Several algorithms based on homogeneous polynomials for multiplication of large integers are described in the paper. The homogeneity of polynomials provides several simplifications: reduction of system of equations an...Several algorithms based on homogeneous polynomials for multiplication of large integers are described in the paper. The homogeneity of polynomials provides several simplifications: reduction of system of equations and elimination of necessity to evaluate polynomials in points with larger coordinates. It is demonstrated that a two-stage implementation of the proposed and Toom-Cook algorithms asymptotically require twice as many standard multiplications than their direct implementation. A multistage implementation of these algorithms is also less efficient than their direct implementation. Although the proposed algorithms as well as the corresponding Toom-Cook algorithms require numerous algebraic additions, the Generalized Horner rule for evaluation of homogeneous polynomials, provided in the paper, decrease this number twice.展开更多
In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the ...In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.展开更多
Purpose: To understand the multiple signs of Horner syndrome and to recommend protocols for pediatricians to obtain an accurate diagnosis of Horner syndrome. Methods: The medical records of 17 pediatric patients with ...Purpose: To understand the multiple signs of Horner syndrome and to recommend protocols for pediatricians to obtain an accurate diagnosis of Horner syndrome. Methods: The medical records of 17 pediatric patients with Horner syndrome, neonates to eighteen years of age, were collected and analyzed. Data recorded included age, presenting symptoms, other medical history, allergies, medications, pupil size, presence of anhidrosis, and presence of ptosis. From the available pupil sizes, average degree of anisocoria was calculated. Results: All 17 patients had other clinical findings of Horner syndrome in addition to anisocoria. On initial evaluation, 100% had ptosis and 25% had anhidrosis. Of the available pupil size data, the average level of anisocoria was 2.06 mm, with a standard deviation of 1.17 mm. Conclusion: Physicians are reminded to measure pupil size to determine the degree of anisocoria when present, as it may help distinguish benign conditions from underlying pathology. Educating pediatricians on measurement of anisocoria and additional signs of Horner syndrome will help with proper referral patterns.展开更多
The present paper deals with the facile synthesis of 6 E geranylgeraniol 19 oic acid(1), a naturally occuring alicyclic diterpene acid, by a Horner Wadsworth Emmons olefination of two readily available fragments 7 and 3.
We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,thi...We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,this method saves most of the multiplications in the price of little increase of additions comparing to Horner's method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.展开更多
苏格兰,是这么个地方:风笛、格子裙、高尔夫和威士忌。苏格兰风笛享誉世界,这只要不是土鳖都知道。在经典的《My Heart Will Go on》中,苏格兰风笛的优雅点缀可谓妙笔生花,而在电影《勇敢的心》(BRAVEHEART)中,美国王牌配乐大师詹姆斯&#...苏格兰,是这么个地方:风笛、格子裙、高尔夫和威士忌。苏格兰风笛享誉世界,这只要不是土鳖都知道。在经典的《My Heart Will Go on》中,苏格兰风笛的优雅点缀可谓妙笔生花,而在电影《勇敢的心》(BRAVEHEART)中,美国王牌配乐大师詹姆斯·霍纳(James Horner)让我们看到了苏格兰音乐的灵魂,那就是爱与自由。当然在苏格兰除了老辈人的传授,21世纪工业文明下的苏格兰,看似传统(我是说那的爷们还保持着穿裙子的风俗)的苏格兰男人也玩摇滚乐,这多少让人觉得不可思议,而实际上,在苏格兰,有无数的摇滚从业者在玩着这种在卫道士眼中大逆不道却让人激情彭湃的音乐,他们用乐器在酿造着让爱摇人民狂饮的威士忌。展开更多
Horner＇s syndrome （HS） results from interruption of sympathetic nervous supply to the eye and manifests clinically with partial ptosis, miosis and enophthalmos, along with anhidrosis of face on the affected side.
文摘Several algorithms based on homogeneous polynomials for multiplication of large integers are described in the paper. The homogeneity of polynomials provides several simplifications: reduction of system of equations and elimination of necessity to evaluate polynomials in points with larger coordinates. It is demonstrated that a two-stage implementation of the proposed and Toom-Cook algorithms asymptotically require twice as many standard multiplications than their direct implementation. A multistage implementation of these algorithms is also less efficient than their direct implementation. Although the proposed algorithms as well as the corresponding Toom-Cook algorithms require numerous algebraic additions, the Generalized Horner rule for evaluation of homogeneous polynomials, provided in the paper, decrease this number twice.
文摘In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.
文摘Purpose: To understand the multiple signs of Horner syndrome and to recommend protocols for pediatricians to obtain an accurate diagnosis of Horner syndrome. Methods: The medical records of 17 pediatric patients with Horner syndrome, neonates to eighteen years of age, were collected and analyzed. Data recorded included age, presenting symptoms, other medical history, allergies, medications, pupil size, presence of anhidrosis, and presence of ptosis. From the available pupil sizes, average degree of anisocoria was calculated. Results: All 17 patients had other clinical findings of Horner syndrome in addition to anisocoria. On initial evaluation, 100% had ptosis and 25% had anhidrosis. Of the available pupil size data, the average level of anisocoria was 2.06 mm, with a standard deviation of 1.17 mm. Conclusion: Physicians are reminded to measure pupil size to determine the degree of anisocoria when present, as it may help distinguish benign conditions from underlying pathology. Educating pediatricians on measurement of anisocoria and additional signs of Horner syndrome will help with proper referral patterns.
基金Supported bytheNational Natural Science Foundation of China( No.2 0 0 72 0 12 ) and the Special Research Grant forDoctoral Sites in Chinese U niversities( No.2 0 0 10 730 0 0 1)
文摘The present paper deals with the facile synthesis of 6 E geranylgeraniol 19 oic acid(1), a naturally occuring alicyclic diterpene acid, by a Horner Wadsworth Emmons olefination of two readily available fragments 7 and 3.
基金Supported by the Graduate Starting Seed Fund of Northwestern Polytechnical University(Z2012030)
文摘We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,this method saves most of the multiplications in the price of little increase of additions comparing to Horner's method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.
文摘苏格兰,是这么个地方:风笛、格子裙、高尔夫和威士忌。苏格兰风笛享誉世界,这只要不是土鳖都知道。在经典的《My Heart Will Go on》中,苏格兰风笛的优雅点缀可谓妙笔生花,而在电影《勇敢的心》(BRAVEHEART)中,美国王牌配乐大师詹姆斯·霍纳(James Horner)让我们看到了苏格兰音乐的灵魂,那就是爱与自由。当然在苏格兰除了老辈人的传授,21世纪工业文明下的苏格兰,看似传统(我是说那的爷们还保持着穿裙子的风俗)的苏格兰男人也玩摇滚乐,这多少让人觉得不可思议,而实际上,在苏格兰,有无数的摇滚从业者在玩着这种在卫道士眼中大逆不道却让人激情彭湃的音乐,他们用乐器在酿造着让爱摇人民狂饮的威士忌。
文摘Horner＇s syndrome （HS） results from interruption of sympathetic nervous supply to the eye and manifests clinically with partial ptosis, miosis and enophthalmos, along with anhidrosis of face on the affected side.
