This article concerns  with  the  construction of the  analytical traveling  wave so- lutions  for the Generalized-Zakharov System  by the Riccati-Bernoulli Sub- ODE technique. Also, we will discuss this  technique  in random  case by using random  traveling  wave trans- formation  in order  to  find what  is the  effect of the  randomness  input  for this  technique. We presented the Generalized-Zakharov System as an example to show the difference effect between the deterministic and stochastic Riccati-Bernoulli Sub-ODE technique.  The first moment of random solution is computed for different statistical probability distributions.

The development of critical thinking (CT) enhances academic and professional opportunities. A review of literature reveals the use of fragmented analysis techniques, such as descriptive and correlational methods, among others, which hinder a deeper understanding of CT levels. This research aims to develop a methodology for analyzing Critical Thinking test scores, integrating five phases: exploratory, item analysis, scoring, gap analysis, and correlational. Using a quantitative approach, CT skills were analyzed with the Halpern Critical Thinking Assessment, which includes both open- and closed-ended questions to measure five skills: Verbal Reasoning (VR), Argument Analysis (AA), Hypothesis Testing (HT), Probability Use (PU), and Problem Solving (PS). The sample consisted of 214 students aged 18 and older. The item analysis phase categorized the items into quadrants: satisfactory, for review, or for elimination, based on difficulty and discrimination indices. The gap analysis revealed that Verbal Reasoning and open-ended formats were less satisfactory. The correlational phase, using heat maps, showed a stronger association between Verbal Reasoning and Probability Use. The methodological contributions include a variety of strategies that provide recommended procedures for analyzing tests or questionnaires in general. In today’s digital age, the development of critical thinking is not only a desirable skill but an essential necessity for the higher education system.

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.

In this paper silver nanoparticles (NPs) which are synthesized by a simple plasma arc discharge method, that is a kind of electrochemical methods, are examined. The method is very simple and silver NPs are obtained very fast by means of two polished silver plates and electrochemical cell. The effects of changing some terms of the experiment including using Hydrogen peroxide (H₂O₂), temperature and the medium of experiment on oxygen percent and crystalline structure of silver NPs have been studied by transmission electron microscopy, UV-visible spectrophotometery, and X-ray diffraction. Water medium gets larger nanoparticles with less oxygen content compare to air medium. The size of synthesized nanoparticles become smaller and they also become more spherical by using H₂O₂ in air medium. In water medium, the size and concentration of the silver crystallite increase by temperature growth and adding H₂O₂  respectively.