?pivotal

pivotal發(fā)音

英：[?p?v?tl]　　美：[?p?v?tl]

英：　　美：

pivotal中文意思翻譯

adj.重要的, 關(guān)鍵的, 軸的

pivotal詞形變化

副詞: pivotally |

pivotal常見例句

1 、Permitting rotation, as a pulley or pivot.───允許旋轉(zhuǎn)的，如滑車或樞軸

2 、Because her job had been the pivot of her life, retirement was very difficult.───因為她的工作一向是她生命的支柱，所以退休后日子很不好過。

3 、No, it's the role of a mom, pivotal to the episode.─── 不 是一個母親的角色 劇集的關(guān)鍵

4 、Love plays a pivotal role on out life.───愛在我們的生活中扮演重要的角色。

5 、Like this testimony is pivotal to your case.─── 這項動議對你的案子至關(guān)重要的話

6 、Foreign trade occupies a pivotal position in Mexico's economy.───對外貿(mào)易在墨西哥經(jīng)濟(jì)中占舉足輕重的地位。

7 、Coach Torbett:Front pivot,baseline,bank.───朝底線前轉(zhuǎn)身，打板。

8 、Study on FeRAM and its pivotal integration process.───鐵電存儲器及其關(guān)鍵集成工藝。

9 、The pivotal factor of predicting rolling force is flow stress.───影響軋制力的主要因素是材料的流動應(yīng)力。

10 、It was a pivotal moment in her life.───那是她一生中重要的時刻。

11 、Front pivot baseline,reverse pivot hook.───朝底線前轉(zhuǎn)身，后轉(zhuǎn)身勾手。

12 、Just pivoting off that, this is our ornamental vineyard.─── 換個話題 這是我們家的裝飾性葡萄園

13 、I need you to counter, I need you to pivot.─── 我要你反擊 我要你轉(zhuǎn)動

14 、The gun is pretty much the pivot of their attack.───機(jī)**作為他們的進(jìn)攻的支點表現(xiàn)出色。

15 、Of, relating to, or serving as a pivot.───樞軸的樞軸的、與樞軸相關(guān)的或作為樞軸的

16 、That is the pivot of the whole argument.───這是整個論據(jù)的關(guān)鍵。

17 、The central brass pivot has an agate cap.───指南針的主軸有一個瑪瑙帽兒。

18 、Any deviation from this pivotal task endangers our material base.───離開了經(jīng)濟(jì)建設(shè)這個中心，就有喪失物質(zhì)基礎(chǔ)的危險。

19 、ABP(tm) (Active Braking Pivot) - Why Skid?───（積極制動軸）－為什么打滑?

20 、Pivotal hearing heads into second day in Florida court.───佛州法院關(guān)鍵聽審進(jìn)入第二天。

21 、FFA plays an pivotal role in early diagnosis of DON.───熒光造影檢查對糖尿病視神經(jīng)病變的早期診斷有重要意義。

22 、But when all is said and done, economic development is the pivot.───但是說到最后，還是要把經(jīng)濟(jì)建設(shè)當(dāng)作中心。

23 、So... if I say we have to pivot, we pivot.─── 所以...如果我說要轉(zhuǎn)做別的 那就得轉(zhuǎn)

24 、But the pivotal strategy must be mobile warfare.───但是轉(zhuǎn)換全局的戰(zhàn)略方針，必然要是運動戰(zhàn)。

25 、And as I pivot my wrist, this is the other leg.─── 隨著我手腕的轉(zhuǎn)動 這是另一條腿

26 、Standards are pivotal to the success of digital wallets.───標(biāo)準(zhǔn)化是數(shù)字錢包能否成功的關(guān)鍵。

27 、In this process,the finger is playing the pivotal role.───在此過程中,手指起著舉足輕重的作用。

28 、I don't know why we would wait to pivot.─── 我不知道我們?yōu)槭裁礇]有及時調(diào)整

29 、Deciding on how to divvy up the output cuts is a pivotal detail.───如何分?jǐn)偹鳒p的產(chǎn)量將是決定的關(guān)鍵細(xì)節(jié)所在。

30 、For Haier, logistics management has a pivotal role.───對于海爾來說，物流管理有著舉足輕重的作用。

31 、The father is often the pivot of a family.───父親往往是家庭生活的中心人物。

32 、Stomach is the pivotal organ of digestive system.───胃是重要的消化系統(tǒng)器官之一。

33 、Took both our pivots to break it up.─── 我們用了兩個中樞隊員才把她們拉開

34 、A vertical bolt that joins the body of a wagon or other vehicle to its front axle and usually acts as a pivot.───中心銷連接馬車或其它車輛的車身和它的前軸的垂直栓銷，一般起樞軸作用

35 、Trace wheel through pivot paper, line A to BP.───用擂盤在旋轉(zhuǎn)紙上畫線,從a1點到胸點。

36 、Love plays a pivotal role in life.───愛在生命中起著至關(guān)重要的作用。

37 、The act of turning on or as if on a pivot.───轉(zhuǎn)動，旋轉(zhuǎn)運動在樞軸上或似乎在樞軸上轉(zhuǎn)動的行為

38 、And if we need to pivot, the gear is right there.─── 如果我們需要行動時 防暴警察就在那里

39 、Love plays a pivotal role on our life. Love makes you feel wanted.───愛在生活之外扮演了一個關(guān)鍵的角色。愛使你想要得到些什么。

40 、The mother is often the pivot of family life.───母親往往是家庭生活的中心人物。

41 、In NCAA/FIBA, the first foot to touch is the pivot.───而在ncaa和fiba中，先落的一腳為中樞腳。

