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. D

    Engineering Simplify Circuit: Understand How I1+I2+U1 = Whole Circuit

    [ Mod Note: relocated to homework forum so template is missing ] Hi Iwas soving a problem and the question is to simplify the circuit . Ididnt understand how the whole circuit is the same as the sum of I1 and I2 and U1 (which is a voltage source ) and I3 and R1 don't play a role Thank you
  2. T

    MHB How Can $\frac{\sec\theta}{\tan\theta}$ Be Simplified to $\csc(\theta)$?

    I have $\frac{sec\theta}{tan\theta}$. How can I simplify it to get $\csc\left({\theta}\right)$ ?
  3. E

    Fault analysis -- Simplifying to Thevenin equivalent

    Homework Statement [/B] All voltages and impedances are in per unit values. After all the source transformations, why is the voltage source still 1 ? Homework EquationsThe Attempt at a Solution [/B]
  4. Cocoleia

    Simplifying a circuit w/ multiple resistors & current source

    Homework Statement I am given this circuit...
  5. E

    I Simplifying integral of Gauss' hypergeometric function

    Hello all, I have this integral, and currently I'm evaluating it using Mathematica numerically, which takes time to be evaluated. Can I write it in a way that the integral has a formula in the Table of Integrals? \int_0^{\infty} F\left(a_1,a_2;a_3;a_4-a_5x\right) e^{-x}\,dx where...
  6. C

    MHB Simplifying radicals - Help with basic number manipulation

    Hi I'm trying to give myself a refresher in Leaving Cert maths and I'm running through some problems. Here's one which has me stumped (sorry I can't figure out how to show the actual symbols on the post, it's just showing as raw LaTEX when I try ) Combine terms and simplify the expression of -...
  7. J

    Simplifying Boolean Algebra: How to Simplify Complex Boolean Expressions

    Homework Statement (A OR C) AND NOT(C AND A AND B OR C AND A AND NOT B) or (A + C) (CAB + CAB')' Relevant Equations (A+B)' = A'B' A(B+C) = (AB) + (AC) (AB)' = A' + B' The attempt at a solution I'm not sure how I'm suppose to expand (CAB + CAB')' for simplifying. I keep arriving at false which...
  8. B

    I Simplifying 3 simultaneous equation into one equation

    Dear forum, I'm new here (living in Arizona). I am stuck getting to derive this: F1−F2−F3 = 0, (2.1) F1c1−F2c2−F3c3 = 0, (2.2) F1z1−F2z2−F3z3 = 0. (2.3) Where the only unknowns are F2 and F3. The textbook states that F1, F2 and F3 can be eliminated to get: c1z3 −c1z2+c2z1 −c2z3 −c3z1 +c2z2 =...
  9. T

    MHB Simplifying expression with exponents

    Supposing I have $$(-4x^n)$$ Why does it equal $(-4)^n * x^n$ and not $(-4)^n * (-x) ^ n$? When we have a negative symbol it only applies to the first item in an expression? so $-xbcw$ equals $b * c * w * (-x)$? Which means if we wanted the other items to be negative we would have to do...
  10. T

    MHB Simplifying Expression: $(-1)^n/(4^n)n(-4)^n$ - Explained

    I have $$\frac{(-1)^n}{(4^n)n }(-4)^n$$ (where n is a sufficiently large positive number, I think in this case it only has to be positive). Is $\frac{-4^n}{4^n}$ the same thing as $(-1)^n$? How is this the case?
  11. Z

    Double Check My Work: Simplifying a Homework Statement

    Homework Statement I got the problem down to: \frac{2}{\pi} \left[ \int_{0}^{\pi/2} \frac{2}{\pi}xsin(nx) dx + \int_{\frac{\pi}{2}}^{\pi} (\frac{-2}{\pi}x+2)sin(nx) dx \right] \frac{4}{\pi^2} \left[ \int_{0}^{\pi/2} xsin(nx) dx + \int_{pi/2}^{\pi} -xsin(nx) dx + \int_{pi/2}^{\pi} \pi...
  12. T

    MHB Understanding Squaring Inequalities

    I have $$-1 \le \cos\left({2x}\right) \le 1 $$ If everything is squared, it goes to $$0 \le \cos^2\left({2x}\right) \le 1 $$ and I'm not sure how $(-1)^2$ turns into $0$
  13. T

    MHB Simplifying a square root expression

    I have this expression: $$\sqrt{ 1 - \frac{16}{\sqrt{x^2 + 16}}}$$ And the textbook simplifies it to $$\frac{x}{\sqrt{x^2 + 16}}$$ But I'm not sure how it does this.
  14. T

    MHB How Can I Simplify This Integral Using Long Division?

