Sunday, September 8, 2019

也談數學“黑洞”——關於卡普雷卡爾常數 金彈子 (原創)

也談數學“黑洞”——關於卡普雷卡爾常數      金彈子 (原創)   http://blog.sina.com.cn/s/blog_4d0579fe01000955.html  

美國數學教授Michael W Ecker在《數學“黑洞”》一文中對卡普雷卡爾常數(Kaprekar,s constant)描述道:取任何一個4位數(4個數字均為同一個數字的例外),將組成該數的4個數字重新組合成可能的最大數和可能的最小數,再將兩者的差求出來;對此差值重複同樣的過程(例如:開始時取數8028,最大的重新組合數為8820,最小的為0288,二者的差8532。重複上述過程得出8532-2358=6174),最後總是達到卡普雷卡爾黑洞:6174。 (見美國《新科學家》,1992,12,19,p38。中國《參考消息》,1993,3,14-17)

   稱之“黑洞”是指再繼續運算,都重複這個數,“逃”不出去。

   但是,4位數以外的其它位數的數有沒有“黑洞”?如果有,它們之間有沒有什麼規律性?還有沒有其它更多的內容? 《數學“黑洞”》沒有說到。本文就是對這些進行討論。

   我在這裡把以上計算得出卡普雷卡爾常數的過程簡稱運算,這個現象稱歸斂,其結果6174稱歸斂結果。以下討論,限於自然數(正整數)。

一、 4位數以外的其它位(任意位)的數的歸斂

   舉一些位數的數的運算結果如下:

例1-1 如卡氏常數所述,所有的4位數經運算都歸斂到6174。

例1-2 所有7位數經運算都歸斂到數組

8,429,652

7,619,733

8,439,552

7,509,843

9,529,641

8,719,722

8,649,432

7,519,743

例1—3 所有10位數經運算都歸斂到以下2個數和5個數組:

2個數是: 1) 9,753,086,421

         2) 6,333,176,664

5個數組是:

  1)

8,655,264,432

6,431,088,654

        8,732,087,622

   2)

6,433,086,654

8,332,087,662

8,653,266,432

3)

8,765,264,322

6, 543,086, 544

9,751,088,421

4)

9,775,084,221

9,755,084,421

8,321,088,762

5)

8,633,086,632

8,633,266,632

6,433,266,654

4,332,087,666

8,533,176,642

7,533,086,643

8,433,086,652

此外:

一位數的歸斂數是0(沒有意義)。

二位數的歸斂數是9,但已不是2位數。以後的討論均不含它們。

三位數的歸斂數是495,其特殊性後面述及。

    通過運算知道,任意n位的數經運算後都能歸斂到三類結果,可能是一個數(稱歸斂數),或是一個數組(稱歸斂組),或若干個數和數組兼而有之。少數歸斂結果是唯一的,如3位數、4位數、7位數,其它則不是唯一的,但其個數是可以確定的有限個數。得到歸斂結果以後,繼續運算也是“逃”不出這些歸斂結果的。任意n位的數各位數字相同時(各有9個),運算結果為0。可視0為它們的特殊歸斂結果,這個歸斂結果沒有意義。這個結論是本文最重要的結論之一。

    要計算任意n位數的歸斂結果,理論上必須對該n位數的所有數進行運算,實際上不可能也沒有必要。分析可知,只須少量運算即可得出。例如:

5位數不必運算9×104 個數(10的4次方),只須運算54個數。

10位數不必運算9×109 個數(10的9次方),只須運算2001個數。

17位數不必運算9×1016個數(10的16次方),只須運算48,049個數(或更少)。等等。


二、 歸斂結果之間的聯繫和派生現象

    歸斂結果之間是互相有相關關係的.

1.聯繫位數較少的n位數的歸斂結果可按一定規律嵌入一些特定的數字(以下用黑體字表示)後,派生成位數較多的N位數(N>n)的歸斂結果。原n位數的歸斂結果稱N位的數根。

   用符號К跟在嵌入數後,表示嵌入К個相同的數。如3К表示嵌入К個3,當К=5,表示嵌入5個3:33333。 К為≥0的任意整數。舉例如下。

第一類 歸斂數派生歸斂數

例2—1—1

4位歸斂數 6174 逐次嵌入3和6這2個數,分別得到6位、8位……的歸斂數。

6位: 6 3 17 6 4,

8位: 6 33 17 66 4,

……

N位: 6 3К 17 6К 4 N=4+2К

6174 稱為它們的數根.

例2—1—2 8位歸斂數 97,508,421 逐次嵌入 9和 0 這 2個數,分別得到 10位、12位…… 的歸斂數。

10位: 9,9 75,084,2 0 1

12位: 9 99,750,842,00 1

……

N位: 9 9К 750842 0К 1 N=8+2К

97,508,421 稱為它們的數根.

例2—1—3 8位歸斂數97,508,421逐次嵌入7,2、5,4、1,8這6個數後分別得到14位、20位…… 的歸斂數。

14位: 97,7 5 5,1 08,8 4 4,2 21

20位:97,77 5,55 1,1 08,88 4,4 4 2,2 21

 ……

   N位: 97 7К 5 5К 1К 08 8К 4К 4 2К 21

N=8+6К

97,508,421 稱為它們的數根.

例2—1—4 17位歸斂數98,765,420,987,543,211逐次嵌入8,6,4,2,9,7,5,3,1這9個數後分別得到26位、35位…… 的歸斂數。

26位: 98,876,654,422,099,877,554,332,111

35位:98,887,666,544,4 2 2,2 09,99 8,777,555,433,321,111

……

N位:98 8К 76 6К 54 4К 2 2К 09 9К 8 7К 7 5К 54 3К 32 1К 11

    N=17+9К

98,765,420,987,543,211稱為它們的數根.

例2—1—5 3位歸斂數495逐次嵌入5,9,4(僅第一次嵌入略不同,後述)後,分別得到6位、9位…… 的歸斂數。

6位: 549,94 5 (第一次嵌入略不同)

9位: 5 5 4,9 99,44 5

……

N位: 5 5К 49 9К 4К 5 N=3+3К

549,945稱為它們的數根.

第二類 由歸斂數派生歸斂

例2—2—1 8位歸斂數97,508,421分別逐次嵌入數組

7,2

5,4

1,8

後,分別得到10位、12位…… 的歸斂組(注:嵌入形式有別於例2—1—3)。

10位:

    9,7 7 5,084,2 21

    9,75 5,08 4,421

    9,751,08 8,421

12位:

    97 7,7 50,84 2,2 21

    975,55 0,8 44,421

    975,11 0,8 88,421

……

N位:

     97 7К 5084 2К 21

     975 5К 08 4К 421

     975 1К 08 8К 421

     N=8+2К

     97,508,421稱為它們的數根.

第三類 由歸斂組派生歸斂組

例2—3—1 8位數歸斂組

86,526,432

64,308,654

83,208,762

各數對應逐次嵌加數組

5,4

1, 8

7,2

後分別得到10位、12位…的歸斂組。

10位:

    8,65 5,26 4,432

    6,43 1,08 8,654

    8,7 32,087,6 2 2

12位:

   865,55 2,6 44,432

   643,11 0,8 88,654

   877,320,876,22 2

N位:

   865 5К 26 4К 432

   643 1К 08 8К 654

    8 7К 320876 2К 2

         ……

    N=8+2К

    原8位數歸斂組

   86,526,432

   64,308,654

   83,208,762

就稱為它們的數根.

例2—3—2 11位歸斂組

96,641,975,331

88,431,976,512

87,641,975,322

86,541,975,432

86,420,987,532

各數分別逐次嵌入8,6,4,2,9,7,5,3,1這9個數後分別得到20位、29位、38位…… 的歸斂組。

 20位

98,666,44 2,19 9,7 75,5 3 3,31 1

88,864,4 32,19 9,7 76,5 53,1 12

8 8,76 6,4 4 2,19 9,7 75,53 3,212

8 8,6 6 5,4 42,19 9,7 75,54 3,31 2

8 8,6 6 4,4 2 2,09 9,8 7 7,5 5 3,3 1 2

……

 N位:

9 8К 66 6К 4 4К 2К 19 9К 7 7К 5К 5 3К 33 1К 1

88 8К 6К 4 4К 3 2К 19 9К 7 7К 6 5К 5 3К 1К 12

8 8К 76 6К 4 4К 2К 19 9К 7 7К 5К 5 3К 32 1К 2

8 8К 6 6К 54 4К 2К 19 9К 7 7К 5К 54 3К 3 1К

8 8К 6 6К 4 4К 2 2К 09 9К 8 7К 7 5К 5 3К 3 1К 2

      N=11+9К

原11位歸斂組

96,641,975,331

88,431,976,512

87,641,975,322

86,541,975,432

86,420,987,532

就稱為它們的數根.

第四類 由歸斂組派生歸斂數

例3—1—4 17位歸斂組

97,665,420,,987,543,321

98,654,320,987,654,311

98,764,320,987,653,211

98,765,431,976,543,211

88,754,320,987,654,212

    這歸斂組5個數中任何一個數嵌入(7,2)、(5,4)、(1,8)當中的任何一個數對,經運算後均得到19位歸斂數9,876, 543,209,876,543,211。繼續嵌加,則又成為前述第二類派生。

2. 基礎數根

     由上述可知,任意N位數的歸斂結果都是較少n位數的歸斂結果嵌加某些數派生而成(即如前述),因此,這些較少n位數的歸斂結果是派生所有任意N位數歸斂結果的基礎,稱它們為基礎數根。這又是本文的重要結論之一。

它們是以下8個:

1) n=4 6,174

2) n=6 549,945

3) ( n=6 )數組

860,832

862,632

642,654

420,876

851,742

750,843

840,852

4) n=8 97,508,421

5) (n=8 )數組

86,526,432

64,308,654

83,208,762

6) n=9 864,197,532

7) n=11 數組

86,420,987,532

96,641,975,331

88,431,976,512

87,641,975,322

86,541,975,432

8) n=13 數組

8,733,209,876,622

9,665,429,654,331

3.層狀組數結構

   從歸斂結果可以看出,它們形成了有規律的層狀組數結構。

   把奇位歸斂數的中間那個數稱中位數,偶位的中間那兩個數稱中位數,中位數的前段數字稱前段,後段數字稱後段。

   中位數前、後相同位數上的兩個數稱數層,兩數之和稱層和。層和為8的層及其包容的所有數稱數核。層和為9的層稱普通層。唯有最外層的層和為10,稱飽和層。

   例如 864,197,532 : 是9位數,屬奇位。 9稱中位數;197稱數核,864稱前段,532稱後段;(8,2)稱飽和層,(6,3)、(4,5)稱普通層。

   9,975,084,201 : 是10位數,屬偶位。 08稱中位數;08又稱數核。 9975稱前段,4201稱後段;(9,1)稱飽和層,(9,0)、(7,2)、(5,4)稱普通層。

   555,499,994,445 : 是12位,屬偶位。 99為中位數;499994稱數核。 555稱前段,445稱後段;(5,5)稱飽和層,(5,4)、(5,4)稱普通層。

    總之,所有的歸斂結果都呈層狀組數結構。唯有3位歸斂數495和5位數歸斂組之一的

59,994

53,995

尚未形成完整的層狀組數結構。

4.派生歸斂結果的嵌數規律

(1)嵌入數 嵌入的數是特定的,共有3類。

第一類是數對型,有兩對: 1)9,0 2)3,6

第二類是數組型,有一組:

7,2

5,4

1,8

第三類是數字型,有兩個:

1) 5 9 4

2) 8 6 4 2 9 7 5 3 1

(2)嵌入方法

1)嵌入數的一部分嵌入前段中大於或等於嵌入數的最末一個數字的後鄰位置。另一部分嵌入後段相應位置_____使與嵌入前段的數形成層狀組數結構。

數對型:(9,0)、(3,6)的奇數9,3嵌入前段,偶數0,6嵌入後段。見例2—1—1, 2—1—2。

數組型: 7,2

         5,4

         1,8

的奇數7,5,1嵌入前段,偶數2,4,8嵌入後段。見例2—1—3, 2—2—1。

數字型:9嵌入數核,8642分開嵌入前段,7531分開嵌入後段。見例2—1—4,2—3—2。

594只能嵌入n=3+3К 這類數。 9嵌入數核,5嵌入前段,4嵌入後段。見例2—1—5。

2)飽和層外不能嵌加。 3位歸斂數的最外層層和為9,尚未 “飽和”,視為可嵌加,如例2—1—5。嵌加一次成6位數,最外層飽和了,以後則按上述規律派生。所以本文把549945而不是495作為基礎數根。

3)(9,0)、(3,6)兩對數可以獨對、兩對嵌入或與數組型、數字型組合嵌入。

4)數組

7,2

5,4

1,8

必須“配套”嵌入並按順序:

(7,2)→(5,4)→(1,8)

或 (5,4)→(1,8)→(7,2)

或 (1,8) →(7,2) →(5,4)。

以8位數歸斂組

86,526,432

64,308,654

83,208,762

為例說明。

A,各數均可嵌入(3,6)К,得n=8+2К位數的歸斂組。

865 3К 26 6К 432

643 3К 08 6К 654

83 3К 2087 6К 62

B, 各數可對應嵌入

(7,2) К

(5,4 )К,

(1,8) К

得n=8+2К位數的歸斂組。

8 7К 652643 2К 2

6 5К 430865 4К 4

832 1К 08 8


三、 歸斂結果的特點

   通過以上的討論,可以總結歸斂結果的特點如下。

1.任意數A,其歸斂結果為B,B和A的位數相同。

2.歸斂結果的各數字之和是9的整數倍。如6174:6+1+7+4=18=2×9。

1) 任意奇位數(n=2k-1)和偶位數(n=2k)的歸斂結果,其各數字之和均為 (k+1)×9或k×9。

2)n=3+3k 位這類數的歸斂結果,無論奇、偶位數,其各位數字之和均為(2k×9。

3)前後兩段數字都是由大到小順序排列。

4)運算中,一次就能形成層狀組數結構而無論是否已成為歸斂結果。只有極少數例外。例如:任意n位數,其中一位為a,其餘n-1位為b(a≠b)如266…6。

5)同一個歸斂組中各數可按順序遞進交換。例如:

86,526,432

64,308,654

83,208,762,

可為

64,308,654

83,208,762

86,526,432

或為

83,208,762

86,526,432

64,308,654

6)歸斂結果的派生有如下傳遞性。

①簡單傳遞。如嵌加(3,6)、(9,0)、864297531的各種情況。見前述例子。

②順序傳遞。只有嵌加數組 7,2

                              5,4

                              1,8

    的這一種情況.

    傳遞順序是循環的7,2→5,4→1,8。當嵌入7,2,就必然也得到嵌入5,4和1,8的“配套”結果。當嵌入5,4,就必然也得到嵌入1,8和7,2的“配套”結果,等等。其餘類推。見例3—2—1。

③配套傳遞。嵌入

7,2

5,4

1,8

數對時,可分別嵌入一對、兩對、三對,但必須“配套”對應。例如 97,508,421的如下嵌入結果:

975 555 11 08 88 4 444 21

97 77 5 111 08 888 42 2 2 1

97 777 5 55 08 44 4 2 22 2 1

其中,К1=0,К2=3,К3=2,К=К1+К2+К3=5。

位數N=8+2К=8+2·5=18

可記為

97 7К1 5 5К2 1К3 08 8К3 4К2 4 2К121

97 7К3 5 5К1 1К2 08 8К2 4К1 4 2К3 2 1

97 7К2 5 5К3 1К1 08 8К1 4К34 2К2 2 1

④組合傳遞。以上各種傳遞的組合。例如50位歸斂組之一:

