A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm de...A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures.展开更多
Malaria is still a major public health concern in Cameroon as more than 20 million people are at risk of the disease. Despite the government’s effort to scale up the distribution of long lasting insecticide-treated b...Malaria is still a major public health concern in Cameroon as more than 20 million people are at risk of the disease. Despite the government’s effort to scale up the distribution of long lasting insecticide-treated bed nets (LLINs), full ownership and optimal use is still limited. In 2021, over a million LLINs were made available for distribution in the South West Region. However, the current situation of malaria has not yet been ascertained following the 2021 mass distribution campaign (MDC). Therefore, the aim of this study was to determine LLIN ownership, coverage, usage and the prevalence of malaria following the 2021 MDC in the Tiko Health District (THD), South West Region of Cameroon. A cross-sectional study was carried from May 1 to 27, 2022 in which a multi-stage sampling technique was used to enroll eligible participants. Data were collected from household heads using questionnaires and capillary blood samples collected from consented household members were used to test for malaria. Data were analyzed using SPSS version 25 at 0.05 significance level. From the 150 households surveyed, 96 (64.0%) owned a mosquito net before the recent MDC. There was an overall significant increase (p p = 0.644) in LLINs ownership between areas where door-to-door (79.5%) and fixed “Hit and Run” (75.8%) strategies were used in the distribution of LLINs in THD. The prevalence of malaria was 10.2%. The regular use of LLINs was significantly associated (p = 0.007) with low malaria prevalence. The 2021 MDC had an impact on malaria prevalence in those who properly used them.展开更多
Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number great...Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A<sup>2</sup> + B<sup>2</sup> + C<sup>2</sup> + D<sup>2</sup> + so on =A<sub>n</sub><sup>2 </sup>where all are natural numbers.展开更多
Denote by a non-trivial primitive solution of Fermat’s equation (p prime).We introduce, for the first time, what we call Fermat principal divisors of the triple defined as follows. , and . We show that it is possible...Denote by a non-trivial primitive solution of Fermat’s equation (p prime).We introduce, for the first time, what we call Fermat principal divisors of the triple defined as follows. , and . We show that it is possible to express a,b and c as function of the Fermat principal divisors. Denote by the set of possible non-trivial solutions of the Diophantine equation . And, let<sub></sub><sub></sub> (p prime). We prove that, in the first case of Fermat’s theorem, one has . In the second case of Fermat’s theorem, we show that , ,. Furthermore, we have implemented a python program to calculate the Fermat divisors of Pythagoreans triples. The results of this program, confirm the model used. We now have an effective tool to directly process Diophantine equations and that of Fermat. .展开更多
This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its general...This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. <em>Note that the second solution is very short and does not exceed one and a half pages</em>. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. <em>To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.</em>展开更多
This study is a comparative research based on corpus. This article compares China's English learners with English na?tive speakers about the use of "at last" and "in the end" from three aspects...This study is a comparative research based on corpus. This article compares China's English learners with English na?tive speakers about the use of "at last" and "in the end" from three aspects: frequency of use, location, semantic prosody. The study shows that the use of the two words are greatly different between China's English learners and English native speakers. In addition, this study discusses about causes of obvious differences and teaching enlightenments.展开更多
The Last of the Mohicans is one of the five frontier novels written by famous American novelist James Fenimore Cooper in the early 19thcentury.Although it has been criticized for its narrative flaws,its length and for...The Last of the Mohicans is one of the five frontier novels written by famous American novelist James Fenimore Cooper in the early 19thcentury.Although it has been criticized for its narrative flaws,its length and formal prose style,it was one of the most popular in its time and is of a high literary value nowadays.With the coming of the white European colonialists,the Indians underwent various changes.Some Indians submitted themselves to the white while some Indians rebelled against the invaders and sought their revenge.With a post-colonial approach,the changes of the Indians will be better understood,and people nowadays will also have a better understanding of the Indian history and culture in early American history.展开更多
