K1 digital currency
1. The running speed is different. The running speed of EMU is 160, 200 and 250. Generally, the speed of high-speed railway is not less than 250 per hour, and there are 250, 350, 380 and 400 per hour
The operation range is different. EMUs usually run across provinces; High speed EMU: the transportation distance is different, there are operations in the province, and there are also operations across provinces The signal system is different. EMUs can run on existing lines (the signal system of ordinary EMUs is compatible with existing lines), while high-speed railways must run on newly built passenger dedicated lines (the signal system of high-speed EMUs is not compatible with existing lines)4. Different power modes. EMUs are divided into centralized power and distributed power. The common CRH series EMUs in China are all distributed power, and they are all AC drive. In addition, metro trains can also be regarded as EMUs (generally DC drive)
{rrrrrrr}
extended data:
other types of trains:
1. Intercity multiple unit train (C prefix)
on August 1, 2008, Beijing Tianjin Intercity Railway officially opened to the public. The newly opened train number is C + 4 digits, which means intercity train. At present, the maximum speed is 300km / h, and the railway system standard is "city * * train". The number of trains between Beijing and Tianjin is from c2001 to c2282. For example, Wuhan intercity train number range is c5001 ~ c5720
2. Direct express passenger train (Z prefix)
the maximum speed is 160km / h, and the railway system standard is "direct * * times". Most of them are full train soft seats, and a few of them are equipped with hard sleeper and hard seat. During the whole journey, only some of them stop at the starting station and / or the terminal station in the Railway Bureau. This kind of train is air-conditioned
3. Express passenger train (t prefix)
the maximum speed is 140 km / h, and the railway system standard is "special * * times". Inter Bureau express stops at provincial capital cities, sub provincial cities and a small number of major prefecture level cities and other super stations or through, while tube express stops at prefecture level cities. This kind of train is air-conditioned
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tp38
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"three people travel together for 70 years, five trees and twenty-one plum blossoms,
seven sons get together for the first half of the month, except lingwu."
these interesting mathematical games, in various forms, introce the solution of the world-famous "Sun Tzu problem", and reflect a remarkable achievement of ancient Chinese mathematics“ "Sun Tzu problem" is a congruence problem in modern number theory. It first appeared in the fourth century's mathematical work "Sun Tzu Suanjing" The title of "things don't know the number" in the volume of Sun Tzu's Suan Jing says: there are things that don't know the number, three of them are counted more than two, five of them are counted more than three, seven of them are counted more than two? Obviously, this is equivalent to finding the positive integer solution n of the system of indefinite equations
n = 3x + 2, n = 5Y + 3, n = 7x + 2
or expressed by the symbol of modern number theory, and the answer given in Sunzi Suanjing is n = 23. Because the data of Sun Tzu's question is relatively simple, this answer can also be obtained through trial calculation. But Sunzi Suanjing doesn't do that“ The article points out that the method to solve the problem is mostly three or three numbers, take the number 70 and multiply the remainder two; Take the number 21 and multiply it with the remainder; Take the number of seven, and multiply it by the remainder two. Add the procts and subtract a multiple of 105. The formula is:
n = 70 × 3+21 × 8+15 × 2-2 × 105
here 105 is the least common multiple of molus 3, 5 and 7. It is easy to see that what Sun Tzu Suanjing gives is the smallest positive integer that meets the conditions. In the case of general remainder, it is pointed out in the Shuwen of Sunzi Suanjing that we only need to replace the remainder 2, 8 and 2 in the above algorithm with a new one. If R1, R2 and R3 are used to represent these resials, then Sun Tzu Suanjing is equivalent to giving the formula
n = 70 × R1+21 × R2+15 × R3-P × 105 (P is an integer)
the key of Sun Tzu algorithm is to determine the number of 70, 21 and 15. The words "Seventy rare", "Twenty-one skill" and "half moon" in the song of Sun Tzu, which spread later, allude to these three key figures The origin of these three numbers is not explained in the Sutra. In fact, they have the following characteristics:
that is to say, the three numbers can be changed from the least common multiple M = 3 × five × In 7 = 105, molus 3, 5 and 7 are reced respectively, and then multiplied by integers 2, 1 and 1 respectively. Suppose K1 = 2, K2 = 1, K3 = 1, then the integer ki (I = 1, 2, 3) is selected so that the remainder is 1 when the three numbers 70, 21, 15 are divided by the corresponding molus. From this point of view, we can immediately dece that when the remainder is R1, R2 and R3,
synthesize the above three formulas, we can get that because
because M = 3 × five × 7 can be divided by any of its factors, so there is:
where p is an integer. This proves the formula of Sunzi Suanjing. By using the above reasoning, we can generalize the Sun Tzu algorithm to the general case: let a number n be divided by two mutually prime numbers A1, A2,... An to obtain the remainder R1, R2,... RN, that is,
n ≡ RI (MOD AI) (I = 1, 2,... N),
only one group of numbers K is needed to satisfy
1 (MOD AI) (I = 1, 2,... N) ... n),
then the least positive solution suitable for the given congruence group is
(P is an integer, M = A1) × a2 ×……× This is the famous remainder theorem in modern number theory. As mentioned above, its basic form has been included in the solution of the problem of "things don't know the number" in Sunzi Suanjing. However, Sun Tzu Suanjing does not explicitly state this general theorem
it is not by chance that the problem of Sun Tzu appeared in Chinese arithmetic books in the fourth century A.D. According to the data of ancient Chinese astronomy and calendar, the study of one-time congruence is obviously promoted by the needs of astronomy and calendar, especially closely related to the calculation of so-called "Shangyuan Jinian" in ancient calendar. As we all know, a calendar needs to specify a starting time. Ancient Chinese calendarists called this starting point "Li Yuan" or "Shang Yuan", and called the accumulated time from Li Yuan to calendar year "Shang Yuan Ji Nian". It is necessary to solve a group of first-order congruences for the calculation of the cumulative year of the upper yuan. Take the Jingchu calendar implemented by Wei state in the Three Kingdoms period in the third century AD as an example. This calendar stipulates that the time when the winter solstice, shuodan (shuodan day and night) and Jiazi day meet at zero is regarded as the calendar. Let a be the number of days in a regressive year, B be the number of days in a new moon, the winter solstice of that year is R1 day from zero o'clock of Jiazi day, and the time from Pingshuo is R2 day, then the proct number N in jingchuli is the solution of congruence group
an ≡ RI (MOD 60) ≡ R2 (MOD b)
. In the northern and Southern Dynasties, Zu Chong's Daming calendar (462 A.D.) required that the calendar must be the beginning of Jiazi year at the same time, and that "the sun and the moon merge together" and "the five stars join the Pearl" (that is, the sun, the moon and the five planets are in the same position), and that the moon just passed its perigee and ascending intersection. Under such conditions, it is equivalent to solving ten congruence formulas to calculate the accumulated year of Shangyuan. Astronomical and calendar data are generally very complex, so in the Wei, Jin and southern and Northern Dynasties period before and after the completion of the book, Chinese astrologers have undoubtedly been able to solve the first-order congruence which is much more complex than the problem of "things don't know the number" in the book, so they must have mastered the method of calculating the first-order congruence according to a certain program This fact is summed up and reflected in the form of the comparative examples in Sunzi Suanjing. In the future, Sun Tzu's algorithm will be used to calculate the accumulated year of Shangyuan in astronomical calendar calculation, which will certainly cause more in-depth discussion. In the 13th century, Qin Jiushao, a great mathematician, made a brilliant achievement in the study of congruence
Qin Jiushao, an ancient Chinese character, lived in the Southern Song Dynasty. He was fond of mathematics when he was a child. After long-term accumulation and painstaking study, he wrote nine chapters of mathematical books in 1247. This masterpiece of mathematics in the middle ages is creative in many aspects. Among them, the great derivation method of solving the first-order congruence group and the positive and negative square method of solving the numerical solution of higher-order equation are achievements of world significance< This paper mainly introces Qin Jiushao's great contribution to a congruence theory
