Primal cutting plane algorithms revisited

Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutting planes is to enable a feasible solution to the original problem to be improved. Research on these algorithms has been almost non-existent.  In this paper we argue for a re-examination of these primal methods. We describe a new primal algorithm for pure 0-1 problems based on strong valid inequalities and give some encouraging computational results. Possible extensions to the case of general mixed-integer programs are also discussed.     

Packing into the smallest square: Worst-case analysis of lower bounds

We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature.     

pp interactions in P-wave and related topics

The nucleon-antinucleon (NN) annihilation process provides a fertile testing ground for microscopic hadron exchange and/or quark models. TheNN system offers a rich ensemble of annihilation channels, whose relative BRs provide strong constraints on dynamical models. Recent experiments show that values of BRs display a significant dependence onL, S andI. These dynamical selection rules,i.e. the suppression of transitions alloweda priori by conservation of quantum numbers, provide key signatures of the annihilation mechanism, and suggest dynamical content beyond simple statistical or flavour symmetry models.     

Integer linear programming models for 2-staged two-dimensional Knapsack problems

 We are given a unique rectangular piece of stock material S, with height H and width W, and a list of m rectangular shapes to be cut from S. Each shape's type i (i = 1, ..., m) is characterized by a height , a width , a profit , and an upper bound ub _i indicating the maximum number of items of type i which can be cut. We refer to the Two-Dimensional Knapsack (TDK) as the problem of determining a cutting pattern of S maximizing the sum of the profits of the cut items. In particular, we consider the classical variant of TDK in which the maximum number of cuts allowed to obtain each item is fixed to 2, and we refer to this problem as 2-staged TDK (2TDK). For the 2TDK problem we present two new Integer Linear Programming models, we discuss their properties, and we compare them with other formulations in terms of the LP bound they provide. Finally, both models are computationally tested within a standard branch-and-bound framework on a large set of instances from the literature by reinforcing them with the addition of linear inequalities to eliminate symmetries. Received: October 17, 2000 / Accepted: December 19, 2001 Published online: September 27, 2002 Key words. packing – cutting – integer linear programming     

Solvent-dependent host–guest complexation of two homologous merocyanines by a water-soluble calix[8]arene: Spectroscopic analysis and structural calculations

The sulfonated calixarene I₈C₁₂ acts as a host for homologous merocyanines Mc1 and Mc2 in organic solvents, exhibiting neither selectivity towards the guest dyes nor solvent dependence of the complexation equilibria. In water, on the contrary, only the lower homologue, Mc1, is solubilized in the presence of the calixarene. A combination of UV–visible and fluorescence spectroscopic and photophysical analysis and MD structural simulation of the calixarene-dye complexes was employed to account for the observations, and suggests that a radical change in the complexation mode occurs upon moving from an organic to an aqueous environment.     

Comparison of the sequential simplex method and linear solvent strength theory in HPLC gradient elution optimization of multicomponent flavonoid mixtures

Summary Using a camomile flavonoid extract as the sample and four different reversed-phase partition systems, the ability of the Simplex procedure to produce optimum gradient separation of unknown multicomponent mixtures was checked against the linear solvent strength (LSS) gradient elution theory. On the same partition systems the mean solvent strenghts were measured by experimentally determined logk vs. mobile phase composition plots. These mean solvent strengths are compared to those inferred from the optimum gradients and the usefulness of LSS theory in multicomponent mixture gradient elution optimization is discussed.Dadicated to Prof. Dr. A Liberti on the occasion of his 70th birthday.     

Characterisation of folic acid by mass balance versus quantitative NMR

Accreditation and Quality Assurance - Two approaches were used to determine the mass fraction of a sample of folic acid, one indirect (mass balance) where the components other than folic acid were...     

Simple,Copper(I)-Catalyzed Oxidation of Benzylic/Allylic Alcohols to Carbonyl Compounds: Synthesis of Functionalized Cinnamates in One Pot

An environmentally benign [Cu(I)]-catalyzed oxidation of activated (benzylic/allylic) alcohols to the corresponding carbonyl compounds is presented. Interestingly, the reaction was also compatible with benzylic alcohols containing ortho-bromo substituents on the aromatic ring without competing with the expected intermolecular Buchwald coupling. Significantly, the catalytic system enables the synthesis of cinnamate-esters in a sequential domino one-pot fashion via oxidation followed by Wittig–Horner protocol.     

The ASACUSA CUSP: an antihydrogen experiment

In order to test CPT symmetry between antihydrogen and its counterpart hydrogen, the ASACUSA collaboration plans to perform high precision microwave spectroscopy of ground-state hyperfine splitting of antihydrogen atom in-flight. We have developed an apparatus (“cusp trap”) which consists of a superconducting anti-Helmholtz coil and multiple ring electrodes. For the preparation of slow antiprotons and positrons, Penning-Malmberg type traps were utilized. The spectrometer line was positioned downstream of the cusp trap. At the end of the beamline, an antihydrogen beam detector was located, which comprises an inorganic Bismuth Germanium Oxide (BGO) single-crystal scintillator housed in a vacuum duct and surrounding plastic scintillators. A significant fraction of antihydrogen atoms flowing out the cusp trap were detected.     

An approximation scheme for the two-stage,two-dimensional knapsack problem

We present an approximation scheme for the two-dimensional version of the knapsack problem which requires packing a maximum-area set of rectangles in a unit square bin, with the further restrictions that packing must be orthogonal without rotations and done in two stages. Achieving a solution which is close to the optimum modulo a small additive constant can be done by taking wide inspiration from an existing asymptotic approximation scheme for two-stage two-dimensional bin packing. On the other hand, getting rid of the additive constant to achieve a canonical approximation scheme appears to be widely nontrivial.