Search Results (9)

We explore the realm of uncertainty theory by investigating diverse notions of convergence and statistical convergence concerning complex uncertain sequences. Complex uncertain variables can be described as measurable functions mapping from an uncertainty space to the set of complex numbers. They are employed to represent and model complex uncertain quantities. We introduce the concept of lacunary almost statistical convergence of order $\alpha$$(0<\alpha \le 1)$ for complex uncertain sequences, examining various aspects of uncertainty such as distribution, mean, measure, uniformly almost sure convergence and almost sure convergence. Additionally, we establish connections between the constructed sequence spaces by providing illustrative instances. Importantly, lacunary almost statistical convergence provides a flexible framework for handling sequences with irregular behavior, which often arise in uncertain environments with imprecise data. This makes our approach particularly useful in practical fields such as engineering, data modeling and decision-making, where traditional deterministic methods are not always applicable. Our approach offers a more flexible and realistic framework for approximating functions in uncertain environments where classical convergence may not apply. Thus, this study contributes to approximation theory by extending its tools to settings involving imprecise or noisy data. Full article

Studies on difference sequences was introduced in the 1980s, