Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
In this paper we study the Oscillatory behaviour of the second order delay differenceequation.（1）△（r<sub>n</sub>△A<sub>n</sub>）+P<sub>n</sub>A<sub>n-k</sub>=0,n=n&...In this paper we study the Oscillatory behaviour of the second order delay differenceequation.（1）△（r<sub>n</sub>△A<sub>n</sub>）+P<sub>n</sub>A<sub>n-k</sub>=0,n=n<sub>0</sub>,n<sub>0</sub>+1……where{P<sub>n</sub>}（?）is a nonnegative Sequenceof real number,（?）is a positive sequence of real number with sum from n=n<sub>0</sub> to +∞（1/r<sub>n</sub>）=+∞,K is a positive integer and △A<sub>n</sub>=A<sub>n+1</sub>-A<sub>n</sub> we prove that each one of following conditions.imples that al solutions of Eq（1）oscillate,where R<sub>n</sub>=sum from i=n<sub>0</sub> to n（1/r<sub>i</sub>展开更多
By utilizing the first order behavior of the device,an equation for the frequency of operation of the submicron CMOS ring oscillator is presented.A 5-stage ring oscillator is utilized as the initial design,with differ...By utilizing the first order behavior of the device,an equation for the frequency of operation of the submicron CMOS ring oscillator is presented.A 5-stage ring oscillator is utilized as the initial design,with different Beta ratios,for the computation of the operating frequency.Later on,the circuit simulation is performed from 5-stage till 23-stage,with the range of oscillating frequency being 3.0817 and 0.6705 GHz respectively.It is noted that the output frequency is inversely proportional to the square of the device length,and when the value of Beta ratio is used as 2.3,a difference of 3.64%is observed on an average,in between the computed and the simulated values of frequency.As an outcome,the derived equation can be utilized,with the inclusion of an empirical constant in general,for arriving at the ring oscillator circuit’s output frequency.展开更多
文摘Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
文摘In this paper we study the Oscillatory behaviour of the second order delay differenceequation.（1）△（r<sub>n</sub>△A<sub>n</sub>）+P<sub>n</sub>A<sub>n-k</sub>=0,n=n<sub>0</sub>,n<sub>0</sub>+1……where{P<sub>n</sub>}（?）is a nonnegative Sequenceof real number,（?）is a positive sequence of real number with sum from n=n<sub>0</sub> to +∞（1/r<sub>n</sub>）=+∞,K is a positive integer and △A<sub>n</sub>=A<sub>n+1</sub>-A<sub>n</sub> we prove that each one of following conditions.imples that al solutions of Eq（1）oscillate,where R<sub>n</sub>=sum from i=n<sub>0</sub> to n（1/r<sub>i</sub>
文摘By utilizing the first order behavior of the device,an equation for the frequency of operation of the submicron CMOS ring oscillator is presented.A 5-stage ring oscillator is utilized as the initial design,with different Beta ratios,for the computation of the operating frequency.Later on,the circuit simulation is performed from 5-stage till 23-stage,with the range of oscillating frequency being 3.0817 and 0.6705 GHz respectively.It is noted that the output frequency is inversely proportional to the square of the device length,and when the value of Beta ratio is used as 2.3,a difference of 3.64%is observed on an average,in between the computed and the simulated values of frequency.As an outcome,the derived equation can be utilized,with the inclusion of an empirical constant in general,for arriving at the ring oscillator circuit’s output frequency.