99,988,776,655,554,433,333,322,099,877,666,666,554,444,332,211,001

99,988,766,554,433,333,322,111,099,888,877,666,666,554,433,211,001

99,988,777,766,544,333,333,221,099,887,766,666,655,433,222, 211,001

分析可知,它是以n=8 的 8位數的歸斂數 97,508,421 作為數根,嵌加

(9,0) 2次

(К′=2),

(3,6)6次(К″=6),

(864297531) 2次(К′″=2),

以及數組 7,2(К1=1),

          5,4(К2=3)

          1,8(К3=0)。

  N=8+2×2+2×6+9×2+2×1+2×3+2×0=50(位)。

當然該歸斂組還可以分析為其它的數根和派生。

⑤唯一傳遞。僅有n=3+3k類嵌加594的情況。見例2—1—5。

   歸斂結果的以上特點可用於運算或者派生結果的設計、檢查、驗證等。


四、 歸斂的成因

   例如n=10時共有9×109個數(10的9次方),其歸斂結果也為10位,其歸斂結果的那兩個數和三個數組的數必然包羅在這9×109個數(10的9次方)之中,即已“隱藏”其中,運算只不過是把它們找出來。

   歸斂有以下幾點是顯而易見的:

1.若干個數字相同而數字的位序不同的數,運算中重新排序必然得到同一個max和同一個min,max-min也就相同,必然歸斂得同一結果。

例如n=8的9×107個數,其中的一個數12,345,678,它的排列有8﹗ =40320個數,這40320個數運算必然歸斂為同一個結果(max-min=87654321-12345678的最後歸斂結果)。

    2.一些“對稱性”數,會歸斂到同一結果。

    例如1,111,000,000排列成的84個數和1,111,110,000排列成的126個共210個數;

3,339,999,999排列成的210個數和3,333,333,999排列成的210個共420個數;

99,911,000,99,922,000,99,933,000…,99,988,000分別排列成的350個共2800個數。它們的max-min分別相同,必然分別歸斂到各自的同一個結果。等等.

3.同一個數,各位分別加1或減1(加、減中不能進位或借位),其max-min相同,也必然歸斂到同一個結果。如6位數的543210,其全排列有6﹗ -5﹗ =600個數,各位加1得到654321,繼續加1得到765432,876543,987654,分別各排列成720個共3480個數。它們必然歸斂到同一個結果(max-min=530865的最後歸斂結果)。

所有的數的歸斂結果的形成,都是運算中重新排序為max、min及max-min使之逐漸“逼近”、“靠攏”到歸斂結果。

四、 結論

由本文以上的討論,可以提出以下結論:任意n位的數,經過卡普雷卡爾運算都能得到具有前述特點的歸斂結果(形成“黑洞”並“落”入“黑洞”)。

還可以提出如下可能性:

1.在確定數根以後,不經運算就能設計出(即直接派生出)任意指定位數的某些歸斂結果。

2.給出任意位數的歸斂結果,可以推算出其前的較少位數或其後的較多位數的歸斂結果的派生路線、派生結果和數根。

   本文以上的討論及其結論,筆者還推及負整數,正、負實小數(排除無限小數),均可適用。

   以上討論,運算均獲成功,但尚未嚴密論證。供有興趣者共同探索和指正。

參考文章:

1, 美國《新科學家》,1992,12,19

2, 中國《參考消息》,1993,3,14-17

(注:打字中和數字校核中可能有錯誤,敬請指正)


-- 
/mwchuang

Friday, August 23, 2019

11 Steps to Becoming a Successful YouTuber

11 Steps to Becoming a Successful YouTuber
how to become a successful youtuberhow to become a successful youtuber

There seems to be a consensus that starting a YouTube channel is no longer ‘worth it’ due to the fact that all of the millionaires have already been born out of the platform. Yes, it’s true that you have a better chance of making “fetch” happen than becoming an overnight YouTube sensation, but that doesn’t mean you can’t have your cake and eat it too. The success of YouTube influencers of the past have made marketers shift how they can potentially reach their audience, so it’s actually a very relevant dream to have for your own channel. The video platform has weaved itself into the marketing fold of many businesses or really anyone looking to share their voice with the world.
Here are the 11 steps you need to take in order become a successful YouTuber:

Define what success means to you and remember it
Develop your channel’s goals and content
Map it out
Make sure your channel page is welcoming
Mind your SEO
Be consistent. Be-be consistent
Get to the point
Keep up with your niche
Manage your community like a boss
Spread the word with a killer website
Learn from your analytics

01. Define what success means to you and remember it
Many define success monetarily, but there’s so much more to it than money in the bank. If you make a ton of money doing a job you hate, would you consider yourself successful despite your lack of fulfillment? Success comes in different forms, and it’s up to you to determine where you consider yourself successful. If you define success outside of greenbacks for your YouTube channel, remember that’s what you’re in it for. Whether its a higher view count for your videos, more subscribers, or just an overall increase of engagement across your channel, keep this as your focus, anything else is just bonus.

