In this paper we analyse the Kaczmarz projection algorithm with Remotest set and Random control of projection indices and provide a suficient condition such that each projection index appears infinitely many times during the iterations.
Recent developments in the field of image reconstruction have given rise to the use of projective iterative methods, such as Kaczmarz and Jacobi, when solving inconsistent linear least squares problems. In this paper we try to generalize previous results concerning extended block versions of these two algorithms. We replace the inverse operator with the Moore-Penrose pseudoinverse and try to prove convergence under weaker assumptions. In order to accomplish this task, we show that these algorithms are special cases of a general iterative process for which convergence is already established.
In a nanobiotechnology world with many applications in biomedicine, a novel combination of inorganic-organic materials is needed to prove a novel functionality. Natural compounds from bee pollen extract coated on magnetite nanoparticles could open up a new way in apitherapy field. Iron oxide nanoparticles have proved special requirements for biological applications like superparamagnetic properties, high biocompatibility and nontoxic material. Magnetite nanoparticles functionalized with natural bioactive substances extracted from bee pollen have been characterised and investigated for antimicrobial activity. Previous findings demonstrate that magnetite nanoparticles (MNPs) and pollen ethanolic extracts (PEE) exhibited antimicrobial activity against a large antimicrobial spectrum, including Grampositive, Gram-negative and antifungal microorganisms.
This study aims to characterize the corrosion behavior of steel by static immersion tests in biodiesel obtained from three different types of vegetable oils (sunflower oil, rapeseed oil and corn oil) at room temperature for 49 days. At the end of the test, corrosion behavior was investigated by weight loss measurements and changes in physical and chemical properties of biodiesel. Biodiesel samples were analyzed to investigate density, dynamic viscosity, acidity index, refractive index and saponification index. Results showed that under the experimental conditions, steel was more susceptible to corrosion in biodiesel from corn oil as compared to biodiesel from sunflower oil and rapeseed oil.
Huge amounts of used lubricating oils from automotive sources are disposed of as a harmful waste into the environment. For this reason, means to recover and reuse these wastes need to be found. Problems arising from acid treatment include environmental problems associated with the disposal of acid sludge and spent earth, low product yield (45-65%) and incomplete removal of metals. The processes of re-refining of used lubricating oils depend greatly on the nature of the oil base stock and on the nature and amount of contaminants in the lubricant resulting from operations. The study was carried out on a sample of 15W40 type used oil collected from one automobile. The re-refining process of used oil consists of dehydration, solvent extraction, solvent stripping and vacuum distillation. This study aims to investigate a process of solvent extraction of an alcohol-ketone mixture as a pre-treatment step followed by vacuum distillation at 5 mmHg. The primary step was conducted before the solvent extraction that involves dehydration to remove the water and fuel contaminants from the used oil by vacuum distillation. The solvent extraction and vacuum distillation steps were used to remove higher molecular weight contaminants. The investigated solvent to oil ratios were 2, 3, 4, 5 and 6. The solvent composition is 25% 2-propanol, 50% 1- butanol and 25% butanone or methyl ethyl ketone (MEK). The percentage of oil recovery for the solvent to oil ratio of 6:1 is further improved, but for the ratio values higher than 6:1, operation was considered economically not feasible. Finally, the re-refined oil properties were compared with the commercial virgin lubricating oil properties.
The concept of generalized exponential trichotomy for linear time-varying systems is investigated in relationship with the classical notion of uniform exponential trichotomy. Some key properties of generalized exponential trichotomy are explored through supplementary projections. These results are also extended to the case of projection sequences, while certain applications for adjoint systems are suggested.
In an earlier paper [J. of Appl. Math. and Informatics, 29(3-4)(2011), 697-712] we proposed a general projection-type algorithm with corrections and proved its convergence under a set of special assumptions. In this paper we prove convergence of this algorithm under a much weaker set of assumptions. This new framework gives us the possibility to obtain as a particular case of our method the two-step algorithm analysed in [B I T, 38(2)(1998), 275-282].
The present paper shows the advantages in using this prototype of tension and compression test machine proposed by the authors. The mechanical behaviour of different materials and components can be easily obtained by using this type of device. The equipment enables a simplified change between the types of testing performed. The operators can quickly and easily change elements and accessories used in testing. This equipment is the suitable choice for evaluating different types of friction dampers.
In this report we show that the iterated regularization scheme due to Riley and Golub, sometimes also called the iterated Tikhonov regularization, can be generalized to damped least squares problems where the weights matrix D is not necessarily the identity but a general symmetric and positive definite matrix. We show that the iterative scheme approaches the same point as the unique solutions of the regularized problem, when the regularization parameter goes to 0. Furthermore this point can be characterized as the solution of a weighted minimum Euclidean norm problem. Finally several numerical experiments were performed in the field of rigid multibody dynamics supporting the theoretical claims.