Walking an unknown street with bounded detour

A polygon with two distinguished vertices, s and g, is called a street if the two boundary chains from s to g are mutually weakly visible. For a mobile robot with on-board vision system we describe a strategy for finding a short path from s to g in a street not known in advance, and prove that the length of the path created does not exceed 1 + π times the length of the shortest path from s to g. Experiments suggest that our strategy is much better than this, as no ratio bigger than 1.8 has yet been observed. This is complemented by a lower bound of 1.41 for the relative detour each strategy can be forced to generate.     

A system of coupled partial differential equations exhibiting both elevation and depression rogue wave modes

Analytical solutions are obtained for a coupled system of partial differential equations involving hyperbolic differential operators. Oscillatory states are calculated by the Hirota bilinear transformation. Algebraically localized modes are derived by taking a Taylor expansion. Physically these equations will model the dynamics of water waves, where the dependent variable (typically the displacement of the free surface) can exhibit a sudden deviation from an otherwise tranquil background. Such modes are termed ‘rogue waves’ and are associated with ‘extreme and rare events in physics’. Furthermore, elevations, depressions and ‘four-petal’ rogue waves can all be obtained by modifying the input parameters.     

On Weierstrass semigroups and sets: a review with new results

In this work we present a survey of the main results in the theory of Weierstrass semigroups at several points, with special attention to the determination of bounds for the cardinality of its set of gaps. We also review results on applications to the theory of error correcting codes. We then recall a generalization of the concept of Weierstrass semigroup, which is the Weierstrass set associated to a linear system and several points. We finish by presenting new results on this Weierstrass set, including some on the cardinality of its set of gaps.      

Canonical maps to twisted rings

If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring , which is surjective in large degree. This result is a key step in the study of projectively simple rings. The proof relies on some results concerning the growth of graded rings which are of independent interest. D. Rogalski was partially supported by NSF grant DMS-0202479. J. J. Zhang was partially supported by NSF grant DMS-0245420 and Leverhulme Research Interchange Grant F/00158/X (UK).     

Non-existence of a massive scalar field for the Marder universe in Lyra and Riemannian geometries

In this paper, we have studied a massive scalar field for a Marder type universe in the context of Lyra and Riemannian geometries. From the exact solutions obtained we show that the massive scalar field does not survive in Lyra and Riemannian geometries for an anisotropic Marder type universe. Therefore we have solved the massless scalar field problem in Lyra and Riemann geometries for two cases. Also we have obtained vacuum solutions for homogeneous and anisotropic Marder space-time in Lyra geometry and the solutions obtained are compared by considering Lyra and Riemann geometries. Finally, some physical and kinematical properties are discussed by using graphics.     

TRAJELIX: A Computational Tool for the Geometric Characterization of Protein Helices During Molecular Dynamics Simulations

Summary We have developed a computer program with the necessary mathematical formalism for the geometric characterization of distorted conformations of alpha-helices proteins, such as those that can potentially be sampled during typical molecular dynamics simulations. This formalism has been incorporated into TRAJELIX, a new module within the SIMULAID framework (http://inka.mssm.edu/~mezei/simulaid/) that is capable of monitoring distortions of alpha-helices in terms of their displacement, global and local tilting, rotation around their axes, compression/extension, winding/unwinding, and bending. Accurate evaluation of these global and local structural properties of the helix can help study possible intramolecular and intermolecular changes in the helix packing of alpha-helical membrane proteins, as shown here in an application to the interacting helical domains of rhodopsin dimers. Quantification of the dynamic structural behavior of alpha-helical membrane proteins is critical for our understanding of signal transduction, and may enable structure-based design of more specific and efficient drugs.     

Preparation and Molecular Structure of Binuclear Nickel (I) Complex Bridged by 1,2,4, 5‐Benzenetetracarboxylato Tetravalent Anion

The title complex [(H₂O)₂(IMI)₃Ni(TCB)Ni(IMI)₃‐(H₂O)₂] H₂O (TCB = 1,2,4,5‐benzenetetracarboxylato te‐travalent anion; IMI = imidazole) has been prepared by the reaction of Ni(IMI)₃(Ac)₂ and TCB in aqueous solution. The crystal structure has been determined by single‐crystal X‐ray diffraction method. It crystallizes in the monoclinic system, space group P2₁/c(# 14), a = 1.2714(4) nm, b = 0.9411 (3) nm, c = 1.5869(4) nm, β= 108.54(2)°, V= 1.8001(9) nm³, Z = 2. The main feature of the crystal structure is a symmetric binuclear unit made up of two slightly distorted coordination octahedrons, which are bridged by TCB in monodentate fashion to each metal ion. Moreover three nitrogen atoms from three imidazoles, three oxygen atoms from two water molecules and one carboxylate group of TCB coordinated to a nickel (I) ion are found on a face of the octahedron respectively, so the octahedron is a facial isomer.     

Bonding Energies and Structural Study of Alkylaluminium

Neutral aluminium alkyls are well known to act as ethylene oligomerization and polymerization catalysts and cocatalysts.On the basis of the full optimization of alkylaluminium compounds with Gaussian 98 program package at the B3LYP/6-31G** level,the selected structures and bonding energies were investigated extensively.The geometries and bonding energies of AlR3(R = H,CH3,C2H5,C3H7,C4H9) and Al(C2H5)2R'(R' = C2H5,C3H7,C4H9,C5H11,C6H13) were investigated extensively,and we found that,along with the prolongation of carbon chains the terminal C-C bond is shortened gradually until to a constant value of about 0.1532 nm in C4H9;and the bonding energy almost remains constant.The dative bonding of C2H4 to Al(C2H5)3,whose bonding energy is only 15.30 kJ/mol,is very weak.     

PERI-INTERACTIONS IN NAPHTHALENES, 21. SUBSTITUENT EFFECTS IN (8-DIMETHYLAMINO-NAPHTH-1-YL)- AND [2-DIMETHYLAMINO-METHYL)PHENYL] - PHOSPHINES ON THE 31P-NMR SIGNAL POSITIONS

Abstract

Contrary to claims in the literature, the ³¹P NMR signal positions of ortho-dimethylaminomethyl-substituted triarylphosphines do not provide evidence for hypercoordination at phosphorus; the observed highfield shifts relative to triphenylphosphine are rather due to the ortho-effect. In (8-dimethylamino-naphth-1-yl)phosphines, the signal positions similar to that of triphenylphosphine are the result of the highfield ortho-effect and a lowfield peri-substituent effect of about the same magnitude whose nature remains to be explored.     

On the automatic restricted-step rational-function-optimization method

The rational function optimization algorithm is one of the widely used methods to search stationary points on surfaces. However, one of the drawbacks of this method is the step reduction procedure to deal with the overstepping problem. We present and comment on a method such that the step obtained from the solution of the rational function equations possesses the desired correct length. The analysis and discussion of the method is mainly centered on the location and optimization of transition states. Received: 18 June 1998 / Accepted: 17 September 1998 / Published online: 23 November 1998