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A New Proof for Congruent Number’s Problem via Pythagorician Divisors

Advances in Pure Mathematics 2024年第4期14卷 283-302页

作者： léopold Dèkpassi Keuméan François Emmanuel.tanoé UFR Mathematics and Computer Science F&#233lix Houphou&#235t Boigny University Abidjan Cote d&#8217Ivoire

Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ ∗ , called congruent numbers, characterized by the fact that there exists a right-angled triangle with rational sides: ( A α ) 2 + ( B β ) 2 = ( C γ ) 2 , such that its area Δ= 1 2 A α B β =n;or in an equivalent way, to that of the existence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equivalent to the existence of: ( a,b,c )∈ ℕ 3∗ prime in pairs, and f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic progression of reason n;And this problem is also equivalent to that of the existence of a non-trivial primitive integer right-angled triangle: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and this last equation can be written as follows, when using Pythagorician divisors: (1) Δ= 1 2 ab= 2 S−1 d e ¯ ( d+ 2 S−1 e ¯ )( d+ 2 S e ¯ )=n f 2;Where ( d, e ¯ )∈ ( 2ℕ+1 ) 2 such that gcd( d, e ¯ )=1 and S∈ ℕ ∗ , where 2 S−1 , d, e ¯ , d+ 2 S−1 e ¯ , d+ 2 S e ¯ , are pairwise prime quantities (these parameters are coming from Pythagorician divisors). When n=1 , it is the case of the famous impossible problem of the integer right-angled triangle area to be a square, solved by Fermat at his time, by his famous method of infinite descent. We propose in this article a new direct proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an particular induction method of resolution of Equation (1) (note that this method is efficient too for general case of prime numbers n=p≡a ( ( mod8 ) , gcd( a,8 )=1 ). To prove it, we use a classical proof by induction on k , that shows the non-solvability property of any of the following systems ( t=0 , corresponding to case n=1 (resp. t=1 , corresponding to case n=2 )): ( Ξ t,k ){ X 2 + 2 t ( 2 k Y ) 2 = Z 2 X 2 + 2

关键词： Prime Numbers-Diophantine Equations of Degree 2 & 4 Factorization Greater Common Divisor Pythagoras Equation Pythagorician Triplets Congruent Numbers Inductive Demonstration Method Infinite Descent BSD Conjecture

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Effect of Pre-Sowing Treatments on Mamalis (Pittosporum pentandrum Blanco Merr.) Seeds Germination under Nursery Condition

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Open Journal of Ecology 2023年第2期13卷 106-118页

作者： raffy l. tano College of Agriculture Forestry and Environmental Sciences Aklan State University Banga Philippines

Seeds were subjected to three different pre-sowing seed treatments: immersion in lukewarm water for 2 hours, immersion in concentrated sulfuric acid (H2SO4) for 5 minutes, hilar removal, and a control in which the seeds were sown without being treated. The experiment was laid out in the Completely Randomized Design (CRD) with four replicates and 60 seeds per treatment. Seeds were sown in an improvised Seedbox in October 2019. Germination was monitored daily for one month. The results showed that Mamalis seeds treated with lukewarm water have the earliest germination of twelve days, with a germination percentage of 66.67%. The germination rate of another treatment ranges from 0 - 44 percent, compared to 45 percent for the control treatment. It seems prudent to conclude that to enhance the vegetative propagation methods is to soaking in warm water at 37.5˚C for 2 hours could provide the best growth.

关键词： Pittosporum pentandrum Seed Germination Pre-Treatments Sulfuric Acid Seed Dormancy

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Quantifying Arborescent Flora Diversity in a Secondary Forest Ecosystem: A Comprehensive Assessment in Nambalan, Mayantoc, Tarlac, Philippines

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Open Journal of Ecology 2023年第6期13卷 387-408页

作者： Baby Jean l. Herbulario raffy l. tano Mileatte P. Omaney College of Agriculture and Forestry Tarlac Agricultural University Camiling Philippines College of Agriculture Forestry and Environmental Sciences Aklan State University Banga Philippines

