922 resultados para Riccati matrix differential equation
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Glass transition temperature of spaghetti sample was measured by thermal and rheological methods as a function of water content.
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A novel voltammetric method for simultaneous determination of the glucocorticoid residues prednisone, prednisolone, and dexamethasone was developed. All three compounds were reduced at a mercury electrode in a Britton-Robinson buffer (pH 3.78), and well-defined voltammetric waves were observed. However, the voltammograms of these three compounds overlapped seriously and showed nonlinear character, and thus, it was difficult to analyze the compounds individually in their mixtures. In this work, two chemometrics methods, principal component regression (PCR) and partial least squares (PLS), were applied to resolve the overlapped voltammograms, and the calibration models were established for simultaneous determination of these compounds. Under the optimum experimental conditions, the limits of detection (LOD) were 5.6, 8.3, and 16.8 µg l-1 for prednisone, prednisolone, and dexamethasone, respectively. The proposed method was also applied for the determination of these glucocorticoid residues in the rabbit plasma and human urine samples with satisfactory results.
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A simple and sensitive spectrophotometric method for the simultaneous determination of acesulfame-K, sodium cyclamate and saccharin sodium sweeteners in foodstuff samples has been researched and developed. This analytical method relies on the different kinetic rates of the analytes in their oxidative reaction with KMnO4 to produce the green manganate product in an alkaline solution. As the kinetic rates of acesulfame-K, sodium cyclamate and saccharin sodium were similar and their kinetic data seriously overlapped, chemometrics methods, such as partial least squares (PLS), principal component regression (PCR) and classical least squares (CLS), were applied to resolve the kinetic data. The results showed that the PLS prediction model performed somewhat better. The proposed method was then applied for the determination of the three sweeteners in foodstuff samples, and the results compared well with those obtained by the reference HPLC method.
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The Node-based Local Mesh Generation (NLMG) algorithm, which is free of mesh inconsistency, is one of core algorithms in the Node-based Local Finite Element Method (NLFEM) to achieve the seamless link between mesh generation and stiffness matrix calculation, and the seamless link helps to improve the parallel efficiency of FEM. Furthermore, the key to ensure the efficiency and reliability of NLMG is to determine the candidate satellite-node set of a central node quickly and accurately. This paper develops a Fast Local Search Method based on Uniform Bucket (FLSMUB) and a Fast Local Search Method based on Multilayer Bucket (FLSMMB), and applies them successfully to the decisive problems, i.e. presenting the candidate satellite-node set of any central node in NLMG algorithm. Using FLSMUB or FLSMMB, the NLMG algorithm becomes a practical tool to reduce the parallel computation cost of FEM. Parallel numerical experiments validate that either FLSMUB or FLSMMB is fast, reliable and efficient for their suitable problems and that they are especially effective for computing the large-scale parallel problems.
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This article explores two matrix methods to induce the ``shades of meaning" (SoM) of a word. A matrix representation of a word is computed from a corpus of traces based on the given word. Non-negative Matrix Factorisation (NMF) and Singular Value Decomposition (SVD) compute a set of vectors corresponding to a potential shade of meaning. The two methods were evaluated based on loss of conditional entropy with respect to two sets of manually tagged data. One set reflects concepts generally appearing in text, and the second set comprises words used for investigations into word sense disambiguation. Results show that for NMF consistently outperforms SVD for inducing both SoM of general concepts as well as word senses. The problem of inducing the shades of meaning of a word is more subtle than that of word sense induction and hence relevant to thematic analysis of opinion where nuances of opinion can arise.
