235 resultados para COMPACTNESS


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For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset of B1 (M, E) is relatively compact, etc. We also show that our class includes Gulko compact. In the second part of the paper we examine under which conditions a bounded linear operator T : X ∗ → Y so that T |BX ∗ : (BX ∗ , w∗ ) → Y is a Baire-1 function, is a pointwise limit of a sequence (Tn ) of operators with T |BX ∗ : (BX ∗ , w∗ ) → (Y, · ) continuous for all n ∈ N. Our results in this case are connected with classical results of Choquet, Odell and Rosenthal.

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2000 Mathematics Subject Classification: 54C60, 54C65, 54D20, 54D30.

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There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the precompactness of sets in the Lebesgue spaces $L_p(\Rn)$, $1 \leq p < \infty$, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces $B^s_{p,q}(\Rn)$, $0

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Despite recent developments in fixed-film combined biological nutrients removal (BNR) technology; fixed-film systems (i.e., biofilters), are still at the early stages of development and their application has been limited to a few laboratory-scale experiments. Achieving enhanced biological phosphorus removal in fixed-film systems requires exposing the micro-organisms and the waste stream to alternating anaerobic/aerobic or anaerobic/anoxic conditions in cycles. The concept of cycle duration (CD) as a process control parameter is unique to fixed-film BNR systems, has not been previously investigated, and can be used to optimise the performance of such systems. The CD refers to the elapsed time before the biomass is re-exposed to the same environmental conditions in cycles. Fixed-film systems offer many advantages over suspended growth systems such as reduced operating costs, simplicity of operation, absence of sludge recycling problems, and compactness. The control of nutrient discharges to water bodies, improves water quality, fish production, and allow water reuse. The main objective of this study was to develop a fundamental understanding of the effect of CD on the transformations of nutrients in fixed-film biofilter systems subjected to alternating aeration I no-aeration cycles A fixed-film biofilter system consisting of three up-flow biofilters connected in series was developed and tested. The first and third biofilters were operated in a cyclic mode in which the biomass was subjected to aeration/no-aeration cycles. The influent wastewater was simulated aquaculture whose composition was based on actual water quality parameters of aquacuture wastewater from a prawn grow-out facility. The influent contained 8.5 - 9:3 mg!L a111monia-N, 8.5- 8.7 mg/L phosphate-P, and 45- 50 mg!L acetate. Two independent studies were conducted at two biofiltration rates to evaluate and confirm the effect of CD on nutrient transformations in the biofilter system for application in aquaculture: A third study was conducted to enhance denitrification in the system using an external carbon- source at a rate varying from 0-24 ml/min. The CD was varied in the range of0.25- 120 hours for the first two studies and fixed at 12 hours for the third study. This study identified the CD as an important process control parameter that can be used to optimise the performance of full-scale fixed-film systems for BNR which represents a novel contribution in this field of research. The CD resulted in environmental conditions that inhibited or enhanced nutrient transformations. The effect of CD on BNR in fixed-film systems in terms of phosphorus biomass saturation and depletion has been established. Short CDs did not permit the establishment of anaerobic activity in the un-aerated biofilter and, thus, inhibited phosphorus release. Long CDs resulted in extended anaerobic activity and, thus, resulted in active phosphorus release. Long CDs, however, resulted in depleting the biomass phosphorus reservoir in the releasing biofilter and saturating the biomass phosphorus reservoir in the up-taking biofilter in the cycle. This phosphorus biomass saturation/depletion phenomenon imposes a practical limit on how short or long the CD can be. The length of the CD should be somewhere just before saturation or depletion occur and for the system tested, the optimal CD was 12 hours for the biofiltration rates tested. The system achieved limited net phosphorus removal due to the limited sludge wasting and lack of external carbon supply during phosphorus uptake. The phosphorus saturation and depletion reflected the need to extract phosphorus from the phosphorus-rich micro-organisms, for example, through back-washing. The major challenges of achieving phosphorus removal in the system included: (I) overcoming the deterioration in the performance of the system during the transition period following the start of each new cycle; and (2) wasting excess phosphorus-saturated biomass following the aeration cycle. Denitrification occurred in poorly aerated sections of the third biofilter and generally declined as the CD increased and as the time progressed in the individual cycle. Denitrification and phosphorus uptake were supplied by an internal organic carbon source, and the addition of an external carbon source (acetate) to the third biofilter resulted in improved denitrification efficiency in the system from 18.4 without supplemental carbon to 88.7% when the carbon dose reached 24 mL/min The removal of TOC and nitrification improved as the CD increased, as a result of the reduction in the frequency of transition periods between the cycles. A conceptual design of an effective fixed-film BNR biofilter system for the treatment of the influent simulated aquaculture wastewater was proposed based on the findings of the study.

