Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal ...Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.展开更多
The closed forms of two kinds of generating functions for the Pascal-type triangle are derived.A certain of properties like the Pascal triangle are found.Explicit expression of any element and closed forms of several ...The closed forms of two kinds of generating functions for the Pascal-type triangle are derived.A certain of properties like the Pascal triangle are found.Explicit expression of any element and closed forms of several kinds of sums are given.A number of combinatorial identities associated with the triangle are constructed.展开更多
Thousands of landslide data being taken as the nation wide statistics of sampling and the two state variables of landslide being processed with two methods described in the references, the main types of lithologica...Thousands of landslide data being taken as the nation wide statistics of sampling and the two state variables of landslide being processed with two methods described in the references, the main types of lithological groups of landslides in China have been sieved and selected.On the other hand, through the displacement table of Pascal Yanghui triangle used in the information encoding theory, the mark weight of sampling can be calculated and the main lithological groups which have close relationship with landslide occurrence can be gained.In comparison with the both results, the characteristics of main sliding lithological groups are determinated, and the main distribution regions of landslides can be prognosticated.展开更多
Objective:We through the anatomy of cadavers to study the"Kambin’s triangle"in the safe working area of lumbar intervertebral foramen and to provide anatomical reference for clinical lumbar fusion through K...Objective:We through the anatomy of cadavers to study the"Kambin’s triangle"in the safe working area of lumbar intervertebral foramen and to provide anatomical reference for clinical lumbar fusion through Kambin’s triangle approach.Methods:five complete cadaveric specimens were taken,the soft tissue of the lumbar back was removed,the transverse process,upper and lower articular processes and part of the vertebral lamina were bitten,the Kambin’s triangle area of the lumbar spine was completely exposed,the bottom edge and height of the Kambin’s triangle were measured,and the area of the Kambin’s triangle was calculated;Using Kirschner wire,pull and fix the traveling nerve root to make the Kambin’s triangle into a rectangle,measure the length of the bottom edge and height again,calculate the area,and compare the two groups of data.Results:the average height of the Kambin’s triangle was 11.20mm±2.10mm,and the average height of the improved four corners was 11.19mm±1.93mm.The height of the improved four corners was slightly shorter than that of the Kambin’s triangle.There was a significant correlation between the two,but the difference was not statistically significant.The average bottom of Kambin’s triangle is 10.78mm±1.95mm,and the average bottom of improved four corners is 12.14mm±1.78mm.The length of the bottom edge of improved four corners is greater than that of Kambin’s triangle.There is a significant correlation between them,and the difference is statistically significant;The average area of Kambin’s triangle is 61.79mm^(2)±20.71mm^(2),and the area of improved four corners is 137.71mm^(2)±38.20mm^(2).The area of improved four corners is significantly larger than that of Kambin’s triangle.There is a significant correlation between the two,and the difference is statistically significant.Conclusion:there is a narrow right angle triangle area surrounded by traveling nerve root,dural sac and superior endplate of lower vertebral body in the lumbar intervertebral foramen.If the traveling nerve root is pulled and fixed to turn the traditional Kambin’s triangle into a quadrilateral,the bottom edge of the Kambin’s triangle area can be significantly longer and the area can be significantly expanded,which can be operated more safely.展开更多
Over the years the defense industry has become a de facto participant in the policy-making process. As in other areas dominated by big business interests, a policy sub-government of "iron triangle" has emerg...Over the years the defense industry has become a de facto participant in the policy-making process. As in other areas dominated by big business interests, a policy sub-government of "iron triangle" has emerged. In the view of some American scholars, such an "iron triangle" as a political relationship that brings together .展开更多
The Pascal matrix and the Fibonacci matrix are among the most well-known and the most widely-used tools in elementary algebra. In this paper, after a brief introduction where we give the basic definitions and the hist...The Pascal matrix and the Fibonacci matrix are among the most well-known and the most widely-used tools in elementary algebra. In this paper, after a brief introduction where we give the basic definitions and the historical backgrounds of these concepts, we propose an algorithm that will generate the elements of these matrices. In fact, we will show that the indicated algorithm can be used to construct the elements of any power series matrix generated by any polynomial (see Definition 1), and hence, it is a generalization of the specific algorithms that give us the Pascal and the Fibonacci matrices.展开更多
The paper critically examines and refutes some of the standard arguments against Pascal＇s Wager, particularly, the ＂Many Gods Objection＂. The paper argues that Pascal＇s philosophical and theological opponents proc...The paper critically examines and refutes some of the standard arguments against Pascal＇s Wager, particularly, the ＂Many Gods Objection＂. The paper argues that Pascal＇s philosophical and theological opponents proceed far too quickly in dismissing his argument as implausible. Their determined attempts to tear down Pascal＇s Wager have caused them to miss its power and force. While the Wager may not be sound for today＇s multi culturally sophisticated audience, the Wager is quite cogent relative to Pascal＇s time, when theism and agnosticism were the only genuine possibilities. Thus, the paper concludes that Pascal＇s Wager is less vulnerable than most detractors seem to think.展开更多
Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I ex...Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.展开更多
At the point of death,a human being only has had the experience of nonexistence before birth and the experience of having lived his/her life after they were born.In the final analysis from the perspective of strict em...At the point of death,a human being only has had the experience of nonexistence before birth and the experience of having lived his/her life after they were born.In the final analysis from the perspective of strict empiricism,the individual only has two options:the nonexistence before birth or the eventual reliving of one’s life.The return of one’s life is supported by the paradigm of a multiverse and an antimatter universe.This is atheism’s logical certainty.展开更多
文摘Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.
