The electro-magnetic (EM) waves transmitted through a thin object with fine structures are observed by a microsphere located above the thin object. The EM radiation transmitted through the object produces both evanescent waves, which include information on the fine structures of the object (smaller than a wavelength), and propagating waves, which include the large image of the object (with dimensions larger than a wavelength). The super-resolutions are calculated by using the Helmholtz equation. According to this equation, evanescent waves have an imaginary component of the wavevector in the z direction, leading the components of the wavevector in the transversal directions to become very large so that the fine structures of the object can be observed. Due to the decay of the evanescent waves, only a small region near the contact point between the thin object and the microsphere is effective for producing the super resolution effects. The image with super-resolution can be increased by a movement of the microsphere over the object or by using arrays of microspheres. Both propagating and evanescent waves arrive at the inner surface of the microsphere. A coupling between the transmitted EM waves and resonances produced in the dielectric sphere, possibly obtained by the Mie method, leads to a product of the EM distribution function with the transfer function. While this transfer function might be calculated by the Mie method, it is also possible to use it as an experimental function. By Fourier transform of the above product, we get convolution between the EM spatial modes and those of the transfer function arriving at the nano-jet, which leads the evanescent waves to become propagating waves with effective very small wavelengths and thus increase the resolution.

Xylene isomers are notorious chemical hazards, and their efficient removal from water solutions is still challenging. The current study reports a polymer nanocomposite as a potential adsorbent for successfully removing dissolved xylene isomers from contaminated water. Polystyrene-1D multiwall carbon nanotube nanocomposite (PS-MWCNT) adsorbent was prepared using the one-step bulk polymerization method. Mesoporous PS-MWCNT was prepared using the nano-crystallization phase separation method. The sulfonation of the mesoporous PS-MWCNT nanocomposites was carried out by treating the samples with concentrated sulfuric acid at elevated temperatures. The sulfonated PS-MWCNT (HO₃S-PS-MWCNT) was found to be a potential adsorbent for dissolved xylene isomers from water solution. In addition, the HO₃S-PS-MWCNT can be efficiently recycled for up to 10 consecutive cycles with negligible decline in adsorption values. The exhibited equilibrium adsorption, rate of adsorption, and rapid regeneration of the HO₃S-PS-MWCNT are clear indications for the possibility of practical utilization of these adsorbents in large-scale water treatment plants.

There are several methods in the literature to find the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems. However, in all these methods, it is assumed that the product of two trapezoidal (triangular) fuzzy numbers will also be a trapezoidal (triangular) fuzzy number. Fan et al. (“Generalized fuzzy linear programming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach”, Information Sciences, Vol. 241, pp. 12–27, 2013) proposed a method for finding the fuzzy optimal solution of FFLP problems without considering this assumption. In this paper, it is shown that the method proposed by Fan et al. (2013) suffer from errors and to overcome these errors, a new method (named as Mehar method) is proposed for solving FFLP problems by modifying the method proposed by Fan et al. (2013) . To illustrate the proposed method, some numerical problems are solved.

Potassium dihydrogen phosphate, KH2PO4 (KDP) crystal is an excellent electro-optical nonlinear optical crystal with large electro-optical nonlinear coefficient, high laser damage threshold, and laser frequency doubling effect, electro-optical effect , Piezoelectric effects and other special features, widely used in inertial confinement fusion engineering (ICF) and electro-optical switching devices. Therefore, its growth mechanism, growth process and performance have been systematically studied. In the process of KDP crystal growth, it is found that the stability of the growth solution is an important factor affecting the quality of crystal growth. Therefore, in recent years, more and more research on the stability of the solution, such as the study of ph, doping, supersaturation, overheating time on the stability of the solution. Among them, the research on the doping is mostly reported, and the research on this aspect is mainly focused on two aspects. On the one hand, it is the study of the stability of the solution under doping, and the other is the effect of doping on the optical quality of the crystal. In fact, the stability of the growth solution and the quality of crystal growth is directly related to the quality, but the existing research to isolate the two researches. Therefore, the experiment will be carried out in the case of double-doped KDP solution stability, KDP crystal growth and crystal optical quality and other experiments, and in-depth analysis of the impact of solution stability and crystal optical quality of the reasons, while the solution stability and The relationship between the optical quality of the crystal is briefly analyzed.

This study explores approaches to optimizing inclusive education through international and local perspectives. It examines the role of educators in inclusive settings, highlights strategies for early detection of children’s developmental needs, and evaluates inclusive school management practices. Using qualitative case study methods, the research includes comprehensive observations and interviews at Fatma Kenanga Islamic Character School. Findings emphasize the importance of individualized learning plans, shadow teacher involvement, and collaborative stakeholder engagement. Integrating global insights, this study contributes to advancing inclusive education practices in Indonesia and beyond.