Some Problems In Algebra And Topology A Study Of Fuzzy Convexity With Special Reference To Separation Properties

This thesis is a study of abstract fuzzy convexity spaces and fuzzy topology fuzzy convexity spaces No attempt seems to have been made to develop a fuzzy convexity theoryin abstract situations. The purpose of this thesis is to introduce fuzzy convexity theory in abstract situations

Folding of graphene slit like pore walls—a simple method of improving CO2 separation from mixtures with CH4 or N2

We report for the first time a detailed procedure for creating a simulation model of energetically stable, folded graphene-like pores and simulation results of CO2/CH4 and CO2/N2 separation using these structures. We show that folding of graphene structures is a very promising method to improve the separation of CO2 from mixtures with CH4 and N2. The separation properties of the analyzed materials are compared with carbon nanotubes having similar diameters or S/V ratio. The presented results have potential importance in the field of CO2 capture and sequestration.

To what extent can mutual shifting of folded carbonaceous walls in slit-like pores affect their adsorption properties?

We have performed systematic Monte Carlo studies on the influence of shifting the walls in slit-like systems constructed from folded graphene sheets on their adsorption properties. Specifically, we have analysed the effect on the mechanism of argon adsorption (T = 87 K) and on adsorption and separation of three binary gas mixtures: CO2/N2, CO2/CH4 and CH4/N2 (T = 298 K). The effects of the changes in interlayer distance were also determined. We show that folding of the walls significantly improves the adsorption and separation properties in comparison to ideal slit-like systems. Moreover, we demonstrate that mutual shift of sheets (for small interlayer distances) causes the appearance of small pores between opposite bulges. This causes an increase in vapour adsorption at low pressures. Due to overlapping of interactions with opposite walls causing an increase in adsorption energy, the mutual shift of sheets is also connected with the rise in efficiency of mixtures separation. The effects connected with sheet orientation vanish as the interlayer distance increases.

Flow regime, hydrodynamics, floc size distribution and sludge properties in activated sludge bubble column, air-lift and aerated stirred reactors

This paper presents a comparative study how reactor configuration, sludge loading and air flowrate affect flow regimes, hydrodynamics, floc size distribution and sludge solids-liquid separation properties. Three reactor configurations were studied in bench scale activated sludge bubble column reactor (BCR), air-lift reactor (ALR) and aerated stirred reactor (ASR). The ASR demonstrated the highest capacity of gas holdup and resistance, and homogeneity in flow regimes and shearing forces, resulting in producing large numbers of small and compact floes. The fluid dynamics in the ALR created regularly directed recirculation forces to enhance the gas holdup and sludge flocculation. The BCR distributed a high turbulent flow regime and non-homogeneity in gas holdup and mixing, and generated large numbers of larger and looser floes. The sludge size distributions, compressibility and settleability were significantly influenced by the reactor configurations associated with the flow regimes and hydrodynamics.

Unfolding kernel embeddings of graphs:enhancing class separation through manifold learning

In this paper, we investigate the use of manifold learning techniques to enhance the separation properties of standard graph kernels. The idea stems from the observation that when we perform multidimensional scaling on the distance matrices extracted from the kernels, the resulting data tends to be clustered along a curve that wraps around the embedding space, a behavior that suggests that long range distances are not estimated accurately, resulting in an increased curvature of the embedding space. Hence, we propose to use a number of manifold learning techniques to compute a low-dimensional embedding of the graphs in an attempt to unfold the embedding manifold, and increase the class separation. We perform an extensive experimental evaluation on a number of standard graph datasets using the shortest-path (Borgwardt and Kriegel, 2005), graphlet (Shervashidze et al., 2009), random walk (Kashima et al., 2003) and Weisfeiler-Lehman (Shervashidze et al., 2011) kernels. We observe the most significant improvement in the case of the graphlet kernel, which fits with the observation that neglecting the locational information of the substructures leads to a stronger curvature of the embedding manifold. On the other hand, the Weisfeiler-Lehman kernel partially mitigates the locality problem by using the node labels information, and thus does not clearly benefit from the manifold learning. Interestingly, our experiments also show that the unfolding of the space seems to reduce the performance gap between the examined kernels.

