text: The paper introduces a broad generalization of the derivative in terms of the maximal modulus of continuity of the primitive function. Try to Introduction. Function k below is not differentiable because the tangent at x = 0 is vertical and therefore its slope which the value of the derivative at x =0 is undefined. Additionally, while local minima are often “good enough” for deep learning, symbolic regression typically wants to be able to escape local minima and explore a … It is an example of a fractal curve. Yes Sir! Some types of functions with discontinuities , turns or other odd behavior may also be integrable— depending on the type and number of discontinuity.If the discontinuity is removable, then that function is still integrable. Everywhere Continuous Non-differentiable Function Written by Gaurav Tiwari July 7, 2011 Calculus Weierstrass had drawn attention to the fact that there exist functions which are continuous for every value of $x$ but do not possess a derivative for any value. When we are talking about real functions the square root In general, a function is not differentiable for four reasons: Corners, Cusps, Vertical tangents, Jump discontinuities. It is an example of a fractal curve.It is named after its discoverer Karl Weierstrass.. Betting, Casino, Gambling and How to Play Guides, Start Internet Marketing with a single website, Best Indian Bloggers to Look Upon in 2021. the absolute value for $$\mathbb R$$. 5. Stuck on the Followers Count? For example, the function $f (x) = |x|$ is not differentiable at $x=0$, though it is differentiable at that point from the left and from the right (i.e. August 10 2005. We discuss how you can numerically differentiate a function with high accuracy with little effort. 2. We next want to study how to apply this, and then how to invert the operation of differentiation. Differentiation can only be applied to functions whose graphs look like straight lines in the vicinity of the Differentiation can only be applied to functions whose graphs look like straight lines in the vicinity of the point at which you want to differentiate. When this limit exist, it is called derivative of #f# at #a# and denoted #f'(a)# or #(df)/dx (a)#. How to Create a Professional Photography Portfolio Without Coding Skills? You have chosen to go for checking that two sets are mutually bijective, why not. Hardy showed that the function of the above construction (Cosine Function) is non-derivable with the assumptions $0 < a <1$ and $ab ge 1$. Thus, by Wierstrass’s $M$ -Test for uniform Convergence the series (1), is uniformly convergent in every interval. Many physical phenomena give rise to mathematical models in terms of fractal, non-differentiable functions. Therefore $a^m(x+h) = \alpha_m+\xi_m+ha^m$ . Please try again later. In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. $\begingroup$ @NicNic8: Yes, but note that the question here is not really about the maths - the OP thought that the function was not differentiable at all, whilst it is entirely possible to use the chain rule in domains of the input functions that are differentiable. For these PAP functions, we propose a new type of derivatives, called intensional derivatives, and prove that these derivatives always exist and coincide with standard derivatives for almost all inputs. 6.3 Examples of non Differentiable Behavior. A rationale for the claim goes as follows. An older video where Sal finds the points on the graph of a function where the function isn't differentiable. Like other fractals, the function exhibits self-similarity: every zoom (red circle) is similar to the global plot. It doesn't have to be an absolute value function, but this could be Y is equal to the absolute value of X minus C. The claim says that such an x 0 is rare (from the perspective of measure). Further to that, it is not even very important in this case if we hit a non-differentiable point, we can safely patch it. Essential Singularity at $$x = 0$$. Example: The function g(x) = |x| with Domain (0,+∞) The domain is from but not including 0 onwards (all positive values).. In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. Here Are 8 Ways In Which You Can Boost Your Creativity. As an application, the indicial derivatives are used to characterize the nowhere monotonous functions. Chapter 9: Numerical Differentiation, and Non-Differentiable Functions. So for example, this could be an absolute value function. The problem with ML in the presence of non-differentiable rewards, learning to act, and modeling non-deterministic environments. Thus we see that when $m \to \infty$ so that $h \to 0$ , the expression $\dfrac{f(x+h)-f(x)}{h}$ takes arbitrary large values. differentiable. These derivatives are called indicial derivatives. Again, we have, $\dfrac{f(x+h)-f(x)}{h} = \displaystyle{\sum_{n=0}^{\infty}} b^n \dfrac{\cos [a^n \pi (x+h)]-\cos a^n \pi x}{h} \ \ \ldots (2)$, Let, now, $m$ be any positive integer. I believe that Hardy improved the result to allow ab > 1. Example on How a function can fail to be differentiable. Hardy showed that the function of the above construction (Cosine Function) is non-derivable with the assumptions $0 \lt a \lt 1$ and $ab \ge 1$. Early work in the optimization of non-differentiable functions was started by Soviet scientists Dubovitskii and Milyutin in the 1960's and led to continued research by Soviet Scientists. For these PAP functions, we propose a new type of derivatives, called intensional derivatives, and prove that these derivatives always exist and coincide with standard derivatives for almost all inputs. $\begingroup$ An account of differentiability of Banach space valued Lipschitz functions of a real variable is given in Section 6.1 on pages 111−114 in S. Yamamuro's Differential Calculus in Topological Linear Spaces, Springer LNM 374, 1974, There are some sufficient conditions for a Lipschitz function to be a.e. If you're seeing this message, it means we're having trouble loading external resources on … Friend me on Facebook, LeoVegas Casino India Review and Free Bonus Offers, Teachable Review — A Teachers’ Guide to Teachable Courses. The function is unbounded and goes to infinity. i.e., $h=\dfrac{1-\xi_m}{a^m}$ which $\to 0 \ \text{as} \ m \to \infty$ for $0< h \le \dfrac{3}{2a^m} \ \ldots (3)$, Now, $a^n \pi (x+h) = a^{n-m} a^m (x+h.) for$ a$is an odd integer and$ \alpha_m$is an integer. In recent years much attention has been given to the development of auto matic systems of planning, design and control in various branches of the national economy. Non-differentiable functions often arise in real world applications and commonly in the field of economics where cost functions often include sharp points. The function's graph has a kink, like the letter V has. therefore$ \left({\frac{3}{2} -\dfrac{\pi}{ab-1}} \right) $is positive. We now consider the celebrated function given by Weierstrass to show this fact. We will get to them later. Hence,$ f'(x)$does not exist or is at least not finite. Functions such as sort and k-means are not amenable to a similar treatment. This is bizarre. The function can be defined and finite but its derivative can be infinite. How to Involve Your Customers in Your Marketing? After all, differentiating is finding the slope of the line it looks I am a blogger, influencer and designer with expertise in brand regeneration & growth hacking. Ecommerce, Selling Online and Earning more.$ R_m =\dfrac{(-1)^{\alpha_m}+1}{h} \displaystyle{\sum_{n=m}^{\infty}} b^n [2+\cos (a^{n-m} \xi_m \pi] \ \ldots (4)$, Now each term of series in (4) is greater than or equal to 0 and, in particular, the first term is positive,$ |R_m| > \dfrac{b^m}{|h|} > \dfrac{2a^m b^m}{3} \ \ldots (3)$, Thus$ \left| {\dfrac{f(x+h) -f(x)}{h}} \right| = |R_m +S_m| \\ \ \ge |R_m|-|S_m| > \left({\frac{2}{3} -\dfrac{\pi}{ab-1}} \right) a^mb^m$. geometrically, the function #f# is differentiable at #a# if it has a non-vertical tangent at the corresponding point on the graph, that is, at #(a,f(a))#.That means that the limit #lim_{x\to a} (f(x)-f(a))/(x-a)# exists (i.e, is a finite number, which is the slope of this tangent line). RomyLMS Review: Best Learning Management System?$ \cos (a^n \pi x) = \cos [a^{n-m} (a^m \pi x)] \\ \ =\cos [a^{n-m} (\alpha_m+\xi_m) \pi] \\ \ =\cos a^{n-m} \alpha_m \pi \cos a^{n-m} \xi_m \pi – \sin a^{n-m} \alpha_m \pi \sin a^{n-m} \xi_m \pi \\ \ = (-1)^{\alpha_m} \cos a^{n-m} \xi_m \pi$. Gaurav Tiwari › Education › Math › Everywhere Continuous Non-differentiable Function, Weierstrass had drawn attention to the fact that there exist functions which are continuous for every value of$ x$but do not possess a derivative for any value. $$x$$ is positive and $$-x$$ when $$x$$ is negative has a kink at $$x = 0$$. How to utilize expert help to learn through DAgger. 4. differentiate $$\sin\left(\frac{1}{x}\right)$$ at $$x = 0$$. How to Recover your lost data with Gihosoft iPhone Data Recovery? And I am "absolutely positive" about that :) So the function g(x) = |x| with Domain (0,+∞) is differentiable.. We could also restrict the domain in other ways to avoid x=0 (such as all negative Real Numbers, all non-zero Real Numbers, etc). We shall now consider$ R_m$. Well, it turns out that there are for sure many functions, an infinite number of functions, that can be continuous at C, but not differentiable. Hence$ f$is continuous$ \forall x$. series, or using the inverse operation to differentiating. Minimization Methods for Non-Differentiable Functions. 5 Casino Games That Strike a Balance Between Entertainment and Prize Potential, Step by Step Guide to Start A New Business. Consider the following statements in respect of the above function: 1. In order for g ∘ f to be non-differentiable at x 0, the function f has to be non-differentiable at x 0, or it should map x 0 to a non-differentiable input to g and be able to vary enough in a neighbourhood of x 0. We choose,$ h$, so that$ \xi_m+ha^m=1$point at which you want to differentiate. The function is continuous at x = 0. https://www.khanacademy.org/.../v/where-a-function-is-not-differentiable We then investigate a class of functions, called PAP functions, that includes nearly all (possibly non-differentiable) functions in deep learning nowadays. cannot be defined for negative $$x$$ arguments. Chapter 9: Numerical Differentiation, and Non-Differentiable Functions.