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Biomineralization is a process encompassing all mineral containing tissues produced within an organism. The most dynamic example of this process is the formation of the mollusk shell, comprising a variety of crystal phases and microstructures. The organic component incorporated within the shell is said to dictate this remarkable architecture. Subsequently, for the past decade considerable research have been undertaken to identify and characterize the protein components involved in biomineralization. Despite these efforts the general understanding of the process remains ambiguous. This study employs a novel molecular approach to further the elucidation of the shell biomineralization. A microarray platform has been custom generated (PmaxArray 1.0) from the pearl oyster Pinctada maxima. PmaxArray 1.0 consists of 4992 expressed sequence tags (ESTs) originating from the mantle, an organ involved in shell formation. This microarray has been used as the primary tool for three separate investigations in an effort to associate transcriptional gene expression from P. maxima to the process of shell biomineralization. The first investigation analyzes the spatial expression of ESTs throughout the mantle organ. The mantle was dissected into five discrete regions and each analyzed for gene expression with PmaxArray 1.0. Over 2000 ESTs were differentially expressed among the tissue sections, identifying five major expression regions. Three of these regions have been proposed to have shell formation functions belonging to nacre, prismatic calcite and periostracum. The spatial gene expression map was confirmed by in situ hybridization, localizing a subset of ESTs from each expression region to the same mantle area. Comparative sequence analysis of ESTs expressed in the proposed shell formation regions with the BLAST tool, revealed a number of the transcripts were novel while others showed significant sequence similarities to previously characterized shell formation genes. The second investigation correlates temporal EST expression during P. maxima larval ontogeny with transitions in shell mineralization during the same period. A timeline documenting the morphologicat microstructural and mineralogical shell characteristics of P. maxima throughout larval ontogeny has been established. Three different shell types were noted based on the physical characters and termed, prodissoconch I, prodissoconch 11 and dissoconch. PmaxArray 1.0 analyzed ESTs expression of animals throughout the larval development of P. maxima, noting up-regulation of 359 ESTs in association with the shell transitions from prodissoconch 1 to prodissoconch 11 to dissoconch. Comparative sequence analysis of these ESTs indicates a number of the transcripts are novel as well as showing significant sequence similarities between ESTs and known shell matrix associated genes and proteins. These ESTs are discussed in relation to the shell characters associated with their temporal expression. The third investigation uses PmaxArray 1.0 to analyze gene expression in the mantle tissue of P. maxima specimens exposed to sub-lethal concentrations of a shell-deforming toxin, tributyltin (TBT). The shell specific effects of TBT are used in this investigation to interpret differential expression of ESTs with respect to shell formation functions. A lethal and sublethal TBT concentration range was established for P. maxima, noting a concentration of 50 ng L- 1 TBT as sub-lethal over a 21 day period. Mantle tissue from P. maxima animals treated with 50 ng L- 1 TBT was assessed for differential EST expression with untreated control animals. A total of 102 ESTs were identified as differentially expressed in association with TBT exposure, comparative sequence identities included an up-regulation of immunity and detoxification related genes and down-regulation of several shell matrix genes. A number of transcripts encoding novel peptides were additionally identified. The potential actions of these genes are discussed with reference to TBT toxicity and shell biomineralization. This thesis has used a microarray platform to analyze gene expression in spatial, temporal and toxicity investigations, revealing the involvement of numerous gene transcripts in specific shell formation functions. Investigation of thousands of transcripts simultaneously has provided a holistic interpretation of the organic components regulating shell biomineralization.
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In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis
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Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.
ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation
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In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.
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In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.
