In this paper, some properties of solutions of linear differential equations f^（k）＋A（z）f = 0 and f（k）＋ A（z）f = F（z） are discussed. Our results are a generalization of the original results.
The growth of solutions of the following differential equation f^(k)+Ak-z(z)f^(k-1)+…+A1(z)f′+A0(z)f=0 is studied,where Aj(z)is analytic in the unit disc D={z:|z|<1}for j=0,1,...,k-1.Some precise estimates of[p,q...The growth of solutions of the following differential equation f^(k)+Ak-z(z)f^(k-1)+…+A1(z)f′+A0(z)f=0 is studied,where Aj(z)is analytic in the unit disc D={z:|z|<1}for j=0,1,...,k-1.Some precise estimates of[p,q]-order of solutions of the equation are obtained by using a notion of new[p,q]-type on coefficients.展开更多
Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)i...Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.展开更多
In this paper, we investigate the growth of solutions to some linear diferential equations with analytic coefcients in the unit disc. When the coefcients of these equations have some special properties near a point on...In this paper, we investigate the growth of solutions to some linear diferential equations with analytic coefcients in the unit disc. When the coefcients of these equations have some special properties near a point on the boundary of the unit disc, the order and the hyper order of the solutions to these equations are estimated accurately. Especially, our conditions on the coefcients are more general and the results on the hyper order of the solutions are new to some extent.展开更多
In this paper, we study the growth of the solutions for 1st kind of differential equations of higher order in the unit disc. We give a sufficient condition for all solutions of second order linear differential equatio...In this paper, we study the growth of the solutions for 1st kind of differential equations of higher order in the unit disc. We give a sufficient condition for all solutions of second order linear differential equation to be inadmissible and a sufficient condition for all solutions of higher order linear differential equation to be of infinite order.展开更多
The frequency of any periodic event can be defined in terms of units of Time. Planck constructed a unit of time called the Plank time from other physical constants. Vyasa defined a natural unit of time, kshana, or mom...The frequency of any periodic event can be defined in terms of units of Time. Planck constructed a unit of time called the Plank time from other physical constants. Vyasa defined a natural unit of time, kshana, or moment based on the motion of a fundamental particle. It is the time taken by an elementary particle, to change its direction from east to north. According to Vyasa, kshana is discrete, exceedingly small, indivisible, and is a constant time quantum. When the intrinsic spin angular momentum of an electron was related to the angular momentum of a simple thin circular plate, spherical shell, and solid sphere model of an electron, we found that the value of kshana in seconds was equal to ten to a power of minus twenty-one second. The disc model for the spinning electron provides an accurate value of the number of kshanas per second as determined previously and compared with other spinning models of electrons. These results indicate that the disk-like model of spinning electrons is the correct model for electrons. Vyasa’s definition of kshana opens the possibility of a new foundation for the theory of physical time, and perspectives in theoretical and philosophical research.展开更多
目的观察单节段Discover人工颈椎间盘置换术及颈椎前路减压融合术后颈椎整体曲度和置换节段活动度的变化情况,分析其临床效果。方法回顾性分析2008年3月至2013年3月治疗的48例颈椎病及颈椎间盘突出症患者,其中18例行Discover人工颈椎间...目的观察单节段Discover人工颈椎间盘置换术及颈椎前路减压融合术后颈椎整体曲度和置换节段活动度的变化情况,分析其临床效果。方法回顾性分析2008年3月至2013年3月治疗的48例颈椎病及颈椎间盘突出症患者,其中18例行Discover人工颈椎间盘置换术（置换组）,男8例,女10例,年龄31-58岁,平均44.2岁;30例行颈椎前路减压融合术（融合组）,男13例,女17例,年龄35-68岁,平均49.8岁。测量手术前后和末次随访时置换节段活动度（range of motion,ROM）,置换节段脊柱功能单位（functional spinal unit,FSU）Cobb角和颈椎整体曲度（C2-7Cobb角）。结果两组患者均获得12个月以上随访,末次随访置换节段屈伸活动度置换组较术前稍增加,左右侧屈活动度无明显变化,而融合组屈伸及左右侧屈活动度较术前明显减小,差异有统计学意义（P〈0.05）;两组间末次随访相比较,融合组屈伸及左右侧屈活动度明显减小,差异有统计学意义（P〈0.05）。末次随访FSU置换组较术前明显增加,差异有统计学意义（P〈0.05）,而融合组无明显变化;两组间末次随访相比较,置换组明显增加,差异有统计学意义（P〈0.05）。末次随访颈椎曲度置换组较术前稍增加,而融合组较术前明显减小,差异有统计学意义（P〈0.05）;两组间末次随访相比较,融合组明显减小,差异有统计学意义（P〈0.05）。结论单节段Discover人工颈椎间盘置换术后对颈椎整体曲度及置换节段活动度的影响小,与传统前路减压融合术相比,可以较好发挥其对颈椎的保护作用。展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130123211171119)+1 种基金the Youth Science Foundation of Education Bureau of Jiangxi Province(Grant No.GJJ12207)the Natural Science Foundation of Jiangxi Province(Grant No.20132BAB211009)
文摘In this paper, some properties of solutions of linear differential equations f^（k）＋A（z）f = 0 and f（k）＋ A（z）f = F（z） are discussed. Our results are a generalization of the original results.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11861023,11501142)the Foundation of Science and Technology Project of Guizhou Province(Grant No.20185769-05)+1 种基金the Foundation of Doctoral Research Program of Guizhou Normal University 2016the Foundation of Science and Technology of Guizhou Province(Grant No.20152112)。
文摘The growth of solutions of the following differential equation f^(k)+Ak-z(z)f^(k-1)+…+A1(z)f′+A0(z)f=0 is studied,where Aj(z)is analytic in the unit disc D={z:|z|<1}for j=0,1,...,k-1.Some precise estimates of[p,q]-order of solutions of the equation are obtained by using a notion of new[p,q]-type on coefficients.