02. Develop your channel’s goals and content
YouTube is video. There’s a lot of good content, and a ton of terrible content out there. To stand out in this raging sea, obviously you will need to keep paddling and keep your head above water but you need to have a plan to get to shore. Developing your content is the fun part, but it’s also a job. Here, you’re defining your channels’ voice and your content should align with it. Even if it’s just you and your camera, you’re building your brand’s personality. The easiest way to develop your channel is to be yourself. But what if you’re not particularly interesting even though the content you’re producing is? Well, then there’s nothing wrong with being a little “extra” to add some pep to your videos. (Read: a little – you’re going for pep, not obnoxious. Also, always consider your audience.)

You’ll need to decide what type of content you will be offering up on your channel. The range is huge, from how-to videos, to humor, to reviews. Once you choose that, backtrack to see how you can make the videos unique using your brand’s personality. Depending on your channel’s content and niche, you want to make sure you give yourself some wiggle room to cover trending topics in your industry. If some big news breaks out or there’s a subject you know others with similar channels are talking about, don’t hesitate to ride the wave. It’s important to stay relevant. Even if you’re covering the same topics as others, it gives you an opportunity to add your valuable input on a subject.

03. Map it out
Now with your content type secured, make a plan as to how you will not only execute its creation, but everything in this venture. Think of this as a business plan of sorts and return to it every now and then to make sure you’re adhering to the standards that you set up for yourself. You can also treat this part as a checklist of the things you will need in the creation of your YouTube channel, including any and all equipment you will need to produce quality videos. This is also a good time to figure out who else will be involved with the your channel, if anyone. In essence, build a realistic timeline for your posting schedule, gather topics for your content, and make sure you follow this timeline consistently along your journey.

04. Make sure your channel page is welcoming
You know what’s not cute? An incomplete YouTube profile. If you’re trying to make YouTube “happen” for you, be sure to mind your p’s and q’s. Since the medium is a visual one, presentation is key. Your profile photo or logo needs to be set in the correct place and your channel banner image needs to be the correct dimensions. Other things to think about are the style of your video thumbnails. Do they have their own visual style that you will continue to consistently reproduce? To ensure all your elements are in place and are the correct size take a look at our ultimate social media size guide. You’re welcome.
Brunch Boys successful youtubersBrunch Boys successful youtubers
05. Mind your SEO
Properly setting up SEO for your YouTube videos is beyond important. Since you took the time to produce your videos don’t start slacking now. YouTube is a very sophisticated search engine, and people use it a lot to discover new content. Which means that, by choosing the right keywords, you’ll embetter your chance to be found, seen, and enjoyed. If there are videos similar to one you’re looking to create, take a look at the exact words you typed in for the results. Then try a slight variation to see how the results change just so you can see what a word or two of difference can make. Research the keywords you’d like to use, their popularity, and the keywords your competition uses.

06. Be consistent. Be-be consistent
It doesn’t matter how many of these articles about being successful on YouTube you read through, you will always find this one. You must be consistent to see any kind of success. It’s that or hedge your bets on instant viral success. Don’t get me wrong, that would cool, but the viral route is not a guaranteed one in the least bit. No matter what type of content you’re producing, stay consistent with your timing and type. Set a schedule as to when you will release your videos and try to stick to it. Consistently releasing videos on the same day and time not only tells your audience when they can expect your new content, but it gives you a schedule to work with and abide by. Consistency isn’t just about timing. It’s about ensuring steady, on-brand content.
Let’s say you follow a baking channel on YouTube and it’s your go-to source for all things baking, but the latest episode, without explanation, is all about their trip to a monster truck rally. (Really?) The stark contrast in content, especially without warning, is jarring and will leave your loyal viewers confused. If you want to experiment with your content it would be wise to give your audience a heads up first..

07. Get to the point
You know what’s absolutely, completely unnecessary for a YouTube video? A five minute explanation for something you can (and intend to) show your viewer that only takes 30 seconds. Sounds funny when worded like that, right? Unfortunately, this is terribly common. I’m sorry, but people do not have time for you to waste their time, so just get right to it. If you release how-to videos, it’s an absolute must to get to your point as soon as you can. Explain what the video is going to be about and then dive right in. The point of a video is to “show” your viewer something (If they just want to listen, they would listen to a podcast.) Of course, there will be instances where further elaboration or troubleshooting may need to be mentioned, but save that for later in the video. Your audience will thank you.
how to become a successful youtuberhow to become a successful youtuber
08. Keep up with your niche
When presenting (recording) to your audience, you want to be seen as knowledgeable about your industry. This entails staying up with news about your niche and your video making peers. Keeping up with the news and happenings of your industry (including your competition) allows you to make relevant and fresh content for your viewers. By watching your competitions videos you can see the points and opinions they make before you make your own video. Allowing you to follow up with your own counter argument (if you live for drama) or your own spin to keep it unique. This will also help to establish yourself as a “go-to” channel for someone who wants to stay up to date with a certain subject.