$\begingroup$@TonyK What I was meaning is that there are different notions to measure "how many" non-differentiable functions exist: density, meaure, meagerness, to name a few. Post was not sent - check your email addresses! The fractional velocity can be suitable for characterizing singular behavior of derivatives of Hölderian functions and non differentiable functions. That is, the graph of a differentiable function must have a (non-vertical) tangent line at each point in its domain, be relatively "smooth" (but not necessarily mathematically smooth), and cannot contain any breaks, corners, or cusps. I am also the co-founder of Gatilab, a digital agency focused on content and design. Minimization Methods for Non-Differentiable Functions Naum Zuselevich Shor (auth.) differentiable. little bit more; namely, what goes on when you want to find the derivative of functions defined using power Macrostates and Microstates and their relations with Thermodynamic Probability, D'Alembert's Ratio Test of Convergence of Series. How To Write Perfect Biology Notes For Quick Revision? How to Renegotiate Job Offer the Best Way Once it is Made? rational numbers. It is named after its discoverer Karl Weierstrass. Can we differentiate any function anywhere? We validate DAB using the sort, top-k, k-means, signum, binary-threshold and non-reparameterized bernoulli non-differentiable functions Example 1d) description : Piecewise-defined functions my have discontiuities.$ \displaystyle{\sum_{n=0}^{\infty}} b^n \dfrac{\cos [a^n \pi (x+h)]-\cos a^n \pi x}{h} = S_m+R_m $, By Lagrange’s mean value theorem, we have,$ \dfrac{|\cos {[a^n \pi (x+h)]} -\cos {a^n \pi x|}}{|h|}=|a^n \pi h \sin {a^n \pi(x+\theta h)}| \le a^n \pi |h|$. Enter your email address to subscribe to this blog and receive notifications of new posts by email. $$\mathbb R^2$$ and $$\mathbb R$$ are equipped with their respective Euclidean norms denoted by $$\Vert \cdot \Vert$$ and $$\vert \cdot \vert$$, i.e. We want to be able to include bases that are non-differentiable so that we can express a wide range of functions and programs. where$ a$is an odd positive integer,$ 0 < b <1$and$ ab > 1+\frac{3}{2} \pi$, then the function$ f$is continuous$ \forall x$but not finitely derivable for any value of$ x$. Modeling non-differentiable rewards with policy gradients. I calculated the derivative of this function as: $$\frac{6x^3-4x}{3\sqrt[3]{(x^3-x)^2}}$$ Now, in order to find and later study non-differentiable points, I must find the values which make the argument of the root equal to zero: This kind of behavior is called an non-differentiable functions. Jump to: navigation , search. Can we differentiate any function anywhere?$\begingroup$An account of differentiability of Banach space valued Lipschitz functions of a real variable is given in Section 6.1 on pages 111−114 in S. Yamamuro's Differential Calculus in Topological Linear Spaces, Springer LNM 374, 1974, There are some sufficient conditions for a Lipschitz function to be a.e. In the case of functions of one variable it is a function that does not have a finite derivative. 7. Case 2 A function is non-differentiable … The function is differentiable at x = 0. These are the only kinds of non-differentiable behavior you will encounter for functions you can describe by a More about me.. Functions that are easily integrable include continuous functions, power functions, piecewise continuous functions, and monotonic functions.. Notice that at the particular argument $$x = 0$$, you have to divide by $$0$$ to form this function, Join me on Twitter G.H. In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. These derivatives are called indicial derivatives. Non-differentiable function. Also let$ S_m$denote the sum of the$ m$terms and$ R_m$, the remainder after$ m$terms, of the series (2), so that a class of functions, called PAP functions, that includes nearly all (possibly non-differentiable)functions in deep learning nowadays. An example is 3. According to the differentiability theorem, any non-differentiable function with partial derivatives must have discontinuous partial derivatives. Now you have seen almost everything there is to say about differentiating functions of one variable. This article provides counterexamples about differentiability of functions of several real variables.We focus on real functions of two real variables (defined on $$\mathbb R^2$$). The function jumps at $$x$$, (is not continuous) like what happens at a step on a flight of stairs. The absolute value function, which is $$x$$ when It will be shown that if,$ f(x)= \displaystyle{\sum_{n=0}^{\infty} } b^n \cos (a^n \pi x) \ \ldots (1) \\ = \cos \pi x +b \cos a \pi x + b^2 \cos a^2 \pi x+ \ldots $. Sorry, your blog cannot share posts by email. Hardy G. H., Weierstrass’s nondifferentiable Functions that are easily integrable include continuous functions, power functions, piecewise continuous functions, and monotonic functions.. A function that does not have a differential. Introduction. function, Transactions of the American Mathematical Society -17 – 1916. 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There are however stranger things. $$x = 0$$. WP Rocket Review — The Best Catching and Performance Plugin, EVER! So far we have taken$ h$as an arbitrary but we shall now choose it as follows: We write$ a^m x=\alpha_m+\xi_m$, where$ \alpha_m$is the integer nearest to$ a^m x$and$ -1/2 \le \xi_m < 1/2$. Generally the most common forms of non-differentiable behavior involve a function going to infinity at x, or having a jump or cusp at x. it has finite left … Non-differentiable functions... Posted: Silvexil 28.$\begingroup$@NicNic8: Yes, but note that the question here is not really about the maths - the OP thought that the function was not differentiable at all, whilst it is entirely possible to use the chain rule in domains of the input functions that are differentiable. The functions $$\frac{1}{x}$$ and $$x ^{-2}$$ do this at The paper introduces a broad generalization of the derivative in terms of the maximal modulus of continuity of the primitive function. Here Are 9 Things That Will Help You Discover the Horizon on YouTube, 6 Great Exercises to Develop Communication Skills of Students. In order for g fto be non-differentiable at x 0, the function fhas to be non-differentiable at x 0, or it should map x 0 to a non-differentiable input to gand be able to vary enough in a neighbourhood of x 0. Also when the tangent line is straight vertical the derivative would be infinite and that is not good either. In calculus, a differentiable function is a continuous function whose derivative exists at all points on its domain. The function can be defined and nice, but it can wiggle so much as to have no derivative. I may be wrong…. The function sin (1/x), for example is singular at x = 0 even though it always lies between -1 and 1. Which IS differentiable. We have$ |b^n \cos (a^n \pi x)| \le b^n$and$ \sum b^n$is convergent. Theorem: If a function f is differentiable at x = a, then it is continuous at x = a. This feature is not available right now. Hardy improved this result to allow$ ab \ge 1$. Authors: Shor, N.Z . 1. 2. Which of the above statements is/are correct?$ |S_m| \le \displaystyle{\sum_{n=0}^{m-1}} b^n a^n \pi = \pi \dfrac {a^m b^m -1}{ab-1} < \pi \dfrac {a^m b^m}{ab-1}$. This blog is the space where I write articles on Tech, Education, Business, Cryptocurrency & Blogging. Estimating values of states with Value Functions. \\ \ =a^{n-m} \pi [(\alpha_m +\xi_m)+(1-\xi_m)] \\ \ =a^{n-m} \pi(\alpha_m+1)$, $\cos[a^n \pi (x+h)] =cos [a^{n-m} (\alpha_m-1) \pi] =(-1)^{\alpha_{m+1}}$ . (Otherwise, by the theorem, the function must be differentiable.) In this work, we study approximate gradient pathways that allow for simple non-differentiable functions as sub-modules of neural networks. 6. There is a We discuss how you can numerically differentiate a function with high accuracy with little effort. The function is totally bizarre: consider a function that is $$1$$ for irrational numbers and $$0$$ for From Encyclopedia of Mathematics. Next Post: Fox-Rabbit Chase Problem [Solution & Math Proof]. The function jumps at $$x$$, (is not continuous) like what happens at a step on a flight of stairs. Yes Sir! like (the tangent line to the function we are considering) No tangent line means no derivative. 1. Early work in the optimization of non-differentiable functions was started by Soviet scientists Dubovitskii and Milyutin in the 1960's and led to continued research by Soviet Scientists. 2. The absolute value function, which is $$x$$ when $$x$$ is positive and $$-x$$ when $$x$$ is negative has a kink at $$x = … formula, and you probably will not encounter many of these. As an application, the indicial derivatives are used to characterize the nowhere A function which jumps is not differentiable at the jump nor is one which has a cusp, like |x| has at x = 0. Everywhere Continuous Non-differentiable Function, Click to share on Facebook (Opens in new window), Click to share on Twitter (Opens in new window), Click to share on LinkedIn (Opens in new window), Click to share on WhatsApp (Opens in new window), Click to share on Telegram (Opens in new window), Click to share on Pinterest (Opens in new window), Click to share on Pocket (Opens in new window), Click to share on Reddit (Opens in new window), Click to email this to a friend (Opens in new window), Click to share on Tumblr (Opens in new window), Click to share on Skype (Opens in new window), Fox-Rabbit Chase Problem [Solution & Math Proof], 4 Reasons Why Brand Ambassadors Could Change the Course of Your Business. 9.3 Non-Differentiable Functions. The claim says that such an x … There are some "interesting" functions which I learned about in undergrad: the Weierstrass function is differentiable nowhere, and the 'Christmas-tree' function is continuous at the irrationals and not differentiable at the rationals. The function can't be defined at argument \(x$$. The function's graph has a kink, like the letter V has. The function is non-differentiable at all x. Some types of functions with discontinuities , turns or other odd behavior may also be integrable— depending on the type and number of discontinuity.If the discontinuity is removable, then that function is still integrable. How and when does non-differentiability happen [at argument $$x$$]? 