Forest plays a crucial role in providing essential ecosystem services, including water supply, climate regulation, and biodiversity conservation. This study aimed to assess the current state of the forest in Barangay Nambalan, Mayantoc, Tarlac. The specific objectives were to identify tree species in the area and determine the tree diversity index, with a focus on endemism and conservation status. Two transect lines, each spanning one kilometer, were established and a total of 10 sampling quadrats were surveyed. Ecological parameters (relative frequency, relative density, relative dominance, and importance value index) and diversity indices (Shannon-Weiner index, Simpson’s index) were computed using the Paleontological Statistic Software Package for Educational Analysis (PAST 4.03). A comprehensive inventory revealed a total of 756 individuals representing 52 species, 46 genera, and 25 families. Among the recorded species, 10 (17.2%) were endemic and 11 (21.6%) were classified as threatened. The Fabaceae (20.8%), Moraceae (14.6%), and Euphorbiaceae (8.3%) were identified as the most abundant families. The computed diversity indices indicated that Barangay Nambalan retains a diverse forest cover;however, species composition was found to be relatively low. Based on the finding, this study recommends the strict enforcement of protective measures and legislation to mitigate further degradation of the remaining forest in Barangay Nambalan.

关键词： Forest Diversity Tree Species Endemism Conservation Status Transect Survey Diversity Indices

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Assessment of Physical Characteristics of Bugang River Watershed in Pandan, Antique, Philippines

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Open Journal of Ecology 2022年第6期12卷 360-376页

作者： Melba l. Raga-as Roberto l. Saladar Jerson C. Calaguio raffy l. tano Glaiza Mae C. Unlayao College of Agriculture Forestry and Environmental Science Aklan State University (Banga Campus) Aklan Philippines

Sustainable and appropriate watershed management strategies require the determination of biophysical information which includes the floral characteristics of the watershed. This study was conducted to characterize the floral composition of the Bugang River watershed. Data gathering was done by conducting an inventory for trees, palms, and bamboos with Quadrant Sampling using a stratified random sampling method in the forested area of the watershed with 50 m × 20 m sampling plots. Floral species were identified and classified through local experts, published books, journals, the internet, and available references. A total of 60 species belonging to 31 families and 52 genera were found using this method. Gogo (Entada phaseoloides) had the highest number of species with 222 or 14% of the total species. Trees with dbh 10 cm and above have a total estimated volume of 102.31 m3. The average diameter and average height of species decrease as the elevation increases. The result showed that the Bugang River watershed has a diverse floral composition, with vertical stratification and a dense canopy. The advocacy and awareness campaign should be done and strengthen the protection and conservation efforts of concerned agencies for the sustainability of the watershed.

关键词： Barangay Pandan Floral Characteristics Watershed Stratification Antique Philippines

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Aboveground Blue Carbon Stock Assessment of Bakhawan Eco-Park Mangrove Plantation in New Buswang, Kalibo, Aklan, the Philippines

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Open Journal of Ecology 2022年第12期12卷 773-787页

作者： Melba l. Raga-as raffy l. tano Floramae Q. Polaron Roberto l. Saladar Nenia N. Bohulano Jea-Ann A. Morales Eric R. Gregorio Jose Adonis N. Nacionales Forestry Department College of Agriculture Forestry and Environmental Sciences Aklan State University Banga The Philippines Agriculture Department College of Agriculture Forestry and Environmental Sciences Aklan State University Banga The Philippines Forestry Department College of Agriculture Forestry and Food Science University of Antique Hamtic The Philippines

The purpose of this study was to determine the aboveground biomass density, blue carbon stock, and monetary value of the mangroves at Bakhawan Eco-Park Mangrove Plantation in New Buswang, Kalibo, Aklan. There were 21, 45 × 45-meter sampled plots established, equivalent to 5% sampling intensity of the plantation’s total area. The number of sample plots was distributed in proportion to the area of the plantation in the specific year it was established. The quadrant and random sampling methods were used. All trees in a quadrant were identified, and the biomass density was calculated using the wood density of various mangrove species. Carbon stock was calculated by multiplying the biomass density by 0.46 or 0.5. The monetary value of C was calculated using the benefits transfer method at $5/ton. The results showed that the plantation established in 1990 had the highest biomass density (Mg/ha) and carbon stock (Mg/ha) with 132 Mg/ha and 66.02 Mg/ha, while the plantation established in 2015 had the lowest biomass density and carbon stock (Mg/ha) with 69.98 Mg/ha and 34.99 Mg/ha. Overall, the estimated total monetary value of Bakhawan Eco-Park of 250 hectares mangrove plantation in New Buswang, Kalibo, Aklan is PhP 2994771.63.

