The Nature of Nothing - Unified Field Equation. The nature of nothing: If you take away everything that is physical (matter/energy), you are left with nothing (no thing).
Nothing is completely empty space, absolute cold, silence and darkness. Nothing is infinite, eternal and indestructible. It does not move; it does not have to. Lec23_ps_96. 香港數碼學堂 The Hong Kong Digital Academy. Det(AB) = Det(A) Det(B) Proof of the third theorem about determinants. Kenneth Shum's scrapbook. The purpose of this note is to record an implementation of the Berlekamp-Massey algorithm in Matlab, and illustrate the similarity to the approximation of real numbers by fractions.
It is well-known that the value of can be approximated by continued fractions. The first few approximations are As we go down the list, the denominator increases, and the accuracy also increases. The approximation has been known since antiquity, and was known to Zu Chongzhi in the 5th century. A one-line proof of det(AB) = det(A) det(B) – Kenneth Shum's scrapbook. The theorem that the determinant function is multiplicative, i.e.
. , Linear algebra - How to show that $\det(AB) =\det(A)\det(B)$ Lines and Distance of a Point to a Line. Distance computations are fundamental in computational geometry, and there are well-known formulas for them.
Nevertheless, due to differences in object representations, there are alternative solutions to choose from. We will give some of these and indicate the situations they apply to. Throughout, we need to have a metric for calculating the distance between two points. We assume this is the standard Euclidean metric “L2 norm” based on the Pythagorean theorem. That is, for an n-dimensional vector , its length |v| is given by: and for two points and , the distance between them is: Lines. I seek not to know the answers, but to understand the questions. Distance from a point to a line. Facebook knows you better than your friends do - because Likes reveal so much about your character - News - Gadgets and Tech - The Independent. A study of more than 86,000 users of Facebook has demonstrated the power of intelligent machines to predict an individual’s character based on what they have listed as their Likes.
Researchers said that the day when computers are able to judge a person’s personality accurately has almost arrived and even suggested that science fiction films like Her, based on a man’s emotional attachment to an intelligent computer, are closer than we think. “In the future, computers could be able to infer our psychological traits and react accordingly, leading to the emergence of emotionally-intelligent and socially-skilled machines,” said Wu Youyou of Cambridge University. Read more: All-knowing Facebook: Am I really a miserable Catholic with (slight) lesbian tendencies?
“People may choose to augment their own intuitions and judgements with this kind of data analysis when making important life decisions such as choosing activities, career paths or even romantic partners,” she said. 求證一條ln. Math Forum - Ask Dr. Math. Are all limits solvable without L'Hospital Rule or Series Expansion. Finding volume of region with cross sections. How to solve $\lim\limits_{x\to 0} \frac{x - \tan(x)}{x^2}$ Without L'Hospital's Rule? $ \mathop {\lim }\limits_{x \to + \infty } \frac{{\log \left( {\frac{{x - 1}}{x}} \right)}}{{\log \left( {\frac{{x + 1}}{x}} \right)}} = - 1.
Where does $r = 1 + 2\cos(\theta)$ have tangents? Limits of function without using L'Hopital's Rule $\mathop {\lim }\limits_{x \to 1} \frac{{x - 1 - \ln x}}{{x\ln x+ 1 - x}} = 1$ Real analysis - Sequence and series problem. Real analysis - Limit of $\left(\frac{x^2+x+1}{2x+1}\right)^{1/(x^2-1)}$ when $x\to1$ Real analysis - Putnam Problem A-1 2008 3 variable function. Calculating $ \lim_{n\to \infty} (1+\sin({1}/{n}))^{n}$ without L'Hopital or series expansions. Continuity and differentiability of two variables function. How find this diophantine equation integer solution $a^3+b^3=(2ab+1)^2$
Movie Review: Salt. Fantasy, Music, scifi I love sleeper spy agent movies!
