Anisotropic adaptive resolution of boundary layers for heat conduction problems

We deal with the numerical solution of heat conduction problems featuring steep gradients. In order to solve the associated partial differential equation a finite volume technique is used and unstructured grids are employed. A discrete maximum principle for triangulations of a Delaunay type is developed. To capture thin boundary layers incorporating steep gradients an anisotropic mesh adaptation technique is implemented. Computational tests are performed for an academic problem where the exact solution is known as well as for a real world problem of a computer simulation of the thermoregulation of premature infants.

Resolution of sharp fronts in the presence of model error in variational data assimilation

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong constraint 4DVar (L2-norm)method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

On the resolution of the generalized nonlinear complementarity problem

Minimization of a differentiable function subject to box constraints is proposed as a strategy to solve the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone. It is not necessary to calculate projections that complicate and sometimes even disable the implementation of algorithms for solving these kinds of problems. Theoretical results that relate stationary points of the function that is minimized to the solutions of the GNCP are presented. Perturbations of the GNCP are also considered, and results are obtained related to the resolution of GNCPs with very general assumptions on the data. These theoretical results show that local methods for box-constrained optimization applied to the associated problem are efficient tools for solving the GNCP. Numerical experiments are presented that encourage the use of this approach.

Algorithms for super-resolution of images based on Sparse Representation and Manifolds

lmage super-resolution is defined as a class of techniques that enhance the spatial resolution of images. Super-resolution methods can be subdivided in single and multi image methods. This thesis focuses on developing algorithms based on mathematical theories for single image super­ resolution problems. lndeed, in arder to estimate an output image, we adopta mixed approach: i.e., we use both a dictionary of patches with sparsity constraints (typical of learning-based methods) and regularization terms (typical of reconstruction-based methods). Although the existing methods already per- form well, they do not take into account the geometry of the data to: regularize the solution, cluster data samples (samples are often clustered using algorithms with the Euclidean distance as a dissimilarity metric), learn dictionaries (they are often learned using PCA or K-SVD). Thus, state-of-the-art methods still suffer from shortcomings. In this work, we proposed three new methods to overcome these deficiencies. First, we developed SE-ASDS (a structure tensor based regularization term) in arder to improve the sharpness of edges. SE-ASDS achieves much better results than many state-of-the- art algorithms. Then, we proposed AGNN and GOC algorithms for determining a local subset of training samples from which a good local model can be computed for recon- structing a given input test sample, where we take into account the underlying geometry of the data. AGNN and GOC methods outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings. Next, we proposed aSOB strategy which takes into account the geometry of the data and the dictionary size. The aSOB strategy outperforms both PCA and PGA methods. Finally, we combine all our methods in a unique algorithm, named G2SR. Our proposed G2SR algorithm shows better visual and quantitative results when compared to the results of state-of-the-art methods.

PRACTICAL RESOLUTION OF DIFFERENTIAL SYSTEMS

3. PRACTICAL RESOLUTION OF DIFFERENTIAL SYSTEMS by Marilia Pires, University of Évora, Portugal This practice presents the main features of a free software to solve mathematical equations derived from concrete problems: i.- Presentation of Scilab (or python) ii.- Basics (number, characters, function) iii.- Graphics iv.- Linear and nonlinear systems v.- Differential equations

Resolution of the chiral (1R,2S) enantiomer of cis-cyclohexane-1,2-dicarboxylic acid in the brucinium salt 2,3-dimethoxy-10-oxostrychnidinium (1R,2S)-2-carboxycyclohexane-1-carboxylate dihydrate

The structure of the 1:1 brucinium salt of cis-cyclohexane-1,2-dicarboxylic acid, 2,3-dimethoxy-10-oxostrychnidinium (1R,2S)-2-carboxycyclohexane-1-carboxylate dihydrate, has revealed the resolved (1R,2S) enantiomer of the acid. Crystals of the compound are orthorhombic, space group P212121, with unit cell dimensions a = 8.1955(3), b = 12.4034(3), c = 29.9073(9)Å, and Z = 4. The asymmetric unit comprises the brucinium cation, the hydrogen cis-cyclohexane-1,2-dicarboxylate cation, in which the carboxylate group is disordered over two sites (58, 42%), and two water molecules of solvation, one of which is occupies two 50% occupancy sites. The classic undulating brucinium cation substructures are present with the anion and the water molecules occupying the interstitial cavities and are hydrogen-bonded to them in a two-dimensional network structure.

