Simplifying Definition and 498 Threads

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

    Need help simplifying units of slope for an angular acceleration vs torque graph

    In a lab we conducted in class we graphed angular acceleration vs torque, and found a positive linear correlation-easy enough. However I am getting rather stuck in simplifying the units of slope in terms of Kg, m, and s... I am fairly sure this will give me that angular acceleration equals...
  2. S

    Simplifying a boolean expression

    Homework Statement Simplify the following boolean expression: Homework Equations B'D' + A + BD + AD + B'C'D' + B'C + CD The Attempt at a Solution --line 1-- A(1+D') + B'D' + BD + B'C'D' + B'C + CD --line 2-- A + B'D' + BD + B'C'D' + B'C + CD --line 3-- A + B'(D' + C'D' +...
  3. S

    Simplifying with rational and negative exponents

    Homework Statement Simplify the expression completely 3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2 The Attempt at a Solution My attempt is totally wrong. I can't quit figure out what to do or where to start 3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2 3(y)(1/3)-6x(y)(-2/3) / y(2/3)...
  4. P

    Simplifying boolean expressions

    Homework Statement Simplify the following Boolean expressions to a minimum number of literals (a+b+c')(a'b'+c) 2. The attempt at a solution Whenever I tried this I made no progress in reducing the number of literals, I just reordered the expression. (a+b+c')(a'b'+c)...
  5. I

    Simplifying equations. Orders of operation.

    Simplify the following expression. (2+1×2)−4×6 =(2+2)−4×6 =4−4×6 =4−24 =−20 My answer was 20 and it was wrong. When i look at this i see, 2 plus 1 times 2 minus 4 times 6 The part I am getting wrong is the minus, which in this case means a -4 instead of a 4. I don't understand how you can you...
  6. D

    Simplifying a sum involving lnx

    Homework Statement I need to show that the lim n->inf ( [(1/n) * sum from k=1 to n of ln(k) ] - ln(n) ) is equal to the lim n->inf ( (1/n) sum from k=1 to n of ln(k/n) ) The Attempt at a Solution I showed that the sum of ln(n) from k=1 to n is ln(n!) using ln(a) + ln(b) = ln(a+b). I...
  7. B

    Boolean algebra: Simplifying logical expression

    I was trying a while ago to prove associativity of the XOR operator. That led me to the following problem: I am trying to prove \overline{(\overline{A}*B+\overline{B}*A)}*B + \overline{B}*(\overline{A}*B+\overline{B}*A) = B Obviously it can be solved by just creating a truth table...
  8. N

    Engineering Simplifying a circuit in order to find the current

    Homework Statement I solved my original question so I posted another one. http://i.imgur.com/dpevY.png Find R_{eq} at terminals (c,d) Homework Equations R_{eq} in series = Ʃ R R_{eq} in parallel = \frac{1}{R_{1}} + \frac{1}{R_{2}} + ...+ \frac{1}{R_{n}} The Attempt at a Solution I don't...
  9. B

    Simplifying the Conditional probability

    P(S1 \cap S2 \cap S3 | r) How do I simplfy the above equation if S2 and S3 are independent of r ?
  10. B

    Simplifying finite geometric series expression

    Homework Statement I've come across the type of sum in several places/problems but seem to be making no progress in trying to simplifying it further. We have a finite series of some exponential function. \sum_{n=0}^{N}e^{-na} Where a is some constant, a quantum of energy or a...
  11. N

    How can I simplify a summation with constant variables A and B?

    Homework Statement Hello! I'm guessing this is precalculus. There is an intermediate step in a simplifying process and I got to: \sum_{x=1}^n xA^{-Bx} Where A is a constant and B is a constant. Homework Equations I was wondering how to write this without the summation sign...
  12. L

    Simplifying the result of integration

    Homework Statement The original problem is \int \, \frac {xe^{2x}}{(1+2x)^2} dx . I utilized integration by parts to get: -\frac {xe^{2x}}{2(1+2x)} \, + \, \frac {1}{4}e^{2x} \, + \, C which I know is correct. However, I am told by the book that this may also be expressed as...
  13. B

    Is There a Faster Way to Prove Part (b) Using Radon-Nykodim?