关键词： Biomass Density Monetary Value Mangrove Species GSP Device KASAMA

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Outlining a stepwise,multi-parameter debris flow monitoring and warning system:an example of application in Aizi Valley,China

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Journal of Mountain Science 2016年第9期13卷 1527-1543页

作者： CHEN Ning-sheng Javed Iqbal.tano lI HU Gui-sheng WANG Feng-niang YANG Cheng-lin DING Hai-tao HE Na WANG Tao Institute of Mountain Hazards and Environment Chinese Academy of SciencesChengdu 610041China University of Chinese Academy of Sciences Beijing 100049China Department of Earth Sciences COMSATS Institute of Information TechnologyAbbottabad 22060Pakistan

In recent years, the increasing frequency of debris flow demands enhanced effectiveness and efficiency of warning systems. Effective warning systems are essential not only from an economic point of view but are also considered as a frontline approach to alleviate hazards. Currently, the key issues are the imbalance between the limited lifespan of equipment, the relatively long period between the recurrences of such hazards, and the wide range of critical rainfall that trigger these disasters. This paper attempts to provide a stepwise multi-parameter debris flow warning system after taking into account the shortcomings observed in other warning systems. The whole system is divided into five stages. Differentwarning levels can be issued based on the critical rainfall thresholds. Monitoring starts when early warning is issued and it continues with debris flow near warning, triggering warning, movement warning and hazard warning stages. For early warning, historical archives of earthquake and drought are used to choose a debris flow-susceptible site for further monitoring. Secondly, weather forecasts provide an alert of possible near warning. Hazardous precipitation, model calculation and debris flow initiation tests, pore pressure sensors and water content sensors are combined to check the critical rainfall and to publically announce a triggering warning. In the final two stages, equipment such as rainfall gauges, flow stage sensors, vibration sensors, low sound sensors and infrasound meters are used to assess movement processes and issue hazardwarnings. In addition to these warnings, communitybased knowledge and information is also obtained and discussed in detail. The proposed stepwise, multiparameter debris flow monitoring and warning system has been applied in Aizi valley China which continuously monitors the debris flow activities.

关键词：监测预警系统泥石流应用中国临界雨量运动过程压力传感器水分传感器

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Rainfall Variability and Trends in West Africa

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Atmospheric and Climate Sciences 2023年第1期13卷 72-83页

作者： Anoumou Réné tano François-Xavier Djézia Bella Bouo Justin Koffi Kouamé Yao Tchétché Sylvain Djédjé Zézé Bafétigué Ouattara Equipe de la Physique pour l’Environnement Laboratoire de Physique Fondamentale et Appliquée Université NANGUI ABROGOUA Abidjan C&#244 te d’Ivoire laboratoire de Physique Université de Man Man C&#244 te d’Ivoire

Rainfall variability associated with climate change has enormous impacts on ecosystems, agriculture and people in West Africa but few studies have been devoted to it. Monthly rainfall data from 1901 to 2013, provided by the Global Precipitation Climatology Center dataset, were analyzed using segmentation and empirical modal decomposition (EMD) methods to increase our knowledge on past and recent spatio-temporal rainfall trends and their impacts on the West African region. The results obtained showed that the peak of rainfall during the short rainy season is observed in September in Côte d’Ivoire, Ghana and liberia. The temporal variability of this rainfall is marked by several breakpoints whose durations range from 2 to 70 years. The periods of change in the rainfall regime, characterized by the appearance of breakpoints, vary from one country to another and are of unequal duration. The main breakpoint appears after 1960. Periods of relative or normal increase or decrease in precipitation are observed before and after 1960. The long-term variability of this rainfall is characterized by a decrease in the amount of rainfall over all West African countries. The results of this study can be used as a tool to help raise awareness among populations for sustainable management of water resources in response to climate change and its adverse effects.

关键词： Rainfall Variability Segmentation Method Empirical Mode Decomposition Method West Africa

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Tenomodulin蛋白对血管内皮细胞增生的抑制作用

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眼科研究 2010年第7期28卷 617-621页

作者：王蔚大岛佑介田野保雄首都医科大学附属北京朝阳医院眼科北京100020 日本大阪大学医学部眼科

目的研究tenomodulin(TeM)蛋白对血管内皮生长因子(VEGF)诱导的人视网膜血管内皮细胞(RECs)和人脐静脉内皮细胞(UVECs)增生及其对体外血管样结构形成的作用。方法将传代至3～6代的人RECs和人UVECs生长至融合时用含质量分数0.5%胎牛血清(... 详细信息

