Quantitative stability of full random two-stage stochastic programs with recourse

In this paper, we consider quantitative stability analysis for two-stage stochastic linear programs when recourse costs, the technology matrix, the recourse matrix and the right-hand side vector are all random. For this purpose, we first investigate continuity properties of parametric linear programs. After deriving an explicit expression for the upper bound of its feasible solutions, we establish locally Lipschitz continuity of the feasible solution sets of parametric linear programs. These results are then applied to prove continuity of the generalized objective function derived from the full random second-stage recourse problem, from which we derive new forms of quantitative stability results of the optimal value function and the optimal solution set with respect to the Fortet–Mourier probability metric. The obtained results are finally applied to establish asymptotic behavior of an empirical approximation algorithm for full random two-stage stochastic programs.     

On a convex set with nondifferentiable metric projection

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with \(C^{1,1}\) boundary which possesses the same property.     

Ragnar Frisch and interior-point methods

The distinguished econometrician Ragnar Frisch (1895–1973) also played an important role in optimization theory. In fact, he was a pioneer of interior-point methods. This note reconsiders his contribution, relating it to history and modern developments.     

Vinyl Polymerization. 418. Polymerization of Vinyl Monomer Initiated by Betaine-Type Polymers in Aqueous Solution

Abstract

Three kinds of betaine-type polymers, which are macromolecular amphoteric electrolytes, were found to be able to polymerize vinyl monomers in aqueous solution through a radical mechanism without any further initiator. Betain-type polymers form hydrophobic areas (HA) in water. Vinyl polymerization commenced in the HA. The effect of the pH of the aqueous solution on polymerization was investigated.     

Vinyl Polymerization. 431. Vinyl Polymerizations Initiated by Block and Random Poly(Styrene-co-Sodium Methacrylate)

Abstract

The polymerization of some kinds of vinyl monomer was found to occur without an ordinary initiator in aqueous solutions of AB-type block or random copolymers of sodium methacrylate with styrene as a so-called “uncatalyzed polymerization.” Although the spin trapping technique showed that the initiation mechanism by the block copolymer was the same as that by the random copolymer, the initiating ability of the block copolymer was lower than that of the random copolymer. Such results are attributable to the difference in the incorporating ability of monomer into the micelles formed by the block copolymer and into the hydrophobic areas formed by the random copolymer.     

Random Copolymers of 1,5-Dioxepan-2-one

ABSTRACT

Copolymers of 1,5-dioxepan-2-one (DXO) and e-caprolactone (?-CL), δ-valerolactone (δ-VL) or L-lactide (LLA) have been synthesized and characterized. High molecular weight copolymers were obtained using stannous-2-ethyl hexanoate as catalyst in bulk. Reactivity ratios for the copolymerization of DXO and δ-VL were determined at 110°C as r_VL=0.5 and r_DXO=2.3. At high conversion, depolymerization of δ-VL occurred, resulting in lower molecular weight and variations in the copolymer composition.

Physical properties, such as crystallinity and melting temperature of the DXO-copolymers proved to be strongly dependent on the choice of comonomer and on the molar composition of the copolymers. DXO appears to be incorporated into the poly-?-caprolactone (PCL) crystals and to some extent into the poly-δ-valerolactone (PVL) crystals, resulting in a more gradual decrease in crystallinity with increasing amount of DXO.     

Vinyl Polymerization. 436. Effect of Magnetic Field on Uncatalyzed Polymerization

The radical polymerization of vinyl monomers initiated with several kinds of hydrophilic macromolecule was carried out in a magnetic field. The magnetic field promoted the polymerization; the conversion of monomers and the molecular weight of the polymers obtained increased with increasing field strength in the range of 0–0.1 T. The dependence of the composition and tacticity of the mother polymer on the magnitude of the magnetic field was studied. Using graft or block copolymers, which consisted of hard and soft segments, the effect of a magnetic field was further investigated. The degree of hardness and tightness of the hydrophobic areas (reaction areas) formed by the mother polymer in the aqueous solution was found to affect the magnetic field effect on the uncatalyzed polymerization. The overall activation energy obtained in the magnetic field was almost equal to that obtained without a magnetic field.     