    I have this integral $$6\int_{}^{} \frac{u^3 - 1 + 1}{u - 1}\,d$$ And I need to simplify it to $$6\int_{}^{}u^2 + u + 1 \frac{1}{u - 1}\,du$$ But I don't know how to get to this step.
  15. T

    MHB What are the steps to simplify this integral?

    I have this integral: $$\int_{}^{} \frac{x^2}{x^2 + 9} \,dx$$ And I'm trying to simplify it to: $$\int_{}^{}\,dx - 9\int_{}^{} \frac{1}{x^2 + 9}\,dx$$ But I'm not sure of the steps necessary to do this.
  16. T

    MHB Simplifying an expression with exponents

    I have this expression $$\frac {1} { e^x + \frac {1} {e^x}}$$ and it simplifies to $$\frac {e^x} { e^{2x} + 1}$$ And I'm not sure how to get this simplification or what rules to apply to get to this simplification.
  17. I

    Simplifying Product Homework: Combinatorics Problem on Object Arrangements

    Homework Statement This is a child thread I'm creating from a previous topic: https://www.physicsforums.com/threads/combinatorics-problem.871661/#post-5473920 In that thread, I was helped to come up with the expression for the number of arrangements of R distinct types of objects given the...
  18. T

    B Simplifying the factors of a complex number's imaginary part

    My question boils down to wondering if there is a way to simplify the imaginary part of a complex-valued function composed of n factors if the real and imaginary component for each of the factors is known but the factors may take on the value of their conjugate as well. For example, is there a...
  19. H

    I Simplifying a fractional factorial with variables

    I am trying to work through a simplication of this factorial with variables: (n/2)!/[(n+2)/2]! I get, 2[n(n-1)]/2[(n+2)(n+1)n(n-1)] cancelling the 2[n(n-1)] leaves me with 1/[(n+2)(n+1)] However, Wolfram Alpha tells me this can be simplified as 2/(n+2) and I don't see that. Thanks
  20. YellowBelliedMarmot

    Engineering Simplifying a Circuit w/ Parallel Resistors

    The goal of this problem is to find the equivalent resistance of all the resistors. Each resistor shown in the image has a conductance of 1 mS which I believe is equal to 1000 ohms. I attached a picture of the circuit diagram in which I show some of my work in order to convey my erroneous...
  21. E

    MHB Simplifying (k + 7/k^2 + 6K + 9) + (k - 5/k^2 - 5k - 24)

    (k + 7/k^2 + 6K + 9) + (k - 5/k^2 - 5k - 24)
  22. P

    Simplifying a log expression with identities

    I was supposed to simplify the expression ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## and apparently it’s wrong. Where’s the mistake? Is it not simplified enough or . . . ? ##\ln |\cot {x}|+\ln |\tan {x}\cos {x}|## ##=\ln |\frac {\cos {x}}{\sin {x}}|+\ln |\frac {\sin {x}}{\cos {x}}\cdot \cos...
  23. P

    Simplifying output for a XOR gate using Boolean Algebra

    Homework Statement I'm trying to show that the output of this XOR circuit is ##F=A'B+AB'##, Homework Equations ##(A+B)'=A'\cdot B'## ##(A\cdot B)'=A'+B'## The Attempt at a Solution From the gates the output is ##[(A\cdot B)+(A+B)']'##, using De Morgan's laws this becomes ##[(A\cdot...
  24. L

    Square Root Simplified: Understanding the Result as a Single Nonnegative Number

    How is it equal to v in the end? I'm sorry for asking such questions. But I'm just trying to understand
  25. Spitfire

    MHB Which simplifying method should be used to simplify 2x^2y^2 times 5xy^4?

    Hello, I have already studied first year mathematics but I am doing some basic revision incase I missed anything, (I skipped two grades and am thus missing some small simple things I should know) When simplifying the single term expression, 2x^2y^2 times 5xy^4 my initial thought was they...
  26. 1729

    Simplifying SI Units: What Quantity Does JNW⁻¹kg⁻¹ Denote?