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This paper presents a robust stochastic model for the incorporation of natural features within data fusion algorithms. The representation combines Isomap, a non-linear manifold learning algorithm, with Expectation Maximization, a statistical learning scheme. The representation is computed offline and results in a non-linear, non-Gaussian likelihood model relating visual observations such as color and texture to the underlying visual states. The likelihood model can be used online to instantiate likelihoods corresponding to observed visual features in real-time. The likelihoods are expressed as a Gaussian Mixture Model so as to permit convenient integration within existing nonlinear filtering algorithms. The resulting compactness of the representation is especially suitable to decentralized sensor networks. Real visual data consisting of natural imagery acquired from an Unmanned Aerial Vehicle is used to demonstrate the versatility of the feature representation.

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Previous research has put forward a number of properties of business process models that have an impact on their understandability. Two such properties are compactness and(block-)structuredness. What has not been sufficiently appreciated at this point is that these desirable properties may be at odds with one another. This paper presents the results of a two-pronged study aimed at exploring the trade-off between compactness and structuredness of process models. The first prong of the study is a comparative analysis of the complexity of a set of unstructured process models from industrial practice and of their corresponding structured versions. The second prong is an experiment wherein a cohort of students was exposed to semantically equivalent unstructured and structured process models. The key finding is that structuredness is not an absolute desideratum vis-a-vis for process model understandability. Instead, subtle trade-offs between structuredness and other model properties are at play.

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This paper describes a novel method for determining the extrinsic calibration parameters between 2D and 3D LIDAR sensors with respect to a vehicle base frame. To recover the calibration parameters we attempt to optimize the quality of a 3D point cloud produced by the vehicle as it traverses an unknown, unmodified environment. The point cloud quality metric is derived from Rényi Quadratic Entropy and quantifies the compactness of the point distribution using only a single tuning parameter. We also present a fast approximate method to reduce the computational requirements of the entropy evaluation, allowing unsupervised calibration in vast environments with millions of points. The algorithm is analyzed using real world data gathered in many locations, showing robust calibration performance and substantial speed improvements from the approximations.

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Modelling video sequences by subspaces has recently shown promise for recognising human actions. Subspaces are able to accommodate the effects of various image variations and can capture the dynamic properties of actions. Subspaces form a non-Euclidean and curved Riemannian manifold known as a Grassmann manifold. Inference on manifold spaces usually is achieved by embedding the manifolds in higher dimensional Euclidean spaces. In this paper, we instead propose to embed the Grassmann manifolds into reproducing kernel Hilbert spaces and then tackle the problem of discriminant analysis on such manifolds. To achieve efficient machinery, we propose graph-based local discriminant analysis that utilises within-class and between-class similarity graphs to characterise intra-class compactness and inter-class separability, respectively. Experiments on KTH, UCF Sports, and Ballet datasets show that the proposed approach obtains marked improvements in discrimination accuracy in comparison to several state-of-the-art methods, such as the kernel version of affine hull image-set distance, tensor canonical correlation analysis, spatial-temporal words and hierarchy of discriminative space-time neighbourhood features.

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Microscopic changes occur in plant food materials during drying significantly influence the macroscopic properties and quality factors of the dried food materials. It is very critical to study microstructure to understand the underlying cellular mechanisms to improve performance of the food drying techniques. However, there is very limited research conducted on such microstructural changes of plant food material during drying. In this work, Gala apple parenchyma tissue samples were studied using a scanning electron microscope for gradual microstructural changes as affected by temperature, time and moisture content during hot air drying at two drying temperatures: 57 ℃ and 70 ℃. For fresh samples, the average cellular parameter values were; cell area: 20000 μm2, ferret diameter: 160 μm, perimeter: 600 μm, roundness: 0.76, elongation: 1.45 and compactness: 0.84. During drying, a higher degree of cell shrinkage was observed with cell wall warping and increase in intercellular space. However, no significant cell wall breakage was observed. The overall reduction of cell area, ferret diameter and perimeter were about 60%, 40% and 30%. The cell roundness and elongation showed overall increments of about 5% and the compactness remained unchanged. Throughout the drying cycle, cellular deformations were mainly influenced by the moisture content. During the initial and intermediate stages of drying, cellular deformations were also positively influenced by the drying temperature and the effect was reversed at the final stages of drying which provides clues for case hardening of the material.

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Plant based dried food products are popular commodities in global market where much research is focused to improve the products and processing techniques. In this regard, numerical modelling is highly applicable and in this work, a coupled meshfree particle-based two-dimensional (2-D) model was developed to simulate micro-scale deformations of plant cells during drying. Smoothed Particle Hydrodynamics (SPH) was used to model the viscous cell protoplasm (cell fluid) by approximating it to an incompressible Newtonian fluid. The visco-elastic characteristic of the cell wall was approximated to a Neo-Hookean solid material augmented with a viscous term and modelled with a Discrete Element Method (DEM). Compared to a previous work [H. C. P. Karunasena, W. Senadeera, Y. T. Gu and R. J. Brown, Appl. Math. Model., 2014], this study proposes three model improvements: linearly decreasing positive cell turgor pressure during drying, cell wall contraction forces and cell wall drying. The improvements made the model more comparable with experimental findings on dried cell morphology and geometric properties such as cell area, diameter, perimeter, roundness, elongation and compactness. This single cell model could be used as a building block for advanced tissue models which are highly applicable for product and process optimizations in Food Engineering.

