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.

The reduction of biodiversity and the decline in wildlife populations are urgent environmental issues with devasting consequences for ecosystems and human health. As a result, the protection of wildlife and biodiversity has emerged as one of humanity’s greatest goals, not only for protecting and maintaining human health but also for environmental, economic, and social well-being. In recent years, people have become increasingly aware of the importance and effectiveness of wildlife conservation efforts alongside environmental protection measures, sustainable agricultural practices and non-harmful production procedures and services. This study describes the development and implementation of a labeling scheme for wildlife and biodiversity protection for products or services. The label is designed to encourage the adoption of sustainable and environmentally friendly production methods and services that will contribute to biodiversity conservation and the harmonic coexistence of human-wildlife. Moreover, using a case study approach, the research presents an innovative information system designed to streamline the label-awarding process, ensuring transparency and efficiency. The established system evaluates the sustainability practices and measures implemented by businesses, with a focus on honey production in this case. Additionally, the study explores the broader social implications of the label, particularly its potential to engage consumers and promote awareness of biodiversity conservation.

ZrO₂ thin film samples were produced by the sol-gel dip coating method. Four different absorbed dose levels (such as ~ 0.4, 0.7, 1.2 and 2.7 Gray-Gy) were applied to ZrO₂ thin films. Hence, the absorbed dose of ZrO₂ thin film was examined as physical dose quantity representing the mean energy imparted to the thin film per unit mass by gamma radiation. Modification of the grain size was performed sensitively by the application of the absorbed dose to the ZrO₂ thin film. Therefore the grain size reached from ~50 nm to 87 nm at the irradiated ZrO₂ thin film. The relationship of the grain size, the contact angle, and the refractive index of the irradiated ZrO₂ thin film was investigated as being an important technical concern. The irradiation process was performed in a hot cell by using a certified solid gamma ray source with 0.018021 Ci as an alternative technique to minimize the utilization of extra toxicological chemical solution. Antireflection and hydrophilic properties of the irradiated ZrO₂ thin film were slightly improved by the modification of the grain size. The details on the optical and structural properties of the ZrO₂ thin film were examined to obtain the optimum high refractive index, self-cleaning and anti-reflective properties.

This paper presents the state of displacement of a multilayered composite laminate subjected to transverse static load with varying balance, symmetric and anti-symmetric angle-ply and cross-ply staking sequences. Higher-order shear deformation theory (HSDT) is considered in the finite element formulation of nine-noded isoparametric element with seven degrees of freedom at each node. The finite element formulation is transformed into computer codes. A convergence study is carried out first to obtain the optimal mesh size for minimizing the computational time. The maximum deflection at the center of plate for both fixed and simply supported edges is verified with reported literature and a good conformity is found. An attempt has been made to observe the minimum value of maximum deflection in the laminate for attaining the maximum strength of laminate with a suitable combination of stacking sequences with a constant volume of material.

The present article reports the applications of Caputo-Fabrizio time-fractional derivatives. This article generalizes the idea of unsteady MHD free convective flow in a Walters.-B fluid with heat and mass transfer study over an exponential isothermal vertical plate embedded in a porous medium. The governing equations are converted into dimensionless form and extended to fractional model. The generalized Walters-B fluid model has been solved analytically using the Laplace transform technique. From the general solutions we reduce limiting solutions when to the similar motion for Newtonian fluid. The corresponding expressions for and Nusselt and Sherwood numbers are also assessed. Numerical results for velocity, temperature and concentration are demonstrated graphically for various factors of interest and discussed. As a result, we have plotted the influence of fractional parameter on fluid flow and drawn comparison between fractional Walters’-B and fractional Newtonian fluid and found that fractional Newtonian fluid is faster than fractional Walters’-B fluids.

Synthesis of macro-mesoporous Titania (Titanium dioxide-TiO₂) nanospheres was successfully achieved using a modified template-free methodology to incorporate macroporous channels into a mesoporous TiO₂ framework to form mixed macro-mesoporous TiO₂ spheres (MMPT), which were doped with carbon dots (C-dots) to form improved nanocomposites (C-dots@MMPT). Elemental composition, surface bonding and optical properties of these nanocomposites were characterized by X-ray diffraction (XRD), Fourier transforms infrared spectroscopy (FTIR) and ultraviolet-visible absorption spectroscopy (UV-VIS). Evaluation of photocatalytic activity for each (C-Dots@MMPT) sample was performed via degrading the Methylene Blue (MB) dye compared with bare samples (MMPT) under visible light irradiation using 300 Watt halogen lamp.