Extreme transcendental differential equations are found in many applications including geophysical climate change models. Solution of these systems in continuous time has only been feasible with the recent development of Runge−Kutta sampling transcendental differential equation solvers with Chebyshev function output such as Mathematica 9÷s NDSolve function. This paper presents the challenges an...

A multivariate study was conducted on 23 subjects practicing the Transcendental Meditation technique and participating in a six-month Age of Enlightenment advanced training program. The electroencephalogram of each subject was recorded before and during the Transcendental Meditation technique, and compressed spectral arrays of coherence above a threshold of0.95 were subsequently generated by co...

We prove a value distribution result which has several interesting corollaries. Let k ∈ N, let α ∈ C and let f be a transcendental entire function with order less than 1/2. Then for every nonconstant entire function g, we have that (f ◦ g) −α has infinitely many zeros. This result also holds when k = 1, for every transcendental entire function g. We also prove the following result for normal fa...

A heuristic method to construct uniform approximations to analytic transcendental functions is developed as a generalization of the Hermite-Padé interpolation to infinite intervals. The resulting uniform approximants are built from elementary functions using known series and asymptotic expansions of the given transcendental function. In one case (Lambert’s W function) we obtained a uniform appr...

When proving it is impossible to ‘square’ the circle by a ruler–and–compass construction we have to appeal to the theorem that π is transcendental. It is our goal to prove this theorem. Since the algebraic numbers are the roots of integer polynomials, they are countably many. Cantor’s proof in 1874 of the uncountability of the real numbers guaranteed the existence of (uncountably many) transcen...

In this paper a modified transcendental equation is proposed, and we analyzed its chaotic characteristics and periodic. It is a simple non-linear mode, l but it has complex dynam ics.Then it was used in gray image encryption. This is a digital image encryption algorithm, dual scrambling that based on chaos of pixel position and pixel value.Compared with the traditional transcendental equation, ...

in this article, the compatibility of the opinion on the impossibility of reincarnation and belief in bodily resurrection in transcendental philosophy is studied. to this end, while defining and mentioning different types of reincarnation, some impediments that caused the transcendental philosophers consider reincarnation as impossible are compiled. then it is specified, with regard to the opin...

It is known that, for a transcendental entire function f, the Hausdorff dimension of J( f ) satisfies 1% dim J( f )% 2. For each d ` (1, 2), an example of a transcendental entire function f with dim J( f ) ̄ d is given. It is then indicated how this function can be modified to produce a transcendental meromorphic function F with one pole with dim J(F ) ̄ d. These appear to be the first examples o...

Marcus and Davis’s Rebooting AI: Building Artificial Intelligence We Can Trust (2019) describes the narrowness of current artificial intelligence, posits constituents human intelligence it contends (AI) must reproduce to achieve a general (broad) formulation, envisages contributions AI living. This article (1) reviews argument, (2) phenomenologically evaluates their interpretation (3) discloses...