Region Iv E: Fill & Download for Free

To check if [math]e^{y+ix}[/math] is analytic or not we will use the Cauchy-Riemann Equations theorem.Cauchy-Riemann Equations:A necessary and sufficient condition for a function W = f(z) = u( x,y )+ i v( x,y ) be analytic in a region R is that the Cauchy-Riemann Equations[math]\frac {\delta u}{\delta x} = \frac {\delta v}{\delta y}[/math] and [math]\frac {\delta u}{\delta y} = - \frac {\delta v}{\delta x}[/math]are satisfied in R , where it is supposed that these partial derivatives are continuous in R.Now, we will proceed to examine the functionLet,[math]f(z) = u + [/math][math]iv[/math][math] = e^{y+ix}[/math][math]u+iv = e^y e^{ix} = e^y ( \cos x + i \sin x)[/math][math]u+iv = e^y \cos x +i e^y \sin x[/math]Now, we can equate the real and imaginary parts on both sides of the equation, then we will get[math]u = e^y \cos x[/math][math]v = e^y \sin x[/math]Here, we will use the Cauchy-Riemann Equations,[math]\frac {\delta u}{\delta x} = - e^y \sin x[/math][math]\frac {\delta v}{\delta y} = e^y \sin x[/math]Therefore,[math]\frac {\delta u}{\delta x} ≠ \frac {\delta v}{\delta y}[/math]Again,[math]\frac {\delta u}{\delta y} = e^y \cos x[/math][math]\frac {\delta v}{\delta x} = e^y \cos x[/math]Therefore,[math]\frac {\delta u}{\delta y} ≠ - \frac {\delta v}{\delta x}[/math]Thus, the function does not satisfy the Cauchy-Riemann Equations and therefore is not analytic.

Some of my friends were in a similar dilemma and so I visited the KEA website. Karnataka Examination Authority conducts the counseling for the PG seats in Karnataka.Their rules for eligibility have the following text-Karnataka Domicile certificate issued by the concerned Tahasildar (candidate or either of his/her parent has been a resident of Karnataka State for a period of not less than TEN years) OR A study certificate for either of the parents having studied for at least 10 years in Karnataka from the Head of the educational institution where he/she had studied.ii. If claiming caste eligibility benefits: (only for Karnataka candidates) Caste/ Caste Income Certificate issued by Concerned Tahasildar‐ For SC/ST in Form‐D, Category‐I in Form‐E and 2A, 2B, 3A and 3B in Form‐F. (In case of married candidate, income of the spouse and his family to be included in the annual income, and in the case of married woman, certificate has to be in the name of candidate along with husband and including the income of the spouse family)iii. Certificates issued by the competent authority for claiming reservation under 371(j) (Hyderabad ‐ Karnataka Region).iv. Certificate issued by the Competent Authority to claim Minority status (Religious /Linguistic) and domicile certificateSo as you can see, it states that either you or your parents should have studied in Karnataka for 10 years.Hope this helps.

It doesn’t break any laws within the bounds of science, but it does fall totally outside science. This is an extract on the E-R bridge from the classic text Gravitation by Misner, Thorne, and Wheeler (pp. 839–840): “One proposal [of modifying the E-R bridge topology] is that the earlier and later singularities be identified with each other, so that a particle which falls into the singularity of region II [the infalling black hole], instead of being destroyed [by the accepted topology], will suddenly reemerge, being ejected, from the singularity of region IV [the emergent BH]. One cannot overstate the objections to this viewpoint; the region r = 0 is a physical singularity of infinite tidal gravitation forces and infinite Riemann curvature. Any particle that falls into that singularity must be destroyed by those forces …… to postulate that the particle reemerges … is to make up an ad hoc mathematical rule, one unrelated to physics.” So the entertaining and fanciful idea that wormholes might be a future means of interstellar, and even intergalactic, transport is total fantasy —- it will never happen, regardless of what you see on the big (or little ) screen. As for the second question, there is of course no evidence for this, but it’s difficult to even venture a guess as to how often it might be discussed. Probably very often among scifi enthusiasts who seem to hold the false belief that what they see in CGI entertainment has even a tiny speck of real factual science embedded somewhere inside, but very rarely among professional physicists, who treat it for what it is —- fascinating cocktail party conversation and nothing more.