Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the...Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the standard forward column/row recurrence equation based on the isolated singular factor method and extended-range arithmetic.Isolating a singular factor is a special normalization method that can improve the universality of the standard forward row recurrence equation to a certain extent,its universality can up to degree hundreds.However,it is invalid for standard forward column recurrence equation.The extended-range arithmetic expands the double-precision number field to the quad-precision numberfield.The quad-precision numberfield can retain more significant digits in the operation process and express larger and smaller numbers.The extended-range arithmetic can significantly improve the applicability and universality of the standard forward column/row recurrence equations,its universality can up to degree several thousand.However,the quad-precision numberfield operation needs to occupy more storage space,which is why its operation speed is slow and undesirable in practical applications.In this paper,the X-number method is introduced in the standard forward row recurrence equation for thefirst time.With the use of the X-number method,fnALFs can be recursed to 4.2 billion degree by using standard forward column/row recurrence equations.展开更多
To the editor： Ventral spinal schwannoma is not a frequently encountered disease and its surgical treatment is difficult.1,2 It has not been reported that the arachnoid adhesions caused by SURGICEL after operation fo...To the editor： Ventral spinal schwannoma is not a frequently encountered disease and its surgical treatment is difficult.1,2 It has not been reported that the arachnoid adhesions caused by SURGICEL after operation for ventral spinal schwannoma.A 45-year-old man was admitted to our clinic with complaints of intermittent lumbar pain for 12 months. Physical examination： The patient＇s lower extremity muscle strength was Ⅲ-Ⅳ grade, the bilateral knee tendon reflexes was hyperactive, the bilateral Babinski sign was positive, the sensory dysfunction level was at T11, the anal reflex was positive, the bilateral cremasteric reflex was positive.展开更多
文摘Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the standard forward column/row recurrence equation based on the isolated singular factor method and extended-range arithmetic.Isolating a singular factor is a special normalization method that can improve the universality of the standard forward row recurrence equation to a certain extent,its universality can up to degree hundreds.However,it is invalid for standard forward column recurrence equation.The extended-range arithmetic expands the double-precision number field to the quad-precision numberfield.The quad-precision numberfield can retain more significant digits in the operation process and express larger and smaller numbers.The extended-range arithmetic can significantly improve the applicability and universality of the standard forward column/row recurrence equations,its universality can up to degree several thousand.However,the quad-precision numberfield operation needs to occupy more storage space,which is why its operation speed is slow and undesirable in practical applications.In this paper,the X-number method is introduced in the standard forward row recurrence equation for thefirst time.With the use of the X-number method,fnALFs can be recursed to 4.2 billion degree by using standard forward column/row recurrence equations.
文摘To the editor： Ventral spinal schwannoma is not a frequently encountered disease and its surgical treatment is difficult.1,2 It has not been reported that the arachnoid adhesions caused by SURGICEL after operation for ventral spinal schwannoma.A 45-year-old man was admitted to our clinic with complaints of intermittent lumbar pain for 12 months. Physical examination： The patient＇s lower extremity muscle strength was Ⅲ-Ⅳ grade, the bilateral knee tendon reflexes was hyperactive, the bilateral Babinski sign was positive, the sensory dysfunction level was at T11, the anal reflex was positive, the bilateral cremasteric reflex was positive.
