What is Simplifying: Definition and 498 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. FlowiwGhar

    Physics problem - Salmon jumping waterfall

    m * g * h + (1/2) * m * v² = m * g * y Simplifying the equation: g * h + (1/2) * v² = g * y Substituting the values: g * 0.614 + (1/2) * v² = g * 2.73 * sin(26.7°) Now, let's solve for v: (1/2) * v² = g * 2.73 * sin(26.7°) - g * 0.614 v² = 2 * (g * 2.73 * sin(26.7°) - g * 0.614) v = √(2...
  2. C

    Simplifying this complicated fraction

    How did they get y^7 in the bottom fraction? I got their answer except I had y^6. Would some please be able to help? Many thanks!
  3. homeworkhelpls

    Help simplifying this algebraic expression please

    14) here i tried 3x^3 + 3/8x^3 to to get 27/8x^3 but the answer is 3/2 x^3, why? 15) here i did 9x^3/2 - 1/x^3/2 to get 9x^9/4 - 1/x^3/2 but that's not in the right form, how do i do it correctly?
  4. T

    I Simplify Tricky Equation for Purely Imaginary C with Complex Constants

    Hey all, I am currently trying to solve the following equation for C: where C is a purely imaginary value, ##F_{+}##, ##F_{-}## and ##G_{+}## and ##G_{-}## are all complex valued constants (so ##G_{+}^{*}## just means complex conjugate of ##G_{+}##. I am not really sure where to start with...
  5. A

    A Simplifying a double summation

    Is it possible to simplify the function below so that the sums disappear. $$\displaystyle g \left(x \right) \, = \, \sum _{j=-\infty}^{\infty} \left(-A +B \right) \sum _{k=-\infty}^{\infty} \frac{1}{2}~\frac{\sqrt{2}~e^{-\frac{1}{2}~\frac{\left(x -k \right)^{2}}{\sigma...
  6. T

    A Help with simplifying an integral

    I am not seeing how the v goes away in the third equal sign of equation (1.8). It seems to be that it must be cos(z*sinh(u+v)), not cos(z*sinh(u)). In the defined equations (1.7), the variable "v" can become imaginary, so a simple change of variables would change the integration sign by adding...
  7. hackedagainanda

    Quick question about simplifying radical expressions

    So I simplify the expression and get 2 x 3^2 x 7 = 84 and get ##2 \sqrt{21(y−2)^{3/2}}## I don't follow how the answer is ##2(y -2) \sqrt{21 ( y - 2) }##
  8. p1ndol

    I Trouble simplifying the Lagrangian

    Hello, I have posted a similar thread on this question before, but I'd like to get some help to simplify the answers I've got so far in order to match the solutions provided. If anyone could help me, I would really appreciate it. Since (c) is quite similar to (b), I'll leave here what I've done...
  9. B

    I Is there a way to simplify this integral involving an exponential function?

    Hello! I have a function ##f(t)## such that ##\int_a^b{f(t)dt}=f_0##. Is there a way to calculate (or bring it to a simpler form) ##\int_a^b{f(a)e^{t}}dt##? Thank you!
  10. B

    MHB Help Needed: Solving x and Simplifying Equations

    having trouble with the following, if anyone could provide assistance it would be appreciated. Solve for x: and Simplify the following:
  11. C

    I Simplifying a nested radical that includes a complex number

    Dear Everyone, This post is not a homework assignment... I want to use the quartic formula. In one step is to solve the resolvent cubic. I know that there is 3 real solutions this particular resolvent cubic. I want to know how Bombelli got his answers before the discovery of the trigonometric...
  12. L

    MHB Simplifying lagrange interpolation polynomial

    Now $\sum_{i=0}^{10}(x_{i}+1) L _{10,i}(5) = (x_{0}+1) L _{10,0}(5) + (x_{1}+1) L _{10,1}(5) + ... + (x_{10}+1) L _{10,10}(5)$ Which I can further decompose into $\frac{(x_{0}+1)(5-x_{1})(5-x_{2})...(5-x_{10})}{(x_{0}-x_{1})(x_{0}-x_{2})...(x_{0}-x_{10})} +...
  13. L