The goal of this research study is to describe academic issues which have been debated in the field of Chinese geosciences for a century. In 1922, Jonquei S. Lee(Li Siguang) discovered Quaternary glacial relics at Tai...The goal of this research study is to describe academic issues which have been debated in the field of Chinese geosciences for a century. In 1922, Jonquei S. Lee(Li Siguang) discovered Quaternary glacial relics at Taihang Mountainin eastern China. In 1947, he published his research findings in the magazine Mount Lushan in Glacial Age. The research results had established three Ice Ages: Poyang(Gonzi), Dagu(Minde), and Lushan(Lisi). However, at that time, no Wurm glacial relics of the last Ice Age had been found in Lushan Mountain. Since then, the research team represented by Shi Yafeng, who is considered to be "the father of glaciers in China", questioned Jonquei S. Lee’s research results and concluded that "Professor Jonquei S. Lee’s Quaternary glacier research in Lushan Mountain having misread the debris flow". In 2005, the "middle-low mountains" in eastern China were finally defined as follows: "We clearly and unambiguously believe that there were no glacial activities in the middle-low mountainous areas of eastern China(east of 102° to 104°E;below 3,000 and 2,500 m) during the Quaternary Period". Currently, the long-standing academic debate appears to have come to a conclusion. As of 2015, the author and others began to investigate and study the Quaternary glacial relics in Mengshan Mountain(1,156 m above sea level), Shandong Province, one of the "middle-low mountains" of eastern China. The relics have been observed to posses the systematic features of glacial erosion, trough and valley striations, and moraine deposits. The applied dating method shave confirmed that there were not only glacial relics of the last Ice Age(Wurm), but also Holocene glacial relics in the Mengshan Mountain area. Therefore, in order to further establish the corresponding relationship between the glacier, loess, stream sediment series, and MIS in the Mengshan Mountain area, a large number of chronological studies have been carried out regarding the various types of sediments in the area, and 24 dating datahave been obtained using OSL, CRN, and 14 Cmethods.On this basis, the corresponding relationship between the sedimentary sequences and the MIS was established for the first time in eastern China, which in dicates the environmental changes which had occurred in eastern China since 80 ka. These discoveries s and chronological study results confirm the existence of the Last Ice Age, as well as Holocene glacial relics at Mengshan Mountain, there by confirming that Quaternary glaciation had occurred in the middle-low mountain areas of eastern China.展开更多
Reconstruction of the desert paleoclimate is important to understand the mechanisms that triggered and/or enhanced climate change.Through optically stimulated luminescence(OSL)dating,grain size,magnetic susceptibility...Reconstruction of the desert paleoclimate is important to understand the mechanisms that triggered and/or enhanced climate change.Through optically stimulated luminescence(OSL)dating,grain size,magnetic susceptibility,X-ray powder diffraction(XRD)and geochemical indicators,we provide a welldated record of a sedimentary outcrop on the southeast margin of the Bardain Jaran Desert,Northwest China,during the last glacial period.Four Qz-OSL ages are obtained,41.0±3.4 ka,54.7±4.4 ka,59.5±5.0 ka and 66.8±5.8 ka,corresponding to the depths of 35 cm,70 cm,150 cm and 200 cm respectively.Indicators like grain size,clay content,magnetic susceptibility,XRD and geochemical index(e.g.Sr,Ba,Sr/Ca)jointly indicate abrupt climate changes at the depth of 35 cm(age,ca.41.0 ka)and200 cm(age,ca.67 ka).Namely,the 280 cm sedimentary outcrop perfectly records a warm wet climate stage,corresponding to the late Marine Isotope Stages(MIS)4 to the early MIS 3.Besides,there is a trend of grain size increase after around 40ka BP,which is most likely a signal of wind strength change.Our research supports that enhancing Siberian High pressure system during the late MIS 3played a key role in NW East Asia climate evolution.展开更多
This paper will try to apply Andre Lefevere's rewriting theory to study subtitling.Through the analysis of The Last Emperor and its two Chinese translations,we will explore how ideology manipulates subtitle transl...This paper will try to apply Andre Lefevere's rewriting theory to study subtitling.Through the analysis of The Last Emperor and its two Chinese translations,we will explore how ideology manipulates subtitle translation.展开更多
