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.

One functional class is described in terms of one-sided modulus of continuity and the modulus of positive (negative) variation on which there
is a uniform convergence of the truncated cardinal Whittaker functions.

In this review are developed insights from the current research work to develop the concept of functional materials. This is understood as real modified substrates for varied applications. So, functional and modified substrates focused on nanoarchitectures, microcapsules, and devices for new nanotechnologies highlighting life sciences applications were revised. In this context, different types of concepts to proofs of concepts of new materials are shown to develop desired functions. Thus, it was shown that varied chemicals, emitters, pharmacophores, and controlled nano-chemistry were used for the design of nanoplatforms to further increase the sizes of materials. In this regard, the prototyping of materials was discussed, affording how to afford the challenge in the design and fabrication of new materials. Thus, the concept of optical active materials and the generation of a targeted signal through the substrate were developed. Moreover, advanced concepts were introduced, such as the multimodal energy approach by tuning optical coupling from molecules to the nanoscale within complex matter composites. These approaches were based on the confinement of specific optical matter, considering molecular spectroscopics and nano-optics, from where the new concept nominated as metamaterials was generated. In this manner, fundamental and applied research by the design of hierarchical bottom-up materials, controlling molecules towards nanoplatforms and modified substrates, was proposed. Therefore, varied accurate length scales and dimensions were controlled. Finally, it showed proofs of concepts and applications of implantable, portable, and wearable devices from cutting-edge knowledge to the next generation of devices and miniaturized instrumentation.

This study focused on the formulation and characterization of silver nanoparticles (AgNP) functionalized with d-limonene. The nanoparticles were functionalized by phase inversion and the synthesis of the nanoparticles was performed in situ; particle size was determined by laser diffraction, zeta potential and optical colloidal stability using Multiscan 20 for a period of 24 hours at 37 °C; the minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) of the formulated material on Escherichia coli ATCC 25922, Staphylococcus aureus ATCC 29213, Klebsiella oxytoca ATCC 700324, Enterococcus casseliflavus ATCC 700327, Escherichia coli BLEE, carbapenem-resistant Pseudomona aeruginosa were determined. The nanoparticles showed colloidal stability at a d-limonene concentration of 3.93%, silver ions at 1.61 × 10⁻³%, non-ionic adjuvant at 24% and ascorbic acid at 5.88%; citric acid/citrate (1:1) 0.48M for a pH of 4.5 was used as a buffer system. The formulation was classified as a polydisperse system (PD = 0.0851), with a zeta potential of −11.6 mV and average particle size of 81.5 ± 0.9 nm. A particle migration velocity of −0.199 ± 0.006 mm∙h⁻¹, a constant transmission profile and backscattering profile with variations of 10% were evidenced, which represents a stable formulation. The nanoparticles presented an MIC and an MBC of 28 μg∙mL⁻¹ (5.6 × 10⁻²% d-limonene and 4.7 × 10⁻⁵% AgNP) against all tested bacteria.

The ways of developing functional textiles based on nanomaterials were introduced, and the latest research achievements of nanomaterials in such aspects as flame retardancy, antibacterial, super-hydrophobic, self-cleaning, UV resistance, and anti-static textiles were reviewed. The main technical obstacles to the large-scale application of nanomaterials in functional textiles were pointed out, the possible solutions were discussed, and the development of functional textiles by nanomaterials has been prospected.