09. Manage your community like a boss
If you measure success by subscriber count, your subscribers are basically gold, so be sure to treat them as such. This goes beyond just answering and liking their comments. Community management can be a job of its own. A great way to engage with your community instantly is to host a live stream. Live video is becoming increasingly more popular, as it allows you to interact directly with your viewers and shows a more candid, off the cuff presentation. This platform is also great for hosting Q&As so your audience can get answers to their burning questions right then and there. You can also flip it and ask your viewers to leave questions in the comments which you can then answer during the session. This may be an article about YouTube, but you should definitely also engage with your community on other social networks as well. Plus, its a great way to take advantage of multiple platforms and tap into new audiences. Being socially present on multiple networks shows that you are availability and committed to your community.
A couple of ways to grow your community include:
Always make sure to link from one social network to the other. A properly placed CTA in your videos can help you achieve this action.
When releasing a new video, announce it on all your other channels. Plus: don’t forget to add a link to your latest vid.
Create a blog to keep your community interested.
Start a forum to keep the conversation going.
Send out newsletters using Wix Email Marketing to promote your weekly blog, announcements or updates.

10. Spread the word with a killer website
When your primary content is made for YouTube, it’s hard to give your brand another home. Sure, you can share your videos on other social networks, and you should, but a stunning video website should be your YouTube channel’s home away from home. The great advantage of a video website is that you’re the owner of everything on your website. Essentially, you’re not confined to what a social media platform has to offer. Therefore, your site has all the benefits of YouTube without any of the limitations. With Wix Video, you can easily sync your YouTube channel to your site, enabling a smooth integration of your videos into your website. That means, more views on your videos straight from your site. From your site, you have the option to sell your videos, rent them or even set up a monthly subscription plan. Best of all, it’s all free.
make-up brand website designmake-up brand website design

11. Learn from your analytics
Even the best can do it better. YouTube offers up a dedicated analytics section for your channel so you can see how your videos are performing. Analytics will allow you to get insight on the people who are watching your videos, which allows you to hone into your target demographic even further. It will also give you a better idea as to why one video may have performed better than another. Basically, it’s a powerful tool you should take advantage of for your budding channel.

