Advertisement allocation for generalized second-pricing schemes

Recently, there has been a surge of interest in algorithms that allocate advertisement space in an online revenue-competitive manner. Most such algorithms, however, assume a pay-as-you-bid pricing scheme. In this paper, we study the query allocation problem where the ad space is priced using the well-known and widely used generalized second-price (GSP) scheme. We observe that the previous algorithms fail to achieve a bounded competitive ratio under the GSP scheme. On the positive side, we present online constant-competitive algorithms for the problem.     

On the neutron-to-proton ratio on the surface of heavy nuclei

The results of a computer simulation study of K^? capture in emulsion nuclei are used to reappraise experimental data pertaining to the question of existence of a ‘neutron halo’ on the surface of heavy nuclei. Our results indicate that the conclusion of the experimental study that there is an excess of neutrons on the surface of heavy nuclei is substantially correct though the neutron-to-proton ratio may be lower (～ 3) than its initially estimated value (～ 5).     

Class two analogue of T. Y. Thomas's theorem and different types of embeddings of static spherically symmetric space-times

A Riemannian space of embedding class two is characterised by two symmetric tensors a _ij , b _ij and a vector s_i, satisfying the equations of Gauss, Codazzi and Ricci. It is proved that the Gauss equations together with one set of Codazzi equations imply the other set of Codazzi equations and the Ricci equations, provided that the matrix of the tensor b _ij (or a _ij ) is nonsingular. (The class m generalisation of the result has also been suggested). The result so proved has further been utilized in finding explicitly the a _ij 's and b _ij 's in the case of the static spherically symmetric line element. It is further indicated that the a _ij 's and b _ij 's so obtained are responsible for the different types of embeddings of the spacetime considered.     

A fourth order method for y″ = ƒ(x,y, y′)

A fourth order numerical method for solving the general second order differential equation $\text{y″ = ?(x, y, y′)}$ is suggested. This method is self starting, P-stable (when applied to $\text{y″ = ?(x, y)}$), and it involves only two function evaluations per step. Easily calculable and simple truncation error estimates are given, which can be used for automatic error control in computations. The method is illustrated on numerical examples.     

Metal derivatives of amidoximes V. Dialkyl- or diphenyl-silyl derivatives of amidoximes

New monomeric dialkyl- or diphenyl-silylbisamidoximes and dialkyl(ethoxy)silylamidoximes have been characterised. Their infrared spectra have been interpreted and diamagnetic susceptibility of some of them has been determined.     

Infrared absorption spectra of 2,3- and 3,5-dichloroaniline

The infrared absorption spectra of 2,3- and 3,5-dichloroanilines have been recorded in the region 250–4000 cm⁻¹. The spectra of the latter are recorded in solid phase (KBr and Nujol mull) and in CS₂/CCl₄ and CHCl₃ solutions while that of the former in thin film only. The spectra have been analysed assuming C ₃ and C_2v point group symmetry respectively and a tentative assignment of the observed bands to different fundamental modes has been made.     

Hyperfragments produced from K− capture

Characteristics of hyperfragments produced from K^? capture in nuclear emulsion are investigated through computer simulation and compared with corresponding experimental results. The nuclear cascade is completely simulated and the nucleus is de-excited through evaporation after estimating the excitation energy. Characteristics of hyperfragments particularly their mass distribution and the prong distribution of their production star can be used in favour of the peripheral hypothesis of K^? absorption. The calculated and the observed range distributions of the heavy hyperfragments are not in complete agreement, a feature leading to the inference that spallation may not be the only process responsible for the production of such hyperfragments.     

Synthesis of aminonicotinonitriles and diaminopyridines through base-catalyzed ring transformation of 2H-pyran-2-ones

An efficient and convenient synthesis of 2-amino-6-aryl-4-methylsulfanylnicotinonitriles (2), 2-amino-6-aryl-4-substituted-aminonicotinonitriles (4), and 2-amino-6-aryl-4-substituted-aminopyridines (6) has been delineated and illustrated through base-catalyzed ring transformation of 6-aryl-3-cyano-4-methylsulfanyl/substituted-amino-2H-pyran-2-ones (1, 3, and 5) with cyanamide and ammonium carbonate separately.     

Synthesis, optical resolution, and configurational assignment of novel axially chiral quateraryls

A one-pot general synthesis of highly functionalized quateraryls through carbanion-induced, base-catalyzed ring transformation of 5,6-diaryl-2H-pyran-2-ones and core-substituted phenylacetones is delineated. These conversions were found to give diversely functionalized benzenes bearing peripheral aryl rings, some of which possess inherent atropisomerism. Exemplarily for one of the quateraryls, the optical resolution of the respective atropo-enantiomers by HPLC on a chiral phase and the assignment of their absolute axial configurations succeeded by LC-CD coupling in combination with semiempirical CNDO/S and TDDFT CD calculations. This synthetic approach offers-in a transition metal-free environment-high flexibility in the construction of quateraryls with the desired conformational freedom along the molecular axis, which may help in exploring and developing new potential ligands for asymmetric synthesis.     

The synthesis and structural characterization of novel N-meta-ferrocenyl benzoyl dipeptide esters: The X-ray crystal structure and in vitro anti-cancer activity of N-{meta-ferrocenyl)benzoyl}-l-alanine-glycine ethyl ester

A series of N-meta-ferrocenyl benzoyl dipeptide esters 2-5 have been prepared by coupling meta-ferrocenyl benzoic acid 1b to the dipeptide ethyl esters using the conventional 1,3-dicyclohexylcarbodiimide (DCC), 1-hydroxybenzotriazole (HOBt) protocol. The dipeptides employed in the synthesis were AlaGly(OEt) (2), AlaAla(OEt) (3), AlaLeu(OEt) (4) and AlaPhe(OEt) (5). The compounds were fully characterized by a range of NMR spectroscopic techniques, mass spectrometry (MALDI-MS, ESI-MS), and cyclic voltammetry (CV). In addition, the X-ray crystal structure and cytotoxicity of N-{meta-(ferrocenyl)-benzoyl}-l-alanine-glycine ethyl ester (2) towards lung cancer cells has been determined.