    Hi, I'm trying to work this out. Just a small question: Let (X, m, μ) be a measure-triple (X a set; m a sigma-algebra, μ a measure) , and let, f:X-->ℝ be measurable. For B a Borel set, define : v(B):=μ(f-1(B)). Then show: a)v is a measure in the Borel subsets of R , and...
  14. C

    Derivative of arctan[(1 - x) / (1 + x)] Simplification

    Homework Statement Find the derivative of arctan[(1 - x) / (1 + x)]. Homework Equations Everything in the "Show Steps" section: http://www.wolframalpha.com/input/?i=derivative+arctan%5B%281+-+x%29+%2F+%281+%2B+x%29%5D My problem is that I don't know how Wolfram manages to simplify...
  15. C

    How can I easily simplify a derivative of sin^-1 (2x + 1)?

    Homework Statement Find derivative of sin^-1 (2x + 1) Homework Equations I do everything Wolfram does except I don't know how to simplify to get the final answer. http://www.wolframalpha.com/input/?i=derivative+sin%5E-1+%282x+%2B+1%29 The Attempt at a Solution Everything Wolfram...
  16. C

    Derivative of Exponential Function with Variable Exponent

    Homework Statement Find the derivative of: y = 10^(1 - x^2)Homework Equations I get: y' = (10^(1 - x^2))(ln 10)(-2x) doing everything Wolfram does here: http://www.wolframalpha.com/input/?i=derivative+10%5E%281+-+x%5E2%29 I don't understand why it simplifies to Wolfram's final answer from...
  17. C

    How to Simplify Trigonometric Functions for Derivatives

    Homework Statement Finding the derivative of x^2 sin x tan x. I need to simplify this: x^2 sin x sec^2 x + x^2 tan x cos x + 2x sin x tan x to: x (x sec(x) tan(x) + sin(x) * (x+2 tan(x))) Homework Equations Just what you see above.The Attempt at a Solution I can get it simplified to x(sin...
  18. JJBladester

    Simplifying a resistor network using pi-T (Y-delta) conversion

    Homework Statement Reduce the resistor network to a single resistor. Go step-by-step and indicate the series or parallel combinations being reduced. Homework Equations For series resistors: R_T=R_1+R_2+R_3+\cdot \cdot \cdot +R_N For parallel resistors...
  19. H

    MHB Simplifying trig expression

    I have to simplify (or get it in terms of tan I guess?) \cot (\frac{2\pi }{3} - x) I'm not sure how to get the reference angle and subtract the angle 'x' from it to get an expressional value...how would I do this?
  20. V

    Simplifying an algebraic fraction with factors

    Homework Statement Simplify the following expression: x3(1-x2) / x(x-1) Homework Equations The Attempt at a Solution I know that the top can be factored to x3(1-x)(1+x) to give x3(1-x)(1+x) / x(x-1) . However, after this step I seem to just go round in circles. I got an...
  21. P

    MHB Simplifying (x+3)1/2 - (x+3)3/2 Expression

    Simplify (x+3)1/2 - (x+3)3/2 i honestly am so lost on this one how i approached it was (x+3)1/2 [1 - ((x+3)3/2 / (x+3)1/2)] but again, i have no idea what I'm doing.
  22. J

    Why do I have to multiply by -1 when simplifying (sometimes)

    Homework Statement Solve for s: -4su+7t+9u+2=6t+4u-9 Homework Equations The Attempt at a Solution My answer: s = \frac{-t-5u-11}{-4u} The given answer: s=\frac{t+5u+11}{4u} I know that the right hand side has been multiplied by -1, but this raises some questions in my mind; Why...
  23. H

    Simplifying Factorials: Proving (n+1)(n+1)!+(n+1)! =(n+2)!

    Homework Statement (n+1)(n+1)!+(n+1)! =(n+2)! simplify The Attempt at a Solution I need to know how to simplify this to show it is true. I know that the above statement is true, but I do not understand how to simplify the left hand side to show it. Thanks, I really have no idea where...
  24. S

    Simplifying a transfer function to find overshoot

    Hi, I have question where I am asked to find the % overshoot of a system based only on its transfer function. T(s) = 15(s+2.1) (s+2)(s2+4s+29)(s2+2s+50) I'm assuming I need to use second order assumptions and then find the damping...
  25. T

    Simplifying ln: A Calculus Struggle

    Homework Statement Simplify ln [(e^1-3ln2)/(2∏/e)] Homework Equations I was using the equation e^lnx = x to try and simplify the numerator, but I am unsure if that is correct. The Attempt at a Solution I am very rusty with my calculus and when it comes to using ln, I tend to get stumped...
  26. V

