Using the rank scale rule, taking 47 major port cities in China from 2001 to 2015 as research samples, this paper discusses the rank scale characteristics and hierarchical structure of coastal port city system from a multi-functional perspective, and divides the coupling type of multi-functional development based on shipping logistics. The research shows that: 1) from 2001 to 2015, the scale-free area of manufacturing function order scale distribution in the coastal port city system appeared bifractal structure, the hierarchical segmentation characteristics appeared, and the other functions were single fractal; From the perspective of long-term evolution, only the order and scale distribution of shipping logistics function has developed from centralization to equilibrium, while the business function, manufacturing function (scale-free region I), modern service function and population distribution function are in a centralized situation. 2) The hierarchical structure of coastal port city system has gradually changed from pyramid structure to spindle structure, and generally formed five levels: national hub, regional hub, regional sub center, regional node and local node. 3) From the perspective of multi-functional coupling types, the traditional functions of port cities are generally ahead, while the high-end service functions lag behind, and the improvement speed of urban functions is slow and tends to be flat, indicating that the multi-functional development of China’s coastal port cities is still at a low level, and the industrial system structure needs to be further optimized. 4) From the perspective of port cities at different levels, the functions of regional hub cities and regional sub central cities are in the stage of rapid growth; regional and local node cities are still in the growth stage of traditional functions such as industry and commerce.

The changes the magnetic flux generated (electric, magnetic and electromagnetic waves) on the surface of earth due to sudden changes is a matter of discussion. These emissions occur along the fault line generated due to geological and tectonic processes. When sudden changes occur in the environment due to seismic and atmospheric variations, these sensing was observed by creatures and human bodies because the animals and trees adopt the abnormal signals and change the behavior. We have analyzed the changing behavior of recorded signal by live sensors (i.e., banyan tree). So we use the deep-rooted and long-aged banyan tree. The root of banyan tree (long-aged) has been working as a live sensor to record the geological and environmental changes. We record the low frequency signals propagated through solar-terrestrial environment which directly affect the root system of the banyan tree and changes that have been observed by live sensors. Then, very low frequency (VLF) signal may propagate to the earth-ionosphere waveguide. We have also analyzed the different parameters of live cells which is inbuilt in latex of the tree, so we record the dielectric parameters of green stem latex and found some parameters i.e., dielectric constant (ε) and dielectric loss (ε’) of various trees to verify these natural hazards and found good correlation. Therefore, we can say by regularly monitoring the bio-potential signal and dielectric properties of banyan tree and we are able to find the precursory signature of seismic hazards and environmental changes.

Many questions of control theory are well studied for systems which satisfy to the relative degree definition. If this definition is fulfilled then there exists linear state-space transform reducing system to a very convenient canonical form where zero dynamics is a part of system’s equations. Algorithms of such reduction are well-known. However, there exist systems which don’t satisfy this definition. Such systems are the subject of investigation in the presented paper. To investigate their properties here we suggest to consider an analogue of the classical relative degree definition – the so-called column-wise relative degree. It turned out that this definition is satisfied in some cases when classical relative degree doesn’t exist. We introduce this notion here, investigate it properties and suggest algorithm for reducing systems to the column-wise relative degree compliant form if possible. It is possible to show that systems with column-wise relative degree also can be reduced to a convenient canonical form by a linear state-space transformation. Some problems arise from the fact that some systems which do not have relative degree can be reduced to a form with it using linear inputs or outputs transform. Here we show that this is an interesting mathematical problem, which can be solved with the help of properties of relative degree, formulated and proved in this paper.

An investigation is conducted into how radiation affects the non-Newtonian second-grade fluid in double-diffusive convection over a stretching sheet. When fluid is flowing through a porous material, the Lorentz force and viscous dissipation are also taken into account. The flow equations are coupled partial differential equations that can be solved by MATLAB’s built-in bvp4c algorithm after being transformed into ODEs using appropriate similarity transformations. Utilizing graphs and tables, the impact of a flow parameter on a fluid is displayed. On velocity, temperature, and concentration profiles, the effects of the magnetic field, Eckert number, and Schmidt number have been visually represented. Calculate their inaccuracy by comparing the Nusselt number and Sherwood number values to those from earlier investigations.