Predictability and model selection in the context of ARCH models

Most of the methods used in the ARCH literature for selecting the appropriate model are based on evaluating the ability of the models to describe the data. An alternative model selection approach is examined based on the evaluation of the predictability of the models in terms of standardized prediction errors. Copyright © 2005 John Wiley & Sons, Ltd.     

Random Walks And The Colored Jones Function

It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagram, and another in terms of counting paths of intersecting chords. Electronic supplementary material to this article is available at and is accessible to authorized users. * S. G. was partially supported by an NSF and by an Israel-US BSF grant. † M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education.     

Approximation algorithms for scheduling problems with a modified total weighted tardiness objective

We study the approximability of minimum total weighted tardiness with a modified objective which includes an additive constant. This ensures the existence of a positive lower bound for the minimum value. Moreover the new objective has a natural interpretation in just-in-time production systems.     

The dynamics of Rydberg electron wavepackets in NO

Rydberg electron wavepackets have been studied in molecular NO for a variety of rotational states of the ion core. Predominantly radial motion of the electron wavepacket is observed which is similar to that previously reported in atomic systems. Interference effects similar to those observed in unperturbed Rydberg series are evident and third and fourth order partial revivals are identified. Most interestingly, when the classical period of electronic motion is close to the classical period of rotation of the molecular ion, the molecular dynamics dominates the electronic dynamics.     

Synthesis and antitumor activity of new thiosemicarbazones of 2‐acetylimidazo[4,5‐b]pyridine

A number of thiosemicarbazones of 2‐acetyl‐imidazo[4,5‐b]pyridine were prepared in order to investigate their in vitro antineoplastic activities. Three compounds: (i) 2‐acetylimidazo[4,5‐b]pyridin‐4‐ sec ‐butyl‐3‐thiosemicarbazone [(A₇), NSC674098], (ii) 2‐acetylimidazo[4,5‐b]pyridin‐4‐tert‐butyl‐3‐thiosemi‐carbazone [(A₉), NSC674099], (iii) 2‐acetylimidazo[4,5‐b]pyridin‐4‐cyclohexyl‐3‐thiosemicarbozone [(A₁₁), NSC674101] showed remarkable activity against some of the cell lines tested. The Biological Evaluation Committee of N.C.I. determined that further secondary testing should be carried out (these compounds were tested against prostate cancer).     

ITQ-15: the first ultralarge pore zeolite with a bi-directional pore system formed by intersecting 14- and 12-ring channels, and its catalytic implications

The pore topology of ITQ-15 zeolite consists of an ultra-large 14-ring channel that is intersected perpendicularly by a 12-ring pore; acid sites have been introduced in its framework and this unique structure shows advantages over unidirectional ultralarge pore zeolites for diffusing and reacting large molecules.     

Quick regiospecific analysis of fatty acids in triacylglycerols with GC using 1,3-specific lipase in butanol

A new micro-procedure for the quick regiospecific analysis of triacylglycerols (TAG) with a 1,3-specific lipase, Lipozyme IM 20 (produced from strains of Muccor miehei) is described. After dissolution of triacylglycerols in butan-1-ol or butan-2-ol 250 mg of Lipozyme IM 20 were added and the whole mixture was agitated. This operation was repeated 5-10 times and the esterified fatty acids in the form of butyl esters (FABE) were dissolved in pentane and washed with water. The pentane layer was dried over sodium sulfate and the solvent was removed under vacuum to a constant weight. The residue was analysed using GC-MS. The same triacylglycerols were converted to fatty acid methyl esters (FAME). The FAME were analysed by gas chromatography (GC).     

2,4‐Diamino‐5‐(1‐naphthyl)‐3,5‐diaza‐1‐azoniaspiro[5.5]undeca‐1,3‐diene chloride

The title salt, C₁₈H₂₂N₅⁺·Cl^?, is a member of a new series of lipophilic 4,6‐di­amino spiro‐s‐triazines which are potent in­hib­itors of di­hydro­folate reductase. The protonated triazine ring deviates from planarity, whereas the cyclo­hexane ring adopts a chair conformation. A rather unusual hydrogen‐bonding scheme exists in the crystal. There is a centrosymmetric arrangement involving two amino groups and two triazine ring N atoms, with graph‐set R(8) and an N?N distance of 3.098 (3) Å, flanked by two additional R(8) systems, involving two amino groups, a triazine ring N atom and a Cl^? anion, with N?Cl distances in the range 3.179 (2)–3.278 (2) Å. Furthermore, the Cl^? anion, the protonated triazine ring N atom and an amino group form a hydrogen‐bonding system with graph‐set R(6).     

Improved Bohr’s inequality for locally univalent harmonic mappings

We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form $f=h+\overline{g}$, where $h$ is bounded by 1 and $\left|g^{\prime }\left(z\right)\right|\le \left|h^{\prime }\left(z\right)\right|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk $D(0,r)$ under the mapping $f$ is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.