使用通过型固相萃取小柱PRi ME HLB处理水产品样品,建立了一种水产品中17种磺胺类药物的简单、快速的筛选分析方法。水产品样品经80%乙腈水溶液(含0.2%甲酸)提取,过PRi ME HLB固相萃取柱净化,浓缩后经C_(18)色谱柱梯度洗脱分离,超高效...使用通过型固相萃取小柱PRi ME HLB处理水产品样品,建立了一种水产品中17种磺胺类药物的简单、快速的筛选分析方法。水产品样品经80%乙腈水溶液(含0.2%甲酸)提取,过PRi ME HLB固相萃取柱净化,浓缩后经C_(18)色谱柱梯度洗脱分离,超高效液相色谱-三重四极杆质谱系统进行定量分析。结果表明,17种磺胺类药物在1.0~50.0 ng·mL^(-1)线性关系良好,相关系数R^(2)>0.99;该方法检出限为2μg·kg^(-1);添加浓度为10μg·kg^(-1)时方法回收率在71.3%~118.4%,RSD值均小于20%。展开更多
The advent of gene editing represents one of the most transformative breakthroughs in life science,making genome manipulation more accessible than ever before.While traditional CRISPR/Cas-based gene editing,which invo...The advent of gene editing represents one of the most transformative breakthroughs in life science,making genome manipulation more accessible than ever before.While traditional CRISPR/Cas-based gene editing,which involves double-strand DNA breaks(DSBs),excels at gene disruption,it is less effective for accurate gene modification.The limitation arises because DSBs are primarily repaired via non-homologous end joining(NHEJ),which tends to introduce indels at the break site.While homology directed repair(HDR)can achieve precise editing when a donor DNA template is provided,the reliance on DSBs often results in unintended genome damage.HDR is restricted to specific cell cycle phases,limiting its application.Currently,gene editing has evolved to unprecedented levels of precision without relying on DSB and HDR.The development of innovative systems,such as base editing,prime editing,and CRISPR-associated transposases(CASTs),now allow for precise editing ranging from single nucleotides to large DNA fragments.Base editors(BEs)enable the direct conversion of one nucleotide to another,and prime editors(PEs)further expand gene editing capabilities by allowing for the insertion,deletion,or alteration of small DNA fragments.The CAST system,a recent innovation,allows for the precise insertion of large DNA fragments at specific genomic locations.In recent years,the optimization of these precise gene editing tools has led to significant improvements in editing efficiency,specificity,and versatility,with advancements such as the creation of base editors for nucleotide transversions,enhanced prime editing systems for more efficient and precise modifications,and refined CAST systems for targeted large DNA insertions,expanding the range of applications for these tools.Concurrently,these advances are complemented by significant improvements in in vivo delivery methods,which have paved the way for therapeutic application of precise gene editing tools.Effective delivery systems are critical for the success of gene therapies,and recent developments in both viral and non-viral vectors have improved the efficiency and safety of gene editing.For instance,adeno-associated viruses(AAVs)are widely used due to their high transfection efficiency and low immunogenicity,though challenges such as limited cargo capacity and potential for immune responses remain.Non-viral delivery systems,including lipid nanoparticles(LNPs),offer an alternative with lower immunogenicity and higher payload capacity,although their transfection efficiency can be lower.The therapeutic potential of these precise gene editing technologies is vast,particularly in treating genetic disorders.Preclinical studies have demonstrated the effectiveness of base editing in correcting genetic mutations responsible for diseases such as cardiomyopathy,liver disease,and hereditary hearing loss.These technologies promise to treat symptoms and potentially cure the underlying genetic causes of these conditions.Meanwhile,challenges remain,such as optimizing the safety and specificity of gene editing tools,improving delivery systems,and overcoming off-target effects,all of which are critical for their successful application in clinical settings.In summary,the continuous evolution of precise gene editing technologies,combined with advancements in delivery systems,is driving the field toward new therapeutic applications that can potentially transform the treatment of genetic disorders by targeting their root causes.展开更多
Seed priming is a pre-germinated technique that can enhance seed germination percentage,faster and synchro-nized germination,better seedling growth,and yield under stress conditions.To ascertain the most effective see...Seed priming is a pre-germinated technique that can enhance seed germination percentage,faster and synchro-nized germination,better seedling growth,and yield under stress conditions.To ascertain the most effective seed priming method that would ensure the potential yield of wheat in Bangladesh,two experiments were carried out from December 2021 to March 2022 at the Department of Agronomy,Bangladesh Agricultural University.Two wheat varieties namely BARI Gom-28 and BWMRI Gom-1 were subjected to a range of priming chemicals in both lab and pot tests.These compounds included the following:control(no priming),hydropriming(distilled water),10000 ppm KNO_(3),15000 ppm KNO_(3),40000 ppm Mannitol,60000 ppm Mannitol,10000 ppm NaCl,20000 ppm NaCl,100 ppm PEG,150 ppm PEG,500 ppm NaOCl,1000 ppm NaOCl,10000 ppm CaCl_(2),20000 ppm CaCl_(2),10000 ppm KCl and 20000 ppm KCl.A complete randomized design(CRD)with three repli-cations was used to set up the experiments.The results showed that BARI Gom-28 and BWMRI Gom-1 responded best to KCl priming in terms of rapid seed germination and strong seedling development.On the other hand,the best priming agents for plant growth and productivity turned out to be CaCl_(2) and KCL.The results of this study support the possibility of using seed priming as a technique to improve wheat plant development and output by raising seed emergence and survival rates.展开更多
