Partial regularity of minimizers of a functional involving forms and maps

We discuss the partial regularity of minimizers of energy functionals such as (1)/(p)integral(Omega)[sigma(u)dA(p) + (1)/(2)delu(2p)]dx, where u is a map from a domain Omega is an element of R-n into the m-dimensional unit sphere of Rm+1 and A is a differential one-form in Omega.

Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.

Conservation planning with irreplaceability: does the method matter?

A number of systematic conservation planning tools are available to aid in making land use decisions. Given the increasing worldwide use and application of reserve design tools, including measures of site irreplaceability, it is essential that methodological differences and their potential effect on conservation planning outcomes are understood. We compared the irreplaceability of sites for protecting ecosystems within the Brigalow Belt Bioregion, Queensland, Australia, using two alternative reserve system design tools, Marxan and C-Plan. We set Marxan to generate multiple reserve systems that met targets with minimal area; the first scenario ignored spatial objectives, while the second selected compact groups of areas. Marxan calculates the irreplaceability of each site as the proportion of solutions in which it occurs for each of these set scenarios. In contrast, C-Plan uses a statistical estimate of irreplaceability as the likelihood that each site is needed in all combinations of sites that satisfy the targets. We found that sites containing rare ecosystems are almost always irreplaceable regardless of the method. Importantly, Marxan and C-Plan gave similar outcomes when spatial objectives were ignored. Marxan with a compactness objective defined twice as much area as irreplaceable, including many sites with relatively common ecosystems. However, targets for all ecosystems were met using a similar amount of area in C-Plan and Marxan, even with compactness. The importance of differences in the outcomes of using the two methods will depend on the question being addressed; in general, the use of two or more complementary tools is beneficial.

Achieving completeness: from constructive set theory to large cardinals

This thesis is an exploration of several completeness phenomena, both in the constructive and the classical settings. After some introductory chapters in the first part of the thesis where we outline the background used later on, the constructive part contains a categorical formulation of several constructive completeness theorems available in the literature, but presented here in an unified framework. We develop them within a constructive reverse mathematical viewpoint, highlighting the metatheory used in each case and the strength of the corresponding completeness theorems. The classical part of the thesis focuses on infinitary intuitionistic propositional and predicate logic. We consider a propositional axiomatic system with a special distributivity rule that is enough to prove a completeness theorem, and we introduce weakly compact cardinals as the adequate metatheoretical assumption for this development. Finally, we return to the categorical formulation focusing this time on infinitary first-order intuitionistic logic. We propose a first-order system with a special rule, transfinite transitivity, that embodies both distributivity as well as a form of dependent choice, and study the extent to which completeness theorems can be established. We prove completeness using a weakly compact cardinal, and, like in the constructive part, we study disjunction-free fragments as well. The assumption of weak compactness is shown to be essential for the completeness theorems to hold.

In-fiber microchannel device filled with a carbon nanotube dispersion for passive mode-lock lasing

Fueled by their high third-order nonlinearity and nonlinear saturable absorption, carbon nanotubes (CNT) are expected to become an integral part of next-generation photonic devices such as all-optical switches and passive mode-locked lasers. However, in order to fulfill this expectation it is necessary to identify a suitable platform that allows the efficient use of the optical properties of CNT. In this paper, we propose and implement a novel device consisting of an optofluidic device filled with a dispersion of CNT. By fabricating a microchannel through the core of a conventional fiber and filling it with a homogeneous solution of CNTs on Dimethylformamide (DMF), a compact, all-fiber saturable absorber is realized. The fabrication of the micro-fluidic channel is a two-step process that involves femtosecond laser micro-fabrication and chemical etching of the laser-modified regions. All-fiber high-energy, passive mode-locked lasing is demonstrated with an output power of 13.5 dBm. The key characteristics of the device are compactness and robustness against optical, mechanical and thermal damage.

Influence of downstream processing on the breakage of whey protein precipitates

Whey proteins may be fractionated by isoelectric precipitation followed by centrifugal recovery of the precipitate phase. Transport and processing of protein precipitates may alter the precipitate particle properties, which may affect how they behave in subsequent processes. For example, the transport of precipitate solution through pumps, pipes and valves and into a centrifugal separator may cause changes in particle size and density, which may affect the performance of the separator. This work investigates the effect of fluid flow intensity, flow geometry and exposure time on the breakage of whey protein precipitates: Computational fluid dynamics (CFD) was used to quantify the flow intensity in different geometries. Flow geometry can have a critical impact on particle breakage. Sharp geometrical transitions induce large increases in turbulence that can result in substantial particle breakage. As protein precipitate particles break, they tend to form denser more compact structures. The reduction in particle size and increase in compaction is due to breakage. This makes the particles become more resistant to further breakage as particle compactness increases. The effect of flow intensity on particle breakage is coupled to exposure time, with greater exposure time producing more breakage. However, it is expected that the particles will attain an equilibrium particle size and density after prolonged exposure in a constant flow field where no further breakage will occur with exposure time. © 2005 Institution of Chemical Engineers.

Some Comments on Q-Irresolute and Quasi-Irresolute Functions

The aim of this paper is to continue the study of θ-irresolute and quasi-irresolute functions as well as to give an example of a function which is θ-irresolute but neither quasi-irresolute nor an R-map and thus give an answer to a question posed by Ganster, Noiri and Reilly. We prove that RS-compactness is preserved under open, quasi-irresolute surjections.

Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds

∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.

