New euclidean theorems by the use of Laguerre transformations — Some geometry of Minkowski (2+1)-space

Examples of the use of Laguerre transformations to discover theorems in the Euclidean and Minkowski planes.     

A large scale location-allocation problem in the natural rubber industry

In trying to improve the efficiency of the smallholder sector of the natural rubber industry, the Malaysian government is faced with large-scale location-allocation problems. This involves locating and operating central rubber processing factories producing high quality natural rubber, siting of collection stations to which the smallholders can bring their latex, and the vehicle routing problem of transporting the latex to the central rubber processing factories. We formulate a global model which minimizes the collection and fixed costs of the system, subject to capacity and time constraints. Since real-life problems, from their sheer magnitude, are impossible to solve optimally, heuristic approaches are suggested for a simplified version of the problem.     

Convergence of a class of runge-kutta methods for differential-algebraic systems of index 2

This paper deals with convergence results for a special class of Runge-Kutta (RK) methods as applied to differential-algebraic equations (DAE's) of index 2 in Hessenberg form. The considered methods are stiffly accurate, with a singular RK matrix whose first row vanishes, but which possesses a nonsingular submatrix. Under certain hypotheses, global superconvergence for the differential components is shown, so that a conjecture related to the Lobatto IIIA schemes is proved. Extensions of the presented results to projected RK methods are discussed. Some numerical examples in line with the theoretical results are included.     

Inorganic analysis

AbstractsGeneral analytical chemistry

Inorganic analysis     

Order properties of attractive spin systems

Methods of constructing semigroups of operators describing interacting particle systems are reviewed. A simple proof is given showing the existence of semigroups of operators on the space of bounded Borel measurable functions for nonnegative continuous attractive spin rates along with a proof of the existence of invariant measures for the semigroups so constructed.     

Variable radio frequency proton-electron double-resonance imaging: application to pH mapping of aqueous samples

Proton-electron double-resonance imaging (PEDRI) offers rapid image data collection and high resolution for spatial distribution of paramagnetic probes. Recently we developed the concept of variable field (VF) PEDRI which enables extracting a functional map from a limited number of images acquired at pre-selected EPR excitation fields using specific paramagnetic probes (Khramtsov et al., J. Magn. Reson. 202 (2010) 267-273). In this work, we propose and evaluate a new modality of PEDRI-based functional imaging with enhanced temporal resolution which we term variable radio frequency (VRF) PEDRI. The approach allows for functional mapping (e.g., pH mapping) using specifically designed paramagnetic probes with high quality spatial resolution and short acquisition times. This approach uses a stationary magnetic field but different EPR RFs. The ratio of Overhauser enhancements measured at each pixel at two different excitation frequencies corresponding to the resonances of protonated and deprotonated forms of a pH-sensitive nitroxide is converted to a pH map using a corresponding calibration curve. Elimination of field cycling decreased the acquisition time by exclusion periods of ramping and stabilization of the magnetic field. Improved magnetic field homogeneity and stability allowed for the fast MRI acquisition modalities such as fast spin echo. In total, about 30-fold decrease in EPR irradiation time was achieved for VRF PEDRI (2.4s) compared with VF PEDRI (70s). This is particularly important for in vivo applications enabling one to overcome the limiting stability of paramagnetic probes and sample overheating by reducing RF power deposition.     

From phage display to dendrimer display: insights into multivalent binding

Phage display is widely used for the selection of target-specific peptide sequences. Presentation of phage peptides on a multivalent platform can be used to (partially) restore the binding affinity. Here, we present a detailed analysis of the effects of valency, linker choice, and receptor density on binding affinity of a multivalent architecture, using streptavidin (SA) as model multivalent receptor. For surfaces with low receptor densities, the SA binding affinity of multivalent dendritic phage peptide constructs increases over 2 orders of magnitude over the monovalent species (e.g., K(d,mono) = 120 μM vs K(d,tetra) = 1 μM), consistent with previous work. However, the affinity of the SA-binding phage presenting the exact same peptides was 16 pM when dense receptor surfaces used for initial phage display were used in assays. The phage affinity for SA-coated surfaces weakens severely toward the nanomolar regime when surface density of SA is decreased. A similarly strong dependence in this respect was observed for dendritic phage analogues. When presented with a dense SA-coated surface, dendrimer display affords up to a 10(4)-fold gain in affinity over the monovalent peptide. The interplay between ligand valency and receptor density is a fundamental aspect of multivalent targeting strategies in biological systems. The perspective offered here suggests that in vivo targeting schemes might best be served to conduct ligand selection under physiologically relevant receptor density surfaces, either by controlling the receptor density placed at the selection surface or by using more biologically relevant intact cells and tissues.