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. anemone

    MHB Simplifying a Quotient with Real Number $a>1$

    Simplify \frac{\Large 1+\frac{1}{2^a}+\frac{1}{3^a}+\frac{1}{4^a}+\cdots}{\Large1-\frac{1}{2^a}+\frac{1}{3^a}-\frac{1}{4^a}+\cdots} where $a>1$ is a real number.
  2. S

    MHB Simplifying Boolean Circuits: W NAND X & YNORZ

    Find the simplified equation (SOP FORM) corresponding to the following circuit (i.e. apply Demorgan's theorem to bring the negations inside the parenthesis). So is it saying W NAND X which means (w!x!) + YNORZ so (w!x!) + (y!z!) = wxyz?
  3. N

    MHB Simplifying a Messy Question - Any Help Appreciated!

    Please refer to the attached image. Is there a way to simplify this question? It looks really messy but I have a feeling there is some nifty way around it. Surely they don't want us to integrate that entire function. I also have no idea about part d) how can some values of lambda result in X...
  4. C

    MHB Simplifying polynomial fraction

    so I was reading my textbook and was showing steps on applying the quotient rule to the function: y=ex/(1+x2) it went from (1+x2)(ex)-(ex)(2x)/(1+x2)2 to ex(1-x)2/(1+x2)2 I understand the first step, but don't get how they got to ex(1-x)2 in the numerator. can someone please explain the...
  5. C

    Need help in simplifying circuits with logic gates

    hi, I am new in basic electronics course. i m having some problem with simplifying the circuits using boolean algebra. can you suggest me any good book to practice this? and i also need a short chart of the laws.
  6. I

    Simplifying an integral expression involving Airy functions

    Hello, Is there some way to express the following integral in terms of some simpler functions? f(x,s) = \int^{\infty}_{-\infty} dk\, e^{-ks} \text{Ai}(-k) \text{Ai}(x-k) where the parameter s \in (0,1) and the coordinate x \in (-\infty,+\infty) The best I can come up with is to...
  7. Drakkith

    How to Simplify the Expression (6w2-w-3) + (7w2-4w+5)

    Homework Statement Simplify, if possible. (6w2-w-3) + (7w2-4w+5) Homework Equations The Attempt at a Solution I attempted to factor both expressions, but they don't seem to be factorable. Is this already simplified as much as possible, or am I missing something?
  8. paulmdrdo1

    MHB Simplifying a Fraction with Exponents

    $\displaystyle\frac{-9b^2(a+3b)^{m+2}(2b-4c)^{2+m}}{4(3a+9b)^{2m+2}(b^2-2b^2)^{2-m}}$ my answer to this is $\displaystyle-\left[\frac{2(b-2c)^2b}{9(a+3b)}\right]^m$ i used some factorization of some quantity to arrive to this answer. but I'm not sure how did that technique works. for...
  9. M

    Simplifying a trigonometry expression

    Homework Statement Simplify: [(sec x)(sec2 x) - (tan x - 1)(sec x tan x)] / sec2 x Homework Equations none The Attempt at a Solution [(sec x)(sec2 x) - (tan x - 1)(sec x tan x)] / sec2 x [(sec x)(sec2 x) - tan x (1 -1) sec x ] / sec2 x [(sec x)(sec2 x) - 0 ] /...
  10. S

    Having trouble with simplifying things

    This isn't about any specific problem, I'm just hoping for a bit of advice. I've been out of education for a long time and am now doing an OU degree. I've passed the first level with high marks but have been struggling in some of the maths. Basically, I've been doing calculus and the bit I'm...
  11. K

    Simple algebra/trig expression, simplifying

    Hello, I'm trying to solve this equation. (4-4cos(∏*0.16*4)) - (4-4cos(∏*0.16*3)) It seems like it should be so easy. First I start with the left hand side (∏*0.16*4). Then I take the cosine of that, and then multiply it by 4. Then I do 4 - [answer] to get a value for the full left side...
  12. Saitama

    Simplifying a trigonometric expression

    Homework Statement If ##\displaystyle \tan\left(\frac{\pi}{4}+\frac{y}{2}\right)=\tan^3\left( \frac{\pi}{4}+\frac {x}{2} \right)##, prove that $$\frac{\sin y}{\sin x}=\frac{3+\sin^2 x}{1+3\sin^2x}$$Homework Equations The Attempt at a Solution...
  13. H

