The paper establishes explicit representations of the errors and residuals of approximate
solutions of triangular linear systems by Jordan elimination and of general linear algebraic
systems by Gauss-Jordan elimination as functions of the data perturbations and the rounding
errors in arithmetic floating-point operations. From these representations strict optimal
componentwise error and residual bounds are derived. Further, stability estimates for the
solutions are discussed. The error bounds for the solutions of triangular linear systems are
compared to the optimal error bounds for the solutions by back substitution and by Gaussian
elimination with back substitution, respectively. The results confirm in a very detailed form
that the errors of the solutions by Jordan elimination and by Gauss-Jordan elimination cannot
be essentially greater than the possible maximal errors of the solutions by back substitution
and by Gaussian elimination, respectively. Finally, the theoretical results are illustrated by
two numerical examples.
In general, the importance of cluster analysis is that one can evaluate elements by clustering multiple homogeneous data; the main objective of this analysis is to collect the elements of a single, homogeneous group into different divisions, depending on many variables. This method of analysis is used to reduce data, generate hypotheses and test them, as well as predict and match models. The research aims to evaluate the fuzzy cluster analysis, which is a special case of cluster analysis, as well as to compare the two methods—classical and fuzzy cluster analysis. The research topic has been allocated to the government and private hospitals. The sampling for this research was comprised of 288 patients being treated in 10 hospitals. As t
... Show MoreMany isolated rural communities are located in regions where there is an abundant and reliable supply of solar energy, but where the distance to the nearest power station is many tens or even hundreds of kilometre. It is therefore mainly in these areas that rural electrification is now being provided by PV generators. since Stand-Alone PV generator can offer the most cost-effective and reliable option for providing power needed in remote places. Accordingly these isolated rural canters are fitted with PV for lighting, a refrigerator, a television and socket to supply kitchen appliances
This paper examines a new nonlinear system of multiple integro-differential equations containing symmetric matrices with impulsive actions. The numerical-analytic method of ordinary differential equations and Banach fixed point theorem are used to study the existence, uniqueness and stability of periodic solutions of impulsive integro-differential equations with piecewise continuous functions. This study is based on the Hölder condition in which the ordering , and are real numbers between 0 and 1.
A true random TTL pulse generator was implemented and investigated for quantum key distribution systems. The random TTL signals are generated by low cost components available in the local markets. The TTL signals are obtained by using true random binary sequences based on registering photon arrival time difference registered in coincidence windows between two single – photon detectors. The true random TTL pulse generator performance was tested by using time to digital converters which gives accurate readings for photon arrival time. The proposed true random pulse TTL generator can be used in any quantum -key distribution system for random operation of the transmitters for these systems
Nanopesticides are novel plant protection products offering numerous benefits. Because nanoparticles behave differently from dissolved chemicals, the environmental risks of these materials could differ from conventional pesticides. We used soil–earthworm systems to compare the fate and uptake of analytical‐grade bifenthrin to that of bifenthrin in traditional and nanoencapsulated formulations. Apparent sorption coefficients for bifenthrin were up to 3.8 times lower in the nano treatments than in the non‐nano treatments, whereas dissipation half‐lives of the nano treatments were up to 2 times longer. Earthworms in the nano treatments accumulated approximately 50% more b
Anchusa strigosa - prickly alkanet from Boraginaceae grows in roadsides, and fields of a broad range of habitats from mediterranean woodlands, to steppe vegetation, to true desert. It is commonly known as" him him" or "lisan al thawr". Anchusa can withstand hard weather conditions and hence is widely cultivated. The color of its flowers can range from pure white to deep cobalt blue. Various parts of A. strigosa are used in traditional medicine for treating several diseases or symptoms, such as abdominal pain, bronchitis, cough, and diarrhea. The goal of this study was to examine the cytotoxic effect of the crude extract of A. strigosa roots and leaves and their fractions against various tumor cell lines: adenoc
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