Qin Jiushao clearly and systematically described the general calculation steps of solving the group of first-order congruences in the book of numbers, nine chapters. Qin's method is exactly the resial theorem mentioned above. We know that the resie theorem reces the general problem of first-order congruence to the selection of a group of numbers Ki, which satisfy the conditions. Qin Jiushao named these numbers "multiplication rate", and detailed the method of calculating multiplication rate - "Dayan seeking one technique" in Volume I "Dayan Zongshu" of "Shu Shu Jiu Zhang"
in order to introce "Dayan seeking one technique", we take the calculation of any multiplication factor ki as an example. If GI = > AI, Qin Jiushao first divided AI by GI and got the remainder GI < AI, then
GI ≡ GI (MOD AI),
then kigi ≡ kigi (MOD AI),
but because kigi ≡ 1 (MOD AI),
the problem comes down to finding ki to fit kigi ≡ 1 (MOD
AI). Qin Jiushao called AI "fixed number" and GI "odd number", and his "Da Yan Qiu Yi Shu" was interpreted in modern language. In fact, it was to divide odd number GI and fixed number AI by turns to obtain quotient Q1, Q2,... QN and remainder R1, R2,... RN successively. When dividing by turns, the following C value in the right column was immediately calculated:
Qin Jiushao pointed out that when RN = 1 and N is even number, Finally, CN is the multiplication rate ki. If RN = 1 and N is odd, then divide RN-1 and RN, formally let QN + 1 = rn-1-1, then the remainder RN + 1 is still 1, then CN + 1 = QN + 1cn + Cn-1, QN + 1 = rn-1-1 is even, CN + 1 is the ki. No matter what the situation is, the last step is the remainder 1, and the whole calculation ends here. Therefore, Qin Jiushao called his method "seeking one skill" (as for the meaning of "Dayan", Qin Jiushao himself attached it to "Dayan's number" in the preface of Shushu Jiuzhang). It can be proved that Qin Jiushao's algorithm is completely positive. All these systematic theories and careful consideration, even in today's eyes, are not simple. They fully demonstrate Qin Jiushao's superb mathematical level and computational skills< When Qin Jiushao was a child, he followed his father to Hangzhou, the capital of the Southern Song Dynasty, where he told the Taishi Bureau (in charge of tianque, very strict)
in Qin Jiushao's time, computing still used computing chips. Qin Jiushao placed an odd number G on the top right, a fixed number a on the bottom right, and a 1 on the top left (he called it "Tianyuan 1"). Then he interacted up and down on the right line to divide less by more. The quotient obtained was multiplied by the upper left (or lower) and merged into the lower left (or upper left) until 1 appeared on the upper right. On the right side is a numerical example (g = 20, a = 27, k = C4 = 23)
Qin Jiushao collected a large number of examples in the nine chapters of the book of numbers, such as "the accumulation of the ancient calendar", "the accumulation of the ruler to find the source", "Tuji tugong", "Cheng Xing Ji Di" and so on, and widely used Dayan to solve practical problems such as calendar, engineering, taxation and military. In these practical problems, the molus AI is not always a mutually prime integer. Qin Jiushao distinguished "Yuan" (AI is an integer), "Shou" (AI is a decimal), "Tong" (AI is a fraction) and other different cases, and gave treatment methods for each case“ The "Da Yan Zong Shu" calculates the "received number" and "general number" in the case of "element number". For the case that the element number is not mutually prime, it gives a reliable program, and appropriately selects the factors of those elements as the fixed number to rece the problem to the case that the element number is mutually prime, "Dayan's method of seeking one" is probably the result of his summing up the method of calculating the accumulated years of Shangyuan in the astronomical calendar. However, it seems that "Dayan seeks one skill" has not been fully understood by his contemporaries. It was almost lost after the middle of Ming Dynasty. Until the Qing Dynasty, "Da Yan Qiu Yi Shu" was rediscovered, which aroused the interest of many scholars (Zhang Dunren, Li Rui, Luo Tengfeng, Huang Zongxian, etc.). They explained, improved and simplified the "Da Yan Qiu Yi Shu", in which Huang Zongxian's "general explanation of Qiu Yi Shu" gave a more concise method for the case that molus is not mutually prime, but it was in the late Qing Dynasty
from the title of "things don't know the number" in Sunzi Suanjing to Qin Jiushao's "Da Yan Qiu Yi Shu", ancient Chinese mathematicians' research on a congruence has a glorious position not only in the history of Chinese mathematics, but also in the history of world mathematics. In Europe, Pei bonaci (1170-1250), an Italian mathematician at the same time as Qin Jiushao, first came into contact with first-order congruence. He gave two first-order congruence problems in the book of algorithms, but there was no general algorithm. These two
Train: ordinary train starts with "K" or "t", such as k525
2. Bullet train: Bullet train starts with "d", such as d3101
3. High speed train: high speed train starts with "g", such as g1635
2. Different working principles
1 High speed railway uses multiple units, not locomotives. Almost all the wheels work together, it not only has a strong force of unity and cooperation, but also can flexibly change the speed, so as to improve the speed
Locomotive is by no means the only locomotive with traction motor in high-speed railway and EMU. Almost every car has an electric motor, and almost every wheel has power to turn. With the progress of the European Monetary Union, all the wheels are moving forward at the same time, and the strength of unity is huge. The trains are lighter and faster Three, different seats:1, train: train seats are divided into hard seat, hard sleeper, soft sleeper, no seat
2, EMU: first class seat, second class seat, no seat
3, high-speed railway: business seat, first class seat, second class seat, no seat
Books are divided into social science books and natural science books
It can be divided into Chinese books and foreign books It can be divided into ordinary books and reference books according to their uses
content division: novels, children's books, non novels, professional books, reference books, manuals, bibliographies, scripts, reports, diaries, book collections, photography and painting collections
feature classification: thread bound book, hardcover book, paperback book, bagged book, e-book, audio book, blind book, national language book
Compared with other publications, the characteristics of books are as follows:1
The publishing cycle is long and the speed of information transmission is slowUNESCO defines a book as a printed matter with more than 49 pages, excluding the front cover and back cover, published by a publishing house (business), with a specific title and author's name and an international standard book number. A publication with a price and right protection is called a book
books are works which are recorded on certain forms of materials with words or other information symbols for the purpose of spreading culture. Books are the proct of human thought and a specific and constantly developing tool of knowledge dissemination
= C1 * 100000 + D1 * 10000 + E1 * 1000 + F1 * 100 + G1 * 10 + H1 + I1 * 0.1 + J1 * 0.01
to merge the number into a number
and then enter in any cell:
= substitute (text (fixed (K1)), "[& gt; 0][dbnum2];[& lt; 0] negative [dbnum2]& quot;)& TEXT(RIGHT(FIXED(k1),2)," Yuan [dbnum2] 0 Jiao 0 fen& quot;& IF(ABS(k1)> 1%," Yuan integer & quot;,)& quot; Zero angle;, IF(ABS(k1)< 1,," Zero & quot;)& quot; Zero & quot& quot; Integer (& quot;)
A B C D E F G H I J K L M
1 大写金额数位: 亿 仟 佰 拾 万 仟 佰 拾 元 角 分
2 小写金额定位:
3 数字:
公式设置如下:
C2=IF(ISERR(FIND(C1,$A$1)),,FIND(C1,$A$1))
D2=IF($G2=0,,IF(ISERR(FIND(D1,$A$1)),,IF(FIND(D1,$A$1)>$G2,,FIND(D1,$A$1))))
E2=IF($G2=0,,IF(ISERR(FIND(E1,$A$1)),,IF(FIND(E1,$A$1)>$G2,,FIND(E1,$A$1))))
F2=IF($G2=0,,IF(OR(ISERR(FIND(F1,$A$1)),FIND(F1,$A$1)>$G2),,FIND(F1,$A$1)))
G2=IF(ISERR(FIND(G1,$A$1)),,FIND(G1,$A$1))
H2=IF(ISERR(FIND(H1,$A$1,IF($G2>0,$G2,1))),,FIND(H1,$A$1,IF($G2>0,$G2,1)))
I2=IF(ISERR(FIND(I1,$A$1,IF($G2>0,$G2,1))),,FIND(I1,$A$1,IF($G2>0,$G2,1)))
J2=IF(ISERR(FIND(J1,$A$1,IF($G2>0,$G2,1))),,FIND(J1,$A$1,IF($G2>0,$G2,1)))
K2=IF(ISERR(FIND(K1,$A$1)),,FIND(K1,$A$1))
L2=IF(ISERR(FIND(L1,$A$1)),,FIND(L1,$A$1))
M2=IF(ISERR(FIND(M1,$A$1)),,FIND(M1,$A$1))
C3=IF(C2=0,,FIND(MID($A$1,C2-1,1),"壹贰叁肆伍陆柒捌玖"))
D3=IF(D2=0,,FIND(MID($A$1,D2-1,1),"壹贰叁肆伍陆柒捌玖"))
E3=IF(E2=0,,FIND(MID($A$1,E2-1,1),"壹贰叁肆伍陆柒捌玖"))
F3=IF(F2=0,,FIND(MID($A$1,F2-1,1),"壹贰叁肆伍陆柒捌玖"))
G3=IF(OR(G2=0,ISERR(FIND(MID($A$1,G2-1,1),"壹贰叁肆伍陆柒捌玖"))),,FIND(MID($A$1,G2-1,1),"壹贰叁肆伍陆柒捌玖"))
H3=IF(H2=0,,FIND(MID($A$1,H2-1,1),"壹贰叁肆伍陆柒捌玖"))
I3=IF(I2=0,,FIND(MID($A$1,I2-1,1),"壹贰叁肆伍陆柒捌玖"))
J3=IF(J2=0,,FIND(MID($A$1,J2-1,1),"壹贰叁肆伍陆柒捌玖"))
K3=IF(OR(K2=0,ISERR(FIND(MID($A$1,K2-1,1),"壹贰叁肆伍陆柒捌玖"))),,FIND(MID($A$1,K2-1,1),"壹贰叁肆伍陆柒捌玖"))
L3=IF(L2=0,,FIND(MID($A$1,L2-1,1),"壹贰叁肆伍陆柒捌玖"))
M3=IF(M2=0,,FIND(MID($A$1,M2-1,1),"壹贰叁肆伍陆柒捌玖"))
最后,在A2输入公式=--CONCATENATE(C3,D3,E3,F3,G3,H3,I3,J3,K3,".",L3,M3)
当在A1输入一个大写金额,如:壹亿贰仟叁佰肆拾伍万陆仟柒佰捌拾玖元壹角贰分
A2即可显示123456789.12