Research on climate changes between the last interglacial period and Holocene renders a speculation on the tendency of present climate. Fully understanding the nature of the changes will play a significant role in a b...Research on climate changes between the last interglacial period and Holocene renders a speculation on the tendency of present climate. Fully understanding the nature of the changes will play a significant role in a better understanding of global climate change. This work discussed the climate change of the last interglacial period and Holocene in Beijing area to discover the mechanism of local palaeo-climate change. The palaeo-vegetation of the last interglacial period in Xishan Mountain of Beijing was reconstructed by pollen analysis and thermo-luminescence dating to represent the change of palaeo-climate and palaeo-environment. Palaeo-vegetation indicators demonstrated that the climate change of the last interglacial period included 6 stages and was homologous to that reflected by the records from deep sea depositions and polar ice cores, respectively corresponding to Marine Isotope Stage (MIS) 5e, 5d, 5c, 5b, 5a and the interim from MIS5 to MIS4 from the early to the late. Millennial climate abrupt events occurred in MIS 5e, which had an agreement with the records of GRIP. In addition, a climate warming event appeared in the interim from MIS5 to MIS4 and it also was found in other regions of the world. Compared with the vegetation and environment indicators of Holocene in Beijing area, it was found that the vegetation, climate and environment of the last glacial period were better than those of Holocene. The climate abrupt events not only appeared in the last interglacial period and MIS 5e, but also occurred in Holocene, whose mechanism and pattern were analogical. After analyzing the records of millennial climate abrupt change events from this work, Ice Cores and others, it was concluded that climate was instability in the interglacial period.展开更多
Although extensive lakes and eolian sands within andsurrounding the Hunshandake Sandy Land （HSL） aresensitive to paleoenvironmental variations in arid andsemi-arid eastern Inner Mongolia （e.g., Yang et al., 2013）,...Although extensive lakes and eolian sands within andsurrounding the Hunshandake Sandy Land （HSL） aresensitive to paleoenvironmental variations in arid andsemi-arid eastern Inner Mongolia （e.g., Yang et al., 2013）,these records are commonly confined to the lastdeglaciation, hampering a complete understanding ofclimatic fluctuations on glacial-interglacial time scales.展开更多
Long lasting phosphorescence (LLP) was observed in Eu2+, Ce3+ co-doped strontium borate glasses prepared under the reducing atmosphere due to the emission of both Eu2+ and Ce3+. The methods of photoluminescence, therm...Long lasting phosphorescence (LLP) was observed in Eu2+, Ce3+ co-doped strontium borate glasses prepared under the reducing atmosphere due to the emission of both Eu2+ and Ce3+. The methods of photoluminescence, thermoluminescence and phosphorescence were used to study the samples, and possible mechanism was suggested. The co-doping of Ce3+ ions poisoned the phosphorescence emission of Eu2+ because of the competition to obtain the trapped electron. The phosphorescence of Ce3+ in the sample decays more quickly than that of Eu2+, which is suggested for the reason that the emission energy of Ce3+ is higher or the distance between Ce3+ and electron traps of the glasses is longer.展开更多
文摘A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures.
文摘Malaria is still a major public health concern in Cameroon as more than 20 million people are at risk of the disease. Despite the government’s effort to scale up the distribution of long lasting insecticide-treated bed nets (LLINs), full ownership and optimal use is still limited. In 2021, over a million LLINs were made available for distribution in the South West Region. However, the current situation of malaria has not yet been ascertained following the 2021 mass distribution campaign (MDC). Therefore, the aim of this study was to determine LLIN ownership, coverage, usage and the prevalence of malaria following the 2021 MDC in the Tiko Health District (THD), South West Region of Cameroon. A cross-sectional study was carried from May 1 to 27, 2022 in which a multi-stage sampling technique was used to enroll eligible participants. Data were collected from household heads using questionnaires and capillary blood samples collected from consented household members were used to test for malaria. Data were analyzed using SPSS version 25 at 0.05 significance level. From the 150 households surveyed, 96 (64.0%) owned a mosquito net before the recent MDC. There was an overall significant increase (p p = 0.644) in LLINs ownership between areas where door-to-door (79.5%) and fixed “Hit and Run” (75.8%) strategies were used in the distribution of LLINs in THD. The prevalence of malaria was 10.2%. The regular use of LLINs was significantly associated (p = 0.007) with low malaria prevalence. The 2021 MDC had an impact on malaria prevalence in those who properly used them.
文摘Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A<sup>2</sup> + B<sup>2</sup> + C<sup>2</sup> + D<sup>2</sup> + so on =A<sub>n</sub><sup>2 </sup>where all are natural numbers.
