Cold Equation Narrative There have been many difficult decision that I have had to make in my life. The one I’m going to write about happened recently. The day that it had happened, I had gone with my dad the night before. My step dad's son, daughter- in- law, and their children had just moved in a few months back. They had also moved their dog in with them, he was a rottweiler. At that time I had a chihuahua yorkie mix. When they first moved in, I didn’t think anything of their dog…
at . Next, Hopf bifurcation at : The Jacobian matrix corresponding to is given by (36) where and its nonzero elements are defined as in (14) and (15) with & replaced by & respectively. The characteristic equation corresponding to obeys (37) where the coefficients are defined as in (16). By the Routh–Hurwitz criteria, all the roots of (37) will have negative real parts if , and It is required for a Hopf bifurcation that…
started off by allowing students to solve a quadratic I had written on board. However the quadratic equation I had written on the board was the wrong equation so students got stuck when they tried to use the quadratic equation because they got a negative under the square root. From there, we went to the graph of the quadratic to see if that would be able to help identify the x-intercepts. But, the equation didn’t have any real solutions so there were no x-intercepts for us to use. Next, I…
To give an another definition of complex number, we have to show z= ew for w, where z is any non-zero complex number. If we assume w = u + iv then eueiv = |z|e^i arg z and this means that |z| = e^u , v = arg z . The equation |z| = e^u is a real equation, so we can write u = ln |z|, where ln |z| is the ordinary logarithm with positive real numbers. Hence, w = u + iv = ln |z| + i arg z = ln |z| + i(Arg z + 2n) , n = 0 , ±1 , ±2 , ±3 , . . .6 We profoundly examined the connection between…
Coulomb interaction operator, is a spherically symmetric component of the polarization energy operator, and ( herrU,ˆ ()rVˆ is the dielectric solvation energy operator. To obtain the explicit form of these operators we solve analytically the Poisson equation for a potential due to a point charge in the core/shell structure with the standard boundary conditions that account for discontinuity of the dielectric constant at hetero-interfaces.3 As a result, we obtain the following solutions: 3…
diluted with DI water and reacted to produce an unknown amount of FeSCN2+ ions in an equilibrium reaction. The absorbance of each solution was found using a spectrophotometer, the first five of which was used to create a calibration curve, whose equation relates the concentration and absorbance of FeSCN2+ ions. Theories…
CHML 1046 General Chemistry 2 Laboratory Experiment “The Rate Law of an Iodine Clock Reaction” Objectives: To apply method of initial rates for investigation of influence of concentrations of reactants on the rate of the reaction. Determine the rate law of a particular reaction experimentally. Observe the effect of catalyst on the reaction rate. Examine the influence of temperature on the rate of this reaction. Calculate activation energy for the reaction from rate constants at two…
Questions: (a) Show that: (b) What value of ε ss would you expect at 800°C and 16000 psi? A= 0.0043 Using your Larson-Miller curve, what temperature should you use for a life of 20 years at the lowest stress level? For the extensive length of time, a temperature of approximately 25 oC which is close to room temperature. With increasing stress or temperature, what changes will you notice in a typical creep curve? When you increase temperature or stress, the creep curve will increase in…
Results and discussion 4.1 Material removal rate The material removed from each coupon was determined by measuring its mass before and after electro-polishing. Theoretical values were then obtained using Faraday’s laws of electrolysis as shown in Equation 9. (9) Where m is the mass of material removed in grams, I is the current and t is the electro-polishing time. EW is the equivalent weight which depends on the chemical composition of…
a quartic function can only have 4 rational/irrational zeros, 2 rational/irrational zeros and 2 complex zeros, or 4 complex zeros. I was able to find how many positive and negative zeros I had using the Descartes Rule of Signs. Using the original equation, I counted from left to right, the amount of sign changes, and that gave me number of positive real zeros. I discovered 2 positive and 2 negative real zeros using this method. Now to find the negative number, the exact same process is repeated,…