Polymerization of isatin towards polymers for anion exchange membranes and gas separation applications

In a world where the problem of energy resources, pollution and all aspects related to these issues become more and more dominant, a greater commitment is needed in the search for solutions. The goal of this project is to make a contribution to the research and development of new materials to reduce the environmental impact in some fields. First of all, we tried to synthesize and prepare an isatin-based membrane which has the potential for use in separating industrial gases. Furthermore, ion exchange membranes, specifically hydroxide exchange membranes (HEMs) derived from the same product can be developed for fuel cells (HEMFC) applications. These materials are essential for energy conversion and storage. The most difficult challenge is to guarantee their thermal stability and stability in corrosive environments such as alkali without losing efficiency. In recent years the poly- hydroxyalkylation catalysed with superacids, e.g. TFSA, has become increasingly studied. This reaction is exploited for the synthesis of the compounds of this thesis. After a preliminary optimization of the reaction conditions it was concluded that due to the rigidity and excessive reactivity of the system, it was not possible to obtain the isatin-based membrane to evaluate the gas separation properties. The synthesis of precursor materials for HEMs was successful by using 1-(4-bromobutyl)indoline-2,3-dione (BID) instead of isatin. A characterization of the obtained polymers was carried out using NMR, TGA and DSC analyses, and subsequently the membranes were functionalized with different ammonium-based cations. Unfortunately, this last step was not successful due to the appearance of side reactions. Future studies on the mechanism and kinetics of the reaction solve this obstacle.

Relationship between flocculation of activated sludge and composition of extracellular polymeric substances

Activated sludge floes are a flocculated mass of microorganisms, extracellular polymeric substances (EPS) and adsorbed organic and inorganic material. The structure of the floes is very heterogeneous and floes with very different properties and morphologies may occur, depending on the conditions in the activated sludge treatment plant and wastewater composition. Present thinking suggests that cations, such as calcium, create cationic bridges with EPS excreted by the bacteria and thereby hold the various floe constituents together. However, due to the complex and heterogeneous nature of activated sludge, the mechanisms have neither been thoroughly investigated nor successfully quantified. A better understanding and description of the biological flocculation process is necessary in order to establish more efficient operational strategies. The main aim of this study was to get a comprehensive and unique insight into the floe properties of activated sludge and to assess the relative impact of chemical and physical parameters. A variety of sludges from full scale treatment plants with different settling properties were characterised. The interrelationships between floe parameters such as composition of EPS, surface properties and floe structure, and their effect on the flocculation and separation properties were assessed. The results indicate that the EPS, both in terms of quantity and quality, are very important for the floe properties of the activated sludge. However, presence of filaments may alter the physical properties of the floes considerably. The EPS showed positive correlations to sludge volume index (SVI) if only sludges with low or moderate numbers of filaments were included. The surface properties were more affected by the composition of the EPS than by the number of filaments. The EPS showed positive correlation to negative surface charge and a negative correlation to relative hydrophobicity and flocculation ability. The negative correlation between flocculation ability and amount of EPS was surprising. The shear sensitivity, measured as degree of erosion of floes when subjected to shear, was more affected by floe size and number of filaments than amount of EPS.

Fuzzy Topological Games and Related Topics

The main purpose of study is to extend the concept of the topological game G(K, X) and some other kinds of games into fuzzy topological games and to obtain some results regarding them. Owing to the fact that topological games have plenty of applications in covering properties, it made an attempt to explore some inter relations of games and covering properties in fuzzy topological spaces. Even though the main focus is on fuzzy para-meta compact spaces and closure preserving shading families, some brief sketches regarding fuzzy P-spaces and Shading Dimension is also provided. In a topological game players choose some objects related to the topological structure of a space such as points, closed subsets, open covers etc. More over the condition on a play to be winning for a player may also include topological notions such as closure, convergence, etc. It turns out that topological games are related to the Baire property, Baire spaces, Completeness properties, Convergence properties, Separation properties, Covering and Base properties, Continuous images, Suslin sets, Singular spaces etc.

The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

Synthesis and characterization of silicalite-1 composite membrane

Silicalite-1/carbon-graphite composite membranes have been prepared using a standard hydrothermal synthesis method and characterized by XRD, SEM, TGA, BET and permeation experiments. Single gas permeation fluxes and binary mixtures separation and selectivity data are reported for methane, ethane and propane using the composite membranes. Carbon-graphite oxidized for 4 h prior to membrane preparation had the most promising separation properties. The permeation fluxes for the binary mixtures reflect that of the single component flux ratios. At 20 °C the membranes show high separation selectivity toward lighter component in binary mixtures. Single gas permeances for methane and ethane were found to decrease with increasing temperatures while that of propane fluctuates. © 2007 Elsevier Inc. All rights reserved.

