The E = mc ^ 2, its so hard to prove this equation, when Einstein asked his student to show him where he came out took eight hours to make the entire development, to finally get to the equation .. Well .. and are difficult to prove, that only Einstein could do it, now there is no one that has been demonstrated again ... and hence the reason of that is the hardest equation in the world .... 2 : a ^ n + b ^ n = z ^ n, ie a number (a) your you raise another number (n) then sums the other town differs in number to (a) or either (b) and you raise to (n) be equal to a different number to (b) ie (z) and you raise the (n). You realize that the three of them are raised to the n is high because all three are the same number. The more problems that ma is a theorem (called Fermat theorem) that Fermat discovered it but never found. It is said that there is no Natural number where n> 2 check this ecuacion.Te give the only two solutions: 6 ^ 2 + 8 ^ 2 = 10 ^ 2 and 3 ^ 2 + 4 ^ 2 = 5 ^ 2 3 : equation of Fermats theorem: X + Y ⁿ ⁿ ⁿ = Z has been 356 years without being able to solve. All the great mathematicians proved Fermat post of demostarlo and failed although some came not fully achieved. It was the June 23, 1993, when Dr. A. Wiles mathematics in English I was to release the final resolution of the theorem mythical. The show is captured in 200 pages. 4: an + bn = cn for n = Easy Examples 2 62 + 82 = 102 32 + 42 = 52 For n> 2 there are no natural numbers satisfying the above property 5: Fourier transform is a linear transformation: mathcal { F} {acdot f + b · g = a}, mathcal {F} {f} + b, mathcal {F} {g}. Valen the following properties for an absolutely integrable function f: Scaled: mathcal {F} {f (at)} (xi) = frac {1} {| a |} mathcal {F} cdot {f} bigg (frac { xi} {a} bigg) Translation: mathcal {F} {f (ta)} (x) = e ^ {-a} cdot ixi mathcal {F} {f} (xi) Translating the transformed variable: mathcal {F } {f} (xi-a) = mathcal {F} {e ^ {iat} f (t)} (xi) Transform the derivative: If f and its derivative is integrable mathcal F {f } (xi) = ixi mathcal {F} {cdot} f (xi) Derivative transform: If f and t → f (t) are integrable, the Fourier transform F (f) is differentiable mathcal {F}} {f (xi) = mathcal {F} {(-it) · f (t)} (xi) These identities are shown by a change of variables and integration by parts. In what follows, we define the convolution of two functions f, g in the line is, we define the following: (f * g) (x) = frac {1} {sqrt {2 pi}} int_ {-infty} ^ {+ infty} f (y) · g (x - y) dy. Again the presence of the factor before the integral simplifies the statement of the results as follows: If f and g are absolutely integrable functions, convolution is also integrable, and equality holds: mathcal {F} {f * g} = mathcal { F} {f} cdot mathcal {F} {g} can also enunciated a theorem analogous to the convolution in the transformed variable mathcal {F}} {f · g = mathcal {F} {f} * mathcal {F} { g}. but this requires some care with the domain of definition of the Fourier transform. 6: This model is called Black-Scholes and was used to estimate the current value of a European option to buy (call) or sell (put) shares at a future date. Later the model was extended to stock options that produce dividends, and then adopted for European, American options, and money market. The model concludes that: C = SN (d_i) - Ke ^ {-N} RDT (d_z), P = e ^ {K} N-VDR (-d_z) - SN (-d_i) Where: = frac {d_i ln (S / K) + (rd-re + sigma ^ 2/2) {T} {T}} sigmasqrt d_z = d_i - sigmasqrt {T}. Setting: C is the value of a call option, European option. P is the value of a put option, European option. S is the rate in view of the coin which is the object of choice. K is the price marked on the (Strike price) option. T is the time in years that still have yet to pass on the option. rd is the domestic interest rate. re is the foreign interest rate. σ is the standard deviation of proportionate changes in currency rates. N is the cumulative distribution function of the normal distribution. N (di) and N (dz) are the values of the probabilities of the values of di and dz taken from the tables of the normal distribution. 7: The Pythagorean Theorem states that in any right triangle, the square of the hypotenuse (the longest side of the triangle equals the sum of the squares of the legs (the two smaller sides of the triangle, which form the right angle). Pythagorean Theorem In any right triangle the square of the hypotenuse equals the sum of the squares of the legs. Pythagoras of Samos. If a right triangle has legs of lengths a, b, and the extent of the hypotenuse is c,, it states that: (1) c ^ 2 = a ^ 2 + b ^ 2, from equation (1) easily 3 corollaries of practical application are derived: a = sqrt {c ^ 2 - b b ^ 2} = sqrt {c ^ 2-a ^ 2} c = sqrt {a ^ 2 + b ^ 2}
Posted on: Sat, 15 Mar 2014 20:13:59 +0000
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