The purposes of this article are to discuss the symplectic transformation laws on theta series and to give some explicit formulas for the trace of the symplectic operator.
In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our metho...In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our methods are new and essentially different with the situation of bounded initial value.展开更多
In this paper, we use Lax-Oleinik formula to study the asymptotic behavior for the initial problem of scalar conservation law u_t + F(u)_x = 0. First, we prove a simple but useful property of Lax-Oleinik formula(Lemma...In this paper, we use Lax-Oleinik formula to study the asymptotic behavior for the initial problem of scalar conservation law u_t + F(u)_x = 0. First, we prove a simple but useful property of Lax-Oleinik formula(Lemma 2.7). In fact, denote the Legendre transform of F(u) as L(σ), then we can prove that the quantity F(q)-′qF(q) + L(′F(q)) is a constant independent of q. As a simple application, we first give the solution of Riemann problem without using of Rankine-Hugoniot condition and entropy condition. Then we study the asymptotic behavior of the problem with some special initial data and prove that the solution contains only a single shock for t > T~*. Meanwhile, we can give the equation of the shock and an explicit value of T~*.展开更多
Based on application of " Fenlong tillage technology" in 40 kinds of crops in 26 provinces of China,and saline alkali land and degraded grassland of 10 provinces in the past 10 years, " Fenlong law"...Based on application of " Fenlong tillage technology" in 40 kinds of crops in 26 provinces of China,and saline alkali land and degraded grassland of 10 provinces in the past 10 years, " Fenlong law" that Fenlong depth of various land resources suitable for cultivation in reasonable depth interval and utilization degree of " natural resources" are proportional to increase in agricultural output,ecological environment improvement and increase in economic output is discussed in this paper. Moreover,its formula,8 " effect laws" and their scientific significance are given. " Full-layer tillage" or " bottom-layer tillage" of Fenlong " super deep ploughing,deep loosening and not disturbing soil layer" is expounded,and the way of multiple incremental utilization of " natural resources" is created,which could be applied in various land resources suitable for cultivation,and realizes deep utilization of natural resources in a " big explosion". Additionally,China has 147 million ha of cultivated land,saline alkali land and degraded grassland,and 400 million people can be supported by the newly increased grain and meat,etc. by Fenlong,and 88 billion m^3 of land water resources is added. " Fenlong law" is proposed based on Fenlong phenomenon,and it is conducive to deep enjoyment and protection of natural resources by human beings,and harmonious development between man and nature.展开更多
There are three main mechanisms to cause the red shift of spectrum in physics. The first is gravity which is related to mass. The second is the Compton scattering which is related to the energy transformation of photo...There are three main mechanisms to cause the red shift of spectrum in physics. The first is gravity which is related to mass. The second is the Compton scattering which is related to the energy transformation of photon. The third is the Doppler’s effect which is related to velocity. The basic formula used to calculate the relation of red shift and distance of Ia supernova in cosmology is which is related to the scalar factor of the R-W metric. It is completely different from the Doppler formula of red shift which is related to velocity factor . This kind of inconsistency is not allowed in physics. Because of , when became larger and larger with time increase, z became smaller and smaller, means that space expansion leads to red shift becoming smaller. At present time, we have and , means that there is no red shift for the light emitted from distance celestial bodies at present. The results obviously violate the Hubble law! It is proved strictly in mathematics that the formula is untenable unless constant and . The further study reveals that the essential reason of the mistake is that the R-W metric violates the principle of light’s speed invariable. The time delay caused by relativity velocity between light’s source and observer is neglected. Besides, there exists the problem of time misalignment between theoretical calculation and practical observations in the original documents of Ia supernova projects. So the formula used to calculate the relation between red shift and distance of Ia supernova is wrong and the deduced conclusion about dark energy and the accelerating expansion of the universe are incredible. It is proved in this paper that based on the Doppler’s formula and the method of numerical calculation, the relation of red shift and distance of Ia supernova can be explained well. The hypotheses of dark energy and the accelerating expansion of the universe are completely unnecessary in cosmology.展开更多
The Doppler formula should be used directly to calculate red shift of Cosmology. The first is gravity, the second is the Doppler’s effect and the third is the Compton scattering. The red shift of cosmology is conside...The Doppler formula should be used directly to calculate red shift of Cosmology. The first is gravity, the second is the Doppler’s effect and the third is the Compton scattering. The red shift of cosmology is considered to be caused by the receding motions of celestial bodies, of which essence is the Doppler’s effect. However, the basic formula used to calculate the relationship between red shift and distance for Ia supernova in cosmology is z+1= R(t0)/R(t1)which is based on the R-W metric and related to the scalar factor R(t). This is different from the Doppler formula which is related to speed factor R(t). Because the R-W metric is only a mathematical structure of space, the metric red shift is not an independent law of physics, this inconsistence is not allowed in physics. It is proved strictly in this paper that the formula of metric red shift is only the result of the first order approximation. If higher order approximations are considered, we can obtain a restrict condition R(t). It indicates that if the formula of metric red shift holds, it can only be suitable to describe the spatial uniform expansion, unsuitable for the practical universal process with acceleration. The further study reveals that the R-W metric violates the invariability principle of light’s speed in vacuum. The time delay caused by展开更多
文摘The purposes of this article are to discuss the symplectic transformation laws on theta series and to give some explicit formulas for the trace of the symplectic operator.