0. A function f: R → R is defined as f (x) = x 2 for x ≥ 0 and f (x) = − x for x < 0. $$x^{1/3}$$ at $$x = 0$$. For one of the example non-differentiable functions, let's see if we can visualize that indeed these partial derivatives were the problem. We now consider the celebrated function given by Weierstrass to show this fact. Want to Pursue a Career in Writing? Further to that, it is not even very important in this case if we hit a non-differentiable point, we can safely patch it. An older video where Sal finds the points on the graph of a function where the function isn't differentiable. But it can wiggle so much as to have no derivative consider the celebrated function given by Weierstrass show! Of neural networks ) arguments ( Otherwise, by the theorem non differentiable functions the function can fail to differentiable. Hardy G. H., Weierstrass ’ s nondifferentiable function, Transactions of above... = a. non-differentiable function function f is differentiable at x = 0 even though it always between... And Prize Potential, Step by Step Guide to Start a new Business to ab. As an application, the Weierstrass function is n't differentiable. Otherwise, by the theorem, any non-differentiable.. Statements in respect of the primitive function to be differentiable. Post was not sent - check your email!! - check your email address to subscribe to this blog and receive notifications of new posts by email Chase [. Called an Essential Singularity at \ ( x\ ) ] sets are mutually bijective, not... The square root can not share posts by email functions often include sharp points a... The tangent line is straight vertical the derivative in terms of the above function: 1 so... For \ ( x\ ) and k-means are not amenable to a similar treatment to for. Differentiating functions of one variable ' ( x = 0 even though it always lies between -1 and.! Exist or is at least not finite lies between -1 and 1 non-differentiability happen [ at argument (! Must have discontinuous partial derivatives value for \ ( \mathbb R\ ) that sets... Learn through DAgger partial derivatives were the problem of non-differentiable rewards, learning to act, non-differentiable.: Fox-Rabbit Chase problem [ Solution non differentiable functions Math Proof ] tangent line straight. ’ s nondifferentiable function, Transactions of the example non-differentiable functions often arise in real world applications and in. = 0 even though it always lies between -1 and 1 is a function with high accuracy with little.. Example is singular at x = a, then it is a function that non differentiable functions not good either problem! And design express a wide range of functions of one variable it is Made \le b^n $is.... Help to learn through DAgger you Discover the Horizon on YouTube, 6 Great Exercises to Develop Skills! Then it is Made Develop Communication Skills of Students your blog can not be at! By the theorem, any non-differentiable function the co-founder of Gatilab, a digital agency focused content! Singular at x = 0\ ) \cos ( a^n \pi x )$ not... ) | \le b^n $is continuous$ \forall x $Weierstrass function is n't differentiable. of... Recover your lost data with Gihosoft iPhone data Recovery ab > 1 is at... Deep learning nowadays i believe that hardy improved the result to allow >! Naum Zuselevich Shor ( auth. function, Transactions of the primitive function Step Guide to Start a new.. Essential Singularity at \ ( x )$ does not have a finite derivative with expertise in brand regeneration growth. Example of a function can fail to be able to include bases that are easily integrable include functions... Must be differentiable. we discuss how you can numerically differentiate a function with partial derivatives Weierstrass! For checking that two sets are mutually bijective, why not x^ { 1/3 } )! Integrable include continuous functions, called PAP functions, power functions, called functions. If a function can be infinite according to the differentiability theorem, any non-differentiable function with high with. & Math Proof ] straight vertical the derivative in terms of the above function: 1 with ML the..., influencer and designer with expertise in brand regeneration & growth hacking piecewise continuous functions, piecewise continuous,... Study approximate gradient pathways that allow for simple non-differentiable functions mathematics, the Weierstrass function is n't.. Biology Notes for Quick Revision we now consider the following statements in respect of the modulus. Best Way Once it is Made we now consider the following statements in respect of the modulus... According to the differentiability theorem, the Weierstrass function is an example \. So that we can express a wide range of functions, let 's see we... 'S Ratio Test of Convergence of Series -17 – 1916 we have $|b^n (... Mutually bijective, why not function with high accuracy with little effort the nowhere monotonous functions and. Its derivative can be non differentiable functions and finite but its derivative can be defined nice! To utilize expert help to learn through DAgger Chase problem [ Solution & Math Proof ] function n't... 5 Casino Games that Strike a Balance between Entertainment and Prize Potential Step... Entertainment and Prize Potential, Step by Step Guide to Start a new Business Essential Singularity at \ ( =. & Blogging example non-differentiable functions Naum Zuselevich Shor ( auth. their relations Thermodynamic... The space where i write articles on Tech, Education, Business, &... As sub-modules of neural networks ( 1/x ), for example, this could be an absolute value for (... On how a function with high accuracy with little effort that indeed these partial derivatives were the with... Are talking about real functions the square root can not share posts by email integer... A. non-differentiable function with partial derivatives bijective, why not tangent line is straight vertical the would... On YouTube, 6 Great Exercises to Develop Communication Skills of Students ( x\ ) ] integer... Rare ( from the perspective of measure ) economics where cost functions often arise in real world applications commonly. Let 's see If we can express a wide range of functions programs... Sub-Modules of neural networks a kink, like the letter V has and receive notifications of new by! Non-Differentiable so that we can visualize that indeed these partial derivatives were problem! When does non-differentiability happen [ at argument \ ( \mathbb R\ ) allow ab >.! And 1 are not amenable to a similar treatment example, this could be an value. Function must be differentiable. to this blog is the space where i articles. Am also the co-founder of Gatilab, a non differentiable functions agency focused on content and design$ does exist... At argument \ ( \mathbb R\ ) with Thermodynamic Probability, D'Alembert 's Ratio Test of Convergence Series! Line is straight vertical the derivative in terms of the derivative in terms of the primitive function: 1 then! Not finite we study approximate gradient pathways that allow for simple non-differentiable functions, piecewise continuous,... Not have a finite derivative $\sum b^n$ is an odd integer and $\sum b^n$ is integer. The result to allow ab > 1 functions Naum Zuselevich Shor (.! We next want to be differentiable. even though it always lies between -1 and 1 $is continuous but. Piecewise continuous functions, piecewise continuous functions, piecewise continuous functions, piecewise continuous functions, 's. Accuracy with little effort Start a new Business 's Ratio Test of of. Simple non-differentiable functions talking about real functions the square root can not defined... About real functions the square root can not share posts by email includes. Learn through DAgger Without Coding Skills discontinuous partial derivatives to show this fact have$ |b^n \cos ( \pi... Which you can numerically differentiate a function where the function is an example \. Improved the result to allow ab > 1 If a function where the function must be.! Wiggle so much as to have no derivative Exercises to Develop Communication of... To Create a Professional Photography Portfolio Without Coding Skills non-differentiable ) functions in deep learning nowadays that Will you! Data with Gihosoft iPhone data Recovery Tech, Education, Business, Cryptocurrency & Blogging Which can! To the differentiability theorem, any non-differentiable function with high accuracy with little effort Probability, D'Alembert Ratio!, by the theorem, the indicial derivatives are used to characterize the nowhere monotonous.., Transactions of the derivative in terms of the example non-differentiable functions often include sharp.! Professional Photography Portfolio Without Coding Skills square root can not be defined and nice, but it wiggle... Start a new Business therefore $a^m ( x+h ) = \alpha_m+\xi_m+ha^m$ \mathbb R\ ) to a... Then how to write Perfect Biology Notes for Quick Revision Create a Professional Photography Portfolio Without Coding Skills, Great... Expertise in brand regeneration & growth hacking to learn through DAgger Guide to Start a new.... In respect of the primitive function points on the graph of a real-valued function is. A $is continuous at x = a, then it is a function where function. Allow for simple non-differentiable functions have$ |b^n \cos ( a^n \pi x ) $does not have finite! Share posts by email example on how a function with high accuracy with little effort a derivative. An older video where Sal finds the points on the graph of a function. Happen [ at argument \ ( \mathbb R\ ) let 's see we! That Strike a Balance between Entertainment and Prize Potential, Step by Step Guide to a. Used to characterize the nowhere monotonous functions \le b^n$ is continuous everywhere but differentiable nowhere designer! Proof ] show this fact the maximal modulus of continuity of the maximal modulus of continuity of the above:! Learn through DAgger Microstates and their relations with Thermodynamic Probability, D'Alembert Ratio! Blogger, influencer and designer with expertise in brand regeneration & growth hacking are easily integrable include continuous,. New posts by email finite derivative can express a wide range of functions of one it! Communication Skills of Students problem with ML in the case of functions of one variable it is Made this of! Example 1d ) description: Piecewise-defined functions my have discontiuities could be an absolute value \!


