What is Simplify: Definition and 372 Discussions

Simplified Chinese characters (简化字; jiǎnhuàzì) are standardized Chinese characters used in Mainland China, Malaysia, and Singapore, as prescribed by the Table of General Standard Chinese Characters. Along with traditional Chinese characters, they are one of the two standard character sets of the contemporary Chinese written language. The government of the People's Republic of China in mainland China has promoted them for use in printing since the 1950s and 1960s to encourage literacy. They are officially used in the People's Republic of China and Singapore, while traditional Chinese characters are used in Hong Kong, Macau, the Republic of China (Taiwan) as well as South Korea to a certain extent, and occasionally in the Chinese community of Malaysia and Singapore.
Simplified Chinese characters may be referred to by their official name above or colloquially 简体字; jiǎntǐzì. In its broadest sense, the latter term refers to all characters that have undergone simplifications of character "structure" or "body", some of which have existed for millennia alongside regular, more complicated forms. On the other hand, the official name refers to the modern systematically simplified character set, which (as stated by then-Chairman Mao Zedong in 1952) includes not only structural simplification but also substantial reduction in the total number of standardized Chinese characters.Simplified character forms were created by reducing the number of strokes and simplifying the forms of a sizable proportion of Chinese characters. Some simplifications were based on popular cursive forms embodying graphic or phonetic simplifications of the traditional forms. Some characters were simplified by applying regular rules, for example, by replacing all occurrences of a certain component with a simplified version of the component. Variant characters with the same pronunciation and identical meaning were reduced to a single standardized character, usually the simplest amongst all variants in form. Finally, many characters were left untouched by simplification and are thus identical between the traditional and simplified Chinese orthographies.
A second round of simplifications was promulgated in 1977, but was later retracted in 1986 for a variety of reasons, largely due to the confusion caused and the unpopularity of the second round simplifications.In August 2009, the PRC began collecting public comments for a modified list of simplified characters. The new Table of General Standard Chinese Characters consisting of 8,105 (simplified and unchanged) characters was officially implemented for use by the State Council of the People's Republic of China on June 5, 2013.

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  1. P

    How to simplify the expression -- Boolean algebra

    1. prove that: X'Y'Z + X'YZ' + XY'Z' + XYZ = (X⊕Y)⊕Z Homework Equations Use postulates and theorems. The Attempt at a Solution X'Y'Z + X'YZ' + XY'Z' + XYZ (original expression) X'Y'Z + X'YZ' + X(Y'Z' + YZ) (distributive) X'Y'Z + X'YZ' + X.1 (complement) X'Y'Z + X'YZ' + X (identity)[/B]...
  2. anemone

    MHB Simplify a trigonometric expression

    Simplify $\left(\sqrt{3}\sec \dfrac{\pi}{5}+\tan\dfrac{2\pi}{5}\right)\tan \dfrac{2\pi}{15}$.
  3. E

    How to simplify using stirling approximation?

    Hey! So we're deriving something in Daniel Schroeder's Introduction to Thermal Physics and it starts with this: \Omega \left( N,q\right) =\dfrac {\left( N-1+q\right) !} {q!\left( N-1\right) !} Both N and q are large numbers and q >> N. The derivation is in the book, but I am always...
  4. B

    MATLAB Simplify Matlab for/if statements further

    Hi Folks, This loop code is working fine but I would like to simplify it further. Can anyone help? Basically, i need syntax to automate the numbers highlighted in bold. k is a 3*3 matrix, SE_ans is a 3*1 vector, A is a 3*3 identify matrix. The rests are just constants. for i=1:size(k,1)...
  5. M

    How can I simplify 1-2*sqrt(x)*sin(sqrt(x))*cos(sqrt(x))?

    Homework Statement How to simplify 1-2*sqrt(x)*sin(sqrt(x))*cos(sqrt(x))? Homework Equations None. The Attempt at a Solution I know the identity that sin(2x)=2sin(x)cos(x).
  6. PcumP_Ravenclaw

    Factorizing determinants and rules to simplify them

    Homework Statement 2. Evaluate the determinants ## \begin{vmatrix} 1 & 1 & 1\\ x & a & b \\ x^2 & a^2 & b^2 \\ \end{vmatrix} ## ## \begin{vmatrix} x & a & b \\ x^2 & a^2 & b^2 \\ x^3 & a^3 & b^3 \\ \end{vmatrix} ## and factorize both answers. Homework Equations Rules of determinants are...
  7. J

    Efficiently Simplifying Nested Logarithms: A Scientist's Guide

    Outer log could be any base.
  8. S

    MHB Compute the Wronskian & Simplify

    Compute the Wronskian and simplify. So the first part was easy a) $y_1 = t^2 + 1$ , $y_2 = 3t^2 + k$ =$6t-2kt$ b) for what values of $k$ are the functions linearly independant so would I just solve for $k$? I'm confused What exactly does linearly independant mean?
  9. N

    Find F(7) and F(a^2-2) (a≥2) -- Simplify .

