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periodic function

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periodic function 【數學】周期函數。

【數學】周期函數。 “periodic“ 中文翻譯：   adj. 【化學】高碘的。 “function“ 中文翻譯：   n. 1.功能，官能，機能，作用。 2.〔常 pl.〕職 ...“almost periodic function“ 中文翻譯：   殆周期函數“almost-periodic function“ 中文翻譯：   準周期函數“anti-periodic function“ 中文翻譯：   反周期函數“continuous periodic function“ 中文翻譯：   連續性周期函數“doubly periodic function“ 中文翻譯：   雙周期函數“generalized almost periodic function“ 中文翻譯：   廣義殆周期函數“left almost periodic function“ 中文翻譯：   左殆周期函數“multiply periodic function“ 中文翻譯：   多重周期函數; 復周期函數“non periodic function“ 中文翻譯：   非周期函數“non-periodic function“ 中文翻譯：   非周期函數“periodic forcing function“ 中文翻譯：   周期強制函數“periodic transfer function“ 中文翻譯：   周期傳遞函數“quasi periodic function“ 中文翻譯：   擬周期函數“quasi-periodic function“ 中文翻譯：   擬周期函數“simply periodic function“ 中文翻譯：   簡單周期函數“single periodic function“ 中文翻譯：   單周期函數“singly periodic function“ 中文翻譯：   單周期函數“triply periodic function“ 中文翻譯：   三周期函數“uniformly almost periodic function“ 中文翻譯：   一致殆周期函數“periodic“ 中文翻譯：    periodic1 adj. 1.周期的，回歸的，定期的，定時的；間歇的，時時的。 2.某一時期的。 3.【修辭學】掉尾句的，圓周句的；美詞麗句的。 adj. 【化學】高碘的。 “a function“ 中文翻譯：   絕對函數“and function“ 中文翻譯：   “與”功能; 及函數; 與酌; 與作用“and to or function“ 中文翻譯：   或作用; 與-或“作用

The whole paper consists of three parts : part is about general theory of the least positive period , which argues the necessary and sufficient condition for the existence of the least positive period for a periodic function , and concludes “ the existence of the least positive period for that periodic function , which is continuous at least one point and not equal ever to a constant “ ; part researches the least positive period for the sum of two periodic functions , followed its general expression ; part discusses non - periodicity for the compound function constructed by a periodic function and a non - periodic function , and the corresponding results 全文分為三部份：第一部份是關于最小正周期的一般理論，得到了周期函數有最小正周期的充分必要條件，也獲得了“至少在一個點連續且不恒等于常數的周期函數必有最小正周期”的結論；第二部份分析了兩個周期函數之和的最小正周期的問題，給出了其一般表達式；第三部份討論了周期函數與某些類型的非周期函數構成的復合函數的非周期性問題，并得出相應結論。

The whole paper consists of three parts : part is about general theory of the least positive period , which argues the necessary and sufficient condition for the existence of the least positive period for a periodic function , and concludes “ the existence of the least positive period for that periodic function , which is continuous at least one point and not equal ever to a constant “ ; part researches the least positive period for the sum of two periodic functions , followed its general expression ; part discusses non - periodicity for the compound function constructed by a periodic function and a non - periodic function , and the corresponding results 全文分為三部份：第一部份是關于最小正周期的一般理論，得到了周期函數有最小正周期的充分必要條件，也獲得了“至少在一個點連續且不恒等于常數的周期函數必有最小正周期”的結論；第二部份分析了兩個周期函數之和的最小正周期的問題，給出了其一般表達式；第三部份討論了周期函數與某些類型的非周期函數構成的復合函數的非周期性問題，并得出相應結論。

periodic law

According to the principle of generation of prime number through boolean algebra logic operation and phase angle matrix analysis of the periodic function it comes out that any even number larger than 4 can be expressed as the sum of two prime numbers ， i . e . “ 1 + 1 ” is tenable , and thereby finishes demonstration of the validity of goldbach ' s conjecture 根據素數的形成機理，從布爾代數的邏輯運算和周期函數的相角矩陣分析，都得出了大于4的任何偶數都可表示成兩個素數之和即“ 1 + 1 ”成立，從而完成了哥德巴赫猜想成立的論證。