Mesenchymal stromal/stem cells(MSCs)have garnered significant attention in the field of regenerative medicine due to their remarkable therapeutic potential.MSCs play a pivotal role in maintaining tissue homeostasis an...Mesenchymal stromal/stem cells(MSCs)have garnered significant attention in the field of regenerative medicine due to their remarkable therapeutic potential.MSCs play a pivotal role in maintaining tissue homeostasis and possess diverse functions in tissue repair and recovery in various organs.These cells are charac-terized by easy accessibility,few ethical concerns,and adaptability to in vitro cultures,making them a valuable resource for cell therapy in several clinical conditions.Over the years,it has been shown that the true therapeutic power of MSCs lies not in cell engraftment and replacement but in their ability to produce critical paracrine factors,including cytokines,growth factors,and exosomes(EXOs),which modulate the tissue microenvironment and facilitate repair and regeneration processes.Consequently,MSC-derived products,such as condi-tioned media and EXOs,are now being extensively evaluated for their potential medical applications,offering advantages over the long-term use of whole MSCs.However,the efficacy of MSC-based treatments varies in clinical trials due to both intrinsic differences resulting from the choice of diverse cell sources and non-standardized production methods.To address these concerns and to enhance MSC therapeutic potential,researchers have explored many priming strategies,including exposure to inflammatory molecules,hypoxic conditions,and three-dimensional culture techniques.These approaches have optimized MSC secretion of functional factors,empowering them with enhanced immunomodulatory,angiogenic,and regenerative properties tailored to specific medical conditions.In fact,various priming strategies show promise in the treatment of numerous diseases,from immune-related disorders to acute injuries and cancer.Currently,in order to exploit the full therapeutic potential of MSC therapy,the most important challenge is to optimize the modulation of MSCs to obtain adapted cell therapy for specific clinical disorders.In other words,to unlock the complete potential of MSCs in regenerative medicine,it is crucial to identify the most suitable tissue source and develop in vitro manipulation protocols specific to the type of disease being treated.展开更多
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
Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equa...Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.展开更多
Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , ...Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.展开更多
The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it ...The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it E<sub>sp</sub>. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted E<sub>np</sub>. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted E<sub>p</sub>. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.展开更多
Salt stress is one of the most harmful environmental stresses in recent times and represents a significant threat to food security. Soil salinization is caused by spontaneous natural processes of mineral dissolution a...Salt stress is one of the most harmful environmental stresses in recent times and represents a significant threat to food security. Soil salinization is caused by spontaneous natural processes of mineral dissolution and human activities such as inappropriate irrigation practices. Natural geological progressions like weathering of rocks, arid climate, and higher evaporation, as well as anthropogenic activities, including the use of brackish water for irrigation, and poor tillage operations, are the foremost causes of soil salinization. Typical characteristics of saline soils are salt stress, high pH, and lack of organic carbon, as well as low availability of nutrients. Disruption of precipitation patterns as well as high average annual temperatures due to climate change additionally negatively affects the process of soil salinization. Productivity and ability to support crop growth are reduced on saline soil. Salinity-induced stress reduces plant growth by modulating the antioxidative system and nutrient orchestration. The aim of this work is to show that the mentioned problems can be alleviated in several ways such as the addition of biochar, exogenous application of several elicitors, seed priming, etc. Research has shown that the addition of biochar can significantly improve the recovery of saline soil. The addition of biochar has no significant effect on soil pH, while the cation exchange capacity of the soil increased by 17%, and the electrical conductivity of the saturated paste extract decreased by 13.2% (depends on the initial salinity and the type of biochar raw material). Moreover, biochar enriched with silicon increases the resistance of bananas to salt stress. In addition, exogenous application of several elicitors helps plants to alleviate stress by inducing stress-related physicochemical and molecular changes (selenium, sulfur, silicon, salicylic acid). Finally, seed priming showed positive effects on metabolomics, proteomics and growth of plants subjected to abiotic stress. Priming usually involves immersing the seed in a solution for a period of time to induce physiological and metabolic progression prior to germination.展开更多
Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers...Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers out of a period 2×3×5×7=210 to be the roots of all primes as well as composites without factors of 2, 3, 5, and 7. Each prime, twin primes, or composite without factors of 2, 3, 5, and 7 is an offspring of the 48 integers uniquely allocated on the PTP. Three major establishments made in the article are the Formula of Primes, the Periodic Table of Primes, and the Counting Functions of Primes and Twin Primes.展开更多
The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit form...The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.展开更多
An elementary formula to know the number of primes in the interval (x, 2x) close to the exact figure for a fixed x is given here. A new elementary equation is derived (a relation between prime numbers and composite nu...An elementary formula to know the number of primes in the interval (x, 2x) close to the exact figure for a fixed x is given here. A new elementary equation is derived (a relation between prime numbers and composite numbers distributed in the interval [1, 2x]). An elementary method to know the number of primes in a given magnitude is suitably placed in the form of a general formula, and we have proved it. The general formula is applied to the terms of the equation, and a tactical simplification of the terms gives rise to an expression whose verification envisages scope for its further studies.展开更多
The China Fashion Week A/W 2024,hosted by the China Fashion Designers Association,took place in Beijing from March 23 to 31.Themed“Fu”(Empower),this season’s fashion week continued to focus on Chinese aesthetics,in...The China Fashion Week A/W 2024,hosted by the China Fashion Designers Association,took place in Beijing from March 23 to 31.Themed“Fu”(Empower),this season’s fashion week continued to focus on Chinese aesthetics,innovation in intangible cultural heritage,fusion of Chinese trends.展开更多
The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infini...The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.展开更多
文摘使用通过型固相萃取小柱PRi ME HLB处理水产品样品,建立了一种水产品中17种磺胺类药物的简单、快速的筛选分析方法。水产品样品经80%乙腈水溶液(含0.2%甲酸)提取,过PRi ME HLB固相萃取柱净化,浓缩后经C_(18)色谱柱梯度洗脱分离,超高效液相色谱-三重四极杆质谱系统进行定量分析。结果表明,17种磺胺类药物在1.0~50.0 ng·mL^(-1)线性关系良好,相关系数R^(2)>0.99;该方法检出限为2μg·kg^(-1);添加浓度为10μg·kg^(-1)时方法回收率在71.3%~118.4%,RSD值均小于20%。
文摘The advent of gene editing represents one of the most transformative breakthroughs in life science,making genome manipulation more accessible than ever before.While traditional CRISPR/Cas-based gene editing,which involves double-strand DNA breaks(DSBs),excels at gene disruption,it is less effective for accurate gene modification.The limitation arises because DSBs are primarily repaired via non-homologous end joining(NHEJ),which tends to introduce indels at the break site.While homology directed repair(HDR)can achieve precise editing when a donor DNA template is provided,the reliance on DSBs often results in unintended genome damage.HDR is restricted to specific cell cycle phases,limiting its application.Currently,gene editing has evolved to unprecedented levels of precision without relying on DSB and HDR.The development of innovative systems,such as base editing,prime editing,and CRISPR-associated transposases(CASTs),now allow for precise editing ranging from single nucleotides to large DNA fragments.Base editors(BEs)enable the direct conversion of one nucleotide to another,and prime editors(PEs)further expand gene editing capabilities by allowing for the insertion,deletion,or alteration of small DNA fragments.The CAST system,a recent innovation,allows for the precise insertion of large DNA fragments at specific genomic locations.In recent years,the optimization of these precise gene editing tools has led to significant improvements in editing efficiency,specificity,and versatility,with advancements such as the creation of base editors for nucleotide transversions,enhanced prime editing systems for more efficient and precise modifications,and refined CAST systems for targeted large DNA insertions,expanding the range of applications for these tools.Concurrently,these advances are complemented by significant improvements in in vivo delivery methods,which have paved the way for therapeutic application of precise gene editing tools.Effective delivery systems are critical for the success of gene therapies,and recent developments in both viral and non-viral vectors have improved the efficiency and safety of gene editing.For instance,adeno-associated viruses(AAVs)are