A Common Regularization for Three Reservoir Optimal Control Problems

Four optimal control problems of reservoir release are investigated. The first problem is to minimize the peak release in order to prevent flood and to reduce the flood height. The second problem is to maximize the lowest release in order to ensure irrigation, water supply, shipping and environment downstream. The third problem is to minimize the flooding duration in order to reduce damage to goods, possessions, plants, levees, etc. It is shown that these three problems may possess infinitely many different optimal solutions, but they all have a common optimal solution, which is the unique optimal solution of the fourth problem. Since this unique optimal solution depends continuously on the input data, the fourth problem is well-posed and it can be considered as a common regularization of the three ill-posed problems.     

Outer Γ-Convexity in Vector Spaces

A subset S of some vector space X is said to be outer Γ-convex w.r.t. some given balanced subset Γ ? X if for all x ₀, x ₁ ? S there exists a closed subset Λ ? [0,1] such that {x _λ | λ ? Λ} ? S and [x ₀, x ₁] ? {x _λ | λ ? Λ} + 0.5 Γ, where x _λ: = (1 ? λ)x ₀ + λ x ₁. A real-valued function f:D → ? defined on some convex D ? X is called outer Γ-convex if for all x ₀, x ₁ ? D there exists a closed subset Λ ? [0,1] such that [x ₀, x ₁] ? {x _λ | λ ? Λ} + 0.5 Γ and f(x _λ) ≤ (1 ? λ)f(x ₀) + λ f(x ₁) holds for all λ ? Λ. Outer Γ-convex functions possess some similar optimization properties as these of convex functions, e.g., lower level sets of outer Γ-convex functions are outer Γ-convex and Γ-local minimizers are global minimizers. Some properties of outer Γ-convex sets and functions are presented, among others a simplex property of outer Γ-convex sets, which is applied for establishing a separation theorem and for proving the existence of modified subgradients of outer Γ-convex functions.     

A solution method for regular optimal control problems with state constraints

A method of region analysis is developed for solving a class of optimal control problems with one state and one control variable, including state and control constraints. The performance index is strictly convex with respect to the control variable, while this variable appears only linearly in the state equation. The convexity or linearity assumption of the performance index or the state equation with respect to the state variable is not required.The author would like to express his sincere gratitude to Prof. R. Klötzler, Prof. E. Zeidler, Prof. H. Schumann, Prof. J. Focke, and other colleagues of the Department of Mathematics, Karl Marx University, Leipzig, GDR, for their support during his stay in Leipzig.     

Strictly and Roughly Convexlike Functions

A function is said to be strictly and roughly convexlike with respect to the roughness degree r > 0 (for short, strictly r-convexlike) provided that, for all x ₀, x ₁ D satisfying ||x ₀ – x ₁|| > r, there exists a ]0, 1[ such that

Critical behavior of magnetic thin films

We study the critical behavior of magnetic thin films as a function of the film thickness. We use the ferromagnetic Ising model with the high-resolution multiple histogram Monte Carlo (MC) simulation. We show that though the 2D behavior remains dominant at small thicknesses, there is a systematic continuous deviation of the critical exponents from their 2D values. We explain these deviations using the concept of “effective” exponents suggested by Capehart and Fisher in a finite size analysis. The shift of the critical temperature with the film thickness obtained here by MC simulation is in an excellent agreement with their prediction.     

Experimental and theoretical study of reaction of OH with 1,3-butadiene

The kinetics of the reaction of hydroxyl radical with 1,3-butadiene at 240-340 K and a total pressure of approximately 1 Torr has been studied using relative rate combined with the discharge flow and mass spectrometer technique. The reaction dynamics of the same reaction has also been investigated using ab initio molecular orbital theory. The rate constant for this reaction was found to be negatively dependent on temperature, with an Arrhenius expression of k1 = (1.58 +/- 0.07) x 10(-11) exp[(436 +/- 13)/T] cm3 molecule(-1) s(-1) (uncertainties taken as 2sigma), which was in good agreement with that reported by Atkinson et al. and Liu et al. at 299-424 K. Mass spectral evidences were found for the addition of OH to both the terminal and the internal carbons of 1,3-butadiene. Our computational results suggest that both addition of OH to 1,3-butadiene and the abstraction of hydrogen atom from 1,3-butadiene by the OH radical are exothermic processes and that the addition of OH to the terminal carbon of the 1,3-butadiene is predicted to have an activation energy of 0.7 kcal mol(-1), being the most energetically favored reaction pathway.     

Methacrylate-containing polymer compounds for dentistry

Methacrylate-containing oligosilsesquioxanes were synthesized by acidohydrolytic copolycondensation of γ-methacryloyloxypropyltrimethoxysilane and phenyltrimethoxysilane in a mixture of bismethacrylate monomers, 2,2-bis[4-(2-hydroxy-3-methacryloyloxypropyl)phenyl]propane and triethylene glycol dimethacrylate, and were characterized by NMR spectroscopy and MALDI-TOF mass spectrometry. Performing the process in the bismethacrylate medium favors formation of uniform blends. Their introduction in an amount of 3 wt % into filled methacrylate dental composites considerably improves the physicomechanical characteristics of these composites.     

Six Kinds of Roughly Convex Functions

This paper considers six kinds of roughly convex functions, namely: δ-convex, midpoint δ-convex, ρ-convex, γ-convex, lightly γ-convex, and midpoint γ-convex functions. The relations between these concepts are presented. It is pointed out that these roughly convex functions have two optimization properties: each r-local minimizer is a global minimizer, and if they assume their maximum on a bounded convex domain D (in a Hilbert space), then they do so at least at one r-extreme point of D, where r denotes the roughness degree of these functions. Furthermore, analytical properties are investigated, such as boundedness, continuity, and conservation properties.     

A study of water vapour adsorption on the (110) surface of copper

The adsorption of water vapour on the (110)Cu face has been studied by AES and Δφ measurements in the 5 × 10^?9 to 3 × 10^?7 Torr range between 75 and 500°C. At lower temperatures, an initial physisorption of oriented water dipoles produces a fast initial Δφ decrease. Further adsorption causes no important changes of the Cu surface potential. At higher temperatures (above 100°C) a partial dissociation of the water molecules leads to a dissociative chemisorption producing a Δφ increase after the initial Δφ decrease due to water physisorption.