基金partly supported by Natural Science Foundation of China(11471332 and 11071246)
文摘In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our methods are new and essentially different with the situation of bounded initial value.
基金supported in part by NSFC(11671193)the Fundamental Research Funds for the Central Universities(NE2015005)supported in part by NSFC(11271182 and 11501290)
文摘In this paper, we use Lax-Oleinik formula to study the asymptotic behavior for the initial problem of scalar conservation law u_t + F(u)_x = 0. First, we prove a simple but useful property of Lax-Oleinik formula(Lemma 2.7). In fact, denote the Legendre transform of F(u) as L(σ), then we can prove that the quantity F(q)-′qF(q) + L(′F(q)) is a constant independent of q. As a simple application, we first give the solution of Riemann problem without using of Rankine-Hugoniot condition and entropy condition. Then we study the asymptotic behavior of the problem with some special initial data and prove that the solution contains only a single shock for t > T~*. Meanwhile, we can give the equation of the shock and an explicit value of T~*.
基金Supported by Special Fund Project of Guangxi Innovation Driven Development(Guike AA17204037)Major Science and Technology Projects in Guangxi(Guike AA16380017)Team Project of Guangxi Academy of Agricultural Sciences(2015YT60).
文摘Based on application of " Fenlong tillage technology" in 40 kinds of crops in 26 provinces of China,and saline alkali land and degraded grassland of 10 provinces in the past 10 years, " Fenlong law" that Fenlong depth of various land resources suitable for cultivation in reasonable depth interval and utilization degree of " natural resources" are proportional to increase in agricultural output,ecological environment improvement and increase in economic output is discussed in this paper. Moreover,its formula,8 " effect laws" and their scientific significance are given. " Full-layer tillage" or " bottom-layer tillage" of Fenlong " super deep ploughing,deep loosening and not disturbing soil layer" is expounded,and the way of multiple incremental utilization of " natural resources" is created,which could be applied in various land resources suitable for cultivation,and realizes deep utilization of natural resources in a " big explosion". Additionally,China has 147 million ha of cultivated land,saline alkali land and degraded grassland,and 400 million people can be supported by the newly increased grain and meat,etc. by Fenlong,and 88 billion m^3 of land water resources is added. " Fenlong law" is proposed based on Fenlong phenomenon,and it is conducive to deep enjoyment and protection of natural resources by human beings,and harmonious development between man and nature.
文摘There are three main mechanisms to cause the red shift of spectrum in physics. The first is gravity which is related to mass. The second is the Compton scattering which is related to the energy transformation of photon. The third is the Doppler’s effect which is related to velocity. The basic formula used to calculate the relation of red shift and distance of Ia supernova in cosmology is which is related to the scalar factor of the R-W metric. It is completely different from the Doppler formula of red shift which is related to velocity factor . This kind of inconsistency is not allowed in physics. Because of , when became larger and larger with time increase, z became smaller and smaller, means that space expansion leads to red shift becoming smaller. At present time, we have and , means that there is no red shift for the light emitted from distance celestial bodies at present. The results obviously violate the Hubble law! It is proved strictly in mathematics that the formula is untenable unless constant and . The further study reveals that the essential reason of the mistake is that the R-W metric violates the principle of light’s speed invariable. The time delay caused by relativity velocity between light’s source and observer is neglected. Besides, there exists the problem of time misalignment between theoretical calculation and practical observations in the original documents of Ia supernova projects. So the formula used to calculate the relation between red shift and distance of Ia supernova is wrong and the deduced conclusion about dark energy and the accelerating expansion of the universe are incredible. It is proved in this paper that based on the Doppler’s formula and the method of numerical calculation, the relation of red shift and distance of Ia supernova can be explained well. The hypotheses of dark energy and the accelerating expansion of the universe are completely unnecessary in cosmology.
文摘The Doppler formula should be used directly to calculate red shift of Cosmology. The first is gravity, the second is the Doppler’s effect and the third is the Compton scattering. The red shift of cosmology is considered to be caused by the receding motions of celestial bodies, of which essence is the Doppler’s effect. However, the basic formula used to calculate the relationship between red shift and distance for Ia supernova in cosmology is z+1= R(t0)/R(t1)which is based on the R-W metric and related to the scalar factor R(t). This is different from the Doppler formula which is related to speed factor R(t). Because the R-W metric is only a mathematical structure of space, the metric red shift is not an independent law of physics, this inconsistence is not allowed in physics. It is proved strictly in this paper that the formula of metric red shift is only the result of the first order approximation. If higher order approximations are considered, we can obtain a restrict condition R(t). It indicates that if the formula of metric red shift holds, it can only be suitable to describe the spatial uniform expansion, unsuitable for the practical universal process with acceleration. The further study reveals that the R-W metric violates the invariability principle of light’s speed in vacuum. The time delay caused by