widely used due to their high transfection efficiency and low immunogenicity,though challenges such as limited cargo capacity and potential for immune responses remain.Non-viral delivery systems,including lipid nanoparticles(LNPs),offer an alternative with lower immunogenicity and higher payload capacity,although their transfection efficiency can be lower.The therapeutic potential of these precise gene editing technologies is vast,particularly in treating genetic disorders.Preclinical studies have demonstrated the effectiveness of base editing in correcting genetic mutations responsible for diseases such as cardiomyopathy,liver disease,and hereditary hearing loss.These technologies promise to treat symptoms and potentially cure the underlying genetic causes of these conditions.Meanwhile,challenges remain,such as optimizing the safety and specificity of gene editing tools,improving delivery systems,and overcoming off-target effects,all of which are critical for their successful application in clinical settings.In summary,the continuous evolution of precise gene editing technologies,combined with advancements in delivery systems,is driving the field toward new therapeutic applications that can potentially transform the treatment of genetic disorders by targeting their root causes.
基金The authors are very much grateful to Bangladesh Agricultural University Research System(BAURES)Bangladesh Agricultural University,Mymensingh-2202,Bangladesh for the financial support through the research project entitled“Induction of Heat and Drought Tolerance in Wheat through Seed Priming”(Project No.2021/35/BAU)to carry out the research work.
文摘Seed priming is a pre-germinated technique that can enhance seed germination percentage,faster and synchro-nized germination,better seedling growth,and yield under stress conditions.To ascertain the most effective seed priming method that would ensure the potential yield of wheat in Bangladesh,two experiments were carried out from December 2021 to March 2022 at the Department of Agronomy,Bangladesh Agricultural University.Two wheat varieties namely BARI Gom-28 and BWMRI Gom-1 were subjected to a range of priming chemicals in both lab and pot tests.These compounds included the following:control(no priming),hydropriming(distilled water),10000 ppm KNO_(3),15000 ppm KNO_(3),40000 ppm Mannitol,60000 ppm Mannitol,10000 ppm NaCl,20000 ppm NaCl,100 ppm PEG,150 ppm PEG,500 ppm NaOCl,1000 ppm NaOCl,10000 ppm CaCl_(2),20000 ppm CaCl_(2),10000 ppm KCl and 20000 ppm KCl.A complete randomized design(CRD)with three repli-cations was used to set up the experiments.The results showed that BARI Gom-28 and BWMRI Gom-1 responded best to KCl priming in terms of rapid seed germination and strong seedling development.On the other hand,the best priming agents for plant growth and productivity turned out to be CaCl_(2) and KCL.The results of this study support the possibility of using seed priming as a technique to improve wheat plant development and output by raising seed emergence and survival rates.
文摘Mesenchymal stromal/stem cells(MSCs)have garnered significant attention in the field of regenerative medicine due to their remarkable therapeutic potential.MSCs play a pivotal role in maintaining tissue homeostasis and possess diverse functions in tissue repair and recovery in various organs.These cells are charac-terized by easy accessibility,few ethical concerns,and adaptability to in vitro cultures,making them a valuable resource for cell therapy in several clinical conditions.Over the years,it has been shown that the true therapeutic power of MSCs lies not in cell engraftment and replacement but in their ability to produce critical paracrine factors,including cytokines,growth factors,and exosomes(EXOs),which modulate the tissue microenvironment and facilitate repair and regeneration processes.Consequently,MSC-derived products,such as condi-tioned media and EXOs,are now being extensively evaluated for their potential medical applications,offering advantages over the long-term use of whole MSCs.However,the efficacy of MSC-based treatments varies in clinical trials due to both intrinsic differences resulting from the choice of diverse cell sources and non-standardized production methods.To address these concerns and to enhance MSC therapeutic potential,researchers have explored many priming strategies,including exposure to inflammatory molecules,hypoxic conditions,and three-dimensional culture techniques.These approaches have optimized MSC secretion of functional factors,empowering them with enhanced immunomodulatory,angiogenic,and regenerative properties tailored to specific medical conditions.In fact,various priming strategies show promise in the treatment of numerous diseases,from immune-related disorders to acute injuries and cancer.Currently,in order to exploit the full therapeutic potential of MSC therapy,the most important challenge is to optimize the modulation of MSCs to obtain adapted cell therapy for specific clinical disorders.In other words,to unlock the complete potential of MSCs in regenerative medicine,it is crucial to identify the most suitable tissue source and develop in vitro manipulation protocols specific to the type of disease being treated.