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Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.

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Electropolymerized films of teraaminometallophthalocyanines (MTAPc; M = Ni and Co) with amino groups at α- (4α-MTAPc) and β- (4β-MTAPc) positions were prepared on glassy carbon (GC) and indium tin oxide (ITO) electrodes. It was found that the electropolymerization growth rate of 4α-MTAPc was less than that of 4β-MTAPc prepared under identical conditions. Further, the surface coverage of the polymerized 4β-MTAPc film was greater than that of 4α-MTAPc polymerized film. Atomic force microscopy (AFM), X-ray diffraction (XRD) and UV–visible spectroscopic studies were carried out for the polymerized films of 4α-NiIITAPc (p-4α-NiIITAPc) and 4β-NiIITAPc (p-4β-NiIITAPc) alone because both Ni(II) and Co(II) polymerized films show similar trend in electropolymerization and surface coverage values. AFM images show that p-4α-NiIITAPc film contains islands and the thickness of this film was nearly three times less than that of p-4β-NiIITAPc. XRD patterns for the two polymerized films reveal that p-4β-NiIITAPc film was relatively more crystalline than p-4α-NiIITAPc film. Further, the compactness of these films was scrutinized from their barrier properties toward [Fe(CN)6]3−/4− redox couple. The differences in the polymerization growth rate of 4α-MTAPc and 4β-MTAPc, and the thicknesses of the resultant polymerized films suggest that unlike 4β-MTAPc one or two amino groups might have not involved in electropolymerization in the case of 4α-MTAPc. Further, the influence of surface coverage on the electrocatalytic properties of the polymerized films was studied by taking p-4β-CoIITAPc and p-4α-CoIITAPc films as examples. The electrocatalytic oxygen reduction current was almost same at both the electrodes suggesting that only the surface species were involved in the electrocatalytic reduction of oxygen.

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Porosity is one of the key parameters of the macroscopic structure of porous media, generally defined as the ratio of the free spaces occupied (by the volume of air) within the material to the total volume of the material. Porosity is determined by measuring skeletal volume and the envelope volume. Solid displacement method is one of the inexpensive and easy methods to determine the envelope volume of a sample with an irregular shape. In this method, generally glass beads are used as a solid due to their uniform size, compactness and fluidity properties. The smaller size of the glass beads means that they enter into the open pores which have a larger diameter than the glass beads. Although extensive research has been carried out on porosity determination using displacement method, no study exists which adequately reports micro-level observation of the sample during measurement. This study set out with the aim of assessing the accuracy of solid displacement method of bulk density measurement of dried foods by micro-level observation. Solid displacement method of porosity determination was conducted using a cylindrical vial (cylindrical plastic container) and 57 µm glass beads in order to measure the bulk density of apple slices at different moisture contents. A scanning electron microscope (SEM), a profilometer and ImageJ software were used to investigate the penetration of glass beads into the surface pores during the determination of the porosity of dried food. A helium pycnometer was used to measure the particle density of the sample. Results show that a significant number of pores were large enough to allow the glass beads to enter into the pores, thereby causing some erroneous results. It was also found that coating the dried sample with appropriate coating material prior to measurement can resolve this problem.

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Electrochemical capacitors are electrochemical devices with fast and highly reversible charge-storage and discharge capabilities. The devices are attractive for energy storage particularly in applications involving high-power requirements. Electrochemical capacitors employ two electrodes and an aqueous or a non-aqueous electrolyte, either in liquid or solid form; the latter provides the advantages of compactness, reliability, freedom from leakage of any liquid component and a large operating potential-window. One of the classes of solid electrolytes used in capacitors is polymer-based and they generally consist of dry solid-polymer electrolytes or gel-polymer electrolyte or composite-polymer electrolytes. Dry solid-polymer electrolytes suffer from poor ionic-conductivity values, between 10(-8) and 10(-7) S cm(-1) under ambient conditions, but are safer than gel-polymer electrolytes that exhibit high conductivity of ca. 10(-3) S cm(-1) under ambient conditions. The aforesaid polymer-based electrolytes have the advantages of a wide potential window of ca. 4 V and hence can provide high energy-density. Gel-polymer electrolytes are generally prepared using organic solvents that are environmentally malignant. Hence, replacement of organic solvents with water in gel-polymer electrolytes is desirable which also minimizes the device cost substantially. The water containing gel-polymer electrolytes, called hydrogel-polymer electrolytes, are, however, limited by a low operating potential-window of only about 1.23 V. This article reviews salient features of electrochemical capacitors employing hydrogel-polymer electrolytes.