Salt was non-stop action even though its run-time was only an hour and thirty-nine minutes, which in my opinion definitely goes to show that longer isn’t necessarily better as is the case with many inflated Hollywood movies these days. The spy-thriller plot is complex enough to keep you guessing, and Angelina Jolie turns out a great performance in this film, mixing in a little Lara Croft with some Mrs. Smith action from her acting repertoire. Although it’s only rated at 58% on the Rotten Tomatoes tomatometer, I still enjoyed it from start to finish. Evelyn Salt is a CIA operative, sworn to defend her country. Ersal of what I expected (that she was a good guy), she makes her way to NY, assassinates the Russian President, and then turns herself in.
Smartphones: Sleepless in Singapore - ASIA RESEARCH Online. An omnibus survey by Toluna revealed that Singapore consumers are increasingly addicted to their smartphones.
While as high as 91% of users see technology as a form of happiness, three-quarters (76%) also see it as a source of stress, which highlights the contradictory relationship that Singaporean consumers have with connected devices. As well as seeking to uncover consumer feelings towards technology, the study, which questioned a representative sample of 500 Singaporean Internet users, also aimed to discover which devices consumers use to access the internet, and which activities they undertake using specific devices. Newspaper. Free newspapers are popular with the elderly in Hong Kong who gather in busy streets in the early morning, asking for used copies from passers-by or at the papers' distribution points.
They do not want to know the latest news, but for the little money they earn by selling the newspapers to recycling companies. Standing in the morning rush- hour-crowds at Mass Transit Railway (MTR) stations, scores of elderly people eagerly wait for every opportunity to seize copies of free newspapers from passers-by. Most do not utter a single word, but stand quietly, stare at passersby, and beckon them to give them the papers. With a large grey bag on her shoulders, one of the old ladies, surnamed Li, has been collecting free newspapers for around seven months. Speaking in a mixture of Cantonese and her native Zhaoqing dialect, Li would hardly talk to Varsity as she was busy collecting papers around exit A of Hung Hom MTR station.
"I'm not a professional," laughed Mr Fung. Journalism. Free news paper hong kong - Поиск в Google. Hong-kong-media-worries-over-chinas-reach-as-ads-disappear. Photo HONG KONG — In what may be a major escalation of pressure by mainland China on Hong Kong’s independent-minded news media, two major British banks have stopped advertising with one of the city’s biggest newspapers, a top media executive said.
The executive, Mark Simon, of Next Media Limited, said two London-based banks, HSBC and Standard Chartered, ended longtime advertising relationships late last year with the paper, Apple Daily, after being told to do so by the Chinese government. “The government is running their business now,” Mr. Simon said in an interview. Free Newspaper War to Escalate in Hong Kong. Newspapers declare war. Hong Kong will see its sixth free newspaper later this month.
Shirley Zhao asks if the city-wide circulation war has gone too far... Everyone who works in Hong Kong knows the frustration of the early morning rush hour. On any given day, swarms of people will gush out of the MTR stations and rush through underground tunnels and overcrowded exits. But a peculiar thing is now happening. Many are holding free newspapers they have either grabbed from stands or had thrust in their hands by armies of uniformed distributors who, shouting the names of these publications, block the path of oncoming commuters in order to palm off their products. But the truth is far less ordinary, because Hong Kong’s newspaper industry is in the midst of a bitter and bloody circulation war.This battle between newspapers has escalated dramatically of late, with Hong Kong Economic Times Ltd (HKET) launching its free Sky Daily on July 27 and Next Media Ltd planning to launch its free Sharp Daily on September 17.
Set theory proof with empty set. Math Resources. Note: I only link to pages that I use myself. If you want a page with dozens of math-related links, you could just do a Google search on "math"; I'm being selective to avoid overwhelming people with too many choices. But the fact that I haven't linked to a page doesn't mean I think badly of it.
Notes and pages on topics in math Some of the notes are web pages, usually accompanied by PDF (Adobe Acrobat) files for printing. Some of the older notes are in PostScript format; I plan to convert them to web pages with PDF as time permits. Radius of convergence: Partial derivative - Math Help Forum. Calculation of a limit - Math Help Forum. Why programmers work at night. [This essay has been expanded into a book, you should read it, here] Image via Wikipedia A popular saying goes that Programmers are machines that turn caffeine into code. And sure enough, ask a random programmer when they do their best work and there’s a high chance they will admit to a lot of late nights. Some earlier, some later. A popular trend is to get up at 4am and get some work done before the day’s craziness begins. At the gist of all this is avoiding distractions.
