a historical introduction to calculus

... by means of parallel translations Let a be some arbitrary vector This vector also can be translated to the point O As a result we have four vectors e1 , e2 , e3 , and a beginning at the same point ... vector a form a class, the class of vector a Let’s denote it as Cl (a) Vector a is a representative of its class However, we can choose any other vector of this class as a representative, say ... force a? ??ecting water streams in small rivers and in oceans around the world Though it is usually drawn attached to the North pole, we can translate this vector to any point along any path provided

Ngày tải lên: 31/03/2014, 15:08

... the proof, we shall assume, as clearly we may, that a is real, and we shall apply the mean-value theorem to P, the minimal polynomial for a We have, for any rational p/q (q > O), ... a, sin a and tan a for all non-zero algebraic a In the sense of Lebesgue measure, 'almost all' numbers are transcendental; in fact as Cantor observed in 1874, the set of all algebraic ... quickly became unobtainable; indeed many scholars of the time had to resort to taking handwritten copies. But it was generally regarded as a rather impenetrable work and it was probably not

Ngày tải lên: 31/03/2014, 16:20

... impart flame retardant properties The flame retardant action arises because they are capable to form polyphosphoric acids by condensation... summarize a few examples of the application and ... Likewise, a curing agent and an accelerator may be considered as an additive However,... evaporation and degradation of plasticizers have been developed, with the aim of formulating long-lasting ... Several monographs have been prepared with regard to the topic (3-7) Plasticizers are used for several... seems to be a good alternative to phthalates in flexible toys due to its ease

Ngày tải lên: 02/04/2014, 16:26

... [30] Michael Kearns and Leslie G Valiant Learning Boolean formulae or finite automata is as hard as factoring Technical Report TR-14-88, Harvard University Aiken Computation Laboratory, August 1988 ... Schapire AT&T Labs Research Shannon Laboratory 180 Park Avenue Florham Park, NJ 07932 USA www.research.att.com/ yoav, schapire yoav, schapire @research.att.com Abstract Boosting is a general method ... regard this maximum minimal margin algorithm as an illustrative approximation of AdaBoost. In fact, algorithms that explicitly attempt to maximize minimal margin have not been experimentally as

Ngày tải lên: 24/04/2014, 12:24

... classical picture cannot explain why atoms are stable, why atoms of the same chemical element are always identical or why atoms have a surprisingly small variation in size In fact, atoms can ... the East, say, is observed to have right-hand circular polarization, then the photon moving to the West is certain to be found to have right-hand circular polarization But if the photon ... to the East has a specific polarization and the unobserved photon moving West immediately has the same polarization This system of entangled photons is equivalent to having two ambidextrous...

Ngày tải lên: 24/04/2014, 17:12

... JavaScript provides a thing called a variable var caught = 5 * 5; A variable always has a name, and it can point at a value, holding on to it The previous statement creates a variable ... produces the value it holds Here’s an example: var... var is used to create a new variable After var, the name of the variable follows Variable names can be almost every word, but they may not include ... include spaces Digits can also be part of variable names—catch22 is a valid name, for example—but the name must not start with a digit The characters $ and _ can be used in names as if they

Ngày tải lên: 28/04/2014, 16:57

... manuscripts that have survived are dated to c 1150,... great medieval literature of Iceland and Norway was created, there existed an essential unity of language in the western Scandinavian world, and ... enough as regards the inflexional system and the basic vocabulary), the pronunciation has changed a great deal since the first centuries of the settle- 4 A. .. orthography may be adapted to ... bring it into greater harmony with that of the manuscript source This last practice means that normalisation of Old Norse does not conform to an immutable standard Even between grammars, text

Ngày tải lên: 04/05/2014, 12:47

... as anthrax. Nano skin creams and suntan lotions are already on the market, and nano-enhanced tennis balls that bounce longer appeared at the 2002 Davis Cup. To date, most companies that claim ... the same way that atoms can interact with each other, via electrical charges and Coulomb's law Therefore, although an individual water molecule is a gas at room temperature, many water molecules ... and mathematics. Chapter 5 is a quick grand tour of some of the thematic areas of nanotechnology, via visits to laboratories. Chapters 6 to 9 are the heart of the book. They deal with the topical

Ngày tải lên: 04/06/2014, 15:19

... because he has an especially transparent "clear and distinct" perception of its truth It is generally agreed that Descartes, the mathematician, had a mathematical... toe one day, and make a ... thought-experiment Imagine an advance in science that enables a mad scientist to extract your brain, and then to maintain it in a vat of chemicals that sustain its normal functioning Imagine that the ... can start by thinking... essentially similar Pain is a mental event or state that lends itself fairly readily to the project of analysis, for at least it has a fairly distinctive, natural,

Ngày tải lên: 10/06/2014, 21:30

... York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi São Paulo Shanghai Taipei Tokyo ... means to be a person and to live a. .. But as we listen daily to how he came to have the mean character and perverse motives he did have a sad story of parental neglect, child abuse, ... 2005 kane42077_fm.qxd 1/19/05 16:27 Page iii Oxford University Press Oxford New York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala

Ngày tải lên: 10/06/2014, 23:02

... world of passion and pain.13 For God’s exaltation above man did not affect man’s ability to know him; it was a moral and metaphysical exaltation, not an elevation beyond the range of man’s knowledge; ... same fundamental notion, it was for every reason natural that what had so long been a familiar truth and obvious certitude, should come to be regarded by Hegel as a dogma as indubitable as to ... that at the outset this position was rather a dogmatic assumption, or at least a mere intuition, and not a principle arrived at after a process of preliminary critical inquiry And indeed even to...

