An Interval-Parameter Fuzzy Approach for Multiobjective Linear Programming Under Uncertainty

An interval-parameter fuzzy linear programming method (IFMOLP) is proposed in this study for multiple objective decision-making under uncertainty. As a hybrid of interval-parameter and fuzzy methodologies, the IFMOLP incorporates interval-parameter linear programming and fuzzy multiobjective programming approaches to form an integrated optimization system. The method inherits advantages of interval-parameter programming, and allows uncertainties and decision-makers’ aspirations to be effectively communicated into its programming processes and resulting solutions. Membership functions for both objectives and constraints are formulated to reflect uncertainties in different system components and their interrelationships. An interactive solution procedure has been developed based on solution approaches of the interval-parameter and fuzzy programming techniques, plus necessary measures for handling the multiobjective feature. A didactic example is provided in the paper to illustrate the detailed solution process. Possibilities of further improvements by seeking Pareto optimum and incorporating flexible preference within constraints are also discussed.     

Reply to Comments of Bassi,Ghirardi, and Tumulka on the Free Will Theorem

We respond to criticisms of our paper “The Free Will Theorem”, and produce a new form of the theorem based on weaker assumptions.     

ALTERATIONS OF PROTEOGLYCANS IN ULTRAVIOLET-IRRADIATED SKIN

Abstract— The effect of UVB exposure on the distribution and synthesis of dermal proteoglycans was measured in the skin of hairless mice. Two groups of mice were included: one was irradiated for 10 weeks; the other was kept as control. After intraperitoneal injection of sodium ³⁵S-sulfate, punch biopsies were taken for histology and proteoglycans were extracted from the remaining skin with 4 M guanidinium chloride, containing 3–[(3-cholamidopropyl)dimethylammonio]-1-propanesulfonate (0.5%, weight per volume). Following proteolytic digestion, the glycosaminoglycan constituents were isolated and analyzed by quantitative cellulose acetate electrophoresis and enzymatic digestibility.
Under the influence of UVB radiation, newly synthesized proteoglycans measured by ³⁵SO₄ uptake increased as much as 60%. In addition, the irradiated skin had a higher average content of proteoglycan than had control skin (4981 μg vs 4134 μg/g dry weight). This could be ascribed to an increase in heparin (1400 vs 533 μ g/g dry weight) and heparan sulfate (472 vs 367 μg/g dry weight), whereas no change in the concentration of hyaluronic acid (1243 vs 1372 μg/g dry weight) and dermatan sulfate (1866 vs 1863 μg/g dry weight) was observed. The irradiated animals also exhibited a marked increase in the synthesis of heparan sulfate and heparin (62% and 71%, respectively). These results demonstrate that chronic doses of UVB altered proteoglycan metabolism through both quantitative and qualitative changes.     

On the measure of the spectrum for the almost Mathieu operator

We obtain partial results on the conjecture that for the almost Mathieu operator at irrational frequency, , the measure of the spectrum,S(, , )=|4–2|. For ||2 we show that if _n is rational and irrational, then .Dedicated to Res Jost and Arthur WightmanResearch partially supported by U.S. NSF grant number DMS-8801918 and by BSF under grant number 88-00325