    Simplifying many body operator expressions

    Hello all, Is there any really good software, package or otherwise, that is helpful for simplifying long operator expressions, particularly with (anti-commuting) electron operators? For example, I'd like to be able to transform Hamiltonians, project onto subspaces with specific occupation...
  14. Saitama

    Finding function, simplifying the summation

    Homework Statement Let ## n \geq 2## be a fixed integer. ##f(x)## be a bounded function defined in ##f:(0,a) \rightarrow R## satisfying f(x)=\frac{1}{n^2}\sum_{r=0}^{(n-1)a} f\left(\frac{x+r}{n}\right) then ##f(x)## = a)-f(x) b)2f(x) c)f(2x) d)nf(x) Homework Equations The...
  15. MarkFL

    MHB Can you simplify this surd expression without a calculator?

    Without the use of a calculator, and showing your work, simplify: \frac{1}{2}\left(\left(239+169\sqrt{2}\right)^{ \frac{1}{7}}-\left(29\sqrt{2}-41\right)^{ \frac{1}{5}}\right) edit: My apologies...I was careless in my first statement of the problem...(Nod)
  16. I

    Simplifying the Algebra for Gaussian Curvature

    Homework Statement Hello everyone. :) I'm having trouble simplifying the last little bit of this question that deals with Gaussian curvature. I've taken all the required derivatives, and double checked with my professor to make sure that they're correct. I'm only have trouble with reducing...
  17. Sudharaka

    MHB Simplifying an Expression (Heather Jean's Question from Facebook)

    Heather Jean's of Facebook writes: Simplify, \[-(6y-\gamma)-5(-\gamma+6y)\]
  18. Femme_physics

    How can I simplify this expression without getting confused?

    My basic math is failing me again :( My attempt to simply: My teacher's attempt: Ignore the difference in notation. He writes || which signifies (A x B) / (A + B) = A || B And yes I'm aware there is more to simplify but I fail to follow him on the first step
  19. C

    Statistical Mechanics, Simplifying dq/dT

    Homework Statement \frac{dq}{dT}=\sum_{i} g_i \frac{dq}{dT} e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2}\sum_{i} g_i ε_i e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2} \bar{ε} q Homework Equations q=\sum_{i} e^{-\frac{ε_i}{kT}} or for degenerate states, q=\sum_{I} g_i e^{-\frac{ε_I}{kT}} The Attempt at a...
  20. J

    Fraction Simplification: Solving Equations with Constants C, L, and R

    I have the following two equations C, L, and R are all constants. I need to somehow get the above two equations and get it to look like this: But I can't get mine to look that nice. I have V1(s) = V2(s)(1+sCR) and I substituded it into equation 1 and it ends up looking messy...
  21. O

    Simplifying the Exploring Orthonormal States

    The following was written down as a solution to a problem, \begin{eqnarray} P(\alpha_n) & = & \frac{1}{25} \left[ 9| \langle \phi_n \mid \psi_1 \rangle |^2 + 16 | \langle \phi_n \mid \psi_2 \rangle |^2 + 12 i \langle \phi_n \mid \psi_1 \rangle \langle \phi_n \mid \psi_2 \rangle^* - 12 i...
  22. E

    I in simplifying this boolean expression

    Can someone please show me how to simplify this expression? I have no clue of how it's done so any help would be appreciated. Thank you! x'y'+xz'+yz+x'yz'+xy'z
  23. anemone

    MHB Simplifying Rational Expression

    Simplify \frac{x^2-4x+3+(x+1)\sqrt{x^2-9}}{x^2+4x+3+(x-1)\sqrt{x^2-9}} where x>3.
  24. 9

    How do I simplify this k/l ratio?

    Homework Statement Simplify this: y = ((k^1/2)/(l^1/4))/((l^1/5)/((k^1/8)) Ideally I would like to make rather than (k/l)/(l/k) simply (k/l) Homework Equations y = ((k^1/2)/(l^1/4))/((l^1/5)/((k^1/8)) The Attempt at a Solution y = (k^3/8)/(l^1/20)
  25. O

    Simplifying Integrands: How to Factor Out Constants in the Denominator?