Based on vibration principle , the paper establishes dynamics analysis model of output shaft with elastic support , according to fourer series spread principle of periodic function , the dynamic response formula is derived by separating complex vibration force into sum of many simple harmonic excitation function of whole number times frequency relations . the result shows that response of both sides support is synchronous when load distribution non - uniform coefficient is 1 依據振動理論建立了具有彈性支撐的輸出軸的動力學分析模型，根據周期函數的傅里葉級數展開原理，將復雜的激振力分解成為多個頻率成整倍數關系的簡諧激勵函數，導出了動態響應表達式，結果表明，當載荷分配不均勻系數為1 . 0時的輸出軸兩端支撐同步。

This paper is devoted to nonlinear approximation , namely , m - term approximtion of anisotropic smooth periodic functions . nonlinear approximation is the important part of approximation the - ory . it means that the approximants do not come from linear spaces but rather from nonlinear manifolds . the advantages of nonlinear approximation show that one can achieve a given accuracy of approximation while assuming less smoothness on the function in the nonlinear case than is necessary in the corresponding linear approximation . nonlinear approximation is used significantly in many applications , such as image processing , noise removal and the solution of operation equations and so on 非線性逼近與線性逼近最大的區別在于所用的逼近子空間不是固定的，而是依賴于被逼近的函數其主要優點是對光滑度較低的函數仍可以得到較高的估計階。隨著小波和樣條的廣泛使用非線性( m項)逼近成為較熱門的話題，它在圖象處理，聲的傳播，算子方程的求解等方面都有很多應用。

The arrangement of the article is : in the second section the properties of existence , uniqueness , global attractivity are discussed ; in the third section , the properties of asmptotic periodic function are proved ; in the fourth and the fifth section , on one dimention and multiple - dimention , asmptotic periodic function space are banach space 本文的具體安排如下：第二節給出漸近周期解存在唯一性和全局吸引性；第三節證明了在某些適當的條件下，漸近周期函數的性質；第四，五節分別證明了在一維和高維下，漸近周期函數空間是banach空間

Therefore , we need more concrete function to better discribe the variation of some biological populations in our real world . the two important indexes r ( t ) and k ( t ) of logistic equation are asmptotic periodic function , and discussed by author . the asmptotic solution of the asmptotic periodic logistic function is obtained 因而，為了更好地刻劃客觀世界，我們需要用更加符合客觀實際的函數來描述生物種群的變化，于是作者對logistic方程的兩個重要的參數r ( t ) ， k ( t )分別是漸近周期函數時，研究漸近周期logistic方程的漸近周期解，并且得到了解的存在性，唯一性，全局吸引性等一些良好的性質

Especially in recent score years , in autonomous and nonautonomous systems , the neutral , finite - delay , infinite - delay , diffusive , discrete , discrete - delay , generalized , difference and other style models were discussed on optimal harvesting , osillation , stability , global stability , and other asmptotic behaviors of logistic equation . reference were searched in [ l - 6 ] , [ 10 - 18 ] , [ 20 - 31 ] , [ 34 ] . the periodic and almost periodic function logistic equation , which are widely studied recently , the results about the above are found on many kinds of magazines 尤其是近二十多年來，在自治系統與非自治系統中有關有限時滯型，無限時滯型，中立型，離散型，擴散型，離散時滯型，廣義型，差分型logistic方程的最優捕獲策略，振動性，周期解，概周期解，漸近性態，全局性態等方向進行了各方面的研究，可參見文獻[ 1 - 6 ] ， [ 10 - 18 ] ， [ 20 - 31 ] ， [ 34 ]

