Cutting planes,connectivity, and threshold logic

Originating from work in operations research the cutting plane refutation systemCP is an extension of resolution, where unsatisfiable propositional logic formulas in conjunctive normal form are recognized by showing the non-existence of boolean solutions to associated families of linear inequalities. Polynomial sizeCP proofs are given for the undirecteds-t connectivity principle. The subsystemsCP _q ofCP, forq2, are shown to be polynomially equivalent toCP, thus answering problem 19 from the list of open problems of [8]. We present a normal form theorem forCP ₂-proofs and thereby for arbitraryCP-proofs. As a corollary, we show that the coefficients and constant terms in arbitrary cutting plane proofs may be exponentially bounded by the number of steps in the proof, at the cost of an at most polynomial increase in the number of steps in the proof. The extensionCPLE ⁺, introduced in [9] and there shown top-simulate Frege systems, is proved to be polynomially equivalent to Frege systems. Lastly, since linear inequalities are related to threshold gates, we introduce a new threshold logic and prove a completeness theorem.Supported in part by NSF grant DMS-9205181 and by US-Czech Science and Technology Grant 93-205Partially supported by NSF grant CCR-9102896 and by US-Czech Science and Technology Grant 93-205     

Aurifeuillian factorizations and the period of the Bell numbers modulo a prime

We show that the minimum period modulo of the Bell exponential integers is for all primes and several larger . Our proof of this result requires the prime factorization of these periods. For some primes the factoring is aided by an algebraic formula called an Aurifeuillian factorization. We explain how the coefficients of the factors in these formulas may be computed.

     

Drinfeld algebra deformations, homotopy comodules and the associahedra

The aim of this work is to construct a cohomology theory controlling the deformations of a general Drinfel'd algebra and thus finish the program which began in [13], [14]. The task is accomplished in three steps. The first step, which was taken in the aforementioned articles, is the construction of a modified cobar complex adapted to a non-coassociative comultiplication. The following two steps each involves a new, highly non-trivial, construction. The first construction, essentially combinatorial, defines a differential graded Lie algebra structure on the simplicial chain complex of the associahedra. The second construction, of a more algebraic nature, is the definition of a map of differential graded Lie algebras from the complex defined above to the algebra of derivations on the bar resolution. Using the existence of this map and the acyclicity of the associahedra we can define a so-called homotopy comodule structure (Definition 3.3 below) on the bar resolution of a general Drinfel'd algebra. This in turn allows us to define the desired cohomology theory in terms of a complex which consists, roughly speaking, of the bimodule and bicomodule maps from the bar resolution to the modified cobar resolution. The complex is bigraded but not a bicomplex as in the Gerstenhaber-Schack theory for bialgebra deformations. The new components of the coboundary operator are defined via the constructions mentioned above. The results of the paper were announced in [12].

     

A high performance liquid chromatography – inductively coupled plasma-mass spectrometry interface employing desolvation for speciation studies of platinum in chemotherapy drugs

A novel interface between high performance liquid chromatography (HPLC) and inductively coupled plasma-mass spectrometry (ICP-MS) is described. The eluent from the HPLC is nebulised into a heated cyclone spray-chamber and the solvent removed using a Nafion membrane drier, held at 75 degrees C, and a cryogenic condenser. The condenser consists of 6 Peltier heat pumps connected to liquid cooled aluminium blocks. At a nebuliser gas flow rate of 0.6 l min(-1), the membrane drier removes 58% of the vapour and the Peltier condenser 75% of the remaining vapour, i.e. a total desolvation efficiency of 89%. This enables the use of HPLC solvents which otherwise would destabilise the ICP, e.g. 100% acetonitrile or methanol, and permits the use of solvent gradients with minimal baseline drift. The system has been applied to the determination of platinum species in an organoplatinum drug used for chemotherapy in human plasma ultrafiltrate of patients treated with this new drug (JM-216). The limit of detection for platinum species has been 0.6 ng nl(-1) (i.e. 120 pg of Pt) and several species have been separated with good resolution.     