42 、Their daughter was the pivot of their lives.───女兒是他們生活的中心。

43 、West Africa was the pivot of the cocoa trade.───西非是可可豆貿(mào)易的中心。

44 、Since this is a pivotal question, we must not touch on it lightly.───這是個關(guān)鍵問題，不能輕描淡寫，一筆帶過。

45 、And then we will have Fallaway Reverse &Slip Pivot.───然后跳并退滑軸左轉(zhuǎn)。

46 、Place a pivot pin into the pivot point.───把大頭針扎在旋轉(zhuǎn)點上。

47 、Remove the inboard seatback pivot bolt.───拆卸內(nèi)側(cè)座椅背樞軸螺釘。

48 、You can't keep pivoting to talking points.─── 你總不能一直這么避重就輕吧

統(tǒng)計里的pivotal quantity怎么理解

探索統(tǒng)計學(xué)中的關(guān)鍵概念：什么是Pivotal Quantity？

在統(tǒng)計的世界里，我們常常遇到兩種核心概念：統(tǒng)計量與樞軸量。它們在理解總體參數(shù)估計中起著至關(guān)重要的作用。首先，讓我們來深入剖析。

統(tǒng)計量，作為樣本函數(shù)的靈魂，它的本質(zhì)是樣本的直接反映，不包含任何未知參數(shù)（一旦樣本數(shù)據(jù)確定，統(tǒng)計量的值也隨之固定）。然而，它的分布通常會與未知參數(shù)密切相關(guān)，例如樣本均值可以用來估計總體均值，但其分布會受到總體方差的影響。統(tǒng)計量的特點包括：作為參數(shù)的點估計工具，某些分布形式明確，如卡方分布和t分布等。

然而，樞軸量與統(tǒng)計量有所不同。樞軸量的核心在于，它直接嵌入了總體中的未知參數(shù)，雖然它的值會因樣本變化，但其分布形式卻固定不變，不依賴于任何未知參數(shù)。例如，正態(tài)分布中的標(biāo)準(zhǔn)化隨機(jī)變量，盡管包含未知參數(shù)，但其分布規(guī)則是明確的。樞軸量的主要用途在于區(qū)間估計，而非點估計，因為它們的分布特征使得我們可以直接利用。

想象一下，我們試圖估計一個未知的總體參數(shù)，比如全國人口的平均身高。統(tǒng)計量如樣本平均身高，為我們提供了估算的起點，但其分布依賴于總體的特性。相比之下，樞軸量，如標(biāo)準(zhǔn)化后的身高，盡管包含未知參數(shù)，但其分布形式已知，使我們能夠進(jìn)行更精確的區(qū)間估計。

在比較統(tǒng)計量與樞軸量時，我們可以看到它們的異同。統(tǒng)計量與樣本緊密相連，但其分布可能受未知參數(shù)影響；而樞軸量不僅依賴于樣本，還包含未知參數(shù)，但其分布形式固定。例如，樣本均值是統(tǒng)計量，而標(biāo)準(zhǔn)化后的均值可能就是樞軸量。

具體到問題，例如考慮以下選項：

統(tǒng)計量：樣本方差，因為它的分布包含未知參數(shù)（總體方差）

樞軸量：樣本的標(biāo)準(zhǔn)化值，其分布形式固定，不依賴未知參數(shù)

統(tǒng)計量（部分）：樣本均值，因為除了樣本量，還可能包含總體方差的估計

樞軸量：樣本與某個已知參數(shù)的函數(shù)，如t統(tǒng)計量，其分布與樣本大小相關(guān)，但不依賴未知參數(shù)

總結(jié)來說，統(tǒng)計量與樞軸量在統(tǒng)計學(xué)的海洋中各司其職，前者是參數(shù)估計的基石，后者則是更精確區(qū)間估計的得力工具。理解這兩者，無疑將有助于我們在實際問題中更準(zhǔn)確地解讀和應(yīng)用統(tǒng)計學(xué)原理。

態(tài)密度(Density of States)

1.1 Unveiling the Fundamentals

Density of States (DOS), at its core, signifies the count of electronic states available for occupation by an electron in a given energy level, expressed as the number of states per unit energy and volume. This pivotal concept underpins the electrical and thermal properties of conductive solids, influencing phenomena such as specific heat capacity, paramagnetic susceptibility, and conductivity. By calculating DOS, we gain insights into the general distribution of states and the energy gaps within semiconductors.

1.2 A Wave's Perspective

To grasp the essence of DOS, let's first delve into the realm of elastic waves in solids. These lattice vibrations in crystalline structures manifest as waves that, when wavelength is long, approximate a continuous medium. Starting with the one-dimensional wave equation:

Equation 1: The solution for a plane wave reads:

Where q (wave number) = 2π/λ, A (amplitude), ω (frequency), and Vs (sound speed) define the wave's behavior.

By eliminating the time-dependent factor, we arrive at:

Now, introducing periodic boundary conditions helps us analyze the system more rigorously. With each end point oscillating identically, the state density (g(ω)) emerges, representing the number of modes within an energy range (dω) around a specific frequency (ω).

1.3 Quantifying States in q-Space

In q-space, the interval dq contains a count of modes that can be calculated using the dispersion relation, giving us:

This counting extends to higher dimensions, as we explore the two-dimensional (2D) and three-dimensional (3D) scenarios:

2D DOS: Equation (1) modifies to:

Applying boundary conditions, we find the mode count within a ring in q-space:

And for the 3D case:

With consideration of transverse and longitudinal modes, we arrive at the total state density:

Ultimately, DOS為我們揭示了電子在不同能量層次上的分布情況，是理解材料性質(zhì)和電子行為的關(guān)鍵橋梁。