    Homework Statement What physical quantity does ##\mathrm{J\cdot N\cdot W^{-1}\cdot kg^{-1}}## denote? Homework Equations You can simplify using mechanics equations or ones from electrodynamics. Be creative, I guess. The Attempt at a Solution ##\mathrm{J\cdot N\cdot W^{-1}\cdot kg^{-1}}##...
  27. Euler2718

    Simplifying a Product of Sequences

    Homework Statement [/B] Simplify: \frac{5\cdot 8\cdot 11 \cdots (3i+2)}{2\cdot 5 \cdot 8 \cdots (3i-1)} Homework EquationsThe Attempt at a Solution I realize the numerator and denominator terms cancel besides the 2, however I'm struggling to write this in a proper form. Only just started...
  28. W

    Simplifying an expression using limits

    Homework Statement Given that ##T = \frac{4E(V-E)}{4E(V-E)+V^2\sinh^2 (ka)}## Simplify the expression for T when a is large but not infinite, and again for the case when a tends to zero and the potential tends to infinity, such that ##d = Va## is a real constant. k is a constant, as is E...
  29. O

    Simplifying Trigonometric Antiderivative using Right Triangles?

    Mod note: Moved from a homework section 1. Homework Statement Hello my question more has to do with theory that perhaps deals with algebra. Why is the following true? Homework Equations N/A The Attempt at a Solution N/A[/B]
  30. Euler2718

    Factorizing an 'i' in Exponent: Justified?

    In the attached picture, how is it justified to factor out an 'i' in the exponent of the 2 and the 5?
  31. EsmeeDijk

    Calculating with tensors and simplifying

    Homework Statement I have a tensor which is given by t_{ij} = -3bx_i x_j + b \delta_{ij} x^2 + c \epsilon_{ijk} x_k And now I am asked to calculate (t^2)_{ij} : = t_{ik} t_{kj} Homework EquationsThe Attempt at a Solution At first I thought I had to calculate the square of the original...
  32. E

    Simplifying square root of an irrational

    Homework Statement Find [(3 - 51/2)/2]1/2 Homework EquationsThe Attempt at a Solution My calculator says (-1 + √5)/2 I have no idea how. Rationalising doesn't really do much good. Just tell me where to start.
  33. B

    Simplifying a fraction (block reduction, control)

    Homework Statement 2*3*4*5/4+3*4*4*6 Homework Equations 2*3*4*5/4+3*4*4*6 The Attempt at a Solution 2*3*5/1+3*4*6 Knowledge gap 1 - I do not understand why if top and bottom are divided through by 4 there should be a 4 left in the denominator and why the rest of the numerators and...
  34. olgerm

    Simplifying expression with vectors

    Homework Statement To simplify: ##\mid \vec b -\frac{\vec a*\vec b}{\vec a*\vec c} * \vec c \mid## ##\mid \vec b -\frac{(\vec a*\vec c)*(\vec b*\vec b)-(\vec a*\vec b)*(\vec b*\vec c)}{(\vec a*\vec b)*(\vec c*\vec c)-(\vec a*\vec c)*(\vec b*\vec c)} * \vec c \mid## Vectors may be any...
  35. science_rules

    Simplifying Fraction: (6x+12y)/(10a+5) * (100a^2-25)/(9x^2-81y^2)

    Homework Statement Simplify (6x+12y)/(10a +5) times (100a2 - 25)/(9x2 - 81y2) Homework Equations (6x+12y)/(10a +5) times (100a2 - 25)/(9x2 - 81y2) The Attempt at a Solution (6x+12y)/(10a +5) times (100a2 - 25)/(9x2 - 81y2) = 3(2x+4y)/(10a+5) times (4a - 1)/(3x-27y) =...
  36. science_rules

    Is This the Correct Way to Simplify Complex Fractions?

    Homework Statement Simplify: (a2 + 2ab + b2)/(a2 - b2) times (a2 - 2ab + b2)/(a2 - b2) Homework Equations (a2 + 2ab + b2)/(a2 - b2) times (a2 - 2ab + b2)/(a2 - b2) The Attempt at a Solution Did I simplify this correctly?? (a+b)(a+b)/((a-b)(a+b)) times (a-b)(a-b)/((a-b)(a+b)) = ((a+b)/(a+b))...
  37. B

    MHB How to Simplify Derivatives Using Common Denominators

    Folks, Just struggling to see how this is simplified. \frac{f''(x)}{((1+f'(x)^2)^{1/2}}-\frac{f'(x)^2 f''(x)}{((1+f'(x)^2)^{3/2}}=\frac{f''(x)}{((1+f'(x)^2)^{3/2}} if we let a=(1+f'(x)^2)^{1/2} then I get as far asf''(x)[a^{-1/2}-f'(x)^2a^{-3/2}]=f''(x)[a^{-1/2}-f'(x)^2 a^{-1/2} a^{-1}]...
  38. C

