortage of novel, clinically proven targets has resulted in the development of many distinct therapeutic antibodies against a small number of proven targets, based on the premise that different antibody molecules against the same target antigen have distinct biological and clinical effects from one another. For example, four antibodies against TNF-α have been approved by the FDA -- infliximab, adalimumab, golimumab, and certolizumab pegol -- with many more in clinical and preclinical development. The situation is similar for HER2, CD20, EGFR, and VEGF, each having one or more approved antibodies and many more under development. This review discusses the different binding characteristics, mechanisms of action, and biological and clinical activities of multiple monoclonal antibodies against TNF-α, HER-2, CD20, and EGFR and provides insights into the development of therapeutic antibodies.