目的研究tenomodulin(TeM)蛋白对血管内皮生长因子(VEGF)诱导的人视网膜血管内皮细胞(RECs)和人脐静脉内皮细胞(UVECs)增生及其对体外血管样结构形成的作用。方法将传代至3～6代的人RECs和人UVECs生长至融合时用含质量分数0.5%胎牛血清(FBS)的培养基孵箱中培养6h,加入不同质量浓度的VEGF或VEGF+TeM混合物,继续培养12h,ElISA法检测TeM对VEGF诱导的血管内皮细胞增生的影响。将含10%FBS、1%FBSDMEM培养基的人RECs和人UVECs悬液分别接种于预先放置基质胶的24孔培养板表面,含1%FBS培养基的细胞培养板内分别加入VEGF(100μg/l)或VEGF+TeM混合物37℃继续培养6h,共焦显微镜下观察,图像处理分析软件量化分析TeM蛋白对毛细血管样结构形成的作用。结果随着VEGF质量浓度的增加,血管内皮细胞DNA合成增加,其吸光度(A)值呈明显上升曲线,而添加TeM组的A值比VEGF组降低,差异有统计学意义(P<0.01)。含10%FBS和1%FBS培养基的血管内皮细胞在基质胶表面形成毛细血管样结构,并连接成网状;在基质胶表面同时添加VEGF的血管内皮细胞,其毛细血管样结构明显增多,长度明显变长。添加TeM组的血管内皮细胞和其毛细血管样结构破坏,每个视野内血管内皮细胞毛细血管样结构显著破坏,管形细胞总长度明显变短。结论 TeM蛋白对血管内皮细胞的增生及体外血管样结构的形成有明显抑制作用。

关键词： Tenomodulin 血管内皮细胞增生新生血管血管内皮生长因子

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Protective action of a hydroalcoholic extract of a vinifera grape skin on experimental preeclampsia in rats.

Protective action of a hydroalcoholic extract of a vinifera ...

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第十五届国际药理学大会

作者： Scares de Moura Roberto Castro Resende Angela tano Tania S.Moura Anibal F.Maradei Marcio Miguel de lemos Neto State University of Rio de Janeiro State University of Rio de Janeiro State University of Rio de Janeiro State University of Rio de Janeiro State University of Rio de Janeiro State University of Rio de Janeiro

＜正＞ This study was designed to determine the protective effects of a vinifera grape skins extract （GSE. 200 mg/kg/day） in experimental preeclampsia induced by chronic inhibition of nitric oxide synthesis in pregnant rats. Blood pressure was measured with the tail cuff method on day 20 of pregnant control rats;pregnant rats treated with lNAME,l-NAME plus GSE or GSE from day 13 to day 20 of pregnancy. Glucose was infused in anesthetized pregnant rats at day 20 and blood glucose and insulin was estimated at time zero, 15, 30, 45 and 60 minutes after beginning of glucose infusion. The number of fetus alive was also estimated at day 20 of pregnancy. Increase in arterial pressure,reduction of fetus alive at the end of pregnancy and increase in insulin resistance was observed in pregnant l-NAME rats but not in pregnant l-NAME plus GSE rats or in pregnant GSE rats. The present study demonstrated a protective effect of an extract obtained from skin of a vinifera grape in experimental preeclampsia since the deleterious effect induced by l-NAME that is. increased in stillbirth,hypertension and insulin resistance were significantly reduced by oral treatment with the extract.

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鹤草酚的晶体结构和分子结构

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化学学报 1982年第3期40卷 193-200页

作者：唐有祺李根培金祥林郝润蓉北京大学物理化学研究所物质结构研究室

鹤草酚晶体属三斜晶系,空间群为PI,晶胞参数为a=9.901(3),b=11.195(4),c=11.752(4)A,α=80.74(3),α=75.66(3),γ=76.46(3)°,晶胞内分子数Z=2.用SyntexP3/R3型四圆衍射仪收集到2891个独立衍射强度.以直接法SHElXTl解出晶体结构.结构参数的修正采用了块对角矩阵最小二乘法,最后得偏离因子R=5.7％.晶胞中含有d-,l-两种对映体分子,它们彼此以I连系组成外消旋体.每分子中的两个六环分别同相邻的氧共面,其双面角为14.2°.两个六环通过碳(sp~3)桥相连,并由于形成分子内氢键O—H…O(分别为2.705A和2.745A)而限制了自由转动.

关键词：晶体结构结晶构造固体结构分子结构鹤草酚驱绦虫药晶胞参数氢原子

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