A posteriori error estimates in the finite element method for elliptic BVP with degeneration

We consider a class of elliptic boundary value problems with degenerating coefficients for which we construct FEM schemes with optimal convergence on the basis of multiplicative extraction of the singularity. For a scale of weighted Sobolev norms including the energy norm of the differential operator, we prove a posteriori estimates for the error of the discrete solutions. © 2014 Pleiades Publishing, Ltd

Mechanical Treatment of Raw Waste Lumber an Effective Way to Preserve the Ecology and Resources

Alternative process flowsheet machining of the machining of raw waste lumber were analysed, and it was implemented in a real machine model based on the chosen scheme. The forming process of the treated surface of the stock material was examined, and consequently the mathematical models of the geometric errors in terms of independent factors of the profile milling process were defined. Based on these models is possible to construct a treatment process of the raw waste lumber with minimal errors on the surfaces which were treated. The manufacturing of products from raw waste lumber allows to reduce the volume of deforestation and helps to preserve the ecology and economize the material resources

The Development of Equipment for the Disposal of Solid Organic Waste and Optimization of Its Operation

The paper describes the developed system for the thermal utilization of solid organic waste, which can simultaneously process the paper, wood, rubber, plastic, etc. A method for improving the efficiency of the equipment, due to optimization of the gas extraction system was proposed. The influence of the characteristics of installed equipment and modes of their work on energy savings and efficiency of the gas extraction system was also determined. Optimization work which includes the introduction into the exhauster control system of the frequency converter, can save up to 70% of electricity and increases the life of the equipment

The Development of Experimental Setups And Experimental Studies of The Process of Energy-Technological Processing of Wood

The paper describes the experimental setups for the study of the various stages of the process of energy-technological processing of wood waste with the production of synthesis gas. The systems for the study of conjugated processes of drying, pyrolysis and gasification, that are an integral part of energy-technological processing of wood wastes were developed. Experimental studies of the processes have identified their basic properties and optimum operating parameters, allowing to obtain a synthesis gas suitable for the chemical synthesis of various olefins

High-Order Accuracy Approximation for a Two-Point Boundary Value Problem of Fourth Order with Degenerate Coefficients

© 2018, Pleiades Publishing, Ltd. High-order accurate finite element schemes for a fourth-order ordinary differential equation with degenerate coefficients on the boundary are constructed. The method for solving the problem is based on multiplicative and additive-multiplicative separation of singularities. For right-hand sides of the given class of smoothness, an optimal convergence rate is proved

Scheme of the finite element method with multiplicative separation of the singularity for a spectral boundary value problem for a degenerate differential operator

The paper deals with the numerical solution of a generalized spectral boundary value problem for an elliptic operator with degenerating coefficients. We suggest an approximate method based on the multiplicative separation of the singularity, whereby the eigenfunctions are approximated by piecewise linear functions multiplied by a weight specially chosen depending on the order of degeneration of the coefficients. For this method, we obtain error estimates justifying its optimality. © 2008 MAIK Nauka

Schemes of the finite element method with separation of singularity for a two-point boundary-value problem of the 4th order with degenerate coefficients

In this paper we construct a high accuracy variant of the finite element method for an ordinary differential equation of the fourth order whose coefficients are degenerate on the boundary. The proposed technique is based on the multiplicative and additive-multiplicative separation of singularity. We prove that the convergence rate of the proposed technique is optimal in a given class of smoothness of right-hand sides. © Allerton Press, Inc., 2011

A Hardy inequality with a point-singular weight inside a domain

Sobolev spaces with weights taking infinite values at some interior points of a two-dimensional domain are considered. For functions from these spaces, a Hardy inequality is obtained. Embedding theorems for weighted Lebesgue spaces and equivalent renorming theorems are proved. © 2013 Pleiades Publishing, Ltd

Sharp estimates for the polynomial approximation in weighted Sobolev spaces

© 2015, Pleiades Publishing, Ltd. We obtain sharp estimates for the accuracy of the best approximation of functions by algebraic polynomials on an interval, the half-line, and the entire line in weighted Sobolev spaces with Jacobi, Laguerre, and Hermite weights, respectively. We show that the orthogonal polynomials associated with these weights form orthogonal bases in the respective weighted Sobolev spaces. We obtain sharp estimates of Markov–Bernstein type

Production of Marker-Free Apple Plants Expressing the Supersweet Protein Gene Driven by Plant Promoter

The presence of antibiotic resistance and other marker genes in genetically modified plants causes concern in society because of perceived risks for the environment and human health. The creation of transgenic plants that do not contain foreign genetic material, especially that of bacterial and viral origin, largely alleviates the tension and makes the plants potentially more attractive for consumers. To produce marker-free transgenic apple plants, we used the pMF1 vector, which combines Zygosaccharomyces rouxii recombinaseR and a CodA-nptII bifunctional selectable gene. The thaumatin II gene from the tropical plant Thaumatococcus daniellii, which is under the control of the plant E8 gene (a predominantly fruit-specific promoter) and rbsS3A terminator, was taken as the gene of interest for modification of the fruit taste and enhancing its sweetness. Exploitation of this gene in our laboratory has allowed enhancing the sweetness, as well as improving the taste characteristics, of fruits and vegetables of plants such as strawberry, carrot, tomato and pear. We have obtained three independent transgenic apple lines that have been analyzed by PCR and Southern blot analyses for the presence of T-DNA sequences. Two of them contained a partial sequence of the T-DNA. With one line containing the full insert we then used a delayed strategy for the selection of marker-free plants. After induction of recombinase activity in leaf explants on selective media with 5-fluorocytosine (5-FC) we obtained more than 30 sublines, most of which lost their resistance to kanamycin. Most of the apple sublines showed the expression of the supersweet protein gene in a wide range of levels as detected by RNA accumulation. The plants from the group with the highest transcript level were propagated and grafted onto dwarf rootstocks for early fruit production for future estimates of protein levels and organoleptic analyses. Thus, we developed a protocol that allowed the production of marker-free apple plants expressing the supersweet protein