U6 is unsuitable for normalization of serum miRNA levels in patients with sepsis or liver fibrosis

MicroRNA (miRNA) levels in serum have recently emerged as potential novel biomarkers for various diseases. miRNAs are routinely measured by standard quantitative real-time PCR (qPCR); however, the high sensitivity of qPCR demands appropriate normalization to correct for nonbiological variation. Presently, RNU6B (U6) is used for data normalization of circulating miRNAs in many studies. However, it was suggested that serum levels of U6 themselves might differ between individuals. Therefore, no consensus has been reached on the best normalization strategy in ‘circulating miRNA''. We analyzed U6 levels as well as levels of spiked-in SV40-RNA in sera of 44 healthy volunteers, 203 intensive care unit patients and 64 patients with liver fibrosis. Levels of U6 demonstrated a high variability in sera of healthy donors, patients with critical illness and liver fibrosis. This high variability could also be confirmed in sera of mice after the cecal ligation and puncture procedure. Most importantly, levels of circulating U6 were significantly upregulated in sera of patients with critical illness and sepsis compared with controls and correlated with established markers of inflammation. In patients with liver fibrosis, U6 levels were significantly downregulated. In contrast, levels of spiked-in SV40 displayed a significantly higher stability both in human cohorts (healthy, critical illness, liver fibrosis) and in mice. Thus, we conclude that U6 levels in the serum are dysregulated in a disease-specific manner. Therefore, U6 should not be used for data normalization of circulating miRNAs in inflammatory diseases and previous studies using this approach should be interpreted with caution. Further studies are warranted to identify specific regulatory processes of U6 levels in sepsis and liver fibrosis.     

Application of thermovision for estimation of the optimal and safe parameters of the whole body cryotherapy

Exposure to the extreme low temperatures, ranging between ?60 and ?140 °C, has many beneficial effects on the human body what is exploited for example in sport medicine, for treatment of locomotory system diseases or even some psychiatric disorders. To insure the safe treatment in a cryochamber, careful planning of the procedure and proper qualification of patients, is required. Cardiovascular system, especially skin vasculature plays the major role of the body response to the extreme cold. The changes in skin blood flow are reflected in changes of the temperature distribution. Therefore, the thermal imaging, which allows to analyze the temperature distribution on the human body, may be successfully exploited to examine the influence of extremely low temperatures on the skin vascular system. The aim of this work was to examine the temperature, blood pressure, and heart rate changes after the whole body cryotherapy in healthy subjects to determine the safety conditions of the treatment. 480 healthy students of the Wroc?aw University School of Physical Education were divided into two groups (each 240 persons). All subjects were exposed for 1–3 min to the extremely low temperatures: ?60, ?100, ?120, and ?140 °C. In one group, the thermograms were recorded before and 5 and 30 min after the cryotherapy by means of ThermoVision A20 M thermal camera. In the other one, heart rate and blood pressure were measured before and 5 min after the cryotherapy. It was demonstrated that 3-min exposure in the cryochamber and the temperature ?120 °C are the optimal and safe cryotherapy parameters.     

Investigation of binuclear metal phthalocyanines as electrocatalysts for Li/SOCl<Subscript>2</Subscript> battery

Three novel series of the binuclear metal phthalocyanines M₂Pc₂, M₂Pc₂Hc, and M₂Nc₂ (M?=?Mn(II), Fe(II), Co(II), Ni(II), and Cu(II)) were synthesized and characterized. The electrocatalytic performance of the binuclear compounds to lithium–thionyl chloride battery was evaluated by operating these compounds in the electrolyte of the battery. The results indicated that the binuclear metal phthalocyanines improved the capacity of the battery by an increase of approximately 30–58 %. Of all, Cu₂Pc₂Hc and Fe₂Nc₂ displayed the highest increments of 56 and 57 %, respectively.