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Osteophytes form through the process of chondroid metamorphosis of fibrous tissue followed by endochondral ossification. Osteophytes have been found to consist of three different mesenchymal tissue regions including endochondral bone formation within cartilage residues, intra-membranous bone formation within fibrous tissue and bone formation within bone marrow spaces. All these features provide evidence of mesenchymal stem cells (MSC) involvement in osteophyte formation; nevertheless, it remains to be characterised. MSC from numerous mesenchymal tissues have been isolated but bone marrow remains the “ideal” due to the ease of ex vivo expansion and multilineage potential. However, the bone marrow stroma has a relatively low number of MSC, something that necessitates the need for long-term culture and extensive population doublings in order to obtain a sufficient number of cells for therapeutic applications. MSC in vitro have limited proliferative capacity and extensive passaging compromises differentiation potential. To overcome this barrier, tissue derived MSC are of strong interest for extensive study and characterisation, with a focus on their potential application in therapeutic tissue regeneration. To date, no MSC type cell has been isolated from osteophyte tissue, despite this tissue exhibiting all the hallmark features of a regenerative tissue. Therefore, this study aimed to isolate and characterise cells from osteophyte tissues in relation to their phenotype, differentiation potential, immuno-modulatory properties, proliferation, cellular ageing, longevity and chondrogenesis in in vitro defect model in comparison to patient matched bone marrow stromal cells (bMSC). Osteophyte derived cells were isolated from osteophyte tissue samples collected during knee replacement surgery. These cells were characterised by the expression of cell surface antigens, differentiation potential into mesenchymal lineages, growth kinetics and modulation of allo-immune responses. Multipotential stem cells were identified from all osteophyte samples namely osteophyte derived mesenchymal stem cells (oMSC). Extensively expanded cell cultures (passage 4 and 9 respectively) were used to confirm cytogenetic stability and study signs of cellular aging, telomere length and telomerase activity. Cultured cells at passage 4 were used to determine 84 pathway focused stem cell related gene expression profile. Micro mass pellets were cultured in chondrogenic differentiation media for 21 days for phenotypic and chondrogenic related gene expression. Secondly, cell pellets differentiated overnight were placed into articular cartilage defects and cultured for further 21 days in control medium and chondrogenic medium to study chondrogenesis and cell behaviour. The surface antigen expression of oMSC was consistent with that of mesenchymal stem cells, such as lacking the haematopoietic and common leukocyte markers (CD34, CD45) while expressing those related to adhesion (CD29, CD166, CD44) and stem cells (CD90, CD105, CD73). The proliferation capacity of oMSC in culture was superior to that of bMSC, and they readily differentiated into tissues of the mesenchymal lineages. oMSC also demonstrated the ability to suppress allogeneic T-cell proliferation, which was associated with the expression of tryptophan degrading enzyme indoleamine 2,3 dioxygenase (IDO). Cellular aging was more prominent in late passage bMSC than in oMSC. oMSC had longer telomere length in late passages compared with bMSC, although there was no significant difference in telomere lengths in the early passages in either cell type. Telomerase activity was detectable only in early passage oMSC and not in bMSC. In osteophyte tissues telomerase positive cells were found to be located peri vascularly and were Stro-1 positive. Eighty-four pathway-focused genes were investigated and only five genes (APC, CCND2, GJB2, NCAM and BMP2) were differentially expressed between bMSC and oMSC. Chondrogenically induced micro mass pellets of oMSC showed higher staining intensity for proteoglycans, aggrecan and collagen II. Differential expression of chondrogenic related genes showed up regulation of Aggrecan and Sox 9 in oMSC and collagen II in bMSC. The in vitro defect models of oMSC in control medium showed rounded and aggregated cells staining positively for proteoglycan and presence of some extracellular matrix. In contrast, defects with bMSC showed fragmentation and loss of cells, fibroblast-like cell morphology staining positively for proteoglycans. For defects maintained in chondrogenic medium, rounded, aggregated and proteoglycan positive cells were found in both oMSC and bMSC cultures. Extracellular matrix and cellular integration into newly formed matrix was evident only in oMSC defects. For analysis of chondrocyte hypertrophy, strong expression of type X collagen could be noticed in the pellet cultures and transplanted bMSC. In summary, this study demonstrated that osteophyte derived cells had similar properties to mesenchymal stem cells in the expression of antigen phenotype, differential potential and suppression of allo-immune response. Furthermore, when compared to bMSC, oMSC maintained a higher proliferative capacity due to a retained level of telomerase activity in vitro, which may account for the relatively longer telomeres delaying growth arrest by replicative senescence compared with bMSC. oMSC behaviour in defects supported chondrogenesis which implies that cells derived from regenerative tissue can be an alternative source of stem cells and have a potential clinical application for therapeutic stem cell based tissue regeneration.