This is done because real images have anomalies at some points caused by sensor errors and image deformation caused by errors of the local trajectory and residual scaled differences. The research into which type of restoration approach should be used and the equations presented which will be used was done by (M. Sistiaga, 1998). The selected method was to use Partial Derivative Equations (P.D.E.) as it successfully restored images and replaced linear filtering methods. A scheme that has been developed to restore images is multi-scale morphological analysis proposed by (L. Alvarez, 1992), which was used by (Lucido, 1997), the diffusion is based on an equation in the…
proportional constant (often negligible), hv is photon energy, EQD is bandgap energy, n based on the transition type (n = 1/2 for direct allowed transitions), and α is absorption coefficient. Kubelka-Munk Equation (3): approximation of α .5
Where R is reflectance, k is the molar absorption coefficient, and is scattering coefficient. However, this method…
Once the model was created the formula was used. Finally, a formula was created that could remove the risk from investments. Many financial derivatives were invented to exploit the BS formula. So after the academics received the Nobel price, LTCM (long term capital management) was created (smart guys going to the market). In 1995 the hedge fund LTCM (long term capital management) was created. The Nobel prize winners had no problem raising the capital and became what could be the team of the…
For the application of Hopf’s bifurcation theory to the system (29) (see [Marsden J.E., M. Mckracken, 1976]), it is required to satisfy the following transversality condition
Substituting , and into (31), and calculating the derivatives with respect to , we obtain
Since , we have
Hence there is a Hopf bifurcation at . We have the following result:
Theorem 13. Suppose holds. Then the system (29) undergoes a Hopf…
use of sophisticated financial instruments to reduce the foreign exchange risk. One example of natural hedge is companies try to match revenues with expenditures in the same currency. In other words, companies require their customers to pay them in the same currency as their expenditures. Moreover, companies can build their manufacturing plant in the foreign country so that production costs are in the same currency as sales.
With the increase in hedging costs, Airbus was looking for natural…
CONNECTIONS OF LOGARITHMIC FUNCTIONS
Logarithm and exponential functions have close relationship and they are inverse function of each other in a way. Before explicitly clarifying this inverse relationship, we should analyze their definitions. Logarithm means, in mathematics, “The exponent that indicates the power to which a base number is raised to produce a given number “2 Exponential function means that “mathematical function in which an…
The Mandelbrot and Filled Julia Sets
The Mandelbrot and Filled Julia Sets are sets of numbers that are composed of complex numbers that do not diverge for varying conditions of the function fc(z)=z²+c. For the Mandelbrot set, the function is iterated from z=0. The filled Julia set holds c constant for any complex number to look at the behavior of the iterated functions for each value of z in the complex plane. Both sets are derived from the iterations of simple functions in the complex plane,…
The Cost-of-Carry Model
In the commodity market the Cost of Carry model is used to price the futures and forwards contracts based on the spot price of the traded asset. The cost of carry is all the costs to carry an asset from the present until a certain future period, those are the cost to finance the asset (the interest), the storage costs, the transportation cost, and the insurance costs.
The cost of carry model looks at the price of the future or forwardcontract as a function of the spot…
Profit Maximizer Review
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1. What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given that at least one root is a complex number?
If the equation is 7th degree then it has 7 roots.
Those roots can be complex or real.
Complex roots always come in pairs, so if it has one, then it has 2, the other one being the conjugate of the first one. This in other words, if one complex root is a + bi, then the other complex root is a – bi.
If at least one root were complex, then we would have a…