文摘The closed forms of two kinds of generating functions for the Pascal-type triangle are derived.A certain of properties like the Pascal triangle are found.Explicit expression of any element and closed forms of several kinds of sums are given.A number of combinatorial identities associated with the triangle are constructed.
文摘Thousands of landslide data being taken as the nation wide statistics of sampling and the two state variables of landslide being processed with two methods described in the references, the main types of lithological groups of landslides in China have been sieved and selected.On the other hand, through the displacement table of Pascal Yanghui triangle used in the information encoding theory, the mark weight of sampling can be calculated and the main lithological groups which have close relationship with landslide occurrence can be gained.In comparison with the both results, the characteristics of main sliding lithological groups are determinated, and the main distribution regions of landslides can be prognosticated.
基金Hainan Provincial Natural Science Foundation(No.819QN365)National Natural Science Foundation of China(No.81902270)。
文摘Objective:We through the anatomy of cadavers to study the"Kambin’s triangle"in the safe working area of lumbar intervertebral foramen and to provide anatomical reference for clinical lumbar fusion through Kambin’s triangle approach.Methods:five complete cadaveric specimens were taken,the soft tissue of the lumbar back was removed,the transverse process,upper and lower articular processes and part of the vertebral lamina were bitten,the Kambin’s triangle area of the lumbar spine was completely exposed,the bottom edge and height of the Kambin’s triangle were measured,and the area of the Kambin’s triangle was calculated;Using Kirschner wire,pull and fix the traveling nerve root to make the Kambin’s triangle into a rectangle,measure the length of the bottom edge and height again,calculate the area,and compare the two groups of data.Results:the average height of the Kambin’s triangle was 11.20mm±2.10mm,and the average height of the improved four corners was 11.19mm±1.93mm.The height of the improved four corners was slightly shorter than that of the Kambin’s triangle.There was a significant correlation between the two,but the difference was not statistically significant.The average bottom of Kambin’s triangle is 10.78mm±1.95mm,and the average bottom of improved four corners is 12.14mm±1.78mm.The length of the bottom edge of improved four corners is greater than that of Kambin’s triangle.There is a significant correlation between them,and the difference is statistically significant;The average area of Kambin’s triangle is 61.79mm^(2)±20.71mm^(2),and the area of improved four corners is 137.71mm^(2)±38.20mm^(2).The area of improved four corners is significantly larger than that of Kambin’s triangle.There is a significant correlation between the two,and the difference is statistically significant.Conclusion:there is a narrow right angle triangle area surrounded by traveling nerve root,dural sac and superior endplate of lower vertebral body in the lumbar intervertebral foramen.If the traveling nerve root is pulled and fixed to turn the traditional Kambin’s triangle into a quadrilateral,the bottom edge of the Kambin’s triangle area can be significantly longer and the area can be significantly expanded,which can be operated more safely.
文摘Over the years the defense industry has become a de facto participant in the policy-making process. As in other areas dominated by big business interests, a policy sub-government of "iron triangle" has emerged. In the view of some American scholars, such an "iron triangle" as a political relationship that brings together .
文摘The Pascal matrix and the Fibonacci matrix are among the most well-known and the most widely-used tools in elementary algebra. In this paper, after a brief introduction where we give the basic definitions and the historical backgrounds of these concepts, we propose an algorithm that will generate the elements of these matrices. In fact, we will show that the indicated algorithm can be used to construct the elements of any power series matrix generated by any polynomial (see Definition 1), and hence, it is a generalization of the specific algorithms that give us the Pascal and the Fibonacci matrices.
文摘The paper critically examines and refutes some of the standard arguments against Pascal＇s Wager, particularly, the ＂Many Gods Objection＂. The paper argues that Pascal＇s philosophical and theological opponents proceed far too quickly in dismissing his argument as implausible. Their determined attempts to tear down Pascal＇s Wager have caused them to miss its power and force. While the Wager may not be sound for today＇s multi culturally sophisticated audience, the Wager is quite cogent relative to Pascal＇s time, when theism and agnosticism were the only genuine possibilities. Thus, the paper concludes that Pascal＇s Wager is less vulnerable than most detractors seem to think.
文摘Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.
文摘At the point of death,a human being only has had the experience of nonexistence before birth and the experience of having lived his/her life after they were born.In the final analysis from the perspective of strict empiricism,the individual only has two options:the nonexistence before birth or the eventual reliving of one’s life.The return of one’s life is supported by the paradigm of a multiverse and an antimatter universe.This is atheism’s logical certainty.
