Third Order Lagrangians, Weyl Invariants and Classical Trace Anomaly in Six Dimensions

We have proceeded the analogy (represented in our previous works) of the Einstein tensor and the alternative form of the Einstein field equations for the generic coefficients of the eight terms in the third order of the Lovelock Lagrangian. We have found the constraint between the coefficients into two forms, an independent and a dimensional dependent versions. Each form has three degrees of freedom, and not only the exact coefficients of the third order Lovelock Lagrangian do satisfy the two forms of the constraints, but also the two independent cubic of the Weyl tensor satisfy the independent constraint in six dimensions and yield the dimensional dependent version identically independent of the dimension. Then, we have introduced the most general effective expression for a total third order type Lagrangian with the homogeneity degree number three which includes the previous eight terms plus the new three ones among the all seventeen independent terms. We have proceeded the analogy for this combination, and have achieved the relevant constraint. We have shown that the expressions given in the literature as the third Weyl-invariant combination in six dimensions do satisfy this constraint. Thus, we suggest that these constraint relations to be considered as the necessary consistency conditions on the numerical coefficients that a Weyl-invariant in six dimensions should satisfy. Finally, we have calculated the “classical” trace anomaly (an approach that was presented in our previous works) for the introduced total third order type Lagrangian and have achieved a general expression with four degrees of freedom in more than six dimensions (three degrees in six dimensions). Then, we have demonstrated that the resulted expression contains exactly the relevant coefficient of the Schwinger–DeWitt proper time method (that linked with the relevant heat kernel coefficient) in six dimensions, as a particular case. Of course, this result is a necessary consistency check, nevertheless our approach can be regarded as an alternative (perhaps simpler, and classical) derivation of the trace anomaly which also gives a general expression with the relevant degrees of freedom.     

Synthesis and characterization of new polymer systems containing very bulky tris(trimethylsilyl)methyl substituents as side chains

The 4-chloromethyl styrene (CMS) was copolymerized with different styrenic monomers such as methyl styrene, 4-methoxy styrene and α-methyl styrene by free radical polymerization method at 70 ± 1 °C using α,α^′-azobis(isobutyronitrile) (AIBN) as an initiator and the copolymers I, II and III collected respectively. The very bulky tris(trimethylsilyl)methyl {trisyl} substituents were covalently attached to the obtained copolymers with replacement of all the chlorine atoms in CMS units. The polymers, obtained in quantitative yields, were characterized by FT-IR, ¹H NMR and ¹³C NMR spectroscopy; differential scanning calorimetry (DSC) and GPC studies. All the polymers containing trisyl groups showed a high glass transition temperature (in the range 150-190 °C) in comparison with copolymers I-III (in the range 90-95 °C). The increase of the glass transition temperature reflects the substantial increase in rigidity of new polymers bearing very bulky substituents in side chains.     

Controlled-release of drugs from cross-linked polymers containing cubane as a crosslinking agent

Two anti-inflammatory drugs, indomethacin and aspirin together with cubane-1, 4-dicarboxylic acid (CDA) were covalently linked with 2-hydroxyethyl methacrylate (HEMA). The drug-linked HEMA (indomethacin-linked HEMA) is abbreviated as HI, aspirin-linked HEMA as HA and cubane-1, 4-dicarboxylic acid (CDA) linked to two HEMA group is the cross-linking agent (CA). A difunctional spacer group was introduced between the drugs and acrylic moiety of the monomer through a hydrolyzable ester linkage. Free radical cross-linking polymerization of the monomers with drug effect was carried out in dioxane solution at various CA ratios, using AIBN as initiator in the temperature range 60-70°C. The compositions of the cross-linked three-dimensional polymers were determined by FT-IR spectroscopy. The glass transition temperature (Tg) of the network polymers was determined calorimetrically. The hydrolysis of drug-polymer conjugates was carried out in cellophane membrane dialysis bags containing an aqueous buffer solution (pH 8 and pH 1) at 37°C. Detection of the hydrolysis product by UV spectroscopy shows that the drugs were released by hydrolysis of the ester bond located between the drug and spacer group.     