文摘Denote by a non-trivial primitive solution of Fermat’s equation (p prime).We introduce, for the first time, what we call Fermat principal divisors of the triple defined as follows. , and . We show that it is possible to express a,b and c as function of the Fermat principal divisors. Denote by the set of possible non-trivial solutions of the Diophantine equation . And, let<sub></sub><sub></sub> (p prime). We prove that, in the first case of Fermat’s theorem, one has . In the second case of Fermat’s theorem, we show that , ,. Furthermore, we have implemented a python program to calculate the Fermat divisors of Pythagoreans triples. The results of this program, confirm the model used. We now have an effective tool to directly process Diophantine equations and that of Fermat. .
文摘This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. <em>Note that the second solution is very short and does not exceed one and a half pages</em>. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. <em>To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.</em>
文摘This study is a comparative research based on corpus. This article compares China's English learners with English na?tive speakers about the use of "at last" and "in the end" from three aspects: frequency of use, location, semantic prosody. The study shows that the use of the two words are greatly different between China's English learners and English native speakers. In addition, this study discusses about causes of obvious differences and teaching enlightenments.
文摘The Last of the Mohicans is one of the five frontier novels written by famous American novelist James Fenimore Cooper in the early 19thcentury.Although it has been criticized for its narrative flaws,its length and formal prose style,it was one of the most popular in its time and is of a high literary value nowadays.With the coming of the white European colonialists,the Indians underwent various changes.Some Indians submitted themselves to the white while some Indians rebelled against the invaders and sought their revenge.With a post-colonial approach,the changes of the Indians will be better understood,and people nowadays will also have a better understanding of the Indian history and culture in early American history.
文摘The goal of this research study is to describe academic issues which have been debated in the field of Chinese geosciences for a century. In 1922, Jonquei S. Lee(Li Siguang) discovered Quaternary glacial relics at Taihang Mountainin eastern China. In 1947, he published his research findings in the magazine Mount Lushan in Glacial Age. The research results had established three Ice Ages: Poyang(Gonzi), Dagu(Minde), and Lushan(Lisi). However, at that time, no Wurm glacial relics of the last Ice Age had been found in Lushan Mountain. Since then, the research team represented by Shi Yafeng, who is considered to be "the father of glaciers in China", questioned Jonquei S. Lee’s research results and concluded that "Professor Jonquei S. Lee’s Quaternary glacier research in Lushan Mountain having misread the debris flow". In 2005, the "middle-low mountains" in eastern China were finally defined as follows: "We clearly and unambiguously believe that there were no glacial activities in the middle-low mountainous areas of eastern China(east of 102° to 104°E;below 3,000 and 2,500 m) during the Quaternary Period". Currently, the long-standing academic debate appears to have come to a conclusion. As of 2015, the author and others began to investigate and study the Quaternary glacial relics in Mengshan Mountain(1,156 m above sea level), Shandong Province, one of the "middle-low mountains" of eastern China. The relics have been observed to posses the systematic features of glacial erosion, trough and valley striations, and moraine deposits. The applied dating method shave confirmed that there were not only glacial relics of the last Ice Age(Wurm), but also Holocene glacial relics in the Mengshan Mountain area. Therefore, in order to further establish the corresponding relationship between the glacier, loess, stream sediment series, and MIS in the Mengshan Mountain area, a large number of chronological studies have been carried out regarding the various types of sediments in the area, and 24 dating datahave been obtained using OSL, CRN, and 14 Cmethods.On this basis, the corresponding relationship between the sedimentary sequences and the MIS was established for the first time in eastern China, which in dicates the environmental changes which had occurred in eastern China since 80 ka. These discoveries s and chronological study results confirm the existence of the Last Ice Age, as well as Holocene glacial relics at Mengshan Mountain, there by confirming that Quaternary glaciation had occurred in the middle-low mountain areas of eastern China.
