A Projection Method for the Integer Quadratic Knapsack Problem

In this paper we present a new branch and bound algorithm for solving a class of integer quadratic knapsack problems. A previously published algorithm solves the continuous variable subproblems in the branch and bound tree by performing a binary search over the breakpoints of a piecewise linear equation resulting from the Kuhn-Tucker conditions. Here, we first present modifications to a projection method for solving the continuous subproblems. Then we implement the modified projection method in a branch and bound framework and report computational results indicating that the new branch and bound algorithm is superior to the earlier method.     

Potential of magnetic resonance spectroscopy to detect metastasis in axillary lymph nodes in breast cancer

Focused pathological evaluation of axillary lymph nodes in breast cancer is gaining importance. Nuclear magnetic resonance (NMR) spectroscopy that assesses the whole of the specimen has the potential in evaluating micrometastases. The biochemical changes associated with breast cancer metastases in axillary nodes by in vitro NMR and its use in the detection of axillary metastases in a clinical setting in comparison with conventional histopathology is presented in this study. Eighty-eight lymph nodes obtained from 30 patients with breast cancer were investigated. Histopathology revealed metastases in 20 nodes from 11 patients, while in vitro NMR spectroscopy revealed metastases in 22 nodes. Out of these 22 nodes, 16 were the same, which showed metastases on histopathology, while 6 nodes have shown metastases only on in vitro magnetic resonance spectroscopy (MRS). These 6 nodes with suspicion of metastases on MRS were subjected to reevaluation with serial sectioning and immunohistochemistry, but no additional metastases were revealed. Forty metabolites could be identified from the MR spectrum of lymph nodes. The levels of the glycerophosphocholine-phosphocholine (GPC-PC), choline, lactate, alanine and uridine diphosphoglucose were elevated significantly in nodes with metastases. In addition, the intensity ratio of GPC-PC/threonine (Thr) was higher in nodes with metastases, and using this as marker, MRS detected the axillary metastases with a sensitivity, specificity and accuracy of 80%, 91% and 88%, respectively. Neoadjuvant chemotherapy (NACT) lowered the concentrations of GPC-PC and GPC-PC/Thr ratio. The accuracy of MRS in detecting metastases was 75% in patients who received NACT (n=9) as compared to 96% in those who did not (n=21). Our results demonstrate the potential of in vitro MRS in characterizing the metabolite profile of the axillary nodes with breast cancer metastases. It detected axillary metastases with reasonable accuracy and can be complementary to histopathological evaluation and immunohistochemistry.     

Geometric Conditions on the Type of Matter Determining the Flat Behavior of the Rotational Curves in Galaxies

In an arbitrary axisymmetric stationary spacetime, we determine the expression for the tangential velocity of test objects following a circular stable geodesic motion in the equatorial plane, as function of the metric coefficients. Next, we impose the condition, observed in large samples of disks galaxies, that the magnitude of such tangential velocity be radii independent in the dark matter dominated region, obtaining a constraint equation among the metric coefficients, and thus arriving to an iff (iff means: if and only if.) condition: The tangential velocity of test particles is radii independent iff the metric coefficients satisfied the mentioned constraint equation. Furthermore, for the static case, the constraint equation can be easily integrated, leaving the spacetime at the equatorial plane essentially with only one independent metric coefficient. With the geometry thus fixed, we compute the Einstein tensor and equate it to an arbitrary stress energy tensor, in order to determine the type of energy-matter which could produce such a geometry. Within an approximation, we deduce a constraint equation among the components of the stress energy tensor. We test in that constraint equation several well known types of matter, which have been proposed as dark matter candidates and are able to point for possible right ones. Finally, we also present the spherically symmetric static case and apply the mentioned procedure to perfect fluid stress energy tensor, recovering the Newtonian result as well as the one obtained in the axisymmetric case. We also present arguments on the need to use GR to study types of matter different than the dust one.     

Incompressibility of strange matter

Strange stars (ReSS) calculated from a realistic equation of state (EOS), that incorporate chiral symmetry restoration as well as deconfinement at high density [Phys. Lett. B 438 (1998) 123; Phys. Lett. B 447 (1999) 352, Addendum; Phys. Lett. B 467 (1999) 303, Erratum; Indian J. Phys. B 73 (1999) 377] show compact objects in the mass radius curve. We compare our calculations of incompressibility for this EOS with that of nuclear matter. One of the nuclear matter EOS has a continuous transition to ud-matter at about five times normal density. Another nuclear matter EOS incorporates density dependent coupling constants. From a look at the consequent velocity of sound, it is found that the transition to ud-matter seems necessary.     

Coulomb screening in graphene with topological defects

We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green’s function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green’s function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge but differ for the higher strengths, especially in the presence of the conical defect. For a given subcritical charge, the transport cross-section has a higher value in the presence of the conical defect. In the supercritical regime we show that the coefficient of the power law tail of polarization charge density can be expressed as a summation of functions which vary log periodically with the distance from the Coulomb impurity. The period of variation depends on the conical defect. In the presence of the conical defect, the Fano resonances begin to appear in the transport cross-section for a lower value of the Coulomb charge. For both sub and supercritical regime we derive the dependence of LDOS on the conical defect. The effects of generalized boundary condition on the physical observables are also discussed.     

Investigations into the role of ion pairing in reactions of heteroatom-substituted cyclic oxocarbenium ions

[reaction: see text] The O-to-C rearrangement of vinyl acetals is used to demonstrate that tight ion pairing is not involved in the stereoselective nucleophilic addition reactions of alkoxy-substituted cyclic oxocarbenium ions.     

Direct meta-C−H Perfluoroalkenylation of Arenes Enabled by a Cleavable Pyrimidine-Based Template

The development of efficient and mild methods for the synthesis of organofluorine compounds is of foremost interest in various fields of chemistry. A direct pyrimidine-based selective meta-C−H perfluoroalkenylation of arenes involving several commercially available perfluoroolefins is described. The synthetic versatility of the protocol is demonstrated by an extensive substrate scope including different benzylsulfonyl, alkylarene and phenylacetic acid scaffolds. The generality of this methodology including the meta-C−H perfluoroalkenylation of Ibuprofen, the facile cleavage of the directing group and gram-scale reactions are presented.     

Cerium(III)-Catalyzed Synthesis of Schiff Bases: A Green Approach

The reaction of primary aromatic amines with aryl aldehydes is found to be catalyzed by cerium chloride heptahydrate under solvent-free conditions to give the corresponding Schiff bases in good yields.     

Stereoselective Bromination of 2-Vinyl Chromones Using NBS

A simple one-step synthetic methodology for stereoselective synthesis of E- and Z-3-bromo-2-vinyl chromones in quantitative yield in polar solvents under ambient conditions without the use of catalysts is reported.