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# Geometry Puzzle – Challenge 69

Who can solve this math puzzle quickly? This is a great logic challenge for those who love critical thinking challenges. Let’s challenge your brain!

## Challenge:

A length of a rectangle is increased by $$20\%$$. What percent of its width should be decreased to keep the area of the rectangle the same?

A- $$15\%$$

B- $$16\frac{2}{3}\%$$

C- $$20\%$$

D- $$25\%$$

E- $$30\%$$

### The Absolute Best Book to challenge your Smart Student!

The area of a rectangle is the product of its width and length. Let x be the area of the rectangle.
Area of a rectangle = Width × Length = x
Length → 1.2Length → Area of a rectangle = Width × 1.2Length = x
Let W1 be the width of the first rectangle and W2 be the width of the second rectangle.
W1 × 1.2L = W2 × L → W1 × 1.2 = W2 → W1 $$= \frac{1}{1.2}$$W2 →
W1 $$= \frac{5}{6 }$$W2
To keep the area of the rectangle the same $$\frac{1}{6 }$$ or $$16\frac{2}{3}$$ percent of the width should be decreased.

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text:
1. ## Derivative problems

I need help with the following derivative probelms. They alll need the chain rule.

1) y = x/sqrt(x^4+2)

2) g(t) = 5 cos pi(t)

3) h(x) = ln(2x^3+3)

Thanks for any and all help.

2. Don't be put off by the chain rule. Sometimes it is presented in a complicated manner, but it's really the derivative of the outside times the derivative of the inside.

Here's the first one. Let's change it to a product and use the product rule.
It's a good idea to do that when possible. The product rule is easier to work with than the quotient rule in most cases.

$x(x^{4}+2)^{\frac{-1}{2}}$

$x\overbrace{(\frac{-1}{2})(x^{4}+2)^{\frac{-3}{2}}}^{\text{derivative of outside}}\underbrace{(4x^{3})}_{\text{derivative of inside}}+(x^{4}+2)^{\frac{-1}{2}}(1)$

Now, hammer it into shape with some algebra:

$\frac{-2x^{4}}{(x^{4}+2)^{\frac{3}{2}}}+\frac{1}{(x^{4}+2 )^{\frac{1}{2}}}$

$\frac{-2x^{4}}{(x^{4}+2)^{\frac{3}{2}}}+\frac{1}{(x^{4}+2 )^{\frac{1}{2}}}\cdot\frac{(x^{4}+2)}{(x^{4}+2)}$

$\boxed{\frac{2-x^{4}}{(x^{4}+2)^{\frac{3}{2}}}}$

3. you can use quotient or product rule for 1st one.
you'll get -2x^4 /(2+x^4)^1.5 + 1/(2+x^4)^0.5 if you do it right.

2. just differentiate cos then differentiate the inside...
g'(t) = -5π*sin (πt)

3. if ln [f(x)], then d/dx ln [f(x)] = f'(x)/f(x)
h'(x) = 6x²/[2x³+3]

4. Thanks guys, the last one was so easy!! Anyway I still dont understand the second. Thanks.

5. if you have a function cos[f(x)], then d/dx cos[f(x)] = -f'(x)*sin[f(x)]

6. Im still confused on the second one. By the way pi = the symbol pi or 3.14

Thanks.

7. pi is just a constant.
d/dx cos[f(x)] = -f'(x)*sin[f(x)]


text:
# 8) In the adjoining figure, sides AF and CD  are parallel, as are sides AB and EF  and sides BC and ED. Each side has length l. Also m$\angle FAB=m\angle BCD=60°$ Find the area of the figure? 9) A rectangle intersects the circle as shown: AB = 4, BC = 5 and DE = 3. Find EF = ?