基金financial support from China University of Geosciences, Beijingsupported by the Project of National Nature Science Foundation of China (Grant No. 41572094)+2 种基金the Ph. D Research Start-up Fund of Fuyang Normal University (Grant No. 2016kyqd0004)the Scientific Research Project of Fuyang Normal University (Grant No. 2018FSKJ08ZD)the Key Project of Youth Science Funds of Fuyang Normal University (Gran No. rcxm201907)
文摘Reconstruction of the desert paleoclimate is important to understand the mechanisms that triggered and/or enhanced climate change.Through optically stimulated luminescence(OSL)dating,grain size,magnetic susceptibility,X-ray powder diffraction(XRD)and geochemical indicators,we provide a welldated record of a sedimentary outcrop on the southeast margin of the Bardain Jaran Desert,Northwest China,during the last glacial period.Four Qz-OSL ages are obtained,41.0±3.4 ka,54.7±4.4 ka,59.5±5.0 ka and 66.8±5.8 ka,corresponding to the depths of 35 cm,70 cm,150 cm and 200 cm respectively.Indicators like grain size,clay content,magnetic susceptibility,XRD and geochemical index(e.g.Sr,Ba,Sr/Ca)jointly indicate abrupt climate changes at the depth of 35 cm(age,ca.41.0 ka)and200 cm(age,ca.67 ka).Namely,the 280 cm sedimentary outcrop perfectly records a warm wet climate stage,corresponding to the late Marine Isotope Stages(MIS)4 to the early MIS 3.Besides,there is a trend of grain size increase after around 40ka BP,which is most likely a signal of wind strength change.Our research supports that enhancing Siberian High pressure system during the late MIS 3played a key role in NW East Asia climate evolution.
文摘This paper will try to apply Andre Lefevere's rewriting theory to study subtitling.Through the analysis of The Last Emperor and its two Chinese translations,we will explore how ideology manipulates subtitle translation.
文摘Research on climate changes between the last interglacial period and Holocene renders a speculation on the tendency of present climate. Fully understanding the nature of the changes will play a significant role in a better understanding of global climate change. This work discussed the climate change of the last interglacial period and Holocene in Beijing area to discover the mechanism of local palaeo-climate change. The palaeo-vegetation of the last interglacial period in Xishan Mountain of Beijing was reconstructed by pollen analysis and thermo-luminescence dating to represent the change of palaeo-climate and palaeo-environment. Palaeo-vegetation indicators demonstrated that the climate change of the last interglacial period included 6 stages and was homologous to that reflected by the records from deep sea depositions and polar ice cores, respectively corresponding to Marine Isotope Stage (MIS) 5e, 5d, 5c, 5b, 5a and the interim from MIS5 to MIS4 from the early to the late. Millennial climate abrupt events occurred in MIS 5e, which had an agreement with the records of GRIP. In addition, a climate warming event appeared in the interim from MIS5 to MIS4 and it also was found in other regions of the world. Compared with the vegetation and environment indicators of Holocene in Beijing area, it was found that the vegetation, climate and environment of the last glacial period were better than those of Holocene. The climate abrupt events not only appeared in the last interglacial period and MIS 5e, but also occurred in Holocene, whose mechanism and pattern were analogical. After analyzing the records of millennial climate abrupt change events from this work, Ice Cores and others, it was concluded that climate was instability in the interglacial period.
基金supported by the China Geological Survey (grant no. 121201104000150009)the NSFC (grant no. 41672178)
文摘Although extensive lakes and eolian sands within andsurrounding the Hunshandake Sandy Land （HSL） aresensitive to paleoenvironmental variations in arid andsemi-arid eastern Inner Mongolia （e.g., Yang et al., 2013）,these records are commonly confined to the lastdeglaciation, hampering a complete understanding ofclimatic fluctuations on glacial-interglacial time scales.
基金Project supported by Technological Key Project of Basic Research of Jilin Province (20020601)
文摘Long lasting phosphorescence (LLP) was observed in Eu2+, Ce3+ co-doped strontium borate glasses prepared under the reducing atmosphere due to the emission of both Eu2+ and Ce3+. The methods of photoluminescence, thermoluminescence and phosphorescence were used to study the samples, and possible mechanism was suggested. The co-doping of Ce3+ ions poisoned the phosphorescence emission of Eu2+ because of the competition to obtain the trapped electron. The phosphorescence of Ce3+ in the sample decays more quickly than that of Eu2+, which is suggested for the reason that the emission energy of Ce3+ is higher or the distance between Ce3+ and electron traps of the glasses is longer.
