you've right. Why is phase important? What is you suggestion about a text book on complex analysis for engineers that preparing them in solving application problems in circuits.. etc. The line (-L to L) belongs to real and also note that line B to C is a one slice of it. After several decades of exponential growth of studies on complexity, it seems to me that society remains on the sidelines, as if all research and serious advances were considered a mere academic debate far from people's real needs. That's it. Compute nontrivial zeros of Riemann zeta function is an algebraically complex task. If You want to get our daily basis posts notifications then simply fill provide us your email in, was prepared according to PPSC, FPSC, NTS and other Examination preparation, was prepared according to best method of preparation. of Legal Meterology. In particular, is there a version of Jack's lemma for hyperbolic domains in plane. It is to be specified what g is, and it g denotes a coupling constant, the answer depends on the field g is the coupling constant of. I am looking into the Laurent series. Anyway, thank everybody who would provide answers and who would pay attention on this question. May be the double series calculation will lead to some result. a Hele-Shaw cell. You can see Emzari Papava's page on ABC theorem. Is there a compact notation for the quadratic term of a Taylor-expansion of a vector-valued function? It's related to Rolle’s Theorem and Mean value theorem. Is there a conformal mapping that can transform non-spherical surfaces to spherical ones? Don't show me this again. $$I_t(x)=\int_{-\infty}^{\infty}e^{-\frac{\cosh^2(u)}{2x}}\,e^{-\frac{u^2}{2 t}}\,\cos\left(\frac{\pi\,u}{2t }\right)\,\cosh(u)\,du$$. What is the physical meaning of the adiabatic coupling constant g? there is k such that n|a_k|\geq |b_k-\lambda|. This section will also provide videos of some examples of relevant topics. Then for given $r\in(0,1)$ $|f|$ attains maximum at a point $z_0 \in T_r$. The local formulation of the maximum-modulus principle asserts that the modulus of f(z) does not have a local maximum at a point z_0 in D. Some researchers define closed submanifold as compact without boundary (perhaps, you may clarify the defition). Title "ON THE SCHWARZ-CHRISTOFFEL TRANSFORMATION AND p-VALENT FUNCTIONS by Goodman-1950". When finalizing the whole manuscript, I will post it as an eletronic preprint somewhere and let you know the url address for it. My logo is the three-dimensional graphics of the zeta function,where s=x+iy0,0> T. For classical systems, the subject matter is often discussed under the heading of "Adiabatic Invariance", which can be read about in any reasonable textbook on Classical Mechanics (such as the excellent book Mechanics, by Landau and Lifshitz). What should the complexity research community do to permeate society? Are these calculations Is ok? Then g(y)-g(x) >= g ' (x)(y - x )>0. It is an expression involving an incomplete Beta function (see attached pdf). In the figure lines are on the real axis. By (a1), $\Gamma_g= f_1^{-1}(c_1)$, where $\Gamma_g$ is the graph of $g$ over $(c,d)$. How can I show that the contour in blue line i.e (B to C) is within the integration contour in red line i.e (-L to L)? In other words, if $f(x)$ is a completely monotonic function on the finite interval $I=(a,b)$, is there an integral representation like (1.2) in the picture 1.png for the completely monotonic function $f(x)$ on the finite interval $(a,b)$? Thank you for your help. d. Antibiotics. In higher codimension, we cannot define the regular infinite one type with  tangent vector field and the levy form directly like in C^2. Does it means that. Deals with programming languages and defines 2 graphical (LD=ladder and FBD = function block diagram) and 2 textual (ST = structured text and SFC = sequential function chart). Hence, a set of actions and plans are to be undertaken, I guess. please help me and let me know if there is a good comparative study or article on this subject. What are possible pathways to make our knowledge on complexity actionable in society?