Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision mod...Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx<sub>1</sub>, and slow-jet, vx<sub>2</sub>. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.展开更多
This article introduces a new class of ideals, namely, the sπr ideals. It is shown that every regular square matrix over sπr ideals of a ring admits a diagonal reduction.
Ideal point method is one of the methods to solve multi-objective problem. It is applied to forest harvest regu-lation, and showed very good results by analyzing changes of quantitative indexes of forest resource stru...Ideal point method is one of the methods to solve multi-objective problem. It is applied to forest harvest regu-lation, and showed very good results by analyzing changes of quantitative indexes of forest resource structure before andafter the regulation. This method can be applied as one of the mathematical tools in forest harvest regulation.展开更多
Nearly half of the world’s population comprise youths. However, addressing their Sexual and Reproductive Health (SRH) remains a challenge. Globally countries are mandated to continually provide Youth Friendly Sexual ...Nearly half of the world’s population comprise youths. However, addressing their Sexual and Reproductive Health (SRH) remains a challenge. Globally countries are mandated to continually provide Youth Friendly Sexual and Reproductive Health services (YFSRHs) to the youth. The objective of this study was to assess and describe youth’s perspectives on a sustainable model for the provision of YFSRHs in Kenya. Data was collected among 400 youths aged 18 - 24 years in Embu and Kirinyaga counties, Kenya. A structured questionnaire was utilized as the data collection tool. Collected data was analyzed using SAS statistical software version 9.4. Statistical threshold of P ≤ 0.05 was used. Overall the mean age of the study participants was ±standard deviation (SD) 21.2 ± 1.86 years. Majority of the participants’ perspective on the health care system sustainability was that the waiting time at the facility should be less than an hour, accessible geographically (less than a kilometre), affordable (≤20 Ksh.), and convenient working hours (weekday and weekends ratio 1:1). Advocacy was on health care provider’s attributes of politeness, welcoming, confidential and non-judgmental. The most preferred locations for the youth friendly centres by the participants were community and school based locations. Similarly, parental and community support was reported to highly contribute to sustained utilization and provision of the YFSRHs (P < 0.001). Unlike popular belief, 99.8% did not see the need for recreational facilities at the youth centres to ensure sustainability of the model. To ensure a sustainable model for the provision of YFSRHs, there is need for a multi-sectoral and stakeholder involvement that is;youth, health care system structure, health care service providers, parents and community. Further research is needed on parents and health care service provider’s perspectives on how to sustain the provision of YFSRH services.展开更多
On April 18-20, 2012, 13th China＇s Refractories Youth Symposium was held successfully in Zhengzhou, Henan Province. China＇s Refracto-ries Youth Symposium, an important and influencing conference, is held every two y...On April 18-20, 2012, 13th China＇s Refractories Youth Symposium was held successfully in Zhengzhou, Henan Province. China＇s Refracto-ries Youth Symposium, an important and influencing conference, is held every two years. 13^th China＇s Refractories Youth Symposium was co-sponsored by The Refractories Branch of The Chinese Society for Metals and Henan Society for Metals, co-organized by Beijing Society of Metals, Metallurgy Society of Hebei Province, Liaoning Society for Metals, Shandong Society for Metals and Shanxi Society for Metals, and supported by Sinosteel Luoyang Institute of Refractories Research Co., Ltd., Zhejiang Zili Co., Ltd., etc.展开更多
It is shown that in the Earth’s atmosphere, due to influence of the gravitational field, coefficient of thermal expansion depends on altitude. The altitude intervals for individual gases for which the laws of ideal g...It is shown that in the Earth’s atmosphere, due to influence of the gravitational field, coefficient of thermal expansion depends on altitude. The altitude intervals for individual gases for which the laws of ideal gases can be applied have been determined and it has been established that they are dependent on the adiabatic index and molar mass of these gases.展开更多
In this paper, we consider the Goldbach＇s problem for matrix rings, namely, we decompose an n × n （n 〉 1） matrix over a principal ideal domain R into a sum of two matrices in Mn,（R） with given determinants....In this paper, we consider the Goldbach＇s problem for matrix rings, namely, we decompose an n × n （n 〉 1） matrix over a principal ideal domain R into a sum of two matrices in Mn,（R） with given determinants. We prove the following result： Let n 〉 1 be a natural number and A = （aij） be a matrix in Mn（R）. Define d（A） ：= g.c.d{aij}. Suppose that p and q are two elements in R. Then （1） If n 〉 1 is even, then A can be written as a sum of two matrices X, Y in Mn（R） with det（X） = p and det（Y） = q if and only if d（A） [ p - q; （2） If n 〉 1 is odd, then A can be written as a sum of two matrices X, Y in Mn（R） with det（X） = p and det（Y） = q if and only if d（A） ｜ p ＋ q. We apply the result to the matrices in Mn（Z） and Mn（Q[x]） and prove that if R = 7. or Q[x], then any nonzero matrix A in Mn（R） can be written as a sum of two matrices in Mn（R） with prime determinants.展开更多
When Chen Duxiu founded New Youth, he attached great importance to the “women’s issue” and established the “women’s issue” section, publishing articles on women’s issues and discussing women’s identity, status...When Chen Duxiu founded New Youth, he attached great importance to the “women’s issue” and established the “women’s issue” section, publishing articles on women’s issues and discussing women’s identity, status, and rights deeply. New Youth provided a forum for women to express their ideas, and its existence was a reflection of its advancement. However, from the discussion and promotion of “virtuous mother”, it’s easy to see that the intellectuals at that time had a biased perception of women’s identity and emphasized the intersection of women’s consciousness with the state’s thinking.展开更多
文摘Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx<sub>1</sub>, and slow-jet, vx<sub>2</sub>. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.