基金supported by the National Natural Science Foundation of China(Grant No.11942109).
文摘Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.
基金supported by the National Natural Science Foundation of China(11301233 and 11171119)the Natural Science Foundation of Jiangxi Province(20114BAB211003 and 20122BAB211005)
文摘In this paper, we investigate the growth of solutions to some linear diferential equations with analytic coefcients in the unit disc. When the coefcients of these equations have some special properties near a point on the boundary of the unit disc, the order and the hyper order of the solutions to these equations are estimated accurately. Especially, our conditions on the coefcients are more general and the results on the hyper order of the solutions are new to some extent.
文摘In this paper, we study the growth of the solutions for 1st kind of differential equations of higher order in the unit disc. We give a sufficient condition for all solutions of second order linear differential equation to be inadmissible and a sufficient condition for all solutions of higher order linear differential equation to be of infinite order.
文摘The frequency of any periodic event can be defined in terms of units of Time. Planck constructed a unit of time called the Plank time from other physical constants. Vyasa defined a natural unit of time, kshana, or moment based on the motion of a fundamental particle. It is the time taken by an elementary particle, to change its direction from east to north. According to Vyasa, kshana is discrete, exceedingly small, indivisible, and is a constant time quantum. When the intrinsic spin angular momentum of an electron was related to the angular momentum of a simple thin circular plate, spherical shell, and solid sphere model of an electron, we found that the value of kshana in seconds was equal to ten to a power of minus twenty-one second. The disc model for the spinning electron provides an accurate value of the number of kshanas per second as determined previously and compared with other spinning models of electrons. These results indicate that the disk-like model of spinning electrons is the correct model for electrons. Vyasa’s definition of kshana opens the possibility of a new foundation for the theory of physical time, and perspectives in theoretical and philosophical research.
文摘目的观察单节段Discover人工颈椎间盘置换术及颈椎前路减压融合术后颈椎整体曲度和置换节段活动度的变化情况,分析其临床效果。方法回顾性分析2008年3月至2013年3月治疗的48例颈椎病及颈椎间盘突出症患者,其中18例行Discover人工颈椎间盘置换术（置换组）,男8例,女10例,年龄31-58岁,平均44.2岁;30例行颈椎前路减压融合术（融合组）,男13例,女17例,年龄35-68岁,平均49.8岁。测量手术前后和末次随访时置换节段活动度（range of motion,ROM）,置换节段脊柱功能单位（functional spinal unit,FSU）Cobb角和颈椎整体曲度（C2-7Cobb角）。结果两组患者均获得12个月以上随访,末次随访置换节段屈伸活动度置换组较术前稍增加,左右侧屈活动度无明显变化,而融合组屈伸及左右侧屈活动度较术前明显减小,差异有统计学意义（P〈0.05）;两组间末次随访相比较,融合组屈伸及左右侧屈活动度明显减小,差异有统计学意义（P〈0.05）。末次随访FSU置换组较术前明显增加,差异有统计学意义（P〈0.05）,而融合组无明显变化;两组间末次随访相比较,置换组明显增加,差异有统计学意义（P〈0.05）。末次随访颈椎曲度置换组较术前稍增加,而融合组较术前明显减小,差异有统计学意义（P〈0.05）;两组间末次随访相比较,融合组明显减小,差异有统计学意义（P〈0.05）。结论单节段Discover人工颈椎间盘置换术后对颈椎整体曲度及置换节段活动度的影响小,与传统前路减压融合术相比,可以较好发挥其对颈椎的保护作用。
