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In this work, a novel fuzzy FEM (Finite Elements Method) numerical solution describing the recession flow in unconfined aquifers is proposed. In general, recession flow and drainage problems can be described by the nonlinear Boussinesq equation, while the introduced hydraulic parameters (Conductivity K and Porosity S) present significant uncertainties for various reasons (e.g., spatial distribution, human errors, etc.). Considering the general lack of in situ measurements for these parameters as well as the certain spatial variability that they present in field scales, a fuzzy approach was adopted to include the problem uncertainties and cover the disadvantage of ground truth missing data. The overall problem is encountered with a new approximate fuzzy FEM numerical solution, leading to a system of crisp boundary value problems. To prove the validity and efficiency of the new fuzzy FEM, a comparative analysis between the proposed approach and other well-known and tested approximations was carried out. According to the results, the proposed FEM numerical solution agrees with Karadinumerical method for the crisp case and is in close agreement with the original analytical solution proposed by Boussinesq in 1904 with the absolute reduced error to be 4.6‰. Additionally, the possibility theory is applied, enabling the engineers and designers of irrigation, drainage, and water resources projects to gain knowledge of hydraulic properties (e.g., water level, outflow volume) and make the right decisions for rational and productive engineering studies.

The solution to the second-order fuzzy unsteady nonlinear partial differential one-dimensional Boussinesq equation is examined. The physical problem concerns unsteady flow in a semi-infinite, unconfined aquifer bordering a lake. There is a sudden rise and subsequent stabilization in the water level of the lake; thus, the aquifer is recharging from the lake. The fuzzy solution is presented by a simple algebraic equation transformed in a fourth-degree polynomial approximation for the head profiles. In order to solve this equation, the initial and boundary conditions, as well as the numerous soil properties, must be known. A fuzzy approach is used to solve the problem since the aforementioned auxiliary conditions are vulnerable to various types of uncertainty resulting from human and machine errors. The physical problem described by a partial differential equation and the generalized Hukuhara derivative and the application of this theory for the partial derivatives were chosen as solving methods. In order to evaluate the accuracy and effectiveness of the suggested fuzzy analytical method, this study compares the findings of fuzzy analysis to those obtained using the Runge–Kutta method. This comparison attests to the accuracy of the former. Additionally, this results in a fuzzy number for water level profiles as well as for the water volume variation, whose α-cuts, provide according to Possibility Theory, the water levels and the water volume confidence intervals with probability p = 1 − α.

Very well-drained lands could have a positive impact in various soil health indicators such as soil erosion and soil texture. A drainage system is responsible for properly aerated soil. Until today, in order to design a drainage system, a big challenge remained to find the subsurface drain spacing because many of the soil and hydraulic parameters present significant uncertainties. This fact also creates uncertainties to the overall physical problem solution, which, if not included in the preliminary design studies and calculations, could have bad consequences for the cultivated lands and soils. Finding the drain spacing requires the knowledge of the unsteady groundwater movement, which is described by the linear Boussinesq equation (Glover-Dumm equation). In this paper, the Adomian solution to the second order unsteady linear fuzzy partial differential one-dimensional Boussinesq equation is presented. The physical problem concerns unsteady drain spacing in a semi-infinite unconfined aquifer. The boundary conditions, with an initially horizontal water table, are considered fuzzy and the overall problem is translated to a system of crisp boundary value problems. Consequently, the crisp problem is solved using an Adomian decomposition method (ADM) and useful practical results are presented. In addition, by application of the possibility theory, the fuzzy results are translated into a crisp space, enabling the decision maker to make correct decisions about both the drain spacing and the future soil health management practices, with a reliable degree of confidence.

Linear regression is a simple but powerful tool for prediction. However, it still suffers from some deficiencies, which are related to the assumptions made when using a model like normality of residuals, uncorrelated errors, where the mean of residuals should be zero. Sometimes these assumptions are violated or partially violated, thereby leading to uncertainties or unreliability in the predictions. This paper introduces a new method to account for uncertainty in the residuals of a linear regression model. First, the error in the estimation of the dependent variable is calculated and transformed to a fuzzy number, and this fuzzy error is then added to the original crisp prediction, thereby resulting in a fuzzy prediction. The results are compared to a fuzzy linear regression with crisp input and fuzzy output, in terms of their ability to represent uncertainty in prediction.

We show that in a sliced spacetime ( V , g ) , global hyperbolicity in V is equivalent to T A -completeness of a slice, if and only if the product topology T P , on V, is equivalent to T A , where T A denotes the usual spacetime Alexandrov “interval” topology.

The anticancer activity of acridone derivatives has attracted increasing interest, therefore, a variety of substituted analogs belonging to this family have been developed and evaluated for their anti-cancer properties. A series of N-alkyl-acridones 1−6 and N,N′-dialkyl-9,9′-biacridylidenes 7−12 with variable alkyl chains were examined for their topoisomerase I activity at neutral and acidic conditions as well as for their binding capacity to calf thymus and possible radical trapping antioxidant activity. It was found that at a neutral pH, topoisomerase I activity of both classes of compounds was similar, while under acidic conditions, enhanced intercalation was observed. N-alkyl-acridone derivatives 1−6 exhibited stronger, dose-dependent, cytotoxic activity against MCF-7 human breast epithelial cancer cells than N,N′-dialkyl-9,9′-biacridylidenes 7−12, revealing that conjugation of the heteroaromatic system plays a significant role on the effective distribution of the compound in the intracellular environment. Cellular investigation of long alkyl derivatives against cell migration exhibited 40−50% wound healing effects and cytoplasm diffusion, while compounds with shorter alkyl chains were accumulated both in the nucleus and cytoplasm. All N,N′-dialkyl-9,9′-biacridylidenes showed unexpected high scavenging activity towards DPPH or ABTS radicals which may be explained by higher stabilization of radical cations by the extended conjugation of heteroaromatic ring system.

A list of all possible causal relations in the two-dimensional Minkowski space M is exhausted, based on the duality between timelike and spacelike in this particular case, and thirty topologies are introduced, all of them encapsulating the causal structure of M. Generalisations of these results are discussed, as well as their significance in a discussion on spacetime singularities.

The use of liposomes has been crucial for investigations in biomimetic chemical biology as a membrane model and in medicinal chemistry for drug delivery. Liposomes are made of phospholipids whose biophysical characteristics strongly depend on the type of fatty acid moiety, where natural unsaturated lipids always have the double bond geometry in the cis configuration. The influence of lipid double bond configuration had not been considered so far with respect to the competence of liposomes in delivery. We were interested in evaluating possible changes in the molecular properties induced by the conversion of the double bond from cis to trans geometry. Here we report on the effects of the addition of trans-phospholipids supplied in different amounts to other liposome constituents (cholesterol, neutral phospholipids and cationic surfactants), on the size, ζ-potential and stability of liposomal formulations and on their ability to encapsulate two dyes such as rhodamine B and fluorescein. From a biotechnological point of view, trans-containing liposomes proved to have different characteristics from those containing the cis analogues, and to influence the incorporation and release of the dyes. These results open new perspectives in the use of the unnatural lipid geometry, for the purpose of changing liposome behavior and/or of obtaining molecular interferences, also in view of synergic effects of cell toxicity, especially in antitumoral strategies.