The aim of this study is to prove Goldbach's famous Conjectures known as strong and weak conjectu... more The aim of this study is to prove Goldbach's famous Conjectures known as strong and weak conjectures. Strong Conjecture: "Every even number greater than 2 is the sum of two prime numbers". Weak Conjecture: "Every odd integer greater than 5 can be written as the sum of three prime numbers". Content: Searching prime numbers with predictive formulas is beyond the scope of this work. The program that generates and tests the prime number is a separate study, in this study the proofs of the Strong and Weak Goldbach Conjectures will take place. We only approach Gold-bach's Conjecture, where all required prior knowledge on prime numbers assumed as accepted by Goldbach's works. Therefore, we start with take a look at Goldbach's description of original problem then will try to derive a step by step proof upon that is described as in original letters. Method: Once the sub groups of the set of prime numbers were defined, theoretical framework was proved to be complete. The theoretical framework is very simple and concise, albeit the entire study is based upon that. This study is providing proof on both of conjectures. Findings and Results: In this study, an effective solution to a historical problem known in mathematics but not proven to this day is introduced; the proofs of Goldbach's Conjectures (both in Strong and Weak) are given. These proofs will open many obstacles in number theory and provide a fresh look on prime numbers and their applications. Many assumptions, conjectures in number theory will be re-evaluated. Based on this proof, another theorem on prime number is constructed with its proof. Conclusion: Many assumptions, conjectures about prime numbers will be re-evaluated under the light of given proofs. There is no reason to limit the sum in the theorem above; one can easily say that prime numbers are infinite. As a discussion, albeit there are institutionalized methods on computing prime numbers, a new way of computing bigger prime numbers can be based on this new perspective this paper has shed lights on. Proofs presented will introduce new horizons to relevant academicians on number theory. Defining this new perspective might also help one to expend this study further points related to even if there is a pattern on Prime Numbers so we can exploit that to compute bigger numbers feasibly. The prominence of major prime numbers in cryp-tology is known. Encryption will be redesigned in line with the proofs. The proof will open new horizons on prime numbers, the first one is this explained and proved new Prime Number Theorem: Aksoy Theorem.
20 patients with beta-thalassemia intermedia classified according to the results of genetic studi... more 20 patients with beta-thalassemia intermedia classified according to the results of genetic studies are presented. (1) 9 patients with beta-thalassemia intermedia homozygous for beta-thalassemia with increased Hb-A2 are reported. (2) 8 patients with beta-thalassemia intermedia, 3 homozygous for beta-thalassemia with normal levels of Hbs.A2 and F, 5 heterozygous for both this and beta-thalassemia with increased Hb-A2 are presented. (3) 2 families with beta-thalassemia intermedia heterozygous for both beta-thalassemia with increased HbA2 and 'silent" beta-thalassemia are reported. Two different varieties are presented.
The aim of this study is to prove Goldbach's famous Conjectures known as strong and weak conjectu... more The aim of this study is to prove Goldbach's famous Conjectures known as strong and weak conjectures. Strong Conjecture: "Every even number greater than 2 is the sum of two prime numbers". Weak Conjecture: "Every odd integer greater than 5 can be written as the sum of three prime numbers". Content: Searching prime numbers with predictive formulas is beyond the scope of this work. The program that generates and tests the prime number is a separate study, in this study the proofs of the Strong and Weak Goldbach Conjectures will take place. We only approach Gold-bach's Conjecture, where all required prior knowledge on prime numbers assumed as accepted by Goldbach's works. Therefore, we start with take a look at Goldbach's description of original problem then will try to derive a step by step proof upon that is described as in original letters. Method: Once the sub groups of the set of prime numbers were defined, theoretical framework was proved to be complete. The theoretical framework is very simple and concise, albeit the entire study is based upon that. This study is providing proof on both of conjectures. Findings and Results: In this study, an effective solution to a historical problem known in mathematics but not proven to this day is introduced; the proofs of Goldbach's Conjectures (both in Strong and Weak) are given. These proofs will open many obstacles in number theory and provide a fresh look on prime numbers and their applications. Many assumptions, conjectures in number theory will be re-evaluated. Based on this proof, another theorem on prime number is constructed with its proof. Conclusion: Many assumptions, conjectures about prime numbers will be re-evaluated under the light of given proofs. There is no reason to limit the sum in the theorem above; one can easily say that prime numbers are infinite. As a discussion, albeit there are institutionalized methods on computing prime numbers, a new way of computing bigger prime numbers can be based on this new perspective this paper has shed lights on. Proofs presented will introduce new horizons to relevant academicians on number theory. Defining this new perspective might also help one to expend this study further points related to even if there is a pattern on Prime Numbers so we can exploit that to compute bigger numbers feasibly. The prominence of major prime numbers in cryp-tology is known. Encryption will be redesigned in line with the proofs. The proof will open new horizons on prime numbers, the first one is this explained and proved new Prime Number Theorem: Aksoy Theorem.
20 patients with beta-thalassemia intermedia classified according to the results of genetic studi... more 20 patients with beta-thalassemia intermedia classified according to the results of genetic studies are presented. (1) 9 patients with beta-thalassemia intermedia homozygous for beta-thalassemia with increased Hb-A2 are reported. (2) 8 patients with beta-thalassemia intermedia, 3 homozygous for beta-thalassemia with normal levels of Hbs.A2 and F, 5 heterozygous for both this and beta-thalassemia with increased Hb-A2 are presented. (3) 2 families with beta-thalassemia intermedia heterozygous for both beta-thalassemia with increased HbA2 and 'silent" beta-thalassemia are reported. Two different varieties are presented.
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Papers by Muzaffer Aksoy