Integrable relativistic systems given by Hamiltonians with momentum-spin-orbit coupling

In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit coupling. We integrate the corresponding Hamiltonian equations in quadratures and express their solutions in terms of elliptic functions.Comment: 18 page

q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials

We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace operator. This allows to construct q-deformed Schroedinger equations in higher dimensions. The equivalence of these Schroedinger equations with those defined on q-Euclidean space in quantum variables is shown. We also define the m-dimensional q-Clifford-Hermite polynomials and show their connection with the q-Laguerre polynomials. These polynomials are orthogonal with respect to an m-dimensional q-integration, which is related to integration on q-Euclidean space. The q-Laguerre polynomials are the eigenvectors of an su_q(1|1)-representation

Interacting particles system revisited in the framework of the q-deformed algebra

We discuss the possibility of interpreting a q-deformed non-interacting system as incorporating the effects of interactions among its particles. This can be accomplished, for instance, in an ensemble of $q$-Bosons by means of the virial expansion of a real gas in powers of the deformed parameter. The lowest order virial coefficient reduces to the case of the standard, non-interacting Bose gas, while the higher order virial coefficients contain effects arising from the interaction. The same picture can be drawn in a quantum mechanical system where it is shown that the q-deformed momentum can be expanded in a series contains high-order powers of the standard quantum phase-space variables. Motivated by this result, we introduce, in the classical framework, a transformation relating the momentum of a free system with the momentum of an interacting system. It is shown that the canonical quantization applied to the interacting system imply a q-deformed quantization for the free system.Comment: 13 pages, no figures, accepted on JP

The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Application

Cerebral microdialysis in clinical studies of drugs: pharmacokinetic applications

The ability to deliver drug molecules effectively across the blood–brain barrier into the brain is important in the development of central nervous system (CNS) therapies. Cerebral microdialysis is the only existing technique for sampling molecules from the brain extracellular fluid (ECF; also termed interstitial fluid), the compartment to which the astrocytes and neurones are directly exposed. Plasma levels of drugs are often poor predictors of CNS activity. While cerebrospinal fluid (CSF) levels of drugs are often used as evidence of delivery of drug to brain, the CSF is a different compartment to the ECF. The continuous nature of microdialysis sampling of the ECF is ideal for pharmacokinetic (PK) studies, and can give valuable PK information of variations with time in drug concentrations of brain ECF versus plasma. The microdialysis technique needs careful calibration for relative recovery (extraction efficiency) of the drug if absolute quantification is required. Besides the drug, other molecules can be analysed in the microdialysates for information on downstream targets and/or energy metabolism in the brain. Cerebral microdialysis is an invasive technique, so is only useable in patients requiring neurocritical care, neurosurgery or brain biopsy. Application of results to wider patient populations, and to those with different pathologies or degrees of pathology, obviously demands caution. Nevertheless, microdialysis data can provide valuable guidelines for designing CNS therapies, and play an important role in small phase II clinical trials. In this review, we focus on the role of cerebral microdialysis in recent clinical studies of antimicrobial agents, drugs for tumour therapy, neuroprotective agents and anticonvulsants

Ultrastructural study of the clearance of intracerebrally infused native and modified albumin-gold complexes

The main objective of this ultrastructural study was to gain a better understanding of the involvement of brain vasculature in clearance of proteins from edematous fluid. For this purpose, both native and modified (cationized, glucosylated, and mannosylated) bovine serum albumin-gold complexes (BSA-G, catBSA-G, glucBSA-G and manBSA-G respectively) dissolved in phosphate-buffered saline (PBS) were infused (10 pl) into mouse cerebral cortex. Samples of brain were taken at 30 min, 1 h, and 24 h post-infusion for electron microscopical examination. All BSA-G complexes were rapidly taken up and deposited inside the cytoplasm of pericytes and of various glial cells (microglia and eventually astrocytes) located in the area adjacent to the infusion site. Only glucBSA-G particles also appeared inside the nuclei of some cells. In the applied experimental conditions and at the examined time intervals, neither BSA-G nor catBSA-G and glucBSA-G complexes were transported back to the bloodstream, although they entered vascular basement membrane and were eventually internalized in the endosomes or multivesicular bodies of the endothelial cells. Only a few gold particles representing the manBSA-G complex were found inside the vascular lumen, suggesting their reverse transport to a rather small degrce. The mechanism of this transport, however, remains unclear. Complexes of catBSA-G were apparently trapped by the negatively charged vascular basement membrane and remained in this structure without any further significant uptake by the endothelial cells. These observations suggest that large size and multimeric nature of albumin-gold complexes are limiting factors making it difficult to interpret the results and hampering their relevance to the clearance in vivo of native albumin from brain edematous fluid

Biochemical activity of di- and polyamines in the green alga Chlorella vulgaris Beijerinck [Chlorophyceae]

This study concerns on the influence of diamines (agmatine, putrescine) and polyamines (spermine, spermidine) upon the growth and the content of chlorophyll a and b, monosaccharides and proteins in the cells of alga Chlorella vulgaris Beijerinck (Chlorophyceae). In the experiments agmatine, putrescine, spermine and spermidine in the range of concentrations 10-6-10-3 M were used. At the concentration 10-3 M and the 1st day of cultivation, they have a toxic effect on growth of the algae. It was found that di- and polyamines used within the range of concentration 10-6-10-4 M stimulate the growth and the contents of analysed biochemical parameters in the cells of C. vulgaris. The most stimulating influence on metabolism of the alga was demonstrated by spermidine and putrescine at concentration of 10-4 M. Agmatine and spermine were characterised by a lower biological activity than spermidine and putrescine demonstrated the most stimulating influence

Cytochemical study of the involvement of cell organelles in formation and accumulation of fibrillar amyloid in the pancreas of NORβ transgenic mice

Phosphatase ultrastructural cytochemistry was used to evaluate the participation of cytoplasmic organelles in the accumulation of fibrillar amyloid β (Aβ) in exocrine acinar cells and in macrophages of the pancreas of transgenic mice overexpressing a carboxyterminal fragment of Aβ protein precursor (AβPP). Nucleoside diphosphatase (NDPase) and glucose-6- phosphatase (G6Pase) were used as cytochemical markers of the endoplasmic reticulum (ER), thiamine pyrophosphatase (TPPase) as a marker of the Golgi apparatus (CA), and acid phosphatase (AcPase) as a marker of lysosomes. Monoclonal antibody 4G8 raised against the 17-24 aa sequence of human Aβ protein was used for immunogold localization of fibrillar Aβ. The results of this study indicate that the formation of Aβ in acinar cells occurs directly in the vacuolar areas of the rough ER (RER) without evident participation of the elements of the GA, whereas an intimate structural relation with primary lysosomes suggests their role in modification or digestion of the deposited amyloid. In macrophages, fibrillar amyloid was present in numerous cytoplasmic vacuoles located frequently in close proximity to flattened saccules of the ER. This structural pattern revealed similarity to that observed previously in microglial cells producing fibrillar PrP amyloid in scrapie-infected mice and Aβ in brains of human elderly patients and in Alzheimer's type brain pathology