We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 defined in the articles are: 2;4: and 6. For those whose difference is equal to 6, we showed their ...We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 defined in the articles are: 2;4: and 6. For those whose difference is equal to 6, we showed their origin then we classified them into two categories according to their classes, we showed in which context two prime numbers which differ from 6 are called sexy and in what context they are said real sexy prime. For those whose difference is equal to 4, we showed their origin then we showed that two prime numbers which differ from 4, that is to say two cousin prime numbers, are successive. We made an observation on the supposed prime numbers then we established two pairs of equations from this observation and deduced the origin of the Mersenne number and that of the Fermat number.展开更多
The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the ...The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed.展开更多
In this paper we give an algorithm for polignac numbers. That algorithm is also the base of the proof of the de Polignac's conjecture. The examples of the application present algorithm for twin, cousin, and sexy p...In this paper we give an algorithm for polignac numbers. That algorithm is also the base of the proof of the de Polignac's conjecture. The examples of the application present algorithm for twin, cousin, and sexy primes are included.展开更多
The mammalian protein kinase C-interacting cousin of thioredoxin(PICOT;also termed glutaredoxin 3)is a multi-domain monothiol glutaredoxin that is involved in a wide variety of signaling pathways and biological proces...The mammalian protein kinase C-interacting cousin of thioredoxin(PICOT;also termed glutaredoxin 3)is a multi-domain monothiol glutaredoxin that is involved in a wide variety of signaling pathways and biological processes.PICOT is required for normal and transformed cell growth and is critical for embryonic development.Recent studies in T lymphocytes demonstrated that PICOT can translocate to the nucleus and interact with embryonic ectoderm development,a polycomb group protein and a core component of the polycomb repressive complex 2,which contributes to the maintenance of transcriptional repression and chromatin remodeling.Furthermore,PICOT was found to interact with chromatin-bound embryonic ectoderm development and alter the extent of histone 3 lysine 27 trimethylation at the promoter region of selected polycomb repressive complex 2 target genes.PICOT knockdown in Jurkat T cells led to increased histone 3 lysine 27 trimethylation at the promoter region of CCND2,a cell cycle-regulating gene which encodes the cyclin D2 protein.As a result,the expression levels of CCND2 mRNA and protein levels were reduced,concomitantly with inhibition of the cell growth rate.Analysis of multiple data sets from the Cancer Genome Atlas revealed that a high expression of PICOT correlated with a low expression of CCND2 in a large number of human cancers.In addition,this parameter correlated with poor patient survival,suggesting that the ratio between PICOT/CCND2 mRNA levels might serve as a predictor of patient survival in selected types of human cancer.展开更多
文摘We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 defined in the articles are: 2;4: and 6. For those whose difference is equal to 6, we showed their origin then we classified them into two categories according to their classes, we showed in which context two prime numbers which differ from 6 are called sexy and in what context they are said real sexy prime. For those whose difference is equal to 4, we showed their origin then we showed that two prime numbers which differ from 4, that is to say two cousin prime numbers, are successive. We made an observation on the supposed prime numbers then we established two pairs of equations from this observation and deduced the origin of the Mersenne number and that of the Fermat number.
基金Supported by the National Natural Science Foundation of China(11171298)the Zhejiang Natural Science Foundation of China(Y6110425)
文摘The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed.
文摘In this paper we give an algorithm for polignac numbers. That algorithm is also the base of the proof of the de Polignac's conjecture. The examples of the application present algorithm for twin, cousin, and sexy primes are included.
基金Supported by the USA-Israel Binational Science Foundation,No.2013034the Israel Science Foundation administered by the Israel Academy of Science,No.1235/17+1 种基金the Jacki and Bruce Barron Cancer Research Scholars’ProgramCity of Hope and the Israel Cancer Research Fund,No.87735611.
文摘The mammalian protein kinase C-interacting cousin of thioredoxin(PICOT;also termed glutaredoxin 3)is a multi-domain monothiol glutaredoxin that is involved in a wide variety of signaling pathways and biological processes.PICOT is required for normal and transformed cell growth and is critical for embryonic development.Recent studies in T lymphocytes demonstrated that PICOT can translocate to the nucleus and interact with embryonic ectoderm development,a polycomb group protein and a core component of the polycomb repressive complex 2,which contributes to the maintenance of transcriptional repression and chromatin remodeling.Furthermore,PICOT was found to interact with chromatin-bound embryonic ectoderm development and alter the extent of histone 3 lysine 27 trimethylation at the promoter region of selected polycomb repressive complex 2 target genes.PICOT knockdown in Jurkat T cells led to increased histone 3 lysine 27 trimethylation at the promoter region of CCND2,a cell cycle-regulating gene which encodes the cyclin D2 protein.As a result,the expression levels of CCND2 mRNA and protein levels were reduced,concomitantly with inhibition of the cell growth rate.Analysis of multiple data sets from the Cancer Genome Atlas revealed that a high expression of PICOT correlated with a low expression of CCND2 in a large number of human cancers.In addition,this parameter correlated with poor patient survival,suggesting that the ratio between PICOT/CCND2 mRNA levels might serve as a predictor of patient survival in selected types of human cancer.