Ngày tải lên: 06/11/2012, 15:51

... matchDao.setDataSource(dataSource); DefaultTournamentMatchManager tournamentMatchManager = new DefaultTournamentMatchManager(); tournamentMatchManager.setMatchDao(matchDao); new SwingApplication(tournamentMatchManager); ... class SwingApplication { private TournamentMatchManager tournamentMatchManager; public SwingApplication(TournamentMatchManager tournamentMatchManager) { this.tournamentMatchManager = tournamentMatchManager; ... com.apress.springbook.chapter01.TournamentMatchManager; com.apress.springbook.chapter01.DefaultTournamentMatchManager; public class SwingApplication { private DefaultTournamentMatchManager tournamentMatchManager;...

Ngày tải lên: 05/10/2013, 04:20

... next example is even more convincing (and only somewhat contrived): alf eastman easily yells A| AAAAAAAAAAAAAAAH The encoder creates the token (1,9 ,A) , matching the first nine copies of A in the ... and in an audio file, a string of audio samples may also appear repeatedly A dictionary-based method maintains a dictionary that contains bits and pieces of the data As a string of data symbols ... organizations A close relative of data encryption is the field of data hiding (steganography) A data file A (a payload) that consists of bits may be hidden in a larger data file B (a cover) by taking...

Ngày tải lên: 14/12/2013, 15:15

... 1|010 a2 a2 1|011 a2 1|100 a5 1|101 a4 1|110 a3 a1 1|111 a3 0 T2 11|000 11|001 11|010 11|011 11|100 11|101 11|110 11|111 = 11 a5 a1 a5 a4 a1 a4 a3 a1 a1 a3 a1 a3 a2 a3 1 T3 = 110 110|000 a5 a1 a1 ... a1 45 0.6 a2 345 a2 0.2 a4 0.1 a2 0.2 a3 0.2 a3 45 a2 3 1.0 0.4 0.4 a4 0.1 a4 5 a5 0.1 0.6 a3 0.2 1 a4 5 0.2 a5 0.1 (a) 0.2 (b) Figure 2.1: Huffman Codes smallest variance The variance of a code measures ... (s,i)←Tablei [j]; append s to output; until end-of-input Figure 2.6: Fast Huffman Decoding 000 001 010 011 100 101 110 111 T0 = Λ a1 a1 a1 a1 a1 a1 a2 a1 a2 a1 a2 − a3 T1 = 1|000 a2 a1 a1 1|001 a2 a1 ...

Ngày tải lên: 14/12/2013, 15:15

... a| bbaabbaabaabaaaa 0 0 0 The next three steps hash the strings bba, baa, and aab to, say, 1, 5, and The encoder outputs the three raw symbols b, b, and a, moves the separator, and updates the hash ... 10) They are bba, baa, aab, aba, and baa They hash to 1, 5, 0, 3, and (we arbitrarily assume that aba hashes to 3) Cell of the hash table is set to 9, and cells 0, 1, and become the starts of ... counts Table 4.13b shows the same symbols sorted by count (a) (b) a1 11 a8 19 a2 12 a2 12 a3 12 a3 12 a4 a9 12 a5 a1 11 a6 a7 a8 a9 a1 0 19 12 a1 0 a5 a4 a7 a6 2 Table 4.13: A Ten-Symbol Alphabet...

Ngày tải lên: 14/12/2013, 15:15

... scale of analysis is said to become smaller and smaller A large-scale analysis illustrates the global behavior of the signal, while each small-scale analysis illuminates the way the signal behaves ... camera Once we realize this, we naturally want to compare the resolution of the eye to that of a modern digital camera Current digital cameras have from 500,000 sensors (for a cheap camera) to ... that in a continuous-tone image, adjacent data units of pixels are normally correlated in the sense that the average values of the pixels in adjacent data units are close We already know that...

Ngày tải lên: 14/12/2013, 15:15

... —Tom Clancy, Clear and Present Danger Chapter Summary Images are an important type of digital multimedia data Images are popular, they are easy to create (by a digital camera, scanning a document, ... (5.11) Instead of calculating averages and differences, all we have to is construct matrices A1 , A2 , and A3 , multiply them to get W = A1 A2 A3 , and apply W to all the columns of an image I by ... for private use, followed by a range of compatibility characters The compatibility characters are character variants that are encoded only to enable transcoding to earlier standards and old implementations...

Ngày tải lên: 14/12/2013, 15:15

... (a) , (b), (ab), (aba), (ba), (bab), (abab), (ababa), (baba), and adds the new entries (3: ab), (4: ba), (5: aba), (6: abab), (7: bab), (8: baba), (9: ababa), (10: ababab), (11: babab), to ... is straightforward The result is that strings aa, aaa, aaaa, are added to the dictionary as entries 256, 257, 258, , and the output is 97 (a) , 256 (aa), 257 (aaa), 258 (aaaa), The output ... source, such as sampled sound and scanned images (drawings or photographs) Such data is called digitally sampled analog data (DSAD) (See also Scalar Quantization.) Voronoi Diagrams Imagine a petri...

Ngày tải lên: 14/12/2013, 15:15