Gratings in novel fibre geometry for applications in shape sensing

A long period grating (LPG) fabricated in progressive three-layered (PTL) fibre is described. The grating with a period of 391µm, had dual attenuation bands associated with a particular cladding mode. The dual attenuation bands have been experimentally characterised for their spectral sensitivity to bending, which resulted in the highest sensitivity to bending seen for this particular fibre and temperature. The spectral characteristics of the fibre have been modelled giving good agreement to the experimental data as well as showing that the attenuation bands are both associated with the second order HE/EH2,n cladding mode.

Experimental and theoretical studies on molecular geometry and polymorphism in crystalline drug substances

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Complexity and chirality indices for molecular informatics::differential geometry approach

Novel molecular complexity measures are designed based on the quantum molecular kinematics. The Hamiltonian matrix constructed in a quasi-topological approximation describes the temporal evolution of the modelled electronic system and determined the time derivatives for the dynamic quantities. This allows to define the average quantum kinematic characteristics closely related to the curvatures of the electron paths, particularly, the torsion reflecting the chirality of the dynamic system. A special attention has been given to the computational scheme for this chirality measure. The calculations on realistic molecular systems demonstrate reasonable behaviour of the proposed molecular complexity indices.

The role of lipid geometry in designing liposomes for the solubilisation of poorly water soluble drugs

Liposomes are well recognised for their ability to improve the delivery of a range of drugs. More commonly they are applied for the delivery of water-soluble drugs, but given their structural attributes, they can also be employed as solubilising agents for low solubility drugs as well as drug targeting agents. To further explore the potential of liposomes as solubilising agents, we have investigated the role of bilayer packaging in promoting drug solubilisation in liposome bilayers. The effect of alkyl chain length and symmetry was investigated to consider if using 'mis-matched' phospholipids could create 'voids' within the bilayers, and enhance bilayer loading capacity. Lipid packing was investigated using Langmuir studies, which demonstrated that increasing the alkyl chain length enhanced lipid packing, with condensed monolayers forming, whilst asymmetric lipids formed less condensed monolayers. However, this more open packing did not translate into improved drug loading, with the longer chain, condensed bilayers formed from long-chain, saturated lipids offering higher drug loading capacity. These studies demonstrate that liposomes formulated from longer chain, saturated lipids offer enhanced solubilisation capacity. However the molecular size, rather than lipophilicity, of the drug to be incorporated was also a key factor dominating bilayer incorporation efficiency. © 2012 Elsevier B.V. All rights reserved.

A Differential Game Described by a Hyperbolic System

An antagonistic differential game of hyperbolic type with a separable linear vector pay-off function is considered. The main result is the description of all ε-Slater saddle points consisting of program strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > for this game. To this purpose, the considered differential game is reduced to find the optimal program strategies of two multicriterial problems of hyperbolic type. The application of approximation enables us to relate these problems to a problem of optimal program control, described by a system of ordinary differential equations, with a scalar pay-off function. It is found that the result of this problem is not changed, if the players use positional or program strategies. For the considered differential game, it is interesting that the ε-Slater saddle points are not equivalent and there exist two ε-Slater saddle points for which the values of all components of the vector pay-off function at one of them are greater than the respective components of the other ε-saddle point.

Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems

We present some results on the formation of singularities for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut + A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions (weaker than genuine non-linearity), we prove that the first order derivative of the solution blows-up in finite time.

Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5

∗ Research partially supported by INTAS grant 97-1644

Generalization of a Conjecture in the Geometry of Polynomials

In this paper we survey work on and around the following conjecture, which was first stated about 45 years ago: If all the zeros of an algebraic polynomial p (of degree n ≥ 2) lie in a disk with radius r, then, for each zero z1 of p, the disk with center z1 and radius r contains at least one zero of the derivative p′ . Until now, this conjecture has been proved for n ≤ 8 only. We also put the conjecture in a more general framework involving higher order derivatives and sets defined by the zeros of the polynomials.

Conference on Geometry and Mathematical Physics, Bulgaria, Zlatograd, 28.08-01.09.2005

List of Participants

Gratings in novel fibre geometry for applications in shape sensing

A long period grating (LPG) fabricated in progressive three-layered (PTL) fibre is described. The grating with a period of 391µm, had dual attenuation bands associated with a particular cladding mode. The dual attenuation bands have been experimentally characterised for their spectral sensitivity to bending, which resulted in the highest sensitivity to bending seen for this particular fibre and temperature. The spectral characteristics of the fibre have been modelled giving good agreement to the experimental data as well as showing that the attenuation bands are both associated with the second order HE/EH2,n cladding mode.

One Application of the Informatics in the Descriptive Geometry

This work acquaints with a program for interactive computer training to students on the subject "Mutual intersecting of pyramids in axonometry ”. Our software is a set of three modules, which we call "student", "teacher" and "autopilot". It gives the final solution of the problem, the traceability of various significant moments in its solution and 3D-image of the finished composition of the two intersecting polyhedra, stripped of the working lines and subjected to rotation and translation.

Two Remarkable Points of the Triangle Geometry

It is shown in the paper the discovery of two remarkable points of the triangle by means of “THE GEOMETER’S SKETCHPAD” software. Some properties of the points are considered too.

Geometry over two Arbitrary Arithmetic Progressions

We consider quadrate matrices with elements of the first row members of an arithmetic progression and of the second row members of other arithmetic progression. We prove the set of these matrices is a group. Then we give a parameterization of this group and investigate about some invariants of the corresponding geometry. We find an invariant of any two points and an invariant of any sixth points. All calculations are made by Maple.

Theoretical Hyperbolic Model of a Partial Agonism: Explicit Formulas for Affinity, Efficacy and Amplification

The quantitative analysis of receptor-mediated effect is based on experimental concentration-response data in which the independent variable, the concentration of a receptor ligand, is linked with a dependent variable, the biological response. The steps between the drug–receptor interaction and the subsequent biological effect are to some extent unknown. The shape of the fitting curve of the experimental data may give some in-sights into the nature of the concentration–receptor–response (C-R-R) mechanism. It can be evaluated by non-linear regression analysis of the experimental data points of the independent and dependent variables, which could be considered as a history of the interaction between the drug and receptors. However, this information is not enough to evaluate such important parameters of the mechanism as the dissociation constant (affinity) and efficacy. There are two ways to provide more detailed information about the C-R-R mechanism: (i) an experimental way for obtaining data with new or