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.
文摘Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.
文摘Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.
文摘The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it E<sub>sp</sub>. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted E<sub>np</sub>. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted E<sub>p</sub>. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.
文摘Salt stress is one of the most harmful environmental stresses in recent times and represents a significant threat to food security. Soil salinization is caused by spontaneous natural processes of mineral dissolution and human activities such as inappropriate irrigation practices. Natural geological progressions like weathering of rocks, arid climate, and higher evaporation, as well as anthropogenic activities, including the use of brackish water for irrigation, and poor tillage operations, are the foremost causes of soil salinization. Typical characteristics of saline soils are salt stress, high pH, and lack of organic carbon, as well as low availability of nutrients. Disruption of precipitation patterns as well as high average annual temperatures due to climate change additionally negatively affects the process of soil salinization. Productivity and ability to support crop growth are reduced on saline soil. Salinity-induced stress reduces plant growth by modulating the antioxidative system and nutrient orchestration. The aim of this work is to show that the mentioned problems can be alleviated in several ways such as the addition of biochar, exogenous application of several elicitors, seed priming, etc. Research has shown that the addition of biochar can significantly improve the recovery of saline soil. The addition of biochar has no significant effect on soil pH, while the cation exchange capacity of the soil increased by 17%, and the electrical conductivity of the saturated paste extract decreased by 13.2% (depends on the initial salinity and the type of biochar raw material). Moreover, biochar enriched with silicon increases the resistance of bananas to salt stress. In addition, exogenous application of several elicitors helps plants to alleviate stress by inducing stress-related physicochemical and molecular changes (selenium, sulfur, silicon, salicylic acid). Finally, seed priming showed positive effects on metabolomics, proteomics and growth of plants subjected to abiotic stress. Priming usually involves immersing the seed in a solution for a period of time to induce physiological and metabolic progression prior to germination.
文摘Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers out of a period 2×3×5×7=210 to be the roots of all primes as well as composites without factors of 2, 3, 5, and 7. Each prime, twin primes, or composite without factors of 2, 3, 5, and 7 is an offspring of the 48 integers uniquely allocated on the PTP. Three major establishments made in the article are the Formula of Primes, the Periodic Table of Primes, and the Counting Functions of Primes and Twin Primes.
文摘The Riemann hypothesis is intimately connected to the counting functions for the primes. In particular, Perron’s explicit formula relates the prime counting function to fixed points of iterations of the explicit formula with particular relations involving the trivial and non-trivial roots of the Riemann Zeta function and the Primes. The aim of the paper is to demonstrate this relation at the fixed points of iterations of explicit formula, defined by functions of the form limT∈Ν→∞fT(zw)=zw,where, zwis a real number.
文摘An elementary formula to know the number of primes in the interval (x, 2x) close to the exact figure for a fixed x is given here. A new elementary equation is derived (a relation between prime numbers and composite numbers distributed in the interval [1, 2x]). An elementary method to know the number of primes in a given magnitude is suitably placed in the form of a general formula, and we have proved it. The general formula is applied to the terms of the equation, and a tactical simplification of the terms gives rise to an expression whose verification envisages scope for its further studies.
文摘The China Fashion Week A/W 2024,hosted by the China Fashion Designers Association,took place in Beijing from March 23 to 31.Themed“Fu”(Empower),this season’s fashion week continued to focus on Chinese aesthetics,innovation in intangible cultural heritage,fusion of Chinese trends.
文摘The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.