    This equality is given in an example, in my textbook: \int\frac{1}{a^2+x^2}dx=\frac{1}{a^2}\int\frac{1}{1+(\frac{x}{a})^2}dx So, my question is simply... how? This is really more of an algebra question, but it'd really help me to see some more detail here.
  26. D

    Simplifying total energy equation orbital mechanics

    I am trying to show that $$ \frac{\Delta v}{v_{c_1}} = \frac{1}{\sqrt{R}} - \frac{\sqrt{2}(1 - R)}{\sqrt{R(1+R)}} - 1 $$ where ##R=r_2/r_1##. ##r_1## is the radius of the circular orbit 1 and ##r_2## is the radius of the circular orbit 2. Similarly, ##v_{c_1}## is the velcotiy of the circular...
  27. L

    Simplifying a cosine + cosine with conjugate denominators

    Homework Statement -\frac{1}{2}[cos(\frac{\pi+\pi n}{\pi+\pi n}) + cos(\frac{\pi-\pi n}{\pi-\pi n})] Homework Equations cos(u)cos(v) = \frac{1}{2} cos(u+v)+cos(u-v) The Attempt at a Solution I am attempting to use the above trig function to simplify the first function, but I can't seem to...
  28. G

    Engineering Simplifying a circuit to establish the intesities

    So I'm to calculate the current intensities in the places I put the ammeters in (yeah, I reckon one of them is turned around :)): http://i.stack.imgur.com/PAmmD.jpg And while I can calculate such things for series or parallel circuits, I was taught I should first try to simplify the...
  29. A

    How do I simplify fractions with exponents?

    Homework Statement (2x+3x)/6x = 2-x+3-x I've tried moving the 6 above, splitting it up and so... but i can't figure how to do it. It must be pretty simple, but I am just not seeing it. all helps appreciated!
  30. E

    Simplifying Additive Exponential Terms

    Homework Statement I have developed an equations for calculating some pollutant concentration as a function of x and y. I'm trying to simplify the problem so that I can write the equation for wp as a function of x. All variables except x and wp are known. Homework Equations...
  31. M

    Simplifying and solving surds with two variables

    Homework Statement Find values for x, and y in the following statement: 2x-y+\sqrt{4x-y}=x-2y+3+\sqrt{x+5} The Attempt at a Solution I've managed to rearrange the equation, but I cannot eliminate or equate the square roots on the LHS: \sqrt{4x-y}-\sqrt{x+5}=-x-y+3
  32. M

    How can I simplify this expression using index laws?

    Homework Statement Simplify; expressing with positive indices. \frac{x^{-2} - y^{-2}}{x^{-1} - y^{-1}} The Attempt at a Solution Hello, I'm doing first year uni math and over the holidays, I forgotten my index laws and as a result I'm stuck on this question :rolleyes: I know that...
  33. D

    Problem simplifying the solution of an ODE.

    So, I was following the derivation in my physics book of: x(t) = c_1e^-(\frac{\gamma t}{2})\cos(\omega_d t)+c_2e^-(\frac{\gamma t}{2})\sin(\omega_d t) Until they simply get to this in one step: Ae^-(\frac{\gamma t}{2})\cos(\omega_d t + \phi) I've tried reading many other sources for this...
  34. L

    MHB How Do You Simplify (x^2-2x+1)/(x-1) to x-1?

    Could someone explain how I'd simplify (x2-2x+1)/(x-1) to become x-1? Thanks a bunch!
  35. V

    MHB Simplifying Logical Expressions [SOLVED]

    [SOLVED] Simplifying Expressions Hello all I am a bit confused about the laws I am learning about right now and attempted some of my own exercises to understand them a bit. I have the problem NOT(a < 20 AND (b < 10 OR b > 10)) and I need to simplify it. From my understanding I can use...
  36. T

    How Do You Simplify and Find the Interval of Convergence for a Power Series?

    Edit: Nevermind, figured it out. Thank you for readingOriginal problem: Find the interval of convergence \sum∞n=1 xn / n * √(n) * 3n Ratio Test, right? an+1/a I get to here and I can't figure out how to get rid of the ns: lim n→∞ abs(x/3)* [n*√(n) / (n+1)*√(n+1)] Solution, They break apart...
  37. P

    MHB Where Did I Go Wrong When Simplifying This Exponent Equation?

