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Algebra of Countably Functions and Theorems of Completeness
Issue:
Volume 8, Issue 1, February 2019
Pages:
1-9
Received:
15 February 2019
Accepted:
18 March 2019
Published:
9 April 2019
Abstract: An algebraic approach to the theory of countable functions is given. Compositions (superpositions) of functions are used instead of recursions. Arithmetic and analytic algorithms are defined. All closed sets are founded. Mathematically precise definitions of logic algorithms with quantifiers of existence and universality are given. Logic algorithm for fast-growing function is built as example. Classification of functions is given. There are non-computable functions. These functions are fictitious (useless) and their set is continual. The set of computable functions is countable. Incompleteness of disjunction and negation, conjunction and negation, of Pierce, Sheffer and diagonal Webb functions is proved. The completeness of the set of one-place functions and any all-valued essential function (Slupecki theorem) is proved for computable functions. Existence of generators of all computable functions is proved too.
Abstract: An algebraic approach to the theory of countable functions is given. Compositions (superpositions) of functions are used instead of recursions. Arithmetic and analytic algorithms are defined. All closed sets are founded. Mathematically precise definitions of logic algorithms with quantifiers of existence and universality are given. Logic algorithm ...
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Comparison Between the Production of Hibiscus in Kordofan States Using Matlab
Abdel Radi Abdel Rahman Abdel Gadi,
Ragaa Mohammed Haj Ebrahim,
Nedal Hassan Elbadowi Eljaneid
Issue:
Volume 8, Issue 1, February 2019
Pages:
10-17
Received:
23 January 2019
Accepted:
4 March 2019
Published:
18 April 2019
Abstract: Hibiscus (Karkadi) contains plant acids such as malic, chemical and that indicates its high importance for humans. Many industries depend on Karkadi in most of the areas in Sudan due to its economic and medical benefits . In this study the statistical data of Hibiscus will be analyzed using Matlab. This study aims to compare and analyze the data of Hibiscus production in North Korodfan state, west Korodfan state and south Korodfan state in period 2006 to 2016 and if planted areas and harvested areas affect production or not. The applying mathematical method was followed using Matlab and found it is more accurate because the data is converges with the analysis, and arrived to relation between production, planted areas and harvested areas . All this data passed through code that designed by Matlab program for analysis and counting data in the analysis obtained bar graph for all data for each state. And counting production for select state of hibiscus production (high, low and non-exist). A new algorithm is designed based on the type of data and compared results with each year in one state, Matlab functions results showed excellent efficiency with 95% accuracy for analysis, counting and classification.
Abstract: Hibiscus (Karkadi) contains plant acids such as malic, chemical and that indicates its high importance for humans. Many industries depend on Karkadi in most of the areas in Sudan due to its economic and medical benefits . In this study the statistical data of Hibiscus will be analyzed using Matlab. This study aims to compare and analyze the data of...
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Boundedness for Sublinear Operators with Rough Kernels on Weighted Grand Morrey Spaces
Issue:
Volume 8, Issue 1, February 2019
Pages:
18-29
Received:
23 March 2019
Accepted:
22 April 2019
Published:
9 May 2019
Abstract: In this paper, we study the boundedness of some sublinear operators with rough kernels, satisfied by most of the operators in classical harmonic analysis, on the generalized weighted grand Morrey spaces. More specifically, we show that the sublinear operators with rough kernels are bounded on these spaces under the conditions that the operators and the kernel functions satisfy some size conditions, and the operators are bounded on Lebesgue spaces. This is done by exploiting the well-known boundedness of sublinear operators with rough kernels on Lebesgue spaces, a more explicit decomposition of the generalized weighted grand Morrey spaces and the good properties of the weight functions and the kernel functions. Through combining some properties of Ap weight with the relevant lemmas of operators with rough kernel, we obtain the boundedness for sublinear operators with rough kernels on weighted grand morrey spaces. Furthermore, using the equivalent norm and the properties of BMO functions, an application of the boundedness of the sublinear operators with rough kernels to the corresponding commutators formed by certain operators and BMO functions are also considered. And the boundedness of commutator is obtained by the lemma of function BMO.
Abstract: In this paper, we study the boundedness of some sublinear operators with rough kernels, satisfied by most of the operators in classical harmonic analysis, on the generalized weighted grand Morrey spaces. More specifically, we show that the sublinear operators with rough kernels are bounded on these spaces under the conditions that the operators and...
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