Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Determinants of self-reported smoking and misclassification during pregnancy, and analysis of optimal cut-off points for urinary cotinine: a cross-sectional study

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The BACOMA cod-end. History and recent developments in BACOMA cod-end regulations and a proposal for abetter specification of the BACOMA cod-end for Baltic Sea cod fishery

To improve the cod stocks in the Baltic Sea, a number of regulations have recently been established by the International Baltic Sea Fisheries Commission (IBSFC) and the European Commission. According to these, fishermen are obliged to use nets with escape windows (BACOMA nets) with a mesh size of the escape window of 120 mm until end of September 2003. These nets however, retain only fish much larger than the legal minimum landing size would al-low. Due to the present stock structure only few of such large fish are however existent. As a consequence fishermen use a legal alternative net. This is a conventional trawl with a cod-end of 130 mm diamond-shaped meshes (IBSFC-rules of 1st April 2002), to be increased to 140 mm on 1st September 2003, according to the mentioned IBSFC-rule. Due legal alterations of the net by the fishermen (e.g. use of extra stiff net material) these nets have acquired extremely low selective properties, i. e. they catch very small fish and produce great amounts of discards. Due to the increase of the minimum landing size from 35 to 38 cm for cod in the Baltic, the amount of discards has even increased since the beginning of 2003. Experiments have now been carried out with the BACOMAnet on German and Swedish commercial and research vessels since arguments were brought forward that the BACOMA net was not yet sufficiently tested on commercial vessels. The results of all experiments conducted so far, are compiled and evaluated here. As a result of the Swedish, Danish and German initiative and research the European Commission reacted upon this in June 2003 and rejected the increase of the diamond-meshed non-BACOMA net from 130 mm to 140mm in September 2003. To protect the cod stocks in the Baltic Sea more effectively the use of traditional diamond meshed cod-ends with-out escape window are prohibited in community waters without derogation, becoming effective 1st of September 2003. To enable more effective and simplified control of the bottom trawl fishery in the Baltic Sea the principle of a ”One-Net-Rule“ is enforced. This is going to be the BACOMA net, with the meshes of the escape window being 110 mm for the time being. The description of the BACOMA net as given in the IBSFC-rules no.10 (revision of the 28th session, Berlin 2002) concentrates on the cod-end and the escape window but only to a less extent on the design and mesh-composition of the remaining parts of the net, such as belly and funnel and many details. Thus, the present description is not complete and leaves, according to fishermen, ample opportunity for manipulation. An initiative has been started in Germany with joint effort from scientists and the fishery to better describe the entire net and to produce a proposal for a more comprehensive description, leaving less space for manipulation. A proposal in this direction is given here and shall be seen as a starting point for a discussion and development towards an internationally uniform net, which is agreed amongst the fishery, scientists and politicians. The Baltic Sea fishery is invited to comment on this proposal, and recommendations for further improvement and specifications are welcomed. Once the design is agreed by the Baltic Fishermen Association, it shall be proposed to the IBSFC and European Commission via the Baltic Fishermen Association.

Near-diffraction-limited, 35.4 W laser-diode end-pumped Nd:YVO4 slab laser operating at 1342 nm

A diode stack end-pumped Nd:YVO4 slab laser at 1342 nm with near-diffraction-limited beam quality by using a hybrid resonator was presented. At a pump power of 139.5 W, laser power of 35.4 W was obtained with a conversion efficiency of 25.4% of the laser diode to laser output. The beam quality M-2 factors were measured to be 1.2 in the unstable direction and 1.3 in the stable direction at the output power of 29 W. (C) 2009 Optical Society of America

On a novel method of impact by a front-end-coated bullet to evaluate the interface adhesion between film and substrate

A preliminary experiment was carried out to validate the feasibility of the method of impact by a front-end-coated bullet to evaluate the interface adhesion between film and substrate. The theoretical description of the initiation, propagation and evolution of the stress pulse during impact was generalized and formulized. The effects of the crucial parameters on the interface stress were further investigated with FEM. The results found the promising prospect of the application of such a method and provided useful guidance for experimental design.