    MHB Simplifying and expanding expressions

    I have a test on simplifying and expanding expressions, could someone help me with this. I don't understand the formula and the way you do it
  14. M

    MHB Expanding and simplifying brackets

    Hello, I have been trying to solve the top line equation to get the result (the bottom line). I am searching for a clue (the steps) on how to obtain those four brackets as a result.
  15. L

    I Simplifying limit with Stirling approximation

    I'm trying to determine why $$ \lim_{N \rightarrow +\infty} ln( \frac {N!} {(N-n)! N^n}) = 0$$ N and n are both positive integers, and n is smaller than N. I want to use Stirling's, which becomes exact as N->inf: $$ ln(N!) \approx Nln(N)-N $$ And take it term by term: $$ \lim_{N...
  16. J

    Engineering Simplifying a series / parallel circuit and calculating unknown values

    Given the circuit above, I have to solve for the labelled currents, find V total and R total accordingly. 1A is flowing through the 5Ω resistor as shown. Assuming electron flow (negative terminal to positive) for circuit. The connector in the middle was somewhat confusing. Without it, this...
  17. JD_PM

    I Simplifying an expression given (on-shell & off-shell) conditions

    I was studying how to compute an unpolarized cross-section (QFT Mandl & Shaw, second edition,https://ia800108.us.archive.org/32/items/FranzMandlGrahamShawQuantumFieldTheoryWiley2010/Franz%20Mandl%2C%20Graham%20Shaw-Quantum%20Field%20Theory-Wiley%20%282010%29.pdf) and came across the following...
  18. S

    Simplifying expressions using Euler's formula

    The following is the questions given. I solved the first one, which steps are shown below. But I am not sure if this is how the question wants me to solve the problem. Would you tell me if the way I solved the problem is the proper way of simplifying the expression using euler's formula...
  19. batclocks

    Simplifying a two-particle system to a one-body problem

    The first part is actually fine. You just note that since r=r1+r2 that means r1=r+r2 and r2=r1-r and you substitute that into the center of mass, R, and simplify to get r1=R+(μ/m1)r, and r2=R-(μ/m2)r But the next part is where I'm very confused. The general idea is that you want to prove ∇1 =...
  20. T

    Simplifying a matrix algebra equation (revised)

    I have a matrix equation (left side) that needs to be formatted into another form (right side). I've simplified the left side as much as I could but can't seem to get it to the match the right side. I am unsure if my matrix algebra skills are lacking or if I somehow messed up the starting...
  21. J

    I Simplifying a matrix into an equation

    Hi, Please see the attached image. I have a matrix and would like to split it up into a nice compact equation if possible. Matrix A seems to be a nice pattern that would lend itself to writing in equation form but I’m not sure what to do. Is it possible? Also do you know how I could correctly...
  22. U

    Simplifying fractional indices

    $$10π \left( \frac V {4π} \right)^{2/3} = 5\sqrt[3] {{V^2}\frac π 2}$$Not sure how to deal with the $$10π$$ and how we get $$\frac π 2$$.
  23. A

    Mastering Trig Identities: Simplifying a Trig Expression

    The other day in a fit of boredom I decided to dust off my old math books (high school and undergrad) and see if I can still crank through the basics. 1. Homework Statement Show the following: $$ \frac { 3 cos^2(x) } { 2 - 2 sin(x) } = \frac { 3 }{ 2 } ( sin(x) + 1 ) $$ Homework Equations $$...
  24. F

    Simplifying integral question....

    Homework Statement I have solve the integral for:to be: But I cannot figure out how to simplify the answer to the form shown above. Homework Equations The Attempt at a Solution Here is my progress so far: Any help would be appreciated
  25. S

    Simplifying algebraic fractions x in numerator and denom.

