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
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
In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical...In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .展开更多
After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first...After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.展开更多
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In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .
文摘After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.