Design and synthesis of benzodiazepine-1,2,3-triazole hybrid derivatives as selective butyrylcholinesterase inhibitors

Molecular Diversity - A new series of compounds based on benzodiazepine-1,2,3-triazole were synthesized and evaluated as cholinesterase inhibitors by Ellman’s method. The compounds proved to...     

On the heat flux vector for flowing granular materials—part II: derivation and special cases

Heat transfer plays a major role in the processing of many particulate materials. The heat flux vector is commonly modelled by the Fourier's law of heat conduction and for complex materials such as non‐linear fluids, porous media, or granular materials, the coefficient of thermal conductivity is generalized by assuming that it would depend on a host of material and kinematical parameters such as temperature, shear rate, porosity or concentration, etc. In Part I, we will give a brief review of the basic equations of thermodynamics and heat transfer to indicate the importance of the modelling of the heat flux vector. We will also discuss the concept of effective thermal conductivity (ETC) in granular and porous media. In Part II, we propose and subsequently derive a properly frame‐invariant constitutive relationship for the heat flux vector for a (single phase) flowing granular medium. Standard methods in continuum mechanics such as representation theorems and homogenization techniques are used. It is shown that the heat flux vector in addition to being proportional to the temperature gradient (the Fourier's law), could also depend on the gradient of density (or volume fraction), and D (the symmetric part of the velocity gradient) in an appropriate manner. The emphasis in this paper is on the idea that for complex non‐linear materials it is the heat flux vector which should be studied; obtaining or proposing generalized form of the thermal conductivity is not always appropriate or sufficient. Copyright © 2006 John Wiley & Sons, Ltd.     

On the heat flux vector for flowing granular materials—Part I: effective thermal conductivity and background

Heat transfer plays a major role in the processing of many particulate materials. The heat flux vector is commonly modelled by the Fourier's law of heat conduction and for complex materials such as non‐linear fluids, porous media, or granular materials, the coefficient of thermal conductivity is generalized by assuming that it would depend on a host of material and kinematical parameters such as temperature, shear rate, porosity or concentration, etc. In Part I, we will give a brief review of the basic equations of thermodynamics and heat transfer to indicate the importance of the modelling of the heat flux vector. We will also discuss the concept of effective thermal conductivity (ETC) in granular and porous media. In Part II, we propose and subsequently derive a properly frame‐invariant constitutive relationship for the heat flux vector for a (single phase) flowing granular medium. Standard methods in continuum mechanics such as representation theorems and homogenization techniques are used. It is shown that the heat flux vector in addition to being proportional to the temperature gradient (the Fourier's law), could also depend on the gradient of density (or volume fraction), and D (the symmetric part of the velocity gradient) in an appropriate manner. The emphasis in this paper is on the idea that for complex non‐linear materials it is the heat flux vector which should be studied; obtaining or proposing generalized form of the thermal conductivity is not always appropriate or sufficient. Copyright © 2006 John Wiley & Sons, Ltd.     

Resource allocation in the North Sea demersal fisheries: A goal programming approach

The management of a fishery is a complex task generally involving multiple, often conflicting, objectives. These objectives typically include economic, biological and social goals such as improving the income of fishers, reducing the catch of depleted species and maintaining employment.Multicriteria decision making (MCDM) techniques appear wellsuited to such a management problem, allowing compromises between conflicting objectives to be analysed in a structured framework. In comparison to other fields, such as water resource planning, forestry and agriculture, there have been few applications of MCDM to fisheries.In this paper, a goal programming model of the North Sea demersal fishery is presented. The model is used to demonstrate the potential applicability of this type of approach to the analysis and development of fisheries management plans with multiple objectives. Alternative scenarios are considered for the problem, and tradeoffs between given objectives are also highlighted and discussed.     

Soliton-antisoliton scattering and capture in λφ4 theory

In this work we have investigated the result of collisions of a soliton-antisoliton pair for various incident velocities in λφ⁴ theory through a series of numerical experiments. It is observed for incident velocities less than a critical velocity V_crit that we have two narrow regions in the velocity spectrum where the result of collision is a scattering of particles along with the emission of some radiation. Outside these two narrow windows the incident particles are captured and form resonances. For velocities greater than V_crit scattering is always obtained and it is found that the square of the outcoming velocity is a linear function of the square of the incoming velocity. From the approximate solution found, an effective potential for widely separated solitons is derived.