Tuesday, August 20, 2019

2019郵寄保健食品回台灣新制

  •  iHerb購物教學百萬華人推薦的美國購物網站,首購享數十美金優惠
近年來食安問題在黑心商品,各種食品、藥品添加劑疑雲壟罩下,消費者都成了驚弓之鳥。讓人猜不透的,除了不法商人的良心,還有成份標籤背後難懂的名稱
因此當代消費者必須要有自我提升的認知,面對各種商品促銷的轟炸前,便宜不能是唯一考量,品牌形象、食安法規、網路社群口碑、企業社會責任都該成為購物前的參考指標,唯有做足功課,才能減少成為受害者的機率
而歐美日等國保健食品向來深受華人喜愛,是由於這些國家衛生食安法規相對嚴格,廠商一旦造假造成消費者受害,需面臨的多是天價求償,因此能大大嚇阻不法行為
而這篇將針對台灣民眾在購買歐美保健食品時常面臨的問題
如何分辨成份是保健食品或藥品
*重要訊息:
即日起下單購物請特別留意,免稅額於2018年1月1日限縮至新台幣2000元(含運費)
於iHerb下單時,實際報關金額會包含忠誠獎勵(Loyalty Credits)與積分獎勵(Rewards Credits)
所以計算免稅額時不能單看實際支付金額,請留意以下兩種狀況:
1.若為首單,”實際支付金額(含運費)”請別超過新台幣2千元,超過會有關稅問題(控制在1970以下會較保險,以防匯率波動)
2.第二單後若有使用”10%忠誠獎勵”或”積分獎勵”則須留意,因為此金額在報關時會被加回,故須以(實際支付額+忠誠獎勵+積分獎勵)為基準,同樣別超過新台幣2千元
目錄
保健食品泛指不具藥品療效,不以治療為目的,但具有特定的保養功效,適合部份族群所使用的食品(但前提是對人體無危害)
但在商業導向的操作下,保健食品是否真有保健效果?價格與品質是否對等也令人存疑?若不當使用保健食品也是會傷身的(因此保健食品與藥品的界線在世界各國各有不同規範)
1.海外網購保健食品前,台灣民眾首先要確認(成份及劑量)在食藥署是被歸類為食品或藥品(別擔心,很容易判別)
因為依據食安法第30條規定,輸入食品需向食藥署申請查驗,但符合下列條件者可辦理免驗:
(一) 若為膠囊狀、錠狀保健食品,需符合每種12瓶以下、總和不超過36瓶規定
(二) 屬食品或相關產品,且價值在1千美元以下,重量在6公斤以內者:(常見有膠原蛋白粉、乳清蛋白粉、奶粉、薑黃粉等)
(三) 屬食品添加物且重量在1公斤以內(但香料限量200公克以內) :常見有維他命C粉末、麩醯胺酸粉末
*注意:購買嬰兒奶粉及嬰兒配方食品須申請"貨品進口同意書"才能進口,且每人每年單項累計輸入不得超過30公斤。
 2.查詢時使用以下3種衛生福利部食品藥物管理署網站(中英文字串皆可查詢)
a.食品類
若可查到則視為食品成分,但超過內文描述的限量,則視為藥物成分
b.藥物類
*一般而言郵寄被抽查機率較低(被視為自用,缺點是到貨期較長,約2周),而快遞因被視為商業行為因此抽檢率較高
 3.經查詢後,若確認成分為藥品,則依衛福部規定:寄送少量藥品供自用者:以「每種2瓶(盒)為限,合計不超過6種,可由海關直接放行)。
如超過上述藥品規定的2瓶限量,則需填寫"申請進口同意書"向食品藥物管理署提出申請才可進口(於寄送前辦理或收到補辦通知後辦理均可)
*欲申請進口同意請參照此網頁:個人輸入自用藥品規範專區(內有貨品進口同意書申請書(含範例)及相關注意事項,下載後按規定辦理即可)
*如果申請非處方藥自用進口,規定是不能超過12瓶或總量1,200顆,且6個月內不得重複申請(每年只能申請2次)
4.國外是保健食品,台灣認定為藥品的成分有哪些(常見的)?
不論劑量:
5.超過所列劑量會被列為藥物:若是購買以下成份,請注意劑量,若購買超過2瓶需申請進口同意書:
維生素A(超過10000 I.U.)
維生素B1(超過50 mg)
維生素B2(核黃素)(超過100 mg)
維生素B3 (菸鹼酸)(超過100 mg)
維生素B6(超過80 mg)
維生素B12(超過1000mcg)
維生素D3(高於800I.U.)
鎂(超過600mg)(包括Magnesium Gluconate、Magnesium Oxide、Magnesium Sulfate)
依化粧品衛生管理條例,化粧品係指施用於人體外部,以潤澤髮膚,刺激嗅覺,掩飾體臭或修飾容貌之物品
常見化妝品範圍及種類有以下:
洗髮用品、洗臉卸粧用品、沐浴用品、香皂類、頭髮用化粧品(造型噴霧、髮蠟、潤髮劑、染髮劑、燙髮劑)、化粧水、剃鬍水、護手乳、助曬油、防曬乳
面膜(糊狀或泥膏狀)、香水、爽身粉、制臭劑、止汗劑、唇用化粧品、覆敷用化粧品(粉底液、蜜粉)、眼部用化粧品(眼霜、睫毛膏、眉筆)、指甲化粧品(指甲油)、牙齒美白劑等
購買化妝品前須注意是否為含藥化粧品,若進口含藥化粧品(不管幾瓶),需依藥事法相關規定申請,取得輸入許可文件後方可進口
判定方式以食藥署公告的"含藥化妝品基準表"為主,若含有所列成分,須辦理申請才能進口
可能為含藥化粧品的商品如下方所列,請特別留意:
防曬劑(含Oxybenzone、p-Aminobenzoic acid)、止汗制臭劑(含Aluminum Chlorohydrate)、去角質產品(含Salicylic acid)
抗痘產品(含Sulfur、adapalene、Azelaic acid)、護膚品(含尿囊素Allantoin)
美白商品(含Ascorbyl Tetraisopalmitate)、牙齒美白商品(含Hydrogen peroxide)及抗菌洗劑(含Triclocarban)
脫毛劑(含Thioglycolic acid)、有消毒殺菌等功能的乾洗手劑、抗菌漱口水(含Clorhexidine Gluconate或Cetylpyridinium Chloride)
染髮劑(含p-Phenylenediamine)、燙髮劑(含Thioglycolic acid、Cysteine、Sodium Sulfite、Sodium Bromate)
進口的商品是否屬含藥化粧品或藥品,仍應由實際商品成分判定,如有疑問,可與食藥署諮詢服務專線確認:(02)2787-8200。
自國外網站購買植物產品寄送回國,須符合"植物防疫檢疫法"以及相關規定
如購買商品屬於防檢局所公告"應施植物檢疫品目表"項目,就必須於貨品寄抵臺灣時申請植物檢疫,檢疫合格後始得輸入
(常見需檢疫商品如奇亞籽、藜麥、亞麻子(仁)、紅豆、綠豆,但已磨碎成粉狀之種子,則不須檢疫,可直接輸入)。
常見不須申請植物檢疫項目:(如以下所列,可直接進口,不需申請)
1. 加工乾燥植物產品:如商業包裝之水果乾(如葡萄乾、香蕉乾、芒果乾、龍眼乾等)、乾香菇、乾燥中藥材(不含種子)。
2. 加工或調製完全之植物產品:
罐頭(如水果罐頭、果醬)
3. 乾燥磨粉植物製品:如辛香料粉(如薑黃粉、辣椒粉、胡椒粉、茴香粉等)、中藥粉、穀類及豆類粉狀製品。
常見需申請植物檢疫項目:(進口人應填寫輸入植物或植物產品檢疫申請書,並檢附輸出國植物檢疫證明書,經申辦後才能合法進口)
新鮮植物(指整株植物之根、莖、葉、花、果實之全部或部分,如蔬果、花卉、苗木…等之全部或部份)
新鮮植物產品(指未經加工或未經高溫乾燥等調製處理之植物產品)
植物種子(包含仍具有發芽能力之新鮮或乾燥種子,及種球、鱗莖、球莖等,如:蔬菜種子(如紅豆、綠豆)、花卉種子、穀類種子、稻穀、果樹種子、種子類香料(如茴香籽、芫荽籽等)、奇亞籽、藜麥、種子類鳥飼料等)
其它產品:如新鮮人參、授粉用花粉。
依據"動物及動物產品檢疫條件",如購買商品屬於防檢局所公告"應施動物檢疫品目表"項目,就必須於貨品寄抵臺灣時申請檢疫,並檢附輸出國政府檢疫機關簽發之動物檢疫證明書,待檢疫合格後始得輸入
常見須申報動物產品檢疫項目:
常見不須申報動物產品檢疫項目:(如以下所列,可直接進口,不需檢疫,但輸入貓狗食用品或寵物營養品時仍應向防檢局申報)
1. 不含動物性成分及僅含乳品或水產品成分之犬貓食品(相關成分如明膠、膠原蛋白、軟骨素、葡萄糖胺、磷酸二鈣及乳品,且有清楚之成分標示或原廠說明以茲判定)。
2. 保久乳、奶粉及乳酪(但嬰兒奶粉依其它規定須另行申請才能進口)。
3. 供寵物食用,未含牛源成分且經高溫滅菌罐製之產品
4. 供人食用之高溫滅菌罐頭食品(馬口鐵罐頭或軟式罐頭但須符合衛生福利部
5. 經煮熟蛋類(蛋黃及蛋白須完全凝固,表面應清潔不得帶有泥土、灰等物質)製品。(鴨仔蛋等含胚胎蛋不論是否煮熟均禁止輸入)
6. 已精煉供人食用之動物油脂。
7. 經清潔處理後再凝固乾燥成型或再熱煮成粥狀之燕窩成品及其高溫罐製品。
8. 經乾燥、醃漬、調製等加工處理之水產品及已完全去除內臟之魚產品。
9. 速食麵(或泡麵)、速食粥、固態或粉狀之湯類等食品。
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Wednesday, March 6, 2019