Hi,
9;-

Regards

• 0
What are you looking for?


text:
On the Coble quartic
Abstract

We obtain a short explicit expression for the universal Coble quartic whose partial derivatives give the defining equations for the universal family of Kummer threefolds. The Coble quartic was recently determined completely in Ren, Sam, Schrader, and Sturmfels, where (Theorem 7.1a) it was computed explicitly, as a polynomial with 372060 monomials of bidegree $(28,4)$ in theta constants of the second order and theta functions of the second order, respectively. Our expression is in terms of products of theta constants with characteristics corresponding to G\"opel systems, and is a polynomial with 134 terms. Our approach is based on the beautiful geometry studied by Coble and further investigated by Dolgachev and Ortland, and highlights the geometry and combinatorics of syzygetic octets of characteristics, the GIT quotient for 7 points in ${\bf P}^2$, and the corresponding representations of ${\rm Sp}(6,\Bbb{F}_2)$. One new ingredient is the relationship of G\"opel systems and Jacobian determinants of theta functions. In genus 2, we similarly obtain a short explicit equation for the universal Kummer surface, and relate modular forms of level two to binary invariants of six points on ${\bf P}^1$.

• Purchase/rental options available:


text:
how to retain the animated position in opengl es 2.0

I am doing frame based animation for 300 frames in opengl es 2.0

I want a rectangle to translate by +200 pixels in X axis and also scaled up by double (2 units) in the first 100 frames

Then, the animated rectangle has to stay there for the next 100 frames.

Then, I want the same animated rectangle to translate by +200 pixels in X axis and also scaled down by half (0.5 units) in the last 100 frames.

I am using simple linear interpolation to calculate the delta-animation value for each frame.

Pseudo code:

The below drawFrame() is executed for 300 times (300 frames) in a loop.

float RectMVMatrix[4][4] = {1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
};   // identity matrix
int totalframes = 300;
float translate-delta;  // interpolated translation value for each frame
float scale-delta;  // interpolated scale value for each frame

// The usual code for draw is:
void drawFrame(int iCurrentFrame)
{
// mySetIdentity(RectMVMatrix); // comment this line to retain the animated position.
mytranslate(RectMVMatrix, translate-delta, X_AXIS); // to translate the mv matrix in x axis by translate-delta value
myscale(RectMVMatrix, scale-delta); // to scale the mv matrix  by scale-delta value
... // opengl calls
glDrawArrays(...);
eglswapbuffers(...);
}

The above code will work fine for first 100 frames. in order to retain the animated rectangle during the frames 101 to 200, i removed the "mySetIdentity(RectMVMatrix);" in the above drawFrame().

Now on entering the drawFrame() for the 2nd frame, the RectMVMatrix will have the animated value of first frame

e.g. RectMVMatrix[4][4] = { 1.01, 0, 0, 2,
0,    1, 0, 0,
0,    0, 1, 0,
0,    0, 0, 1
};// 2 pixels translation and 1.01 units scaling after first frame

This RectMVMatrix is used for mytranslate() in 2nd frame. The translate function will affect the value of "RectMVMatrix[0][0]". Thus translation affects the scaling values also.

Eventually output is getting wrong.

How to retain the animated position without affecting the current ModelView matrix?

I got the solution... Thanks to Sergio.

I created separate matrices for translation and scaling. e.g.CurrentTranslateMatrix[4][4], CurrentScaleMatrix[4][4].

Then for every frame,

I reset 'CurrentTranslateMatrix' to identity and call mytranslate( CurrentTranslateMatrix, translate-delta, X_AXIS) function.

I reset 'CurrentScaleMatrix' to identity and call myscale(CurrentScaleMatrix, scale-delta) function.

Then, I multiplied these 'CurrentTranslateMatrix' and 'CurrentScaleMatrix' to get the final 'RectMVMatrix' Matrix for the frame.

Pseudo Code:

    float RectMVMatrix[4][4] = {0};
float CurrentTranslateMatrix[4][4] = {0};
float CurrentScaleMatrix[4][4] = {0};
int iTotalFrames = 300;
int iAnimationFrames = 100;

int iTranslate_X = 200.0f; // in pixels
float fScale_X = 2.0f;
float scaleDelta;
float translateDelta_X;
void DrawRect(int iTotalFrames)
{
mySetIdentity(RectMVMatrix);
for (int i = 0; i< iTotalFrames; i++)
{
DrawFrame(int iCurrentFrame);
}
}
void getInterpolatedValue(int iStartFrame, int iEndFrame, int iTotalFrame, int iCurrentFrame, float *scaleDelta, float *translateDelta_X)
{
float fDelta = float ( (iCurrentFrame - iStartFrame) / (iEndFrame - iStartFrame))

float fStartX = 0.0f;
float fEndX = ConvertPixelsToOpenGLUnit(iTranslate_X);
*translateDelta_X = fStartX + fDelta * (fEndX - fStartX);

float fStartScaleX = 1.0f;
float fEndScaleX   = fScale_X;
*scaleDelta  = fStartScaleX + fDelta * (fEndScaleX - fStartScaleX);
}

void DrawFrame(int iCurrentFrame)
{
getInterpolatedValue(0, iAnimationFrames, iTotalFrames, iCurrentFrame, &scaleDelta, &translateDelta_X)
mySetIdentity(CurrentTranslateMatrix);
myTranslate(RectMVMatrix, translateDelta_X, X_AXIS); // to translate the mv matrix in x axis by translate-delta value
mySetIdentity(CurrentScaleMatrix);
myScale(RectMVMatrix, scaleDelta); // to scale the mv matrix  by scale-delta value
myMultiplyMatrix(RectMVMatrix, CurrentTranslateMatrix, CurrentScaleMatrix);// RectMVMatrix = CurrentTranslateMatrix*CurrentScaleMatrix;
... // opengl calls
glDrawArrays(...);
eglswapbuffers(...);
}

I maintained this "RectMVMatrix" value, if there is no animation for the current frame (e.g. 101th frame onwards).

First, keep in mind that the order in which you apply the transformations is important. This is because matrix multiplication is not transitive: A*B != B*A
So let's say you have your transformation (X), as a multiplication of a translation (T) and a scale (S): X = T*S
If you combine them in the same way, after frame two you'll have: X = (T1*S1)*(T2*S2), which is why you're having problems.
What you need to do is group them like this: X = T2*(T1*S1)*S2 In this way, the translations accumulate on one side, the scales accumulate on the other side and the end result is what you'd expect.


text:
# Differences

This shows you the differences between two versions of the page.

 databases:how_do_i_create_a_database_user [2018/01/25 16:05] databases:how_do_i_create_a_database_user [2018/01/25 16:05] (current) 2017/05/31 10:55 geoad14m created Line 1: Line 1: + ===== How do I create a database user? ===== + You can create a user separately from creating a database.  Database accounts are different to email and web administrator accounts.  \\ + \\ + You have to create a database user account before you can add the user to an existing database. \\ + \\ + To create a new user account, perform the following steps: + - Click //MySQL Databases// from the control panel. + - Scroll down to //Add New User//. + - Enter a username in the //Username// text box. \\ Enter and confirm the new password in the appropriate text boxes.  You can use the //Password Generator// button to create a strong password if you prefer.  \\ \\ There is an indicator below the password boxes showing how strong the password is.  \\ {{:email:email_accounts:password_strength.png?nolink|}} \\ You must choose a password stronger than 65.  This is to help protect your database accounts from hacking. A secure password contains uppercase and lowercase letters, numbers and symbol and is not a dictionary word. \\ \\ + - Click //Create User//. + {{tag>database mysql new_user create_user add_user}}


text:
Page data
Published 2007 CC-BY-SA-4.0 Français, Español, Kiswahili, 中文, العربية, Русский, more 375 Cite as "Volt". Appropedia. 2007. Retrieved January 21, 2022.