Project Management Duration/Resource Tradeoff Analysis: an Application of the Cut Search Approach

The paper presents an application oriented procedure for solving the project management duration/resource tradeoff problem. A procedure is presented for reducing a project from a normal to a crash duration state at a minimum amount of additional resource expenditure assuming a linear utilization functions. The procedure is network based using a graphical Cut Search Approach to locate the minimal resource level at each reduction in total project duration. Activity-on-arc networks and flow networks are utilized. The paper is presented for practical application and for conceptual development as compared to a theoretical treatment.     

Liquid chromatographic determination of diminazene diaceturate (Berenil) in raw bovine milk

A simple liquid chromatographic (LC) method is presented for the determination of diminazene (DZ) in raw bovine milk. DZ is extracted from raw milk by chilled aqueous centrifugation and is isolated from milk components on a cyano solid-phase extraction column. DZ is eluted by using a methanol-ion pairing reagent. A Phenomenex LUNA CN column and an acetonitrile-buffered mobile phase with a counter ion are used for gradient LC. The LC effluent is monitored at a detection wavelength of 372 nm by using a deuterium lamp. Under the parameters described, the retention time of DZ is 8-10 min with a peak area response of 6.5 mAU/ng. The method demonstrated excellent precision over all levels tested (25-400 ppb) with an overall average recovery of 90.4 +/- 14.5%. The method is applicable to the monitoring of milk for DZ residues at the 25 ppb level with a limit of quantitation of 10 ppb.     

Factors influencing proton positions in biomolecules

Results of quantum mechanical calculations are presented that suggest a number of mechanisms whereby protons may be shifted from one group to another along an H bond. The first factor to be considered is a stretching of the bond that drastically raises the energy barrier to transfer. It is possible to predict barriers for an arbitrary system based only on results for a simple system and knowledge of the relevant bond length in the isolated subsystems. Factors that increase the intrinsic basicity of the B group in A-H-B lead not only to a lowering of the energy of the A-HB state relative to AH-B but also to a reduction in the barrier to transfer of the proton from A to B. Ions in the vicinity of the H bond exert a powerful influence and can shift the proton to the less basic group across a gradient of several pK units. Rather than shielding the proton from the external ion, the H bond acts instead to amplify the effects of the electric field. Reorientation of the A and B groups relative to one another, i.e., bends of the H bond, also produce surprisingly large changes in the relative energies of the AH-B and A-HB states. Such bends are capable of pushing the proton across to the normally less basic group, providing a mechanism of coupling conformational changes to proton ‘pumping’ activity. It is found that the high and low pH states of a given H bond can have dramatically differnt relative populations of the AH-B and A-HB configurations. These observations are explained in terms of fundamental concepts involving electrostatic interaction energies.     

The effect of interface deformation due to gravity on line tension measurement by the capillary rise in a conical tube

Much research has been done on line tension measurement and interpretation, and attempts have also been made to measure line tension with simple, cheap and reliable methods that do not require excessive sophistication. Of particular interest is the method of determining line tensions of solid–liquid–vapor systems from the capillary rise in a conical tube. This simple and relatively inexpensive method gives line tension values comparable to those reported in the literature obtained via highly sophisticated instruments or techniques such as the well known axisymmetric drop shape analysis technique. The absolute value of line tension obtained using the conical tube method and assuming a spherical liquid–vapor interface is larger but of the same order of magnitude (1 μJ m⁻¹) as that reported in the literature. A theoretical analysis presented herein shows that by including the deformation of the liquid–vapor interface due to gravity in the conical capillary analysis, the line tension value inferred from the experimental data is reduced by approximately 50% and compares better with values in the literature obtained using other sophisticated methods. Thus a relatively simple, cheap, accurate and reliable method of line tension measurement has been advanced.     

Catalytic oxidation of thiols to disulfides using iodine and CeCl3·7H2O in graphite

A very simple procedure for the efficient oxidation of thiols to disulfides catalyzed by I₂/CeCl₃·7H₂O in graphite and ethyl acetate as the solvent, in an open system at room temperature is described. The reaction proceeds cleanly under mild conditions and was performed with aromatic, aliphatic, and heterocyclic thiols.