Flop 高拋球

You can find many video tutorials for playing a flop shot on YouTube, including these:

Flop Shot ,也稱為Lob Shot,是一種短距離劈起球Pitching,使用非常高的Wedge楔形桿,以便在球的軌跡上創造最大高度。目的是將高爾夫球放到高弧形軌道上,急劇上升並急劇下降,這樣當它落在果嶺上時,它會很快停止,只需很少的滾動。

Flop Shot是高爾夫球的特殊打法,通常是為了讓球在高爾夫球手和旗桿之間的障礙或危險(例如沙坑)上飛越, 或者在高爾夫球手位在離開果嶺短邊short sided,並且需要球一旦在果嶺上能快速停止時。每當高爾夫球處於高爾夫球手需要在陡峭的軌道上快速將球送入空中的位置時,然後將球輕柔地放在果嶺上,Flop Shot 是可以選擇的打法。

Flop Shot通常使用稱為高仰角楔型桿的高位楔形桿Lob Wedge來打。高楔桿有一個大約60到64度的仰角,最初專門用來打lobs,又名Flop。如果高爾夫球手將球桿面敞開以增加桿面傾角,則可以用其他楔桿進行Flop,但是Lob Wedge是理想的球桿。

打Flop/ Lob Shot的技巧
有關此短桿技術的完整說明,請參閱Charlotta Sorenstam如何打Flop Shot/Lob Shot。但是,總結Sorenstam的教程,基礎是這些:

打開你的Lob Wedge桿面,進一步增加仰角。
設置高爾夫球的位置比正常情況下要前一些。
將你的上半身瞄準目標, 但是採取打開放站姿(這樣右打者的腳就會在目標左側對齊)。
重心稍偏在你的前腳球位上。
彎曲膝蓋比平常多一點。
全力以赴,保持下半身靜止不動,讓你的手臂和雙手完成大部分工作。
揮桿擺動到完整的結束。
要全力以赴,加速衝擊,這可能使Flop Shot對許多休閒高爾夫球手來說具有挑戰性。因為這是一個非常短的打擊-  50碼,30碼,甚至果嶺邊緣 - 它可能很容易減速或未能完全致力於揮桿。如果你打得太薄,球可能會飛過目標過長了。

A flop shot, also known as a lob shot, is a short pitch shot played with a very high-lofted wedge in order to create maximum height on the ball's trajectory. The intention is to send the golf ball on a high-arcing trajectory, steeply up and steeply down, so that when it lands on the green it stops quickly, with very little roll.

The flop shot is a specialty shot in golf, typically played in order to get the ball over a hazard (such as a bunker) between the golfer and the flagstick; or from just off the green when the golfer is short-sided and needs the ball to stop very quickly once on the green. Any time the golf ball is in a position where the golfer needs to get the ball into the air quickly on a steep trajectory, then land the ball soft on the green, the flop shot is an option to be played.

A flop shot is typically played with a high-lofted wedge called a lob wedge. A lob wedge has around 60- to 64-degrees of loft and was originally created specifically to play lobs, aka flops. A flop shot can be played with other wedges if the golfer lays the ​clubface wide open in order to add loft, but the lob wedge is the ideal club.

Technique for Playing the Flop Shot/Lob Shot
For a full explanation of this shot's technique, see How to Play a Flop Shot by Charlotta Sorenstam. But, summarizing Sorenstam's tutorial, the basics are these:

Open the face of your lob wedge to increase the loft even more.
Set up with the golf ball a bit more forward in your stance than normal.
Aim your upper body at the target but open your stance (so your feet are aligned left of the target for a right-hander).
Set up on the balls of your feet with a little more weight on your front foot.
Bend your knees a little more than normal.
Make a full swing, keeping the lower body quiet and letting your arms and hands to most of the work.
Swing through to a full finish.
It's that full swing, accelerating into impact, that can make flop shots challenging for many recreational golfers. Since it's a very short shot - 50 yards, 30 yards, even from just off the green - it can be easy to decelerate or fail to fully commit to the swing. And if you catch it thin, the ball might fly the target by a long way.