I think it boils down to three things: the maker’s schedule, the sleepy brain and bright computer screens. The maker’s schedule Paul Graham wrote about the maker’s schedule in 2009 – basically that there are two types of schedules in this world (primarily?). On the other hand you have something PG calls the maker’s schedule – a schedule for those of us who produce stuff. 20 Ways to Strive for Excellence in Life. Most of us are trying hard to juggle it all in life: career, work, family, self-care and then some. We believe that in order to be our best selves, we should “get the most out of it”, and be on the ball in all fields of our lives.
Although this article deals with excellence, you might be surprised that I am not urging you to be at the top of the game in every single aspect of life. Instead, I would like to invite you to excel in those fields where you really can make a difference, so that when you move on, you shall have left behind a better world for those who follow. This is an invitation to find your voice and leave a mark in the world; an invitation to surpass the average and aim for higher levels of excellence; an invitation to tap into your talents more deeply than before and turn yourself into a radiating powerhouse. 50 Ways to Strive for Excellence in Life. The society in which you grow up determines by and large how you perceive excellence and the goal of getting the very best out of your life. Some cultures might attribute excellence to a few brilliant, hard-working, exceptional cases. Other cultures, such as the one in which I grew up, value modesty and urge people to try to be “average”.
Excellence, however, is for all of us. Excellence is about getting the most out of our talents. Excellence is about trying to make a little dent in the world, so that when we move on, we will have left behind a better place for those who follow. You might think that striving for excellence means perfectionism. Differential equations - Laplace Transform... Find the surface area obtained by rotating $y=1+3x^2$ from $x=0$ to $x=2$ about the y-axis. Tsz-Yeung Wong. Why programmers work at night. Laurent series of 1/F(x) - Math Help Forum. I need help to do this integral. - Math Help Forum. 50 Ways to Strive for Excellence in Life. Angular resolution. Angular resolution, or spatial resolution, describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution. Definition of terms[edit] Explanation[edit] Airy diffraction patterns generated by light from two points passing through a circular aperture, such as the pupil of the eye.
Points far apart (top) or meeting the Rayleigh criterion (middle) can be distinguished. Points closer than the Rayleigh criterion (bottom) are difficult to distinguish. The interplay between diffraction and aberration can be characterised by the point spread function (PSF). Two point sources are regarded as just resolved when the principal diffraction maximum of one image coincides with the first minimum of the other.[1] [2] If the distance is greater, the two points are well resolved and if it is smaller, they are regarded as not resolved. ), divided by π. Linear Algebra Thoroughly Explained. Ex7.pdf. The Chinese University of Hong Kong /All Locations. Is the vector cross product only defined for 3D? The Cauchy-Schwarz inequality. The Cauchy-Schwarz inequality is not hard to prove, so there is not much reason for a page devoted to simplifying the usual proof, or rather simplifying the usual presentation of the usual proof. What is more, the idea that follows is so natural that it must be well known to a significant proportion of mathematicians.
Hence the word `tiny' above. Nevertheless, most textbooks and all analysis courses I have attended favour the approach where you write down a quadratic form, use the fact that it is non-negative everywhere, and observe that this implies the Cauchy-Schwarz inequality. No explanation is usually given of where the quadratic form comes from. This page is intended for those who happen not to have observed, or been shown, that more or less the same argument can be made to seem much more natural. First, let us consider the basic, real-analysis version of the inequality, namely. Differential Equations. Differential Equations. Techniques. Linear algebra Archives - Computer vision for dummies. A geometric interpretation of the covariance matrix In this article, we provide an intuitive, geometric interpretation of the covariance matrix, by exploring the relation between linear transformations and the resulting data covariance.
Most textbooks explain the shape of data based on the concept of covariance matrices. Instead, we take a backwards approach and explain the... Why divide the sample variance by N-1? - Computer vision for dummies. Abstract algebra - Proof of $\gcd(a,b)=ax+by$