I. Singular perturbation problems involving singular points and turning points. II. On the averaged Lagrangian technique for nonlinear dispersive waves

In Part I a class of linear boundary value problems is considered which is a simple model of boundary layer theory. The effect of zeros and singularities of the coefficients of the equations at the point where the boundary layer occurs is considered. The usual boundary layer techniques are still applicable in some cases and are used to derive uniform asymptotic expansions. In other cases it is shown that the inner and outer expansions do not overlap due to the presence of a turning point outside the boundary layer. The region near the turning point is described by a two-variable expansion. In these cases a related initial value problem is solved and then used to show formally that for the boundary value problem either a solution exists, except for a discrete set of eigenvalues, whose asymptotic behaviour is found, or the solution is non-unique. A proof is given of the validity of the two-variable expansion; in a special case this proof also demonstrates the validity of the inner and outer expansions.

Nonlinear dispersive wave equations which are governed by variational principles are considered in Part II. It is shown that the averaged Lagrangian variational principle is in fact exact. This result is used to construct perturbation schemes to enable higher order terms in the equations for the slowly varying quantities to be calculated. A simple scheme applicable to linear or near-linear equations is first derived. The specific form of the first order correction terms is derived for several examples. The stability of constant solutions to these equations is considered and it is shown that the correction terms lead to the instability cut-off found by Benjamin. A general stability criterion is given which explicitly demonstrates the conditions under which this cut-off occurs. The corrected set of equations are nonlinear dispersive equations and their stationary solutions are investigated. A more sophisticated scheme is developed for fully nonlinear equations by using an extension of the Hamiltonian formalism recently introduced by Whitham. Finally the averaged Lagrangian technique is extended to treat slowly varying multiply-periodic solutions. The adiabatic invariants for a separable mechanical system are derived by this method.

Synthesis and potency of long end-associative polymers for mist control

Long linear polymers that are end-functionalized with associative groups were studied as additives to hydrocarbon fluids to mitigate the fire hazard associated with the presence of mist in a crash scenario. These polymers were molecularly designed to overcome both the shear-degradation of long polymer chains in turbulent flows, and the chain collapse induced by the random placement of associative groups along polymer backbones. Architectures of associative groups on the polymer chain ends that were tested included clusters of self-associative carboxyl groups and pairs of hetero-complementary associative units.

Linear polymers with clusters of discrete numbers of carboxyl groups on their chain ends were investigated first: an innovative synthetic strategy was devised to achieve unprecedented backbone lengths and precise control of the number of carboxyl groups on chain ends (N). We found that a very narrow range of N allows the co-existence of sufficient end-association strength and polymer solubility in apolar media. Subsequent steady-flow rheological study on solution behavior of such soluble polymers in apolar media revealed that the end-association of very long chains in apolar media leads to the formation of flower-like micelles interconnected by bridging chains, which trap significant fraction of polymer chains into looped structures with low contribution to mist-control. The efficacy of very long 1,4-polybutadiene chains end-functionalized with clusters of four carboxyl groups as mist-control additives for jet fuel was further tested. In addition to being shear-resistant, the polymer was found capable of providing fire-protection to jet fuel at concentrations as low as 0.3wt%. We also found that this polymer has excellent solubility in jet fuel over a wide range of temperature (-30 to +70°C) and negligible interference with dewatering of jet fuel. It does not cause an adverse increase in viscosity at concentrations where mist-control efficacy exists.

Four pairs of hetero-complementary associative end-groups of varying strengths were subsequently investigated, in the hopes of achieving supramolecular aggregates with both mist-control ability and better utilization of polymer building blocks. Rheological study of solutions of the corresponding complementary associative polymer pairs in apolar media revealed the strength of complementary end-association required to achieve supramolecular aggregates capable of modulating rheological properties of the solution.

Both self-associating and complementary associating polymers have therefore been found to resist shear degradation. The successful strategy of building soluble, end-associative polymers with either self-associative or complementary associative groups will guide the next generation of mist-control technology.