    Homework Statement (x+3)(x-2)/x2-2x Homework EquationsThe Attempt at a Solution (x+3)(x-2)/x(x-2) = (x+3)/x What I don't understand is why I can't simplify this further for instance the x's cancel to give 1: (1+3)/1 = 4/1 = 4 Is it because there is no x next to the 3? Many thanks :)[/B]
  26. R

    MHB Simplifying f(a+h)=-5(a+h)^2+2(a+h)-1

    Not sure where the 2ah is coming from in the middle step. f(a+h)=-5(a+h)^2+2(a+h)-1 = -5(a^2 + 2ah +h^2) +2a +2h -1 = -5a^2 - 10ah -5h^2 +2a +2h -1 Please enlighten me
  27. Eclair_de_XII

    Need help simplifying a summation with binomials

    Homework Statement "Prove that ##\sum_{n=0}^\infty s^n e^{-\lambda} \frac{\lambda^n}{n!}\sum_{m=0}^\infty s^m e^{-\mu}\frac{\mu^m}{m!}=\sum_{m+n=0}^\infty s^{n+m} e^{-(\lambda+\mu)} \frac{(\lambda + \mu)^{m+n}}{(m+n)}!## Homework Equations Binomial theorem: ##(x+y)^n=\sum_{k=0}^n x^ky^{n-k}##...
  28. Cheesycheese213

    How to find the square root of a square root?

    Homework Statement Simplify √(53 - 8√15) Homework Equations Numbers can be represented as √a - √b The Attempt at a Solution I had tried to make in an equation where the 2 expressions were equal, but after squaring both sides, I didn’t really know what to do. I had also tried to use something...
  29. Mr Davis 97

    I Simplifying this absolute value

    I have the expression ##|nr^n|^{1/n}##. A quick question is whether I can allow the exponent to go inside of the absolute value. I know that if it were an positive integral exponent then because of the multiplicativity of the absolute value function that would be allowed. But I'm not sure what...
  30. I

    Intuition about simplifying this expression

    Homework Statement I was solving a problem and came to a part where I was dealing with the expression, 1 - e-t -------- 1 - et It turns out that this can be simplified to -e-t but I had no idea from simply looking at the first expression that it could be simplified, and I tried to continue...
  31. opus

    Help Simplifying a Trig Expression

    Homework Statement Simplify: $$sin^2\left(x\right)+sin^2\left(x\right)tan^2\left(x\right)$$ Homework Equations All trigonometric identities. The Attempt at a Solution (i) ##sin^2\left(x\right)+sin^2\left(x\right)tan^2\left(x\right)## (ii)...
  32. The W

    Simplifying Electrical Mathematics in Certain Scenario

    When I was in school for Biomedical Engineering, while playing with numbers I noticed a pattern while calculating an equation, so I tested it. This is for relatively simple equations but maybe there is a way to incorporate it at a higher level. I would imagine while crunching numbers there may...
  33. T

    Simplifying the Natural Convection Heat Transfer Correlation

    Homework Statement An appropriate correlation for heat transfer by natural convection from a horizontal pipe to the atmosphere is Nu=0.53Gr^0.25 Pr^0.25 Where, Gr= (αp^2 d^3 (T_1-T_f )g)/μ^2 And Pr⁡〖= (C_p μ)/k〗 Show the above correlation can be simplified to h...
  34. RoboNerd

    I Question about simplifying Sigma notation

    Hello everyone! I have this expression which I have to simplify: ∑i=1log(n) 1(log(n) - i) And my book apparently simplifies it to being log(n). I am struggling to figure out why this is the case. Could anyone help? Thanks!
  35. J

    I Can the Double Summation be Simplified?

    Hi, I am trying to simplify a double summation and was wondering if anyone would be able to help me. The sum is $$ \sum_{i=1}^{n-1} \sum_{j=i+1}^n a_i a_j $$ Is it possible to simplify it down and maybe lose one of the sigmas? Thank you in advance :)
  36. F

    B Simplifying expressions -- What exactly does it mean to simplify an expression?

    What exactly does it mean to simplify an expression. I understand that an expression becomes more simple when you combine like terms but what other conditions are there? Is x(5x+1) more or less simple than 5x^2 +x? Do square roots need to be moved to the numerator?
  37. S

    I Help with simplifying series of hyperbolic integrals

    Hello. I have this function ## v(x) = -\sum_{i=1} x^i \sqrt{2}^{i-2} \int_{-\infty}^{\infty} m^{i-1} \cosh(m)^{-4} dm## which I can not seem to figure out how to simplify.I tried looking at some partial integration but repeated integration of ## \cosh ## gives polylogarithms which seemed to...
  38. toforfiltum

    Engineering Simplifying switching circuit literals

    Homework Statement The problem is given in the picture attached. It is a network of switches.Homework EquationsThe Attempt at a Solution I managed to simplify the expression to this: ## (S + x'(w+y) + xvz)(x'+y)(v+z') ## but I just can't find a way to simplify it to 9 literals. I've tried all...
  39. R

    B Can this equation be simplified?

