We prove existence of renormalized solutions to general nonlinear elliptic equation in Musielak–Orlicz space avoiding growth restrictions. Namely, we consider−divA(x,∇u)=f∈L1(Ω), on a Lipschitz ...bounded domain in RN. The growth of the monotone vector field A is controlled by a generalized nonhomogeneous and anisotropic N-function M. The approach does not require any particular type of growth condition of M or its conjugate M⁎ (neither Δ2, nor ∇2). The condition we impose is log-Hölder continuity of M, which results in good approximation properties of the space. The proof of the main results uses truncation ideas, the Young measures methods and monotonicity arguments.
The rate-regulation tradeoff, defined between two objective functions, one penalizing the packet rate and one the regulation cost, can express the fundamental performance bound of networked control ...systems. However, the characterization of the set of globally optimal solutions in this tradeoff for multidimensional Gauss-Markov processes has been an open problem. In this article, we characterize a policy profile that belongs to this set without imposing any restrictions on the information structure or the policy structure. We prove that such a policy profile consists of a symmetric threshold triggering policy based on the value of information and a certainty-equivalent control policy based on a non-Gaussian linear estimator. These policies are deterministic and can be designed separately. Besides, we provide a global optimality analysis for the value of information <inline-formula><tex-math notation="LaTeX">\mathbf{{VoI}}_{{\boldsymbol{k}}}</tex-math></inline-formula>, a semantic metric that emerges from the rate-regulation tradeoff as the difference between the benefit and the cost of a data packet. We prove that it is globally optimal that a data packet containing sensory information at time <inline-formula><tex-math notation="LaTeX">{\boldsymbol{k}}</tex-math></inline-formula> be transmitted to the controller only if <inline-formula><tex-math notation="LaTeX">\mathbf{{VoI}}_{{\boldsymbol{k}}}</tex-math></inline-formula> becomes nonnegative. These findings have important implications in the areas of communication and control.
Abstract Ophthalmic drug delivery through eye drops is inefficient because of low corneal bioavailability and short residence time in tears. Contact lenses are ideally suited for extended and ...targeted drug delivery to cornea, but commercial contact lenses release ophthalmic drugs for only 1–2 h. This study focuses on dispersing timolol encapsulating highly crosslinked nanoparticles in contact lenses to increase the duration of drug release from 1 to 2 h to about 2–4 weeks. The highly crosslinked particles were prepared from monomers with multivinyl functionalities such as EGDMA (ethylene glycol dimethacrylate) and PGT (propoxylated glyceryl triacylate). The nanoparticles were about 3.5 nm in size and encapsulated 48–66% of the drug depending on the composition. Drug release studies in a diffusion cell showed that the particles released the drug for a period of about 4 weeks. The drug loaded particles were dispersed in hydroxy methyl methacrylate (HEMA) gels, which are common contact lens materials. The particle loaded gels release timolol in phosphate buffered saline (PBS) for 2–4 weeks at therapeutic dose, which is promising for extended drug release applications. The proposed mechanism of drug transport is hydrolysis of ester bonds that link timolol to the particle matrix which form during the particle formation process. The drug release profiles can be described by a first order reaction model with a temperature dependent rate constant. The rate constant of ester hydrolysis was significantly smaller than that in previous studies on timolol esters possibly due to steric effects and the low water content of the highly crosslinked hydrophobic particles. The results of this study provide evidences that contact lenses loaded with nanoparticles could be very useful for extended delivery of ophthalmic drugs.
This article will examine the current literature, as it relates to contact lens discomfort (CLD) secondary to contact lens solutions. The reader will better understand the characteristics of contact ...lenses, as they uniquely interact with each type of contact lens solution and also gain a better comprehension of the components of contact lens solution such as preservatives, surfactants, and chelating agents, which may contribute to discomfort. By investigating corneal staining theory and the mechanisms that contribute to its presence, the reader will gain insight into this clinical finding, which relates to selection of contact lens solutions. The FDA standards for testing solutions and how this relates to contact lens keratitis will also be appraised in regards to current ISO recommendations. Finally, better selection of multipurpose contact lens solution (MPS) and hydrogen peroxide-based solutions for patients should be accessible to the clinician based on this review and preexisting clinical findings or diagnoses.
A review of current published literature from peer reviewed journals and online journals was conducted to gain an understanding of contact lens solution's impact on contact lens discomfort.
Many studies have been conducted comparing comfort between various types of contact lens solutions. It is challenging to decipher this information and apply it clinically when selecting solutions for patients. By comparing solution components, how contact lens solutions interact with different types of lenses, keratitis related to contact lenses, and preexisting ocular conditions, this review will improve a clinician's ability to eliminate CLD.
This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. It is one of the first ...books on Theory of Boundary Element Methods.
We use a variational approach to deal with the system −Δu+V(x)u+K(x)ϕu=a(x)|u|p−1u,−Δϕ=K(x)u2,x∈R3, with 3<p<5. Under some mild conditions on the sign-changing potentials V and a we obtain two ...nonzero solutions. One of them is nonnegative and the other one changes sign.
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•Zr-Ta-B-SiC coatings with different solid solubility of (Zr,Ta)B2 were prepared by pack cementation and slurry method.•The microstructure evolution and ablation behavior of ...Zr-Ta-B-SiC coatings were investigated.•The content of tantalum brings a remarkable impact on the surface morphology after ablation.•The constitution and micro morphology of Zr-Ta-O layer played a predominant role in ablation resistance.
Zr-Ta-B-SiC multiphase coating was prepared on carbon/carbon composites by pack cementation and slurry method. The (Zr,Ta)B2 solid solution was found to be the key antiablative component. The ablation behavior suggested that the synthesized Zr0.70Ta0.30B2-SiC coating exhibited the best ablation resistance at 2300 °C. It is asserted that the micromorphology and distribution of Zr-Ta-O in the coating played a vital role in the evolution of the protective layer and ablation performance. A coating with ∼30 % Ta was beneficial for stabilizing the t-ZrO2 phase and alleviating the volume change at high temperature. The formation of a thermal barrier and low volatility of Zr-Ta-O layer were responsible for the excellent ablation resistance.
In this study, generalized Jacobi elliptic function method is implemented to strain wave equation in microstructure solids (SWEMSS). This method is based on the elliptic equation which is a powerful ...equation and has abundant of elliptic function solutions. This study found new doubly periodic wave solutions. These doubly periodic wave solutions degenerated as single periodic solutions when m→0 and solitary wave solutions when m→1. The new obtained single periodic solutions and solitary wave solutions of the SWEMSS could help in the understanding of the phenomena in which waves are governed by such equation. We also presented graphical movement of few obtained solutions by using different values for parameters involved in the solutions. Also, the aspects of stability analysis for the considered equations is investigated using the linear stability technique.
•Periodic Soliton Solutions to Strain Wave are presented.•Exact soliton solutions are obtained for some nonlinear partial differential equations.•Graphical analysis has been carried out to study the physical aspects of obtained solutions.
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