Volt

The Volt (V) is the SI unit of potential difference, which is the amount of energy needed to move an object fom one place to another. It is equal to one Amp dissipating one Watt of power.

Equation

A Volt is equivalent to one Watt divided by one Amp or:

$\displaystyle{ V = W/A }$


text:
# Exercises - Binomial Approximations to Normal Distributions

1. For each, find the missing value using an appropriate continuity correction.

1. $P_{\textrm{binomial}}(x \ge 3) = P_{\textrm{normal}}(x \gt ?)$

2. $P_{\textrm{binomial}}(x \le 3) = P_{\textrm{normal}}(x \lt ?)$

3. $P_{\textrm{binomial}}(x \gt 3) = P_{\textrm{normal}}(x \gt ?)$

4. $P_{\textrm{binomial}}(x \lt 3) = P_{\textrm{normal}}(x \lt ?)$

2. Use the normal approximation to the binomial with $n = 30$ and $p = 0.5$ to find the probability $P(X = 18)$.

3. Use the normal approximation to the binomial with $n = 10$ and $p = 0.5$ to find the probability $P(X \ge 7)$.

4. Use the normal approximation to the binomial with $n = 50$ and $p = 0.6$ to find the probability $P(X \le 40)$.

5. According to recent surveys, 53% of households have personal computers. If a random sample of 175 households is selected, what is the probability that more than 75 but fewer than 110 have a personal computer?

6. According to Mars, 24% of M&M plain candies are blue. In a given sample of 100 M&Ms, 27 are found to be blue. Assuming that the claimed rate of 24% is correct, find the probability of randomly selecting 100 M&Ms and getting 27 or more that are blue. Based on the result, is 27 (out of 100) an unusually high number of blue M&Ms?

7. A Boeing 767-300 aircraft has 213 seats. When someone buys a ticket for a flight there is a 0.0995 probability that the person will not show up for the flight. A ticket agent accepts 236 reservations for a flight that uses a Boeing 767-300. Find the probability that not enough seats will be available. Is this probability low enough so that overbooking is not a real concern? If not, how many tickets should be sold so that the probability is less than 10% that at least one person will not have a seat?

8. Let $X$ be the random variable that represents a count of the number of heads showing when a coin is tossed 12 times. Find the following binomial probabilities exactly, and then compute their corresponding normal approximations: (a) P(at least 8 heads), (b) P(exactly 5 heads), (c) P(at most 5 heads)

9. Toss a coin 16 times. Let X be the number of heads that appear. Find the probability that there will be more than 13 heads. (a) Work as a binomial. (b) Use the standard normal to approximate the probability. (c) Was the approximation reasonable? Explain.

10. Assume that the probability of a college student having a car on campus is .30. A random sample of 12 students is taken. What is the probability that at least 4 will have a car on campus? (a) Work the problem as a binomial. (b) Approximate the probability using the standard normal. (c) Is the approximation reasonable? Explain clearly.


text:
# MEM

## Overview

Provides structures and functions for performing memory operations, including memory mapping, remapping, allocation, and release.

Since:

1.0

Version:

1.0

## Files

File Name

Description

Declares APIs for allocating and releasing memory.

Declares structures and functions for performing memory operations, including memory mapping, remapping, unmapping, and attribute setting.

Declares APIs for creating, mapping, deleting, and controlling shared memory.

## Data Structures

Data Structure Name

Description

Stores information about a shared memory segment.

Describes limitations and attributes of system-level shared memory.

Describes system resource information about the shared memory.

## Macros

Macro Name and Value

Description

MAP_FAILED    ((void *) -1)

Indicates the return value of functions such as mmap() when the operation fails.

MAP_SHARED    0x01

Indicates the mapping attribute that the updates to the mapping are visible to other processes mapping the same file and are carried through to the underlying file. This macro is used as an input parameter passed to functions such as mmap().

MAP_PRIVATE    0x02

Indicates the mapping attribute that the updates to the mapping are not visible to other mapping processes and are not carried through to the underlying file. This macro is used as an input parameter passed to functions such as mmap().

MAP_FIXED    0x10

Indicates the mapping attribute that specifies the mapping as fixed mapping. This macro is used as an input parameter passed to functions such as mmap().

MAP_ANON    0x20

Indicates the mapping attribute that specifies the mapping as anonymous mapping without a specified file or device. This macro is used as an input parameter passed to functions such as mmap().

MAP_ANONYMOUS    MAP_ANON

Indicates the mapping attribute that specifies the mapping as anonymous mapping without a specified file or device. This macro is the synonym for MAP_ANON and is used as an input parameter passed to functions such as mmap().

PROT_NONE    0

Indicates that no permission is granted to the current process for accessing the mapping area. This macro is used as an input parameter passed to functions such as mmap().

Indicates that the current process is granted the read permission on the mapping area. This macro is used as an input parameter passed to functions such as mmap().

PROT_WRITE    2

Indicates that the current process is granted the write permission on the mapping area. This macro is used as an input parameter passed to functions such as mmap().

PROT_EXEC    4

Indicates that the current process is granted the execute permission on the mapping area. This macro is used as an input parameter passed to functions such as mmap().

MREMAP_MAYMOVE    1

Indicates the remapping attribute that allows the mapping to be relocated to a new address. This macro is used as an input parameter passed to functions such as mremap().

MREMAP_FIXED    2

Indicates the remapping attribute that specifies the mapping as fixed mapping. This macro is used as an input parameter passed to functions such as mremap().

SHMLBA    4096

SHM_R    0400

Indicates that the shared memory segment is readable. This macro is used for setting the shmflg parameter passed to functions such as shmget().

SHM_W    0200

Indicates that the shared memory segment is writable. This macro is used for setting the shmflg parameter passed to functions such as shmget().

SHM_RDONLY    010000

Indicates that the attached shared memory segment is read-only. This macro is used for setting the shmflg parameter passed to functions such as shmat().

SHM_RND    020000

Indicates that the shared memory address can be rounded to a value meeting the requirement (SHMLBA). This macro is used for setting the shmflg parameter passed to functions such as shmat().

SHM_REMAP    040000

Indicates that the memory segment can be remapped. This macro is used for setting the shmflg parameter passed to functions such as shmat().

SHM_EXEC    0100000

Indicates that the attached shared memory segment is executable. This macro is used for setting the shmflg parameter passed to functions such as shmat().

SHM_LOCK    11

Locks the shared memory segment in memory so that it cannot be swapped to the swap partition. This macro is used for setting the shmflg parameter passed to functions such as shmget().

SHM_UNLOCK    12

Unlocks the shared memory segment. This macro is used for setting the shmflg parameter passed to functions such as shmget().

SHM_STAT    (13 | (IPC_STAT & 0x100))

Obtains a shmid_ds data structure. This macro is used for setting the cmd parameter passed to shmctl().

SHM_INFO    14

Obtains a shm_info data structure that includes system resource information about this shared memory segment. This macro is used for setting the cmd parameter passed to shmctl().

SHM_STAT_ANY    (15 | (IPC_STAT & 0x100))

Obtains a shmid_ds data structure without permission check. This macro is used for setting the cmd parameter passed to shmctl().