Cost-effective and eco-friendly synthesis of novel and stable N-doped ZnO/g-C3N4 core-shell nanoplates with excellent visible-light responsive photocatalysis

N-doped ZnO/g-C3N4 hybrid core–shell nanoplates have been successfully prepared via a facile, cost-effective and eco-friendly ultrasonic dispersion method for the first time. HRTEM studies confirm the formation of the N-doped ZnO/g-C3N4 hybrid core–shell nanoplates with an average diameter of 50 nm and the g-C3N4 shell thickness can be tuned by varying the content of loaded g-C3N4. The direct contact of the N-doped ZnO surface and g-C3N4 shell without any adhesive interlayer introduced a new carbon energy level in the N-doped ZnO band gap and thereby effectively lowered the band gap energy. Consequently, the as-prepared hybrid core–shell nanoplates showed a greatly enhanced visible-light photocatalysis for the degradation of Rhodamine B compare to that of pure N-doped ZnO surface and g-C3N4. Based on the experimental results, a proposed mechanism for the N-doped ZnO/g-C3N4 photocatalyst was discussed. Interestingly, the hybrid core–shell nanoplates possess high photostability. The improved photocatalytic performance is due to a synergistic effect at the interface of the N-doped ZnO and g-C3N4 including large surface-exposure area, energy band structure and enhanced charge-separation properties. Significantly, the enhanced performance also demonstrates the importance of evaluating new core–shell composite photocatalysts with g-C3N4 as shell material.

Synthesis of magnetically separable and recyclable g‑C3N4−Fe3O4 hybrid nanocomposites with enhanced photocatalytic performance under visible-light irradiation

Herein we demonstrate a facile, reproducible, and template-free strategy to prepare g-C3N4–Fe3O4 nanocomposites by an in situ growth mechanism. The results indicate that monodisperse Fe3O4 nanoparticles with diameters as small as 8 nm are uniformly deposited on g-C3N4 sheets, and as a result, aggregation of the Fe3O4 nanoparticles is effectively prevented. The as-prepared g-C3N4–Fe3O4 nanocomposites exhibit significantly enhanced photocatalytic activity for the degradation of rhodamine B under visible-light irradiation. Interestingly, the g-C3N4–Fe3O4 nanocomposites showed good recyclability without loss of apparent photocatalytic activity even after six cycles, and more importantly, g-C3N4–Fe3O4 could be recovered magnetically. The high performance of the g-C3N4–Fe3O4 photocatalysts is due to a synergistic effect including the large surface-exposure area, high visible-light-absorption efficiency, and enhanced charge-separation properties. In addition, the superparamagnetic behavior of the as-prepared g-C3N4–Fe3O4 nanocomposites also makes them promising candidates for applications in the fields of lithium storage capacity and bionanotechnology.

Kinetics of photogenerated carriers in nanostructured semiconductor heterojunctions for solar water splitting

This thesis aims to investigate the fundamental processes governing the performance of different types of photoelectrodes used in photoelectrochemical (PEC) applications, such as unbiased water splitting for hydrogen production. Unraveling the transport and recombination phenomena in nanostructured and surface-modified heterojunctions at a semiconductor/electrolyte interface is not trivial. To approach this task, the work presented here first focus on a hydrogen-terminated p-silicon photocathode in acetonitrile, considered as a standard reference for PEC studies. Steady-state and time-resolved excitation at long wavelength provided clear evidence of the formation of an inversion layer and revealed that the most optimal photovoltage and the longest electron-hole pair lifetime occurs when the reduction potential for the species in solution lies within the unfilled conduction band states. Understanding more complex systems is not as straight-forward and a complete characterization that combine time- and frequency-resolved techniques is needed. Intensity modulated photocurrent spectroscopy and transient absorption spectroscopy are used here on WO3/BiVO4 heterojunctions. By selectively probing the two layers of the heterojunction, the occurrence of interfacial recombination was identified. Then, the addition of Co-Fe based overlayers resulted in passivation of surface states and charge storage at the overlayer active sites, providing higher charge separation efficiency and suppression of recombination in time scales that go from picoseconds to seconds. Finally, the charge carrier kinetics of several different Cu(In,Ga)Se2 (CIGS)-based architectures used for water reduction was investigated. The efficiency of a CIGS photocathode is severely limited by charge transfer at the electrode/electrolyte interface compared to the same absorber layer used as a photovoltaic cell. A NiMo binary alloy deposited on the photocathode surface showed a remarkable enhancement in the transfer rate of electrons in solution. An external CIGS photovoltaic module assisting a NiMo dark cathode displayed optimal absorption and charge separation properties and a highly performing interface with the solution.