Earthquake response of steel braces and braced steel frames

This thesis consists of three parts. Chapter 2 deals with the dynamic buckling behavior of steel braces under cyclic axial end displacement. Braces under such a loading condition belong to a class of "acceleration magnifying" structural components, in which a small motion at the loading points can cause large internal acceleration and inertia. This member-level inertia is frequently ignored in current studies of braces and braced structures. This chapter shows that, under certain conditions, the inclusion of the member-level inertia can lead to brace behavior fundamentally different from that predicted by the quasi-static method. This result is to have significance in the correct use of the quasi-static, pseudo-dynamic and static condensation methods in the simulation of braces or braced structures under dynamic loading. The strain magnitude and distribution in the braces are also studied in this chapter.

Chapter 3 examines the effect of column uplift on the earthquake response of braced steel frames and explores the feasibility of flexible column-base anchoring. It is found that fully anchored braced-bay columns can induce extremely large internal forces in the braced-bay members and their connections, thus increasing the risk of failures observed in recent earthquakes. Flexible braced-bay column anchoring can significantly reduce the braced bay member force, but at the same time also introduces large story drift and column uplift. The pounding of an uplifting column with its support can result in very high compressive axial force.

Chapter 4 conducts a comparative study on the effectiveness of a proposed non-buckling bracing system and several conventional bracing systems. The non-buckling bracing system eliminates buckling and thus can be composed of small individual braces distributed widely in a structure to reduce bracing force concentration and increase redundancy. The elimination of buckling results in a significantly more effective bracing system compared with the conventional bracing systems. Among the conventional bracing systems, bracing configurations and end conditions for the bracing members affect the effectiveness.

The studies in Chapter 3 and Chapter 4 also indicate that code-designed conventionally braced steel frames can experience unacceptably severe response under the strong ground motions recorded during the recent Northridge and Kobe earthquakes.

Modelling the dynamics of phytoplankton with the needs of the end user in mind

How to regulate phytoplankton growth in water supply reservoirs has continued to occupy managers and strategists for some fifty years or so, now, and mathematical models have always featured in their design and operational constraints. In recent years, rather more sophisticated simulation models have begun to be available and these, ideally, purport to provide the manager with improved forecasting of plankton blooms, the likely species and the sort of decision support that might permit management choices to be selected with increased confidence. This account describes the adaptation and application of one such model, PROTECH (Phytoplankton RespOnses To Environmental CHange) to the problems of plankton growth in reservoirs. This article supposes no background knowledge of the main algal types; neither does it attempt to catalogue the problems that their abundance may cause in lakes and reservoirs.

Una aproximación al sector eléctrico

Español:Este TFG pretende exponer de un modo sencillo el mercado eléctrico español. Se trata de un tema de elevada complejidad y gran extensión. Con el fin de alcanzar una idea clara, hemos decidido centrarnos en los puntos de mayor relevancia. En las secciones siguientes abordamos cuestiones relativas al mercado mayorista (pool) y minorista español así como la incipiente reforma eléctrica llevada a cabo por el Gobierno. Después de una breve Introducción, la sección 2 enumera una serie de términos que se utilizan con frecuencia en esta área. La sección 3 proporciona algunos antecedentes sobre el sector eléctrico. La sección 4 se refiere al mercado mayorista, en el cual se realiza la compra-venta diaria de electricidad. En él participan los productores, los distribuidores y los comercializadores de electricidad, así como los consumidores cualificados de energía eléctrica. Dentro de éste nos encontramos el mercado a plazo (o forward), el mercado diario (o spot) y el mercado a corto plazo (o de ajuste). La sección 5 trata del mercado minorista, su diseño y composición. Aquí, las empresas encargadas de comercializar energía (que compran en el mercado mayorista a las empresas generadoras) se la venden a los consumidores finales. En la sección 6 se aborda la Reforma Eléctrica, aclarando los cambios sufridos desde su implantación. Los hechos más llamativos a este respecto son: la eliminación de las subastas CESUR y el cambio de la Tarifa de Último Recurso (TUR) a un Precio Voluntario para el Pequeño Consumidor (PVPC). Por último, hay una sección final con las principales conclusiones.