The whole paper consists of three parts : part is about general theory of the least positive period , which argues the necessary and sufficient condition for the existence of the least positive period for a periodic function , and concludes “ the existence of the least positive period for that periodic function , which is continuous at least one point and not equal ever to a constant “ ; part researches the least positive period for the sum of two periodic functions , followed its general expression ; part discusses non - periodicity for the compound function constructed by a periodic function and a non - periodic function , and the corresponding results 全文分為三部份：第一部份是關于最小正周期的一般理論，得到了周期函數有最小正周期的充分必要條件，也獲得了“至少在一個點連續且不恒等于常數的周期函數必有最小正周期”的結論；第二部份分析了兩個周期函數之和的最小正周期的問題，給出了其一般表達式；第三部份討論了周期函數與某些類型的非周期函數構成的復合函數的非周期性問題，并得出相應結論。

Within the author ' s knowledge , recently , the results are few about the asmptotic logistic equation . the articles , [ 32 - 33 ] discuss the logistic equation , in which the two important indexes r ( t ) and k ( t ) are not only dependent on t . but also asmptotically tend to periodic function 目前，據作者所知，在r ， k是漸近周期函數方面， logistic方程的結果卻相對很少，文獻[ 32 ， 33 ]所討論的系統參數r ， k不僅是與時間t有關，而且是漸近接近于周期函數的

In [ 20 ] , zhang chuanyi has introduced an extension of the almost periodic functions , the so - called pseudo - almost periodic functions . then , the existence of pseudo - almost periodic solutions of some differential equations with piecewise constant argument is considered in some papers ( [ 21 ] ~ [ 25 ] ) 張傳義在文[ 20 ]中推廣了概周期函數的概念，引進了偽概周期函數的概念，之后有些文獻研究了具逐段常變量微分方程的偽概周期的存在性[ 21 ] [ 25 ] 。

The periodic function is separated into the digital quantity . it has the high stability signal sweep frequency using the phase - lock link to carry on to the digital quantity reading , through d / a transformation , the appropriate filter may obtain the high stability signal output 摘要將周期函數離散成為分離的數字量，利用鎖相環產生高穩定度的信號掃描頻率對數字量進行讀取，經過d / a變換及恰當的濾波可以獲得高穩定度的信號輸出。

If the initial photon state is a fock state , the probability density of the electron exhibits bifurcation and confluence and the corresponding photon distribution is a time - periodic function which result from the energy exchange between the electron and field Ck態時，隨著時間的演化，電子的兒率密度呈現分叉現象，相應的光子數分布是時間周期函數，這是由于電子與光場之間有能量交換。在這種情況下，系統是封閉的。

Some fundamental methods in mathematical analysis are applied to prove the unique decomposition theorem : the distance between vector - valued pseudo almost periodic functions in metric spaces and almost periodic functions is an ergodic perturbation 應用數學分析中的基本方法證明了唯一分解定理，即距離空間中的向量值偽概周期函數和概周期函數之間的距離是一個遍歷擾動。

Based on some results for almost periodic functions and almost periodic sequences , some results for asymptotically almost periodic functions on r ( superscript + ) and asymptotically almost periodic sequences on z ( superscript + ) are obtained 摘要主要利用概周期函數和概周期序列的一些結果，給出了r (上標+ )上漸近概周期函數和z (上標+ )上漸近概周期序列的相關結果。

In this paper , we mainly study coexistence problem of nonautonomous predator - prey system with n - predator and one - prey , and study the existence of positive periodic solutions when the coefficients are periodic functions 本文主要研究n + 1維非自治捕食者-食餌系統的共存問題，進一步當系統中的系數為周期函數時研究了系統周期正解的存在性。

Most radar signals are non - stationary signals , but they are cyclostationary signals , namely , the correlation function of radar signals is periodic function of time 大部分的雷達信號都是非平穩信號,但它們都具有循環平穩特性,所謂循環平穩信號是指相關函數為時間的周期函數的一大類非平穩信號。

The properties of asmptotic periodic function and the asmptotic periodic function space are studied , accordingly , we have , the asmptotic periodic function space is banach space 并在此基礎上，進一步研究漸近周期函數所構成的空間，相應的得到漸近周期函數空間是banach空間

3 the effective value of a non sinusoidal periodic function is equal to the square root of the square sum of the constant component value and every harmonic component effective value 非正弦周期函數的有效值等于直流分量與各次諧波分量有效值的平方和的平方根。