    Algebra II Simplifying Radicals Using Product and Quotient Properties

    Homework Statement Simplify. \sqrt[3]{\frac{5}{4}} The answer according to the textbook is: \frac{\sqrt [3]{10}}{2} Homework Equations -- The Attempt at a Solution Separated numerator and deonominator into individual cube roots and multiplied both by \sqrt[3] {4} ...
  27. A

    Simplifying radical in a radical

    How would you approach something like this? \sqrt{-\sqrt{3}+\sqrt{4+\sqrt{5}+\sqrt{17-4\sqrt{15}}}}
  28. AnTiFreeze3

    How do I simplify cubed roots with multiple variables and coefficients?

    Homework Statement Simplify...Homework Equations Starting Equation: ³√9xy^4 * ³√12x³yThe Attempt at a Solution (Sorry ahead of time if this is sloppy) ³√9xy^4 * ³√12x³y - I broke up each part of the cubed roots to try and simplify them³√9 * ³√x * ³√y * ³√y³ * ³√y * ³√12 *...
  29. AnTiFreeze3

    Simplify Radicals: √3 + √2 - √5

    Homework Statement The expression can be simplified. Simplify the following...Homework Equations 1 _____________ - Starting equation √3 + √2 - √5The Attempt at a Solution 1 * [(√3 + √2) + √5] _____________...
  30. C

    Can this Secant-Tangent Equation be Simplified Further?

    Homework Statement Is it possible to simplify this even further? Homework Equations This is a Secant-tangent equation. Secant: AD = 18/radical 3 AC = ?? The Attempt at a Solution I cross multiplied to get 18=324radical 3 (AC) and in the end i got 0 = (18radical3) (AC) which makes...
  31. T

    How Can Trig Double Angle Formulas Simplify This Function?

    Homework Statement Hello, I am trying to simplify the inputted function here http://www.wolframalpha.com/input/?i=sqrt%282%29+sqrt%281-cos%28%282pi%28x-y%29%29%2Fn%29%29 which is \sqrt{2}\sqrt{1-cos[2\pi(x-y)/n]} to the form of 2sin[(x-y)\pi/n] Homework Equations Not sure The Attempt at a...
  32. P

    How Do You Simplify a Cubic Polynomial?

    Homework Statement simplify -x^3 - 3x^2 - 4x - 2 It is equal to -(x-1)(x^2 + 2x + 2) Not sure how to get that answer, nor how to start it.
  33. E

    Reallllly dumb question about Feynman Parameters (and simplifying them)

    I know the generalized formula for Feynman parameters, my problem is in simplifying. What I mean is something like this: Take the simplest 3 parameter equation \frac{1}{ABC} = 2 \int_0^1 dx \int_0^1 dy \int_0^1 dz \frac{ \delta \left( 1-x-y-z \right)}{(xA+yB+zC)^3} And you can take this...
  34. Y

    How do I simplify sigma notation to find the sum in terms of n only?

    Homework Statement I'm actually asked to calculate the area under the curve 5x + x2 over the interval [0,1] using Riemann Sums. I found the formula for the Riemann sum over the interval, it being the following: \sum^{n}_{k=1} (\frac{5k}{n}+\frac{k^{2}}{n^{2}})(\frac{1}{n}) However, I...
  35. C

    How Do You Simplify the Square of Complex Conjugates?

    Homework Statement Simplify (\sqrt{3+4i}+\sqrt{3-4i})^{2} Homework Equations The Attempt at a Solution well I tried expanding it out but I don't think that is the right approach but I have no other idea to tackle the problem? so by expanding I had...
  36. M

    Regarding functions how can simplifying a function change it's domain

    for example if f(x) = \frac{x^{2} - 1}{x+1} they by factoring: f(x) = \frac{x^{2} - 1}{x+1} = \frac{(x + 1)(x - 1)}{x+1} = x - 1 thus the simplified version is x - 1 let's say g(x) = simplified f(x) g(x) = x - 1 meaning g(x) = f(x) but g(-1) ≠ f(-1) am I missing something?
  37. F

    Simplifying arctan(cot(x)) to Terms of x and Constants

    Hello, I need help trying to simplify the equation below, I believe it should be in terms of x and constants only, no trigonometry. "Simplify arctan(cot(x)), assuming 0<x<pi/2" After many attempted solutions and failures, my most recent attempt is below. let arctan(1/tanx) = u ==> tan...
  38. C