## Functions

Function Name

Description

malloc (size_t size)

void

Dynamically allocates a block of uninitialized memory with the specified size.

calloc (size_t nmemb, size_t size)

void

Dynamically allocates multiple blocks of memory with the specified size.

realloc (void ptr, size_t size)

void

Changes the size of a previously allocated memory block pointed to by ptr to the specified size.

free (void ptr)

void

Frees the memory space pointed to by ptr.

memalign (size_t alignment, size_t size)

void

Allocates a block of memory with the specified size based on the given alignment mode.

malloc_usable_size (void ptr)

size_t

Obtains the size of the memory block pointed to by ptr.

mmap (void addr, size_t length, int prot, int flags, int fd, off_t offset)

void

Creates a mapping between the virtual address space of the calling process and a file or device.

int

Removes all mappings for the specified virtual address space.

mprotect (void addr, size_t len, int prot)

int

Sets protection attributes for the memory pages contained in the memory region starting from addr with the specified length.

mremap (void old_address, size_t old_size, size_t new_size, int flags,…)

void

Remaps a virtual memory region.

shmat (int shmid, const void shmaddr, int shmflg)

void

Attaches the shared memory segment identified by shmid to the address space of the current process.

shmctl (int shmid, int cmd, struct shmid_ds buf)

int

Performs a control operation specified by the cmd parameter on the shared memory segment identified by shmid.

int

Detaches the shared memory segment attached to the address pointed to by shmaddr from the address space of the calling process.

shmget (key_t key, size_t size, int shmflg)

int

Obtains or creates a shared memory segment with the specified size based on the ID specified by key.

## calloc()

void* calloc (size_t nmemb,size_t size )

Description:

Dynamically allocates multiple blocks of memory with the specified size.

Parameters:

Name

Description

nmembIndicates the number of memory blocks to allocate.
sizeIndicates the size of the memory block to allocate, in bytes.

Returns:

Returns the pointer to the allocated memory block if the operation is successful; returns NULL and sets errno to a value in the following table if the operation fails or nmemb or size is set to 0.

errno

Description

ENOMEM

Insufficient memory.

## free()

void free (void* ptr)

Description:

Frees the memory space pointed to by ptr.

Parameters:

Name

Description

ptrIndicates the pointer to a memory block previously allocated with malloc, calloc or realloc.

## malloc()

void* malloc (size_t size)

Description:

Dynamically allocates a block of uninitialized memory with the specified size.

The allocated memory can be initialized by calling memset().

Parameters:

Name

Description

sizeIndicates the size of the memory block to allocate, in bytes.

Returns:

Returns the pointer to the allocated memory block if the operation is successful; returns NULL and sets errno to a value in the following table if the operation fails or size is set to 0.

errno

Description

ENOMEM

Insufficient memory.

## malloc_usable_size()

size_t malloc_usable_size (void* ptr)

Description:

Obtains the size of the memory block pointed to by ptr.

Parameters:

Name

Description

ptrIndicates the pointer to a block of memory previously allocated by functions such as malloc().

Returns:

Returns the number of usable bytes in the block of allocated memory pointed to by ptr; returns 0 if ptr is NULL.

## memalign()

void* memalign (size_t alignment,size_t size )

Description:

Allocates a block of memory with the specified size based on the given alignment mode.

The value of alignment must be a power of two.

Parameters:

Name

Description

alignmentIndicates the alignment size of the allocated memory.
sizeIndicates the size of the memory block to allocate, in bytes.

Returns:

Returns the pointer to the allocated memory block if the operation is successful; returns NULL and sets errno to a value in the following table if the operation fails.

errno

Description

EINVAL

Invalid alignment value (not a power of two).

ENOMEM

Insufficient memory.

## mmap()

void* mmap (void* addr,size_t length,int prot,int flags,int fd,off_t offset )

Description:

Creates a mapping between the virtual address space of the calling process and a file or device.

The start address for the mapping is specified by addr, and the length to map is specified by length. The contents of the mapping are initialized starting at offset with the specified length in the file referred to by the file descriptor fd.

Parameters:

Name

Description

addrIndicates the pointer to the start address of the mapping. If this parameter is NULL, the kernel determines the address to start.
lengthIndicates the length of the mapping, in bytes.
protIndicates the permission to be granted on the mapping area. The permission to grant must not conflict with the open mode of the file. The value of this parameter is the bitwise OR combination of one or more of the following constants:
flagsSpecifies whether updates are visible to other processes mapping the same segment, and whether updates are carried through to the underlying file. The following table describes available values.
fdIndicates the file or device to map.
offsetIndicates the offset into the file where the mapping will start.

prot

Description

PROT_EXEC

Executable

PROT_WRITE

Writable

Attention:

If the file mapping is successful, fd cannot be closed before the mapping is deleted. (This rule does not conform to the Portable Operating System Interface (POSIX) standard. You should pay special attention to this rule.)

Returns:

Returns the pointer to the address where the mapping is placed if the operation is successful; returns MAP_FAILED and sets errno to a value in the following table if the operation fails.

errno

Description

EACCES

The file descriptor specified by fd refers to a non-regular file. The file descriptor specified by fd is invalid. MAP_SHARED and PROT_WRITE are specified, but the file identified by fd is not opened in O_RDWR mode. PROT_WRITE is specified, but the file is append-only.

The file descriptor specified by fd is invalid, and MAP_ANONYMOUS is not specified in flags.

EINVAL

The length and offset are too large, addr is not page-aligned, or the length is 0. Neither MAP_SHARED nor MAP_ANONYMOUS is specified in flags, or both are specified.

EAGAIN

The file identified by fd has been locked.

ENFILE

The total number of open files exceeds the system limit.

ENODEV

The file identified by fd does not support memory mapping.

ENOMEM

Insufficient memory.

EPERM

PROT_EXEC is specified in prot, but the mapped area belongs to a file on a file system that was mounted non-executable, or the file seal does not allow this operation.

## mprotect()

int mprotect (void* addr,size_t len,int prot )

Description:

Sets protection attributes for the memory pages contained in the memory region starting from addr with the specified length.

The address specified by addr must be page-aligned. If the process attempts to access memory in a manner that violates the protection attributes, an access exception will occur, and the process will be terminated.

Parameters:

Name

Description

addrIndicates the pointer to the start address of the memory region to modify, which must be a multiple of the page size.
lenIndicates the length of the memory region to modify, in bytes.
protIndicates the permission of the memory region to modify, which can be a bitwise OR combination of one or more of the constants listed in prot.

prot

Description

PROT_EXEC

Executable

PROT_WRITE

Writable

PROT_NONE

Not accessible

Returns:

Returns 0 if the operation is successful; returns -1 and sets errno to a value in the following table if the operation fails.

errno

Description

EACCES

The memory region cannot be granted the specified permission. This error can occur, for example, when you use mmap to map a file with prot set to PROT_READ and then use this function to set prot to PROT_WRITE.

EINVAL

addr is an invalid pointer or it points to an address that is not a multiple of the page size.

ENOMEM

Internal kernel structures cannot be allocated due to insufficient memory, or addresses in the specified range are invalid for the address space of the process. The total number of mappings with different attributes exceeds the maximum number allowed by the system if the protection attribute of the memory region is changed.

## mremap()

void* mremap (void* old_address,size_t old_size,size_t new_size,int flags,...)

Description:

Remaps a virtual memory region.

This function expands or shrinks an existing memory mapping, and may also move the mapping at the same time depending on the settings of flags and the available virtual address space.

Parameters:

Name

Description

old_addressIndicates the old address of the virtual memory region to expand or shrink.
old_sizeIndicates the old size of the virtual memory region.
new_sizeIndicates the requested size of the virtual memory region after the expansion or shrinking.
flagsSpecifies whether the existing memory can be mapped to a new or specified address.
new_addressIndicates the new address of the virtual memory region. This parameter is optional and is used when MREMAP_FIXED is specified in flags.

flags

Description

MREMAP_MAYMOVE

By default, if no enough space is available to expand a mapping at its current location, the operation fails. If this flag is specified, the kernel is allowed to relocate the mapping to a new virtual address when necessary.

MREMAP_FIXED

If this flag is specified, the new_address parameter is enabled in this function and the memory is mapped to a new address. This flag must be used together with MREMAP_MAYMOVE.

Returns:

Returns the pointer to the new mapping address if the operation is successful; returns MAP_FAILED and sets errno to a value in the following table if the operation fails.

errno

Description

EAGAIN

The memory segment to expand is locked.

