Reply to “Comment on ‘Calculation of Two-center Nuclear Attraction Integrals over Integer and Noninteger N-slater-type Orbitals in Nonlined-up Coordinate Systems” ’

The comments of Guseinov on our recent paper (T. Özdo?an, S. Gümü? and M. Kara, J. Math. Chem. 33 (2003) 181) are critically analyzed. It is proved that the expansion formula for the product of two normalized associated Legendre functions and the expressions for two-center nuclear attraction integrals over Slater type orbitals have been obtained independently, by the use of basic mathematical rules.     

Modified Alternating $$\vec{k}$$–generators

This paper deals with a class of pseudorandom bit generators – modified alternating –generators. This class is constructed similarly to the class of alternating step generators. Three subclasses of are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating –generators, designed especially to be more secure, are presented.     

Harnack’s Inequality for Stable Lévy Processes

We prove Harnacks inequality for harmonic functions of a symmetric stable Lévy process on R^d without the assumption that the density function of its Lévy measure is locally bounded from below. Mathematics Subject Classifications (2000) Primary 60J45, 31C05; Secondary 60G51.Research partially supported by KBN (2P03A 041 22) and RTN (HPRN-CT-2001-00273-HARP).     

Linear Orders on General Algebras

We answer the question, when a partial order in a partially ordered algebraic structure has a compatible linear extension. The finite extension property enables us to show, that if there is no such extension, then it is caused by a certain finite subset in the direct square of the base set. As a consequence, we prove that a partial order can be linearly extended if and only if it can be linearly extended on every finitely generated subalgebra. Using a special equivalence relation on the above direct square, we obtain a further property of linearly extendible partial orders. Imposing conditions on the lattice of compatible quasi orders, the number of linear orders can be determined. Our general approach yields new results even in the case of semi-groups and groups.     

A New Route to Light Emitting Organic Materials Based on Triazine Derivatives

Novel light-emitting organic materials comprising conjugated oligomers chemically attached via a flexible spacer to an electron–or hole-conducting core were synthesized by Stille cross-coupling methodology and designed for tunable charge injection and optical properties. The hyperbranched structures have been characterized by ¹H NMR, ¹³C NMR, and UV-VIS spectroscopy. The obtained structures show good stability in common organic solvents such as CHCl₃, toluene, and CH₂Cl₂ and exhibit excellent thermal stability. A preliminary electroluminescence properties were also investigated. This class of materials will help to balance charge injection and transport and to spread out the charge recombination zone, thereby significantly improving the device efficiency and lifetime of unpolarized and polarized OLEDs.     

Nanosensors having dipicolinic acid imprinted nanoshell for Bacillus cereus spores detection

Molecular imprinted polymers (MIPs) as a recognition element for sensors are increasingly of interest and MIP nanoclusters have started to appear in the literature. In this study, we have proposed a novel thiol ligand-capping method with polymerizable methacryloylamido-cysteine (MAC) attached to gold–silver nanoclusters, reminiscent of a self-assembled monolayer and have reconstructed surface shell by synthetic host polymers based on molecular imprinting method for recognition. In this method, methacryloylamidoantipyrine–terbium ((MAAP)₂–Tb(III)) has been used as a new metal-chelating monomer via metal coordination–chelation interactions and dipicolinic acid (DPA) which is main participant of Bacillus cereus spores used as a model. Nanoshell sensors with templates give a cavity that is selective for DPA. The DPA can simultaneously chelate to Tb(III) metal ion and fit into the shape-selective cavity. Thus, the interaction between Tb(III) ion and free coordination spheres has an effect on the binding ability of the gold–silver nanoclusters nanosensor. The binding affinity of the DPA imprinted nanoclusters has been investigated by using the Langmuir and Scatchard methods, and the respective affinity constants (K _affinity) determined were found to be 1.43 × 10⁴ and 9.1 × 10⁶ mol L^?1.     

Stark effect and generalized Bloch-Siegert shift in a strongly driven two-level system

A superconducting qubit was driven in an ultrastrong fashion by an oscillatory microwave field, which was created by coupling via the nonlinear Josephson energy. The observed Stark shifts of the "atomic" levels are so pronounced that corrections even beyond the lowest-order Bloch-Siegert shift are needed to properly explain the measurements. The quasienergies of the dressed two-level system were probed by resonant absorption via a cavity, and the results are in agreement with a calculation based on the Floquet approach.     

Large Deviations for Brownian Particle Systems with Killing

Particle approximations for certain nonlinear and nonlocal reaction–diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is killed independently at a rate determined by the empirical sub-probability measure of the states of the particles alive. A large deviation principle (LDP) for such sub-probability measure-valued processes is established. Along the way a convenient variational representation, which is of independent interest, for expectations of nonnegative functionals of Brownian motions together with an i.i.d. sequence of random variables is established. Proof of the LDP relies on this variational representation and weak convergence arguments.