The basic property of anti-smog masks is to block PM2.5 with excellent air permeability. A multi-layer nanofiber woven fabric with hierarchical structure is the best candidate for this purpose.
The variational iteration method is shown to be applicable to delay differential equations for analytical approximate solutions.
Starting from the initial triality of physics, namely mathematical philosophy, transfinite set theory and number theory we drive the inevitability of a topological quantum vacuum fluctuation of spacetime resulting in the fundamental reality of pair creation and annihilation. Subsequently we give a simple but strong mathematical proof of Dvoretzky‘s marvellous theorem on measure concentration, thus making dark energy and accelerated cosmic expansion not only an astrophysical measurement and observational reality, but also a plausible topological-geometrical fact of a pointless Cantorian actual universe akin to the Penrose fractal tiling space. This space is described accurately via the von Neumann-Conne noncommutative geometry using their golden mean dimensional function and the corresponding bijection of E-infinity theory. The said theory was developed by the authors of the present paper and their group and is based on and starts from the pioneering efforts of the Canadian physicist G. Ord and the French astrophysicist L. Nottale.
Albert Einstein combined continuous space and time into his special relativity, El-Naschie discovered the transfinite discontinuity of space–time in his E-infinity theory where infinity of dimensions was created. We find a partner of both space–time and E-infinity in biology. In our theory, the number of cells in an organism endows an additional dimension in biology, leading to explanation of many complex phenomena.
No abstract is provided for this article.
Electrospinning is a simple method used in the preparation of polymer fibers, the diameter of the electrospun fibers, varying in large from micrometer to nanometer, mainly depends upon the electrical field applied. The non-linear relation between the current of charged jet and the applied voltage is an intriguing and enduring problem. An allometric scaling relation between the current and voltage is obtained. He Chengtian's inequality, which has millennia history, is applied.
No abstract is provided for this article.
Article A Family of Variational Principles for Compressible Rotational Blade-to-Blade Flow Using Semi-Inverse Method was published on June 1, 1998 in the journal International Journal of Turbo & Jet-Engines (volume 15, issue 2).
No abstract is provided for this article.
No abstract is provided for this article.
Hall–Petch strengthening has been widely used in materials science, but its mechanism is not very clear yet, some inverse phenomena were observed. This paper gives a fractal approach to explanation of the Hall–Petch effect, revealing the value of the fractal dimensions is the key factor: when it is larger than one, the Hall–Petch effect is predicted; while when it is smaller than one, an inverse Hall–Petch relationship is obtained. The fractal theory can also explain the nano-effort (size effort) in nanotechnology and spider silk’s strength.
No abstract is provided for this article.
This paper aims to study a two-scale population growth model in a closed system by He–Laplace method together with the fractional complex transform (FCT). The two-scale derivative is described with the help of He’s fractional derivative. The FCT approach is used to convert differential equation of the two-scale fractal order in its traditional partner, which is then readily solved by He–Laplace iterative scheme. The results are computed as a series of easily computed components. The validation of the proposed methodology is illustrated by a quantitative comparison of numerical results with those obtained using other techniques. The results show that the proposed method is fast, accurate, straightforward, and computationally reasonable.
In this paper, Elzaki projected differential transform method (EPDTM) is applied to approximate the solution of fractional-order model of HIV infection of CD4[Formula: see text]T-cells that comprise a system of fractional differential equations (FDEs). By approximating the solution of this system, the unknown parameters of the original fractional HIV model are adjusted. Numerical results demonstrate that this method is simple and precise when applied to a system of FDEs.
Article Treatment Shocks in Transonic Aerodynamics in the Meshless Method Part I: Lagrange Multiplier Approach was published on March 1, 1999 in the journal International Journal of Turbo & Jet-Engines (volume 16, issue 1).
No abstract is provided for this article.
He’s multiple scales method is a couple of the homotopy perturbation method and the multiple scales technology in the classic perturbation method. This method has been proved to be a powerful mathematical tool to various nonlinear equations, and it is extremely effective for forced nonlinear oscillators. This paper shows that the method can be further improved by incorporating some known technologies, e.g., the parameter-expanding technology, the enhanced perturbation method and the homotopy perturbation method with an auxiliary term. Due to the wide application of the homotopy perturbation method, He’s multiple scales method cleans solutions of nonlinear equations while the classic perturbation method fails.