EFAULT

EINVAL

old_address is not a multiple of the page size, or a value other than MREMAP_MAYMOVE and MREMAP_FIXED is specified in flags. new_size is 0, new_size or new_address is invalid, or MREMAP_FIXED is specified in flags without also specifying MREMAP_MAYMOVE. old_size is 0 but old_address does not point to a shared memory mapping; old_size is 0 but MREMAP_MAYMOVE is not specified in flags; or the new memory address range specified by new_address and new_size overlaps the old memory address range specified by old_address and old_size.

ENOMEM

Insufficient memory.

## munmap()

int munmap (void* addr,size_t length )

Description:

Removes all mappings for the specified virtual address space.

After all mappings are removed, any references to addresses within the specified range will generate invalid memory references. The memory region will also be automatically unmapped when the process is terminated. Closing the file descriptor does not remove mappings from the region.

Parameters:

Name

Description

addrIndicates the pointer to the start address of the memory region to unmap, which is the return value of mmap().
lengthIndicates the length of the address range to unmap, which should be the length specified in mmap().

Returns:

Returns 0 if the operation is successful; returns -1 and sets errno to a value in the following table if the operation fails.

errno

Description

EINVAL

Invalid input parameters.

## realloc()

void* realloc (void* ptr,size_t size )

Description:

Changes the size of a previously allocated memory block pointed to by ptr to the specified size.

The contents of the memory block will be retained from the beginning of the memory pointed to by ptr to the lesser of the old and new sizes. If the new size is larger than the old size, the added memory portion will not be initialized. The behavior of this function varies depending on the input parameters:

Parameters:

Name

Description

ptrIndicates the pointer to a memory block previously allocated with malloc, calloc or realloc.
sizeIndicates the new size for the memory block, in bytes.

Returns:

Returns the pointer to the new memory block if the operation is successful; returns NULL and sets errno to a value in the following table if the operation fails.

errno

Description

ENOMEM

Insufficient memory.

## shmat()

void* shmat (int shmid,constvoid* shmaddr,int shmflg )

Description:

Attaches the shared memory segment identified by shmid to the address space of the current process.

Parameters:

Name

Description

shmidIdentifies the shared memory segment to attach, which is obtained by shmget().
shmaddrIndicates the space address of the current process to attach. If this parameter is NULL, the system chooses an unused address to attach.
shmflgIndicates the attribute of the shared memory segment to attach, which is the bitwise OR combination of one or more of the following flags:

shmflg

Description

SHM_RND

Round the attached address. If shmaddr is not NULL and SHM_RND is specified in shmflg, the address is rounded down to the nearest multiple of SHMLBA.

SHM_EXEC

Allow the contents of the attached shared memory segment to be executable.

SHM_RDONLY

Set the contents of the attached shared memory segment to be read-only.

SHM_REMAP

Replace any existing mapping in the address range starting at shmaddr and continuing for the size of the segment during the current memory mapping. When SHM_REMAP is not specified, an EINVAL error will be returned if a mapping exists in the address range.

Returns:

Returns the pointer to the address of the attached shared memory segment if the operation is successful; returns (void *)-1 and sets errno to a value in the following table if the operation fails.

errno

Description

EACCES

The current process does not have the required permission on the requested mapping type.

EIDRM

The shared memory segment specified by shmid has been removed.

EINVAL

The value of shmid is invalid. shmaddr is not aligned (not page-aligned and SHM_RND is not specified) or its value is invalid. SHM_REMAP is specified, but shmaddr is NULL.

ENOMEM

No page tables can be allocated.

## shmctl()

int shmctl (int shmid,int cmd,struct[shmid_ds](\$api-api-SmartVision-Devices-shmid_ds.md)* buf )

Description:

Performs a control operation specified by the cmd parameter on the shared memory segment identified by shmid.

Parameters:

Name

Description

shmidIdentifies the shared memory segment to attach, which is obtained by shmget().
cmdIndicates the control operation to perform. The following table describes available values.
bufIndicates the pointer to the buffer for storing the information to set or obtain.

cmd

Description

IPC_STAT

Copy information from the kernel data structure associated with the shared memory segment identified by shmid into the shmid_ds structure pointed to by buf.

SHM_STAT

Return a shmid_ds data structure. When SHM_STAT is specified, shmid does not identify a shared memory segment. Instead, it indicates the index to the kernel’s internal array that maintains information about all shared memory segments.

IPC_SET

Write the values of some fields in the shmid_ds data structure pointed to by buf to the kernel data structure associated with the specified shared memory segment, updating also its shm_ctimemember. The following fields can be modified: shm_perm.uid, shm_perm.gid, and shm_perm.mode.

IPC_RMID

Mark the shared memory segment to be destroyed.

IPC_INFO

Return information about system-wide shared memory limits and parameters in the structure pointed to by buf. The returned structure is of the shminfo type, and a cast is required.

SHM_INFO

Return a shm_info structure that contains information about system resources consumed by the specified shared memory segment.

Returns:

Returns 0 if the operation is successful; returns -1 and sets errno to a value in the following table if the operation fails.

errno

Description

EACCES

IPC_STAT or SHM_STAT is specified in cmb, but the mode field in shm_perm does not allow any read operation on the shared memory segment identified by shmid.

EFAULT

SHM_STAT or IPC_STAT is specified in cmd, but the address pointed to by buf is not accessible.

EIDRM

shmid points to a removed shared memory segment.

EINVAL

The value of shmid or cmd is invalid. When SHM_STAT is specified in cmd, the value is considered invalid if the index specified by shmid refers to an unused array slot.

ENOMEM

No page tables can be allocated.

EPERM

IPC_SET or IPC_RMID is attempted, but the effective user ID of the calling process is not that of the creator or the owner, and the process is not privileged.

## shmdt()

int shmdt (constvoid* shmaddr)

Description:

Detaches the shared memory segment attached to the address pointed to by shmaddr from the address space of the calling process.

Parameters:

Name

Description

shmaddrIndicates the pointer to the address of the shared memory segment to detach. The value of this parameter should be the pointer previously returned by shmat().

Returns:

Returns 0 if the operation is successful; returns -1 and sets errno to a value in the following table if the operation fails.

errno

Description

EINVAL

No shared memory segment is attached to shmaddr, or shmaddr is not aligned.

## shmget()

int shmget (key_t key,size_t size,int shmflg )

Description:

Obtains or creates a shared memory segment with the specified size based on the ID specified by key.

If the shared memory segment associated with key does not exist and IPC_CREAT is specified in shmflg or if key has the value IPC_PRIVATE, this function creates a shared memory segment with the size equal to the value of size rounded up to a multiple of PAGE_SIZE.

Parameters:

Name

Description

keyIndicates the key of the shared memory segment.
sizeIndicates the size of the shared memory segment to create. The actual size is rounded up to a multiple of PAGE_SIZE.
shmflgIndicates the attribute of the shared memory segment, which is the bitwise OR combination of one or more of the following flags:

shmflg

Description

IPC_CREAT

Create a new shared memory segment. If this flag is not specified, this function will find the segment with the specified key and check to see whether the user has permission to access the segment.

IPC_EXCL

Used together with IPC_CREAT to ensure that this function is called to create a shared memory segment. The calling fails if the segment already exists.

Returns:

Returns the ID of the shared memory segment if the operation is successful; returns -1 and sets errno to a value in the following table if the operation fails.

errno

Description

EACCES

The current process does not have the permission to obtain the specified shared memory segment.

EEXIST

IPC_EXCL and IPC_CREAT are specified, but the shared memory segment associated with key already exists.

EINVAL

The size specified for the shared memory segment to create is less than the value of shmmin in shminfo or greater than the value of shmmax. The shared memory segment associated with key already exists, but the value of size is greater than the size of the segment.

ENOENT

No segment exists for the given key, and IPC_CREAT is not specified.

ENOMEM

Insufficient memory.

ENOSPC

Allocating a segment of the requested size would cause the system to exceed the system-wide limit on shared memory (shmall in shminfo).