This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the incl...This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the inclusion of the zero element as the source of a strong Goldbach conjecture reformulation. A prime Boolean vector is defined, pinpointing the positions of prime numbers within the odd number sequence. The natural unit primality is discussed in this context and transformed into a source of quantum-like indetermination. This approach allows for rephrasing the strong Goldbach conjecture, framed within a Boolean scalar product between the prime Boolean vector and its reverse. Throughout the discussion, other intriguing topics emerge and are thoroughly analyzed. A final description of two empirical algorithms is provided to prove the strong Goldbach conjecture.展开更多
With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harm...With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harmonic numbers. This enables us to construct and prove identities on q-harmonic numbers. Several examples are also given.展开更多
Objective:To analyze the clinical value of non-invasive prenatal testing(NIPT)in detecting chromosomal copy number variations(CNVs)and to explore the relationship between gene expression and clinical manifestations of...Objective:To analyze the clinical value of non-invasive prenatal testing(NIPT)in detecting chromosomal copy number variations(CNVs)and to explore the relationship between gene expression and clinical manifestations of chromosomal copy number variations.Methods:3551 naturally conceived singleton pregnant women who underwent NIPT were included in this study.The NIPT revealed abnormalities other than sex chromosome abnormalities and trisomy 13,18,and 21.Pregnant women with chromosome copy number variations underwent genetic counseling and prenatal ultrasound examination.Interventional prenatal diagnosis and chromosome microarray analysis(CMA)were performed.The clinical phenotypes and pregnancy outcomes of different prenatal diagnoses were analyzed.Additionally,a follow-up was conducted by telephone to track fetal development after birth,at six months,and one year post-birth.Results:A total of 53 cases among 3551 cases showed chromosomal copy number variation.Interventional prenatal diagnosis was performed in 36 cases:27 cases were negative and 8 were consistent with the NIPT test results.This indicates that NIPT’s positive predictive value(PPV)in CNVs is 22.22%.Conclusion:NIPT has certain clinical significance in screening chromosome copy number variations and is expected to become a routine screening for chromosomal microdeletions and microduplications.However,further interventional prenatal diagnosis is still needed to identify fetal CNVs.展开更多
This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmo...This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmology. In Section 2, we have described some equations concerning cosmic evolution in a Cyclic Universe. In Section 3, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang space-time, the M-theory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In Section 4, we have described some equations concerning the generating ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective five-dimensional theory of the strongly coupled heterotic string as a gauged version of N=1five-dimensional supergravity with four-dimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In Section 5, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w>1. In Section 6, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory. In Section 7, we have described various equations concerning the p-adic minisuperspace model, zeta strings, zeta nonlocal scalar fields and p-adic and adelic quantum cosmology. In Section 8, we have shown various and interesting mathematical connections between some equations concerning the p-adic inflation, the p-adic quantum cosmology, the zeta strings and the brane collisions in string and M-theory. Furthermore, in each section, we have shown the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.展开更多
目的：研究核糖体蛋白S15a（ribosomal protein S15a RPS15a）基因在胃癌及癌旁组织中表达差异，为进一步了解胃癌发生、发展的分子机制提供帮助。方法应用荧光定量PCR等方法进一步验证该基因在胃癌及癌旁组织中的表达差异，并在多种肿...目的：研究核糖体蛋白S15a（ribosomal protein S15a RPS15a）基因在胃癌及癌旁组织中表达差异，为进一步了解胃癌发生、发展的分子机制提供帮助。方法应用荧光定量PCR等方法进一步验证该基因在胃癌及癌旁组织中的表达差异，并在多种肿瘤细胞中的表达量进行比较。结果该基因在胃癌组织中的表达量高于其对应的癌旁组织，但在多种肿瘤细胞中的表达量无显著差异。结论 RPS15a基因在胃癌中呈高表达，说明其可能与细胞恶性生物学行为相关。在多种肿瘤细胞中表达量无显著差异，推测其可能在恶性肿瘤中的高表达具有普遍性。展开更多
This article explores the optimization of heat transport in a magnetohydrodynamic nanofluid flow with mixedMarangoni convection by using the Response SurfaceMethodology.The convective flow is studied with external mag...This article explores the optimization of heat transport in a magnetohydrodynamic nanofluid flow with mixedMarangoni convection by using the Response SurfaceMethodology.The convective flow is studied with external magnetism,radiative heat flux,and buoyancy.An internal heat absorption through the permeable surface is also taken into account.The governing system includes the continuity equation,Navier-Stokes momentum equation,and the conservation of energy equations,approximated by the Prandtl boundary layer theory.The entropy generation in the thermodynamic system is evaluated.Experimental data(Corcione models)is used to model the single-phase aluminawater nanofluid.The numerical solution for the highly nonlinear differential systemis obtained via Ralston’s algorithm.It is observed that the applied magnetic field leads to a higher entropy generation which is engendered by the Lorentz force within the fluid system.The thermal radiation leads to a higher Bejan number,indicating the importance of the irreversibility of heat transport.Also,the heat absorption process via a permeable surface can be employed to regulate the thermal field.An optimizedNusselt number of 13.4 is obtained at the high levels of radiation,injection,and heat sink parameters.The modeled fluid flow scenario is often seen in drying,coating,and heat exchange processes,especially in microgravity environments.展开更多
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is determined at its birth and its remaining lifetime decreases at the un...We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is determined at its birth and its remaining lifetime decreases at the unit speed. The models, without or with immigration, are constructed as measure-valued processes by pathwise unique solutions of stochastic equations driven by time-space Poisson random measures. In the subcritical branching case, we give a sufficient condition for the ergodicity of the process with immigration. Two large number laws and a central limit theorem of the occupation times are proved.展开更多
文摘This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the inclusion of the zero element as the source of a strong Goldbach conjecture reformulation. A prime Boolean vector is defined, pinpointing the positions of prime numbers within the odd number sequence. The natural unit primality is discussed in this context and transformed into a source of quantum-like indetermination. This approach allows for rephrasing the strong Goldbach conjecture, framed within a Boolean scalar product between the prime Boolean vector and its reverse. Throughout the discussion, other intriguing topics emerge and are thoroughly analyzed. A final description of two empirical algorithms is provided to prove the strong Goldbach conjecture.