    Simplifying Algebra with power to a half

    Homework Statement 3b^1/2 x 4b^0 / 6b^1/2 3. The Attempt at a Solution [/b] All the solutions i keep getting do not equal the answer which is 2b^-1 = 2/b. I am not sure what i am supposed to minus from the first side and put on the second side of the equation?
  39. R

    Stuck At the Last Step Simplifying A Series

    Homework Statement Find a power series for the function, centered at c, and determine the interval of convergence. Homework Equations g(x) = 2 / (1-x^2) , c=0 The Attempt at a Solution 2 / (1+x)(1-x) = 1/(1+x) + 1/(1-x) 1/(1-(-x)) => Sum [(-1)^n (x^n)], n=0 to infinity. Converges when...
  40. D

    Is (x^2-1)/x^2 More Simplified Than 1-(1/x^2)?

    I don't know if this is calculus or not but this was on a calculus test. It was the last step of a third derivative question. I lost a mark because the teacher says (x^2-1)/x^2 is more simplified than 1-(1/x^2).. is this fair? Is there an official rule that states (x^2-1)/x^2 is more simplified...
  41. C

    Simplifying this differential using product rule?

    Hi, I am trying to simplify this; x \frac{\partial}{\partial x} W(x,y) - \frac{\partial}{\partial x} (xW(x,y)) Am I correct in thinking I can do this with the product rule, as; \frac{\partial}{\partial x} (xW(x,y)) = \left( \frac{\partial x}{\partial x}\right) W(x,y) + x...
  42. V

    Algebra II Simplifying Rational Algebraic Expressions

    Hi everyone and nice to meet you. I'm velox_xox a newbie to PF and a high school correspondence student currently taking Algebra II. Since I'm correspondence, I am basically teaching myself my subjects, which means if I don't understand something it's a big problem. I enjoy math, but I must...
  43. P

    I have troubles simplifying this quotient of factorials

    Homework Statement I'm trying to self-study Mary L. Boas' book Mathematical Methods in the Physical Sciences. One of the exercices asks the reader to find the limit of n -> ∞ (n!)2 / (2n)! Homework Equations None The Attempt at a Solution Instinctively I know that (2n)! grows...
  44. M

    Simplifying with Imaginary Numbers

    Homework Statement I'm trying to see if what I have before the e match up with the correct answer. the correct answer is (2+.5i)e^(1+3i)x + (2-.5i)e^(1-3i)x The Attempt at a Solution This is what I have so far. I don't know how I would simplify anymore. Please help.
  45. G

    Problem simplifying a power function derivation

    Hello All, I can compute the solution, but I fail to see how it further simplifies into the final expression. The solution manual lists both the answer and its simplified formulation. How do I go from step three to step four? Homework Statement Find the derivative of: f(x) =...
  46. S

    IIR - Bilinear transform - simplifying H(z)

    Homework Statement Hello, I'm an audio engineer with an interest in creating/implementing audio processing techniques and I'm trying to learn IIR filter design via the Bilinear Transform method. I've looked through various books and online resources but I keep on getting stuck when it comes...
  47. L

    MHB Simplifying Limit Problem - L'Hôpital and Algebra

    I have the following limit problem: $$\Large\lim_{x \rightarrow \infty}\frac{x^{\frac{5}{3}}}{e^{2x}}$$ I have reduced it to the following using L'Hôpital's rule once and basic algebra: $$\Large\lim_{x \rightarrow \infty}\frac{5}{2e^{2x}3x^{\frac{-2}{3}}}$$ I can tell that the limit is 0, but...
  48. D

    MHB Can the Given Complex Summation be Simplified?

    u is a complex. Can this sum be simplified? If so, how? $\displaystyle \sum_{n}^{\infty}\frac{2u+5}{2}\left(-\frac{u}{2}\right)^n $ Thanks.
  49. D

    Simplifying Equations with Polynomial denominators/numerators

    Homework Statement I uploaded a picture of the question because I didn't want to confuse people from the way it looks because it is pretty long. http://tinypic.com/r/2itpm39/5 Homework Equations -None- The Attempt at a Solution I went from the original equation and took an 'x'...
  50. MathWarrior

    Quick question about simplifying a differential equation?

    I have solved this equation but I am just not quite sure why this final result is the way it is. \frac{2e^{t}+C}{e^{t}} = 2e^{-t} + C Why is it e^{-t} when its simplified ?
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