    System Analysis - Simplifying with Transfer Functions

    Homework Statement Sorry for the pictures, I'd normally write out the problem but it is mostly diagrams. Question and work attached. I am looking for help with part (a) right now, the transfer function I obtain is shown at the end of my work. Homework Equations Knowledge of Laplace transforms...
  39. S

    Simplifying natural log of complex number

    Homework Statement The problem is to sketch lines of constant u and v in the image plane for the function Log[(z+1)/(z-1)]. Homework Equations z=x+iy The Attempt at a Solution In order to do this I have to get the expression into u+iv form, so that I can read off and manipulate the u and v...
  40. T

    Simplifying a 4-term equation using boolean algebra

    So, I have an equation: ~A * B * C * ~D + ~A * B * C * D + A * ~B * ~C * D + A * ~B * C * D + A * B * ~C * D + A * B * C * ~D where * represents "AND" and + represents "OR", ~ being NOT. Part of the reason I'm having trouble is due to the length of the equation. So far, I've managed to use...
  41. Mr Davis 97

    Simplifying a rational expression

    Given that we have the expression ##\displaystyle-\frac{1}{(x-2)(x-2)(x-3)}~\cdot~\sqrt{\frac{(x-2)^{2}}{(x-3)(x-1)}} ##, how do we simplify it, step by step? Specifically, I am concerned about the ##\sqrt{(x-2)^{2}}## term. Are we allowed to cancel this with the ##(x-2)## in the denominator?
  42. karush

    MHB Simplifying a Trigonometric Expression

    $$\frac{\cot^3\left({y}\right)-\tan^3\left({y}\right)} {\sec^2\left({y}\right)+\cot^2\left({y}\right)} =2\cot\left({2y}\right)$$ I tried the LHS but could get it to reduce.
  43. T

    Simplifying Complicated Concepts: Explained with Examples

    I do not understand this even the one in Wikipedia. Can anyone explain it to me as simple as possible as well as give me some simple examples? Thanks a lot!
  44. B

    Simplifying Tensor Equations for Beginners

    Hello, I am very new to tensors and GR and would like to ask for guidance to understand how tensor simplification works. If we have this term $$\frac{1}{2}N_{IJ}F_{\mu\nu}^I\tilde{F}^{J\mu\nu} $$ and I want to derive w.r.t ##F^{\rho\sigma I}## where - ##N_{IJ}## is a symmetric complex matrix -...
  45. earthloop

    Simplifying with trig identities

    Homework Statement [/B] Hi, I am currently working through a textbook, and the following simplification is given for an example question: I can't seem to work out how they have moved from cos(pi+n*pi) to cos(pi)cos(n*pi) so easily? Is there a simple trick I have missed? I understand the...
  46. marcus

    From Aeon to Zeon to Zeit, simplifying the standard cosmic model

    This is take 2.0 of the earlier thread, which got a lot of help from George J., Jorrie, Wabbit, Ken G, and others. I'm exploring this simplification of the flat matter-dominated ΛCDM model (basically anything after year 1 million) to see if there is a presentation that would be suitable for PF...
  47. anemone

    MHB Simplifying Expression: Simplify Expression

    Simplify the expression $\dfrac{\sqrt{1+\sqrt{1-a^2}}((1+a)\sqrt{1+a}-(1-a)\sqrt{1-a})}{a(2+\sqrt{1-a^2})}$.
  48. J

    Simplifying Complex Calculation

    Calculate ( minus ( 2 over 3 ) + ( 2 over 3 ) i ) to the power minus 4, simplifing your answer and giving it in the form a + i b, with a and b given exactly.I found the modulus by: sqrt((-2/3)^2 + (2/3)^2) = (2*sqrt(2))/3 the argument is: pi - 1 (from a sketch in the complex plane) hence...
  49. W

    Simplifying A Fraction That Can't Be Simplified

    So let me start off by saying I am horrible at math and always have been. Despite considering myself highly intelligent, I suck at math. It's what led me into computer programming instead of physics like I wanted. Simply, I want to ask, say I have a fraction or a ratio that can't be simplified...
  50. anemone

    MHB Simplifying Expression: $\frac{z^2(w-x)(x-y)}{(w-x)(x-y)(y-w)}$

    Simplify the expression below: $\dfrac{w^2(z-x)(z-y)}{(w-x)(w-y)}+\dfrac{x^2(z-y)(z-w)}{(x-y)(x-w)}+\dfrac{y^2(z-w)(z-x)}{(y-w)(y-x)}$
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