Cutting down the Cypress leylandii, pittosporums, and cotoneasters on your neighbours' land - the resolution of spite hedges

Queensland, New South Wales, and the United Kingdom have enacted legislation that governs what are colloquially known as spite hedges. These are barriers, commonly horticultural, that once constructed, block the view or sunlight from a neighbouring property. The matter was also recently raised in the Tasmanian Parliament. This article examines whether legislation should be enacted to deal with this issue, and if so, what is the regulatory model that need be adopted. The conclusion is that a layered nuanced response is needed to balance the interests and obligations of neighbouring landowners.

Atomic resolution of dielectric with low temperature coefficient

Ba(6-3x)Nd(8+2x)Ti(18)O(54) (BNTl14) is a high permittivity dielectric with low temperature coefficient (Tcf). Low coefficient of change of dielectric permittivity with temperature (Tcf) is an unusual materials property. The research is aimed at discovering how atomic structure relates to temperature coefficient. Sub-Ångström scanning transmission electron microscopy (STEM) is used to measure mixed occupancy of Nd and Ba in atomic columns. It was expected that phase separation would occur to accommodate mixing of dissimilar ions. However no evidence of phase separation was found. There is a good image match between experiment and high angle annular dark field (HAADF) simulation. Vacancies and excess Ba ions appear to be randomly arranged on the available sites which would result in distortion of TiO6 octahedra. The low Tcf may arise from TiO6 distortion.

Resolution of Cryptic Species Complexes of Tephritid Pests to Enhance SIT Application and Facilitate International Trade

Tephritid fruit flies (Diptera: Tephritidae) are considered by far the most important group of horticultural pests worldwide. Female fruit flies lay eggs directly into ripening fruit, where the maggots feed causing fruit loss. Each and every continent is plagued by a number of fruit fly pests, both indigenous as well as invasive ones, causing tremendous economic losses. In addition to the direct losses through damage, they can negatively impact commodity trade through restrictions to market access. The quarantine and regulatory controls put in place to manage them are expensive, while the on-farm control costs and loss of crop affect the general well-being of growers. These constraints can have huge implications on loss in revenues and limitations to developing fruit and vegetable-based agroindustries in developing, emergent and developed nations. Because fruit flies are a global problem, the study of their biology and management requires significant international attention to overcome the hurdles they pose. The Joint Food and Agriculture Organisation / International Atomic Energy Agency (FAO/IAEA) Programme on Nuclear Techniques in Food and Agriculture has been on the foreground in assisting Member States in developing and validating environment-friendly fruit fly suppression systems to support viable fresh fruit and vegetable production and export industries. Such international attention has resulted in the successful development and validation of a Sterile Insect Technique (SIT) package for the Mediterranean fruit fly. Although demands for R&D support with respect to Mediterranean fruit fly are diminishing due to successful integration of this package into sustainable control programmes against this pest in many countries, there were increasing demands from Member States in Africa, Asia and Latin America, to address other major fruit fly pests and a related, but sometimes neglected issue of tephritid species complexes of economic importance. Any research, whether it is basic or applied, requires a taxonomic framework that provides reliable and universally recognized entities and names. Among the currently recognized major fruit fly pests, there are groups of species whose morphology is very similar or identical, but biologically they are distinct species. As such, some insect populations that are grouped taxonomically within the same pest species, display different biological and genetic traits and show reproductive isolation which suggest that they are different species. On the other hand, different species may have been taxonomically described, but there may be doubt as to whether they actually represent distinct biological species or merely geographical variants of the same species. This uncertain taxonomic status has practical implications on the effective development and use of the SIT against such complexes, particularly at the time of determining which species to mass-rear, and significantly affects international movement of fruit and vegetables through the establishment of trade barriers to important agricultural commodities which are hosts to these pest tephritid species...

Resolution of racemic gossypol and interaction of individual enantiomers with serum albumins and model peptides

Racemic gossypol has been resolved by HPLC separation of diastereomeric (−) norepinephrine adducts on a reverse-phase column. The binding constants for the interaction of the three gossypol forms (+, − and −) with human and bovine serum albumins have been determined by fluoresence quenching studies. The KD values demonstrate that all three forms bind equally effectively to the two proteins, suggesting an absence of chiral discrimination in albumin-gossypol interactions. Circular dichroism studies of (+)-gossypol binding to the model dibasic peptides, Boc-Lys-Pro-Aib-Lys-NHMe and gramicidin S, suggesting that distortions of binaphthyl geometry may occur only for specific orientations of interacting residues at the receptor site.