Multiple-type,two-dimensional bin packing problems: Applications and algorithms

In this paper we consider a class of bin selection and packing problems (BPP) in which potential bins are of various types, have two resource constraints, and the resource requirement for each object differs for each bin type. The problem is to select bins and assign the objects to bins so as to minimize the sum of bin costs while meeting the two resource constraints. This problem represents an extension of the classical two-dimensional BPP in which bins are homogeneous. Typical applications of this research include computer storage device selection with file assignment, robot selection with work station assignment, and computer processor selection with task assignment. Three solution algorithms have been developed and tested: a simple greedy heuristic, a method based onsimulated annealing (SA) and an exact algorithm based onColumn Generation with Branch and Bound (CG). An LP-based method for generating tight lower bounds was also developed (LB). Several hundred test problems based on computer storage device selection and file assignment were generated and solved. The heuristic solved problems up to 100 objects in less than a second; average solution value was within about 3% of the optimum. SA improved solutions to an average gap of less than 1% but a significant increase in computing time. LB produced average lower bounds within 3% of optimum within a few seconds. CG is practical for small to moderately-sized problems — possibly as many as 50 objects.     

Kinetics of nonequilibrium methylsiloxane polymerization and rearrangement

Nonrandom reactions were demonstrated experimentally during the polymerization of (CH₃)₃SiOSi(CH₃)₃ plus [(CH₃)₂SiO]₄ and the rearrangement of (CH₃)₃SiO[(CH₃)₂SiO]₅Si(CH₃)₃ or (CH₃)₃SiO[(CH₃)₂SiO]₈Si(CH₃)₃, using sulfuric acid-treated Fuller's earth as catalyst. Cyclic and linear reaction products were analyzed by gas–liquid chromatography. A four-step polymerization mechanism was proposed to account for the approach to equilibrium from either the forward or reverse direction. Reaction rate expressions for this mechanism were reduced to a finite set of nonlinear ordinary differential equations. These were solved by using a fourth-order Runge-Kutta numerical integration on a Burroughs B5500 computer. The calculated molecular weight distributions thus obtained were found to agree at all times with the distributions from polymerization and rearrangement experiments.     

Embedding in R-closed spaces

Some problems in the theory of R-closed spaces are solved by showing that every regular space can be embedded in a minimal regular space and there is an R-closed space with no coarser minimal regular topology. A class of spaces is found so that when fed into the Jone's machinery for producing non-Tychonoff, regular spaces, the output is non-tychonoff R-closed and minimal regular spaces. Also, an example of a strongly minimal regular space that is not locally R-closed is given.     

Reactions leading to the formation of O-3 on magnesium oxide

Ozonide ions were observed on MgO upon irradiation (254 nm) in the presence of O₂ at 25°C or upon reaction of O^-₂ on the surface with N₂O at 100°C. In the former case on O^-₂ intermediate is photodissociated to O and O^-. The latter subsequently reacts with O₂ forming O^-₃.     

ACTION SPECTRA FOR PHOTOREACTIONS I AND II OF PHOTOSYNTHESIS IN THE BLUE-GREEN ALGA ANACYSTIS NIDULANS

Abstract— Action spectra for photoreactions I and II of photosynthesis were obtained for Anacystis nidulans and three of its variants which had altered chlorophyll/phycocyanin ratios. The spectra are properly scaled to each other. They provide information on contributions of phycocyanin and chlorophyll to initial absorption and final distribution of excitation energy to reaction centers I and II. In normally pigmented cells the light harvesting pigments for photoreaction I include about 40% of the phycocyanin and 84% of the chlorophyll. Both in normal cells and in cells with altered pigmentation excitation energy from phycocyanin is delivered to photoreaction II via a small number of chlorophylls. In response to alterations in chlorophyll/phycocyanin ratio Action I spectra showed large variations whereas Action II spectra were essentially invariant. The result is taken to mean that alteration in chlorophyll components in Anacystis is attended by a special restriction: there are only small changes in amount of chlorophyll accessible to photoreaction II in the face of large changes in amount committed to photoreaction I.