文摘With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harmonic numbers. This enables us to construct and prove identities on q-harmonic numbers. Several examples are also given.
基金Dongguan City Social Development Project(Project number:20161081101023)。
文摘Objective:To analyze the clinical value of non-invasive prenatal testing(NIPT)in detecting chromosomal copy number variations(CNVs)and to explore the relationship between gene expression and clinical manifestations of chromosomal copy number variations.Methods:3551 naturally conceived singleton pregnant women who underwent NIPT were included in this study.The NIPT revealed abnormalities other than sex chromosome abnormalities and trisomy 13,18,and 21.Pregnant women with chromosome copy number variations underwent genetic counseling and prenatal ultrasound examination.Interventional prenatal diagnosis and chromosome microarray analysis(CMA)were performed.The clinical phenotypes and pregnancy outcomes of different prenatal diagnoses were analyzed.Additionally,a follow-up was conducted by telephone to track fetal development after birth,at six months,and one year post-birth.Results:A total of 53 cases among 3551 cases showed chromosomal copy number variation.Interventional prenatal diagnosis was performed in 36 cases:27 cases were negative and 8 were consistent with the NIPT test results.This indicates that NIPT’s positive predictive value(PPV)in CNVs is 22.22%.Conclusion:NIPT has certain clinical significance in screening chromosome copy number variations and is expected to become a routine screening for chromosomal microdeletions and microduplications.However,further interventional prenatal diagnosis is still needed to identify fetal CNVs.
文摘This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmology. In Section 2, we have described some equations concerning cosmic evolution in a Cyclic Universe. In Section 3, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang space-time, the M-theory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In Section 4, we have described some equations concerning the generating ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective five-dimensional theory of the strongly coupled heterotic string as a gauged version of N=1five-dimensional supergravity with four-dimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In Section 5, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w>1. In Section 6, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory. In Section 7, we have described various equations concerning the p-adic minisuperspace model, zeta strings, zeta nonlocal scalar fields and p-adic and adelic quantum cosmology. In Section 8, we have shown various and interesting mathematical connections between some equations concerning the p-adic inflation, the p-adic quantum cosmology, the zeta strings and the brane collisions in string and M-theory. Furthermore, in each section, we have shown the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.
文摘目的：研究核糖体蛋白S15a（ribosomal protein S15a RPS15a）基因在胃癌及癌旁组织中表达差异，为进一步了解胃癌发生、发展的分子机制提供帮助。方法应用荧光定量PCR等方法进一步验证该基因在胃癌及癌旁组织中的表达差异，并在多种肿瘤细胞中的表达量进行比较。结果该基因在胃癌组织中的表达量高于其对应的癌旁组织，但在多种肿瘤细胞中的表达量无显著差异。结论 RPS15a基因在胃癌中呈高表达，说明其可能与细胞恶性生物学行为相关。在多种肿瘤细胞中表达量无显著差异，推测其可能在恶性肿瘤中的高表达具有普遍性。
文摘This article explores the optimization of heat transport in a magnetohydrodynamic nanofluid flow with mixedMarangoni convection by using the Response SurfaceMethodology.The convective flow is studied with external magnetism,radiative heat flux,and buoyancy.An internal heat absorption through the permeable surface is also taken into account.The governing system includes the continuity equation,Navier-Stokes momentum equation,and the conservation of energy equations,approximated by the Prandtl boundary layer theory.The entropy generation in the thermodynamic system is evaluated.Experimental data(Corcione models)is used to model the single-phase aluminawater nanofluid.The numerical solution for the highly nonlinear differential systemis obtained via Ralston’s algorithm.It is observed that the applied magnetic field leads to a higher entropy generation which is engendered by the Lorentz force within the fluid system.The thermal radiation leads to a higher Bejan number,indicating the importance of the irreversibility of heat transport.Also,the heat absorption process via a permeable surface can be employed to regulate the thermal field.An optimizedNusselt number of 13.4 is obtained at the high levels of radiation,injection,and heat sink parameters.The modeled fluid flow scenario is often seen in drying,coating,and heat exchange processes,especially in microgravity environments.
基金supported by the National Key R&D Program of China(2020YFA0712901).
文摘We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is determined at its birth and its remaining lifetime decreases at the unit speed. The models, without or with immigration, are constructed as measure-valued processes by pathwise unique solutions of stochastic equations driven by time-space Poisson random measures. In the subcritical branching case, we give a sufficient condition for the ergodicity of the process with immigration. Two large number laws and a central limit theorem of the occupation times are proved.
