Quantum ball as an example of quantum Kähler manifold

Using the notion of the coherent state map we present a construction of the C^∗$C^{\ast }$-algebra which is considered as a quantum version of the unit ball in C^N${\mathbb{C}}^N$. The structure of the quantum ball as well as its physical interpretation is investigated. Applying the reduction procedure to the quantum ball we obtain the Heisenberg–Weyl algebra.     

Induction for weak symplectic Banach manifolds

The symplectic induction procedure is extended to the case of weak symplectic Banach manifolds. Using this procedure, one constructs hierarchies of integrable Hamiltonian systems related to the Banach Lie–Poisson spaces of k$k$-diagonal trace class operators.     

Operator algebras related to quantum optical systems and integrations

We show that some quantum optical systems generate quantum algebras being the natural generalization of the Heisenberg-Weyl algebra. The importance of these algebras for the integration of the systems under consideration is discussed. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. This work is supported in part by KBN grant 2 PO3 A 012 19.     

A model of conformal kinematics

A new realization of the conformal group in the classical phase space of a positive mass relativistic scalar particle is obtained. A physical interpretation in the spirit of conformal relativity is discussed.     

Stereoselective synthesis of uridine-derived nucleosyl amino acids

Novel hybrid structures of 5'-deoxyuridine and glycine were conceived and synthesized. Such nucleosyl amino acids (NAAs) represent simplified analogues of the core structure of muraymycin nucleoside antibiotics, making them useful synthetic building blocks for structure-activity relationship (SAR) studies. The key step of the developed synthetic route was the efficient and highly diastereoselective asymmetric hydrogenation of didehydro amino acid precursors toward protected NAAs. It was anticipated that the synthesis of unprotected muraymycin derivatives via this route would require a suitable intermediate protecting group at the N-3 of the uracil base. After initial attempts using PMB- and BOM-N-3 protection, both of which resulted in problematic deprotection steps, an N-3 protecting group-free route was envisaged. In spite of the pronounced acidity of the uracil-3-NH, this route worked equally efficient and with identical stereoselectivities as the initial strategies involving N-3 protection. The obtained NAA building blocks were employed for the synthesis of truncated 5'-deoxymuraymycin analogues.     

QCM-D analysis of the performance of blocking agents on gold and polystyrene surfaces

With today's developments of biosensors and medical implants comes the need for efficient reduction of nonspecific binding. We report on a comparison of the ability of traditionally used blocking agents and poly(ethylene glycol) (PEG) derivatives to prevent protein adsorption on both gold and polystyrene surfaces. The adsorption kinetics of blocking molecules and proteins was monitored gravimetrically using quartz crystal microbalance with dissipation (QCM-D). The resistance to nonspecific adsorption was evaluated on gold and polystyrene surfaces coated with bovine serum albumin (BSA) or casein, gold coated with three different 6-11 ethylene glycol (EG) long hydroxyl- or methoxy-terminated PEG-thiolates and polystyrene blocked with a PLL-g-PEG or three different 12 EG long benzyl-PEG-derivatives. The prevention of protein adsorption on the coated surfaces was evaluated by monitoring the mass uptake at the addition of both pure prostate specific antigen (PSA) and seminal plasma. We demonstrate that on pure gold the PEG-thiols are superior to the other blocking molecules tested, with the end group and length of the PEG-thiols used being of minor importance. On polystyrene surfaces blocking with PLL-g-PEG, BSA and casein gave the best results. These results have an impact on further development of an optimized immunoassay protocol.     

Fractional variational calculus with classical and combined Caputo derivatives

We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange equations to the basic and isoperimetric problems as well as transversality conditions are proved.     

Interparticle Charge-Transport-Enhanced Electrochemiluminescence of Quantum-Dot Aerogels

Electrochemiluminescence (ECL) represents a widely explored technique to generate light, in which the emission intensity relies critically on the charge-transfer reactions between electrogenerated radicals. Two types of charge-transfer mechanisms have been postulated for ECL generation, but the manipulation and effective probing of these routes remain a fundamental challenge. Here, we demonstrate the design of quantum dot (QD) aerogels as novel ECL luminophores via a versatile water-induced gelation strategy. The strong electronic coupling between adjacent QDs enables efficient charge transport within the aerogel network, leading to the generation of highly efficient ECL based on the selectively improved interparticle charge-transfer route. This mechanism is further verified by designing CdSe-CdTe mixed QD aerogels, where the two mechanistic routes are clearly decoupled for ECL generation. We anticipate our work will advance the fundamental understanding of ECL and prove useful for designing next-generation QD-based devices.