文摘This article introduces a new class of ideals, namely, the sπr ideals. It is shown that every regular square matrix over sπr ideals of a ring admits a diagonal reduction.
文摘Ideal point method is one of the methods to solve multi-objective problem. It is applied to forest harvest regu-lation, and showed very good results by analyzing changes of quantitative indexes of forest resource structure before andafter the regulation. This method can be applied as one of the mathematical tools in forest harvest regulation.
文摘Nearly half of the world’s population comprise youths. However, addressing their Sexual and Reproductive Health (SRH) remains a challenge. Globally countries are mandated to continually provide Youth Friendly Sexual and Reproductive Health services (YFSRHs) to the youth. The objective of this study was to assess and describe youth’s perspectives on a sustainable model for the provision of YFSRHs in Kenya. Data was collected among 400 youths aged 18 - 24 years in Embu and Kirinyaga counties, Kenya. A structured questionnaire was utilized as the data collection tool. Collected data was analyzed using SAS statistical software version 9.4. Statistical threshold of P ≤ 0.05 was used. Overall the mean age of the study participants was ±standard deviation (SD) 21.2 ± 1.86 years. Majority of the participants’ perspective on the health care system sustainability was that the waiting time at the facility should be less than an hour, accessible geographically (less than a kilometre), affordable (≤20 Ksh.), and convenient working hours (weekday and weekends ratio 1:1). Advocacy was on health care provider’s attributes of politeness, welcoming, confidential and non-judgmental. The most preferred locations for the youth friendly centres by the participants were community and school based locations. Similarly, parental and community support was reported to highly contribute to sustained utilization and provision of the YFSRHs (P < 0.001). Unlike popular belief, 99.8% did not see the need for recreational facilities at the youth centres to ensure sustainability of the model. To ensure a sustainable model for the provision of YFSRHs, there is need for a multi-sectoral and stakeholder involvement that is;youth, health care system structure, health care service providers, parents and community. Further research is needed on parents and health care service provider’s perspectives on how to sustain the provision of YFSRH services.
文摘On April 18-20, 2012, 13th China＇s Refractories Youth Symposium was held successfully in Zhengzhou, Henan Province. China＇s Refracto-ries Youth Symposium, an important and influencing conference, is held every two years. 13^th China＇s Refractories Youth Symposium was co-sponsored by The Refractories Branch of The Chinese Society for Metals and Henan Society for Metals, co-organized by Beijing Society of Metals, Metallurgy Society of Hebei Province, Liaoning Society for Metals, Shandong Society for Metals and Shanxi Society for Metals, and supported by Sinosteel Luoyang Institute of Refractories Research Co., Ltd., Zhejiang Zili Co., Ltd., etc.
文摘It is shown that in the Earth’s atmosphere, due to influence of the gravitational field, coefficient of thermal expansion depends on altitude. The altitude intervals for individual gases for which the laws of ideal gases can be applied have been determined and it has been established that they are dependent on the adiabatic index and molar mass of these gases.
文摘In this paper, we consider the Goldbach＇s problem for matrix rings, namely, we decompose an n × n （n 〉 1） matrix over a principal ideal domain R into a sum of two matrices in Mn,（R） with given determinants. We prove the following result： Let n 〉 1 be a natural number and A = （aij） be a matrix in Mn（R）. Define d（A） ：= g.c.d{aij}. Suppose that p and q are two elements in R. Then （1） If n 〉 1 is even, then A can be written as a sum of two matrices X, Y in Mn（R） with det（X） = p and det（Y） = q if and only if d（A） [ p - q; （2） If n 〉 1 is odd, then A can be written as a sum of two matrices X, Y in Mn（R） with det（X） = p and det（Y） = q if and only if d（A） ｜ p ＋ q. We apply the result to the matrices in Mn（Z） and Mn（Q[x]） and prove that if R = 7. or Q[x], then any nonzero matrix A in Mn（R） can be written as a sum of two matrices in Mn（R） with prime determinants.
基金贵州省2018年度哲学社会科学规划国学单列课题阶段性成果,宋元时期宋人别集的编纂与刊刻研究,Serial Number 18GZGX25《新青年》“译介”类栏目规划与内容判断力研究,Serial Number 22150322016)《点石斋画报》(1884-1898)的图文艺术性、现代性传播与出版研究,Serial Number Eb202008.
文摘When Chen Duxiu founded New Youth, he attached great importance to the “women’s issue” and established the “women’s issue” section, publishing articles on women’s issues and discussing women’s identity, status, and rights deeply. New Youth provided a forum for women to express their ideas, and its existence was a reflection of its advancement. However, from the discussion and promotion of “virtuous mother”, it’s easy to see that the intellectuals at that time had a biased perception of women’s identity and emphasized the intersection of women’s consciousness with the state’s thinking.