Nonsolvent induced phase separation preparation of poly(vinylidene fluoride-co-chlorotrifluoroethylene) membranes with tailored morphology, piezoelectric phase content and mechanical properties

Poly(vinylidene fluoride-co-chlorotrifluoroethylene) – P(VDF-CTFE) membranes are increasingly interesting for a wide range of applications, including battery separators, filtration membranes and biomedical applications. This work reports on the morphology, hydrophobicity, thermal and mechanical properties variation of P(VDF-CTFE) membranes processed by nonsolvent induced phase separation technique (NIPS) as a function of the main processing parameters. All membranes show a porous structure composed of large spherulites, (interconnected) micropores and/or microvoids depending on the processing conditions used that in turn affect their hydrophobicity and mechanical properties. The degree of crystallinity of the membranes remains approximately constant with a value of about 15 %, except for the membranes immediately immersed in ethanol, which is of about 23 %. In turn, the crystalline phases present in the copolymer is mainly affected by the temperature and nonsolvent characteristics of the coagulation bath, the β-phase content ranging from 33 to 100 %, depending on those processing parameters. It was show that the temperature of water-based coagulation bath plays an important role in order to produce structurally uniform and homogeneous porous membranes, which is particularly important from the point of view of technological applications.

Influence of stationary phase and eluent properties on chromatographic separation of carbohydrates

In this thesis, the sorption and elastic properties of the cation-exchange resins were studied to explain the liquid chromatographic separation of carbohydrates. Na+, Ca2+ and La3+ form strong poly(styrene-co-divinylbenzene) (SCE) as well as Na+ and Ca2+ form weak acrylic (WCE) cation-exchange resins at different cross-link densities were treated within this work. The focus was on the effects of water-alcohol mixtures, mostly aqueous ethanol, and that of the carbohydrates. The carbohydrates examined were rhamnose, xylose, glucose, fructose, arabinose, sucrose, xylitol and sorbitol. In addition to linear chromatographic conditions, non-linear conditions more typical for industrial applications were studied. Both experimental and modeling aspectswere covered. The aqueous alcohol sorption on the cation-exchangers were experimentally determined and theoretically calculated. The sorption model includes elastic parameters, which were obtained from sorption data combined with elasticity measurements. As hydrophilic materials cation-exchangers are water selective and shrink when an organic solvent is added. At a certain deswelling degree the elastic resins go through glass transition and become as glass-like material. Theincreasing cross-link level and the valence of the counterion decrease the sorption of solvent components in the water-rich solutions. The cross-linkage or thecounterions have less effect on the water selectivity than the resin type or the used alcohol. The amount of water sorbed is higher in the WCE resin and, moreover, the WCE resin is more water selective than the corresponding SCE resin. Theincreased aliphatic part of lower alcohols tend to increase the water selectivity, i.e. the resins are more water selective in 2-propanol than in ethanol solutions. Both the sorption behavior of carbohydrates and the sorption differences between carbohydrates are considerably affected by the eluent composition and theresin characteristics. The carbohydrate sorption was experimentally examined and modeled. In all cases, sorption and moreover the separation of carbohydrates are dominated by three phenomena: partition, ligand exchange and size exclusion. The sorption of hydrophilic carbohydrates increases when alcohol is added into the eluent or when carbohydrate is able to form coordination complexes with the counterions, especially with multivalent counterions. Decreasing polarity of the eluent enhances the complex stability. Size exclusion effect is more prominent when the resin becomes tighter or carbohydrate size increases. On the other hand,the elution volumes between different sized carbohydrates decreases with the decreasing polarity of the eluent. The chromatographic separation of carbohydrateswas modeled, using rhamnose and xylose as target molecules. The thermodynamic sorption model was successfully implemented in the rate-based column model. The experimental chromatographic data were fitted by using only one adjustable parameter. In addition to the fitted data also simulated data were generated and utilized in explaining the effect of the eluent composition and of the resin characteristics on the carbohydrate separation.