In core logging, each joint set intersects borehole into some segments. In this research, it has been shown that length of the borehole segments created by each joint set could be computed by trigonometrical relations...In core logging, each joint set intersects borehole into some segments. In this research, it has been shown that length of the borehole segments created by each joint set could be computed by trigonometrical relations. By realizing the lengths associated with joint sets, an algorithm has been designed to compute the length of borehole pieces (created by all joint sets) and to calculate RQD. Effect of some factors have been analyzed and applied to the abstract model of the rock mass to have the most similarity to a real rock mass. The program proposed in this study, is a robust platform to calculate the RQD in all directions inside a rock mass without having to deal with the labor of core logging and wrestling with difficulties and inaccuracies of the traditional processes. This is the first algorithmic method for estimating the rock quality which could be employed to develop a new and far more reliable measurement for the degree of jointing inside a rock mass.展开更多
In this paper, we study about trigonometry in finite field, we know that , the field with p elements, where p is a prime number if and only if p = 8k + 1 or p = 8k -1. Let F and K be two fields, we say that F is an ex...In this paper, we study about trigonometry in finite field, we know that , the field with p elements, where p is a prime number if and only if p = 8k + 1 or p = 8k -1. Let F and K be two fields, we say that F is an extension of K, if K⊆F or there exists a monomorphism f: K→F. Recall that , F[x] is the ring of polynomial over F. If (means that F is an extension of K), an element is algebraic over K if there exists such that f(u) = 0 (see [1]-[4]). The algebraic closure of K in F is , which is the set of all algebraic elements in F over K.展开更多
In this paper we show that the author’s Two Nonzero Lemma (TNCL) can be applied to present a simple proof for a very useful equality which was first proved by Karl Gustafson in 1968. Gustafson used Hilbert space meth...In this paper we show that the author’s Two Nonzero Lemma (TNCL) can be applied to present a simple proof for a very useful equality which was first proved by Karl Gustafson in 1968. Gustafson used Hilbert space methods, including convexity of the Hilbert space norm, to prove this identity which was the basis of his matrix trigonometry. By applying TNCL, we will reduce the problem to a simple problem of ordinary calculus.展开更多
In one of his astronomical works the prominent arabic medieval scientists Thabit ibn Qurra （836-901） studied the visible motion of the Sun and found the points, where its velocity is maximum or minimum. He also lbun...In one of his astronomical works the prominent arabic medieval scientists Thabit ibn Qurra （836-901） studied the visible motion of the Sun and found the points, where its velocity is maximum or minimum. He also lbund the points on the ecliptic, where this velocity is equal to the average velocity of the Sun over all the ecliptic. For this purpose he used the idea of infinitely small arcs and their ratios in different points of the circle. The great scientist Leonard Euler （1707-1783） introduced in his works on spherical trigonometry the line-element ds of the surface of the sphere, i.e. the differential of the arc length. He constructed the spherical trigonometry as an inner geometry on the surface of the sphere. He replaced the trigonometry lines, which were in use befbre him, by trigonometric functions.展开更多
文摘In core logging, each joint set intersects borehole into some segments. In this research, it has been shown that length of the borehole segments created by each joint set could be computed by trigonometrical relations. By realizing the lengths associated with joint sets, an algorithm has been designed to compute the length of borehole pieces (created by all joint sets) and to calculate RQD. Effect of some factors have been analyzed and applied to the abstract model of the rock mass to have the most similarity to a real rock mass. The program proposed in this study, is a robust platform to calculate the RQD in all directions inside a rock mass without having to deal with the labor of core logging and wrestling with difficulties and inaccuracies of the traditional processes. This is the first algorithmic method for estimating the rock quality which could be employed to develop a new and far more reliable measurement for the degree of jointing inside a rock mass.
文摘In this paper, we study about trigonometry in finite field, we know that , the field with p elements, where p is a prime number if and only if p = 8k + 1 or p = 8k -1. Let F and K be two fields, we say that F is an extension of K, if K⊆F or there exists a monomorphism f: K→F. Recall that , F[x] is the ring of polynomial over F. If (means that F is an extension of K), an element is algebraic over K if there exists such that f(u) = 0 (see [1]-[4]). The algebraic closure of K in F is , which is the set of all algebraic elements in F over K.
文摘In this paper we show that the author’s Two Nonzero Lemma (TNCL) can be applied to present a simple proof for a very useful equality which was first proved by Karl Gustafson in 1968. Gustafson used Hilbert space methods, including convexity of the Hilbert space norm, to prove this identity which was the basis of his matrix trigonometry. By applying TNCL, we will reduce the problem to a simple problem of ordinary calculus.
文摘In one of his astronomical works the prominent arabic medieval scientists Thabit ibn Qurra （836-901） studied the visible motion of the Sun and found the points, where its velocity is maximum or minimum. He also lbund the points on the ecliptic, where this velocity is equal to the average velocity of the Sun over all the ecliptic. For this purpose he used the idea of infinitely small arcs and their ratios in different points of the circle. The great scientist Leonard Euler （1707-1783） introduced in his works on spherical trigonometry the line-element ds of the surface of the sphere, i.e. the differential of the arc length. He constructed the spherical trigonometry as an inner geometry on the surface of the sphere. He replaced the trigonometry lines, which were in use befbre him, by trigonometric functions.