Pseudo-Compact Semi-Topological Groups

Митрофан М. Чобан, Петър Ст. Кендеров, Уорън Б. Муурс - Полу-топологична група (съответно, топологична група) е група, снабдена с топология, относно която груповата оперция произведение е частично непрекъсната по всяка от променливите (съответно, непрекъсната по съвкупност от променливите и обратната операция е също непрекъсната). В настоящата работа ние даваме условия, от топологичен характер, една полу-топологична група да е всъщност топологична група. Например, ние показваме, че всяка сепарабелна псевдокомпактна полу-топологична група е топологична група. Показваме също, че всяка локално псевдокомпактна полу-топологична група, чиято групова операция е непрекъсната по съвкупност от променливите е топологична група.

A Note on Div-Curl Lemma

2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.

Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions

2010 Mathematics Subject Classification: 47B33, 47B38.

Passive mode locking in erbium-doped fibre laser by carbon nanotubes

Passively mode locked fibre lasers have a variety of applications ranging from telecommunication to medical photonics. Carbon nanotubes (CNTs) have attracted recently a great deal of attention as a promising solution for saturable absorber elements required for laser mode locking (see e.g. [1-3] and references therein). CNTs can be used as a saturable absorber in passively mode locked fibre laser directly [1,2] or as a CNTs polymer composites [3]. An attractive feature of CNT-based solutions in fibre lasers is a possibility to maintain the compactness, robustness of all-fibre format and low cost through using all standard telecom compatible components. The two important technical challenges in such type of lasers are: (i) to achieve stable polarization properties of the generated radiation without using complex control elements, and, (ii) to avoid low frequency instabilities of the mode-locked pulse train. In this paper we report results of the experiments on mode-locked soliton fibre laser using the following standard components: 1m of highly doped erbium fibre (Liekki Er80-8/125) serves as the gain medium with nominal absorption of 80 dB/m at 1530 nm; a 976 nm laser diode providing up to 310mW power is used to pump the laser via a 980/1550 wavelength division multiplexing; an isolator is employed to ensure single direction oscillation; SMF-28 is used to create necessary amount of anomalous dispersion to form soliton pulse making the total cavity length around 7.83 m; the CNT-polyvinyl alcohol polymer saturable absorber sandwiched in the FC/PC connector is used as a mode-locker device (see [3] for details). © 2011 IEEE.

Análise da eficácia de um refrigerador doméstico com condensador modificado: revestimento com meio poroso dissipativo

The development of home refrigerators generally are compact and economic reasons for using simplified configuration. The thermodynamic coefficient of performance ( COP ) is limited mainly in the condenser design for reasons of size and arrangement ( layout ) of the project ( design ) and climatic characteristics of the region where it will operate. It is noteworthy that this latter limitation is very significant when it comes to a country of continental size like Brazil with diverse climatic conditions. The COP of the cycle depends crucially on the ability of heat dissipated in the condenser. So in hot climates like the northeast, north, and west-central dispel ability is highly attenuated compared to the south and southeast regions with tropical or subtropical climates when compared with other regions. The dissipation in compact capacitors for applications in domestic refrigeration has been the focus of several studies, that due to its impact on reducing costs and power consumption, and better use of the space occupied by the components of refrigeration systems. This space should be kept to a minimum to allow an increase in the useful storage volume of refrigerator without changing the external dimensions of the product. Due to its low cost manufacturing, wire on tube condensers continue to be the most advantageous option for domestic refrigeration. Traditionally, these heat exchangers are designed to operate under natural convection. Not always, the benefits of greater compactness of capacitors for forced outweigh the burden of pumping air through the external heat exchanger. In this work we propose an improvement in convective condenser changing it to a transfer mechanism combined in series with conductive pipes and wire to a moist convective porous medium and the porous medium to the environment. The porous media used in the coating was composed of a gypsum plaster impregnated fiber about a mesh of natural cellulosic molded tubular wire mesh about the original structure of the condenser , and then dried and calcined to greater adherence and increased porosity. The proposed configuration was installed in domestic refrigeration system ( trough ) and tested under the same conditions of the original configuration . Was also evaluated in the dry condition and humidified drip water under natural and forced with an electro - fan ( fan coil ) convection. Assays were performed for the same 134- refrigerant charge e under the same thermal cooling load. The performance was evaluated in various configurations, showing an improvement of about 72 % compared with the original configuration proposed in humidification and natural convection.

CUBEs: decoupled, compact, and monolithic spatial translational compliant parallel manipulators

This paper deals with the conceptual design of decoupled, compact, and monolithic XYZ compliant parallel manipulators (CPMs): CUBEs. Position spaces of compliant P (P: prismatic) joints are first discussed, which are represented by circles about the translational directions. A design method of monolithic XYZ CPMs is then proposed in terms of both the kinematic substitution method and the position spaces. Three types of monolithic XYZ CPMs are finally designed using the proposed method with the help of three classes of kinematical decoupled 3-DOF (degree of freedom) translational parallel mechanisms (TPMs). These monolithic XYZ CPMs include a 3-PPP XYZ CPM composed of identical parallelogram modules (a previously reported design), a novel 3-PPPR (R: revolute) XYZ CPM composed of identical compliant four-beam modules, and a novel 3-PPPRR XYZ CPM. The latter two monolithic designs also have extended lives. It is shown that the proposed design method can be used to design other decoupled and compact XYZ CPMs by using the concept of position spaces, and the resulting XYZ CPM is the most compact one when the fixed ends of the three actuated compliant P joints thereof overlap.