    I have this problem to simplify with positive exponents: \[\left[(-4a^{-4}b^{-5})^{-3}\right]^4\] So, working with the interior brackets, I applied -3 to the equation, which resulted in: \[-(-64)x^{12}b^{15}\] **because "-4" was not in brackets, the exponent was applied to the 4 only...
  38. E

    Simplifying an algebra question

    Hello, Ive was reading my literature today and it showed me some algebra, which i did not understand how it went from one step to the next... What was done to simplify V= x^2 ( 75-x^2 / 2x ) into V= x/2 ( 75-x^2 ) & then what was done to simplify ^^^ V= x/2 ( 75-x^2 )...
  39. A

    MHB Simplifying exponential expressions

    Simplify 8p-3 x (4p2)-2/p-5. This is what I got: First thing I did was flip everything to get rid of the negative exponents: p5/8p3x(4p2)2 next thing I did was multiply the 4p2 by 2 p5/ 8p3x16p4Then I subtracted thep5 from the 8p3 p2/8x16p4 and ended up with 1/128p2 I know that the...
  40. I

    Question about simplifying congruences

    Homework Statement I am looking at an example from my book and I have no clue how this is done.Homework Equations I solved the left hand side and got this 125t3+75t2+50t+4 How did they reduce it to 65t+5?The Attempt at a Solution http://i48.tinypic.com/2v2gpap.jpg
  41. J

    Simplifying an expression involving complex exponentials

    Homework Statement Simplify the following expression: \sum_{ \alpha_1 + \cdots + \alpha_n = k} e^{i(\alpha_1 \theta_1 + \cdots + \alpha_n \theta_n)} Homework Equations \alpha_n = k - \sum_{j=1}^{n-1} \alpha_j 0 = \sum_{j=1}^{n} \theta_j The Attempt at a Solution I am trying to simplify...
  42. J

    Simplifying Complex Resistor Circuits

    Simplifying "Complex" Resistor Circuits Homework Statement Question 1: I have an E&M test coming up and I'm having trouble simplifying complex circuits. Our teacher told us something about "pinching" the wires which I didn't really understand. I found the following link...
  43. J

    Implicit Differentiation, chain rule, and simplifying

    Okay so, I am having trouble figuring out what exactly to do in implicit differentiation and usage of the chain rule. Like, I keep getting the wrong answer somehow. See, from what I understand you have to find the derivative of both sides then use the chain rule or something and then solve for...
  44. R

    Why do absolute values appear in the simplification of square roots?

    Homework Statement Simplify. a) \sqrt{x^6} b) 8 \sqrt{x^7y^{10}} - 10 \sqrt{x^7y^{10}} For b, it's y^10. I can't make it look right for some reason. Mod note: Fixed the exponent. Homework Equations The Attempt at a Solution I can simplify all of them but I don't know when or where I need to...
  45. C

    Simplifying the following function

    Homework Statement I have stumbled upon the following equation on wikipedia http://upload.wikimedia.org/math/b/8/d/b8de8bfcdf40f1793e7b72755161d61f.png To clarify, I am not sure how to simplify the equation of the form x^2/(1-x) = 1/(x^2 - x^-2) as demonstrated in the second line of...
  46. C

    Engineering Simplifying Complex Resistor Circuits

    Homework Statement See attached image. Homework Equations The Attempt at a Solution I cannot find any resistors in parallel or series in the circuit. I am confused by the lone branch going from the 10kOhm resistor back to the other end of the same resistor. How do I deal with...
  47. S

    Boolean expression needs simplifying

    I have attached the problem and my working. It would be much appreciated if someone could check through my working and let me know if I have slipped up anywhere. Thanks in advance Steve
  48. J

    Help simplifying a rational expression?

    Homework Statement \frac{x^2}{(x^2 -1)} Homework Equations N/A The Attempt at a Solution I know the solution is supposed to be 1+\frac{1}{2(x-1)}-\frac{1}{2(x+1)} and when I did long division, I got 1+\frac{1}{(x^2-1)} , so I'm making progress, but I'm not quite there. What should...
  49. M

    Simplifying a trigonometric product

    Was just double checking if we can simplify this in the following way, ∫ sinx * √(1 + cos2x) dx = ∫ sinx * (1 + cosx) dx
  50. P

    Simplifying slope-angular acceleration vs torque

    Homework Statement 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...
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