Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil^[1]. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method has resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at p = 2 , r = 2 and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures (μ^*, σ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters β and θ_s is suggesting a greater significant digits to reduce its input uncertainty range.

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.

The potential of nanotechnology to improve human health, optimize natural resource utilization, and reduce environmental pollution is remarkable. With the ever-growing advancement in dentistry, one of the breakthroughs is using nanotechnology. Nanotechnology in periodontics has touched every aspect of treatment modality, from non-surgical therapy to implant procedures, including regenerative procedures. Understanding their mechanism plays a pivotal role in more efficient usage of nanotechnology, better treatment procedures, and eventually better outcomes. In this paper, we review the application of nanotechnology in periodontal therapy. We performed the search for papers in Scopus using the key words and phrases as follows: “nanodentistry”; “dentistry and nanotechnology”; “dentistry and nanoparticles”; “dentistry and nanomedicine”; “dentistry and nanorobots”. There were found 530 papers in total. Some papers belonged to two and more categories. It is revealed that the number of papers versus year does not follow any specific pattern, but the cumulative amount of papers versus year is fitted with the exponential regression. There were also selected papers using certain inclusion/exclusion criteria. Only the selected papers were analyzed. Nanomedicine is subjected to intensive studies nowadays. There are some promising results that will likely be implemented into praxis soon in the fields of medical diagnostics and clinical therapeutics. The appearance of nanotechnology can have a considerable impact on the treatment of periodontal diseases.

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.