    Hi, just wondering if anyone could help me simplify (if possible) the following two equations. x = sin((cos(((1-(cos(θ/2)^2))*360)/2)+1)/2*θ)*(d/2) x = cos((cos(((1-(cos(θ/2)^2))*360)/2)+1)/2*θ)*d/2)*2 My math is pretty crap, so any help would be appreciated. Thanks
  40. Drakkith

    Engineering Simplifying a Circuit Using a Y-to-Δ Transformation

    Homework Statement [/B] A.) Simplify the circuit (Figure 1) by using a Y-to-Δ transformation involving the resistors R2, R3, and R5 as shown in (Figure 2) . Determine the resistances of the equivalent Δ. B.) Determine the equivalent resistance Rab in the circuit. Hopefully these two figures...
  41. S

    Simplifying transfer function block diagram

    Homework Statement Simplify the block diagram. I uploaded a single image as it's the easiest way to do this problem. Homework Equations None at this stage. The Attempt at a Solution Please see the image.
  42. D

    Simplifying Complex Fractions, final step

    Homework Statement Please see attachment. Homework Equations I don't know how to get the final product on the ones with the question marks (textbook answers written next to them). I've gotten to the last step (except for # 29 but don't mind that one, I haven't exhausted all ideas). I've...
  43. Jess Karakov

    Simplifying this derivative....

    Homework Statement Evaluate the derivative of the following function: f(w)= cos(sin^(-1)2w) Homework Equations Chain Rule The Attempt at a Solution I did just as the chain rule says where F'(w)= -[2sin(sin^(-1)2w)]/[sqrt(1-4w^(2)) but the book gave the answer as F'(w)=(-4w)/sqrt(1-4w^(2))...
  44. pairofstrings

    B What is the use of simplifying a question in math?

    Hello. I have been looking into trigonometric identities that helps to simplify a question in mathematics. But the question that I have is, why do I need to simplify a question? For instance: Sin(x) * Cos(x) means Sin(2*x)/2. I have no answer that tells me why I simplify Sin(x) * Cos(x) to its...
  45. M

    I Need help understanding this step in simplifying a limit equation

    I read a paper and i can't understand how can we make the conversion (that attached in photo) i mean how i get formula (5) from previous one
  46. M

    Control systems: Simplifying block diagram

    Homework Statement How to show a block diagram can be simplified to a standard first order form for the diagram shown in the image attached and the question is shown in 1.a Homework Equations Standard first order form K/(1+tD) where K gain and t is time constant The Attempt at a Solution...
  47. P

    MHB Simplifying an Expression: $\sqrt{3} + \sqrt{2} / \sqrt{3} - \sqrt{2}$

    \sqrt{3} + \sqrt{2} / \sqrt{3} - \sqrt{2}
  48. M

    B Simplifying roots of negative numbers

    In this Khan Academy video they say that it is ok to break the square root ##\sqrt{a\cdot b}##, with ##a, b \in \mathbb{R}##, into the product of two square roots ##\sqrt{a}\cdot \sqrt{b}##, only when: (1) both are non negative, (2) one of the two is negative and the other is possitive. I...
  49. Mr Davis 97

    B Simplifying an exponential with a square root

    I have the expression ##e^{\frac{1}{2} \log|2x-1|}##. I am tempted to just say that this is equal to ##\sqrt{2x-1}## and be done with it. However, I am not sure how to justify this, since it seems that then the domains of the two functions would be different, since the latter would be all real...
  50. Charles Henderson

    Boolean Algebra - Simplifying to two different expressions

    For the expression: (B and C) or (not B and not C) or (A and (not B) and not C) I get two different answers depending on the order I do the simplification. 1. If I factor C out of the first and third terms I get (B and C) or (A and C) or (not B and not C) 2. If I factor not B out of the...