    Homework Statement find F(7) and F(a^2-2) (a≥2). Simplify.The Attempt at a Solution Not sure maybe F(7^2-2) therefore F(47)? Not sure what this question is asking me to do. Please help
  10. PcumP_Ravenclaw

    Applying rules to simplify a 3 x 3 determinant

    I have attached the properties/rules that will aid in simplifying the 3 x 3 determinant so that it can be calculated with minimum effort. I am trying to understand rule (2) and (4). I am not so clear about the idea of linearity. Can anyone please explain these two rules with regards to example...
  11. S

    How to simplify behavior of a field-effect transistor

    Are there simple governing equations for FETs like there are for BJTs, and if so, what are they? For example, in the BJT case we have IC = β×IB IE + IC + IB I'm sure it depends on the type - MOSFET, JFET, etc. - so anything anyone could contribute would be helpful. From what I understand, the...
  12. Dr. Ficus

    How can the log in the denominator of the charging equation be simplified?

    Homework Statement Basically, I'm just trying to verify that I can do basic algebraic manipulation correctly. The objective: solve the charging equation of a simple RC circuit for (C), capacitance. Homework Equations v\left(t\right)={v}_{s}\left(1-{e}^{{-t}/{RC}}\right) The Attempt at a...
  13. T

    Learning to Simplify the Curvature Tensor

    I just watched susskind video on EFE but he didnt show us how to convert curvature tensor(the one with 4 indices) to that of Ricci tensor. Can anyone help me with this? Try to simplify it as I just started this.
  14. R

    Approximation question -- How does this approximation simplify the integral?

    how does this aproximation reduse the integral
  15. H

    Simplify the matrix product to the identity

    Homework Statement IF G, H and G+H are invertible matrices and have the same dimensions Prove that G(G^-1 + H^-1)H(G+H)^-1 = I 3. Attempt G(G^-1 +H^-1)(G+H)H^-1 = G(G^-1G +G^-1H + H^-1G + H^-1H)H^-1 = (GG^-1GH^-1 +GG^-1HH^-1 +GH^-1GH^-1 +GH^-1HH^-1) = GH^-1+I +GH^-1GH^-1 +GH^-1 =2GH^-1+...
  16. S

    Simplify the expression -- Electric field in a capacitor

    Homework Statement Between two metal plates a metal strip is inserted as shown on the figure. a) Calculate the electric potential anywhere inside the capacitor. b) Simplifly ##U(x,y)## for ##x>>a##. c) Calculate the electric field in the middle of the capactior. Homework EquationsThe Attempt...
  17. E

    Trying to help someone simplify this: (2ab - 3b^2)/(3b - 4a)

    I managed to get it down to 2ab/(4a-3b)-b, but that doesn't seem very simplified to me. I also added and subtracted terms in the numerator to make it factorable, ect but nothings really worked out.
  18. L

    Functions and Rearranging Help

    Two functions are defined as: f(x) = 1/(-10x+14)+17 g(x) = 1/(-4x-3) Find fg(x) and gf(x) and simplify answer into form (ax+b)/(cx+d) where a,b,c and d are numbers to be found. I know it is common practice to put in some of my own attempts onto here, but I am not even getting remotely close to...
  19. O

    MHB Is this wrong or right? Simplify: -2^2 =-4

    Because on the test the answer given back says the correct answer for -2^2 is -4. Is there a difference between simplifying and solving?
  20. H

    MHB How Can I Simplify This Complex Mathematical Expression?

    Hello, I am having difficulty solving my math problems. Simplify the Expression and show how.. And kalkulate z²+w(2wz)²-(w+4z²-1)w³-(z+w²)(x-w²) And w=2 I know we have many ways doing it, an the more ways i can study, the bether i can understand this..
  21. Rectifier

    Is it possible to simplify this equation?

    Hey there! This isn't actually a problem from a book or something. Its a problem I have stumbled upon when I did some physics. The problem I have come to this equation and I can't seem a way to simplify it $$Q_c^2 =Q^2 \frac{d_1^4+d_2^4}{(d_1d_2)^4} \cdot (d_1^2+d_2^2)^2 $$ The attempt...
  22. KleZMeR

    Simplify with Trigonometric Identities

    Homework Statement I'm trying to simplify some trigonometric expressions, I'm attaching my work here. This comes from a famous physics problem i.e. the rod with two masses spinning on a circle. I've tried many times but I just can't get it. Any help on which identities to use would really...
  23. A

    MHB Are My Answers Correct for These Ratio Math Problems?

    Hellow I did these three math problems and I wonder if my answers are right. (1.03 : 10^-1 + 17) : (4.5^-1 + 5/18)^-2 my answer here is 3. (0.2 : 10^-2 -2 ) : (1/0.9 - 1)^-1 my answer here is 2. Now the last one 1/a^2+a - a+2/a+1 + a+1/a and here my anser is 2. Thank you.
  24. I

    MHB Simplifying Complex Math Expression

    $[\sqrt{4+\pi^2}-2\ln\left({\frac{2+\sqrt{4+\pi^2}}{2}}\right)]-[\sqrt{4+\pi^2/9}-2\ln\left({\frac{2+\sqrt{4+\pi^2/9}}{2}}\right)]$
  25. anemone

    MHB Simplify a trigonometric expression

    Simplify $\tan x\left(1-\sec \dfrac{x}{2} \right) (1-\sec x)(1-\sec 2x)\cdots(1-\sec 2^{n-1} x)$ at $n=8$.
  26. G

    MHB Solve Complex Math Problem: Helping My Middle Schooler

    Helping my middle schooler and got hung up with this one. Simplify and solve: (630*137+2) / (316+315*136) I don't see it. Extract 2 from the numerator? Then what? Any guidance is appreciated.
  27. P

    How to simplify this summation to an incomplete gamma function

    Could someone please explain why the following sum simplifies to the following? = As far as I can see, this sum does not correlate to the formula for incomplete gamma function as a sum. I'd appreciate any help as the incomplete gamma function is somewhat beyond the scope of my current...
  28. E

    MHB How do you simplify this?

    How do you simplify this? -2x[5x-(2x-7)]+6x[3x-(1+2x)] Can someone show the steps? I keep getting the wrong answer.
  29. E

    MHB Simplify (Adding and Subtracting Rational Functions)

    5c) Simplify. \frac{2x}{3y} - \frac{x^2}{4y^3} + \frac{3}{5y^4} This is what I did, which is wrong according to the textbook. Could someone point out what I did wrong and how to correct it? Thanks. \frac{(2x)(4y^3)-(x^2)(3y)}{(3y)(4y^3)} + \frac{3}{5y^4} \frac{8xy^3-3x^2y}{(12y^3)} +...
  30. E

    MHB Simplify and state any restrictions on the variables.

    Simplify 1) Simplify and state any restrictions on the variables: \frac{3a-6}{a+2} ÷ \frac{a-2}{a+2} This is what I did. Can someone tell me what I did wrong? Thanks. \frac{3a-6}{a+2} ⋅ \frac{a+2}{a-2} \frac{3a^2-12}{a^2-4} \frac{(3a+6)(a-2)}{(a+2)(a-2)} \frac{3a+6}{a+2} 3 +...
  31. E

    MHB Simplify and state any restrictions on the variables.

    Simplify and state any restrictions on the variables: \frac{2(x+1)}{3} ⋅ \frac{x-1}{6(x+1)} This is what I did, which is wrong (according to the textbook). \frac{2}{3} ⋅ \frac{x-1}{6} \frac{2x-2}{18} \frac{2(x-1)}{18} Can someone tell me what I've done wrong? Also, how would you find the...
  32. N

    Simplify this expression for an ellipse

    Homework Statement Simplify sqrt(x^2+(y-sqrt(5))^2) = 8 - sqrt(x^2 + (y+sqrt(5))^2) The Attempt at a Solution I know squaring both sides, collecting like terms and simplifying gets the equation but in my solution manual they do it a different way that is a lot shorter and I need help...
  33. P

    MHB Simplify equation using binomial theorem

    I'm sure this is easy but it has got me baffled. I'm told that the binomial theorem can be used to simplify the following formula x = \dfrac{1 - ay/2}{\sqrt{1-ay}} to (approximately) x = 1 + a^2 y^2 / 8 if a << 1. Thanks for any help or pointers on this one in particular, and/or general...
  34. H

    Simplifying an Equation with Taylor Series Expansion

    Homework Statement In a paper I have found there is a simplification of an equation which I do not understand. How did they do this? Can someone explain this step by step? Homework Equations The euqation is as follows: X = e \cos\theta + \sqrt{(R^2 + e^2 \sin^2 \theta)} X =...
  35. Albert1

    MHB How to Simplify Radical Expressions with Multiple Radicals?

    simplify: $\sqrt {21-4 \sqrt 5 +8\sqrt 3 - 4\sqrt {15}}$
  36. M

    Not able to simplify this summation formula?

    Hi, Please see the attached pdf file. Equation 1 and equation 2 are equivalent. Can someone please help me understand how to simplify equation 1 to get to equation 2? Thanks.
  37. G

    MHB How to simplify radicals in the denominator?

    I have some problems I am stuck on. The goal here is to simplify radicals in the denominator. I understand that when there is a binomial in the denominator, you need to multiply both sides by the conjugate. For some reason though, I seem to be having trouble doing that or am making a mistake...
  38. M

    Can the equation be simplified in the third step if it's indeterminate?

    Why can't the equation be simplified in the third step where it specifies that the equation is indeterminate? You could essentially have ln1/(ln1+1-1) if you substitute values in here. This then simplifies to just ln1/ln1 and then they would cancel to equal 1. Yet, the solution uses l'Hospital's...
  39. E

    Solving Complex Math Problems: (-192x^2(4x-3)-4(27-64x^3))/(4x-3)^2

    I am currently stumped with a mental blackout, how do you simplify this again? (-192x^2(4x-3)-4(27-64x^3))/(4x-3)^2 Wolfram Alpha spits out -32x-12, but how do you get there? :(
  40. R

    How does the following simplify?

    1. The problem statement ( F(r) \frac{d}{dr} ( r^{2} \frac{d}{dr} ) ) g(r) 2. The attempt at a solution Does it just melt down to: ( F(r) r^{2} g(r) ) \frac{d^{2}}{dr^{2}}
  41. N

    MHB What has been done here to simplify the integration

    Please refer to the attached image. My lecturer seems to have re-written $e^{-st}$ as $\frac{d}{dt}e^{-st}$ and taken out the $(-\frac{1}{s}$ which I do see is equivalent, but i am unsure how he goes from there onwards. Although, e is the derivative of itself. how does he split the integral...
  42. Z

    Simplify Fraction with same term in Num and Dem, but.

    Homework Statement I'm having a brain fart, how do you factor/simplify a fraction such as \frac{ab}{ab+cd} I keep thinking multiply by ab-bc but I'm not sure.
  43. C

    MHB Can You Simplify the Fraction 2h/h2 + 2h + 2 by Cancelling Out 2h?

    2h/h2 + 2h + 2 does the 2h cancel out?
  44. L

    Simplify the boolean expression #2

    Homework Statement Simplify the expression using boolean algebra postulates, laws, theorems. (\overline{\overline{x + \overline{y})(xz + \overline{y}}) + x (\overline{yz}}) The Attempt at a Solution (\overline{\overline{x + \overline{y})(xz + \overline{y}}) + x (\overline{yz}}) 1. ((x +...
  45. L

    Simplify the boolean expression

    Homework Statement Build the truth tables for the boolean expressions. (x + y' * z)' + (x * y * z' + (y + z)') + (y + (x * z')')' The Attempt at a Solution Given that the expression is so complex I believe that I need to simplify first then proceed to build the truth table? Work so...
  46. G

    Engineering Can You Simplify a Circuit Node with Both Voltage and Current Sources?

    Homework Statement I've been struggling with simplifying this circuit, eliminating a bunch of sources and moving around stuff in general. I'm still very unsure of how to handle nodes with multiple sources though. Like in the picture I've attached. I've got a voltage source and a current...
  47. 1

    Solve Linear ODE Simplify Step

    Homework Statement Solve: ##x\frac{dy}{dx}-4y=x^{6}e^{x}## Homework Equations ##x^{-4}\frac{dy}{dx}-4x^{-5}y=xe^{x}## is equal to ##\frac{d}{dx}[x^{-4}y]=xe^x## The Attempt at a Solution The second equation above simplifies to the third (according to my textbook) but I can't figure out...
  48. B

    MHB Simplify a trig. expression using a right triangle

    I have the expression sin^{-1}(cosx) I'm not sure how to simplify this at all. I've never done a problem like this and it's in my textbook as a review question. A quick boot in the right direction would help
  49. N

    How to simplify double radical when theres fractions involved?

    Homework Statement sqrt((2-sqrt(3))/4) I tried to split whatever is under the radical sign into two separate parts, 1/2 and (-1/4)sqrt(3) I realized that 1.5 times 2 is 3 and 2-1.5 = 1/2 so it seemed like it fulfilled the requirements for solving a double radical. so I put down...
  50. Safinaz

    Mathematica - how to simplify an output formula

    Mathematica -- how to simplify an output formula Hi all, Is there any more options to simplify an out put Mathematica formula. I used //Simplify but the expression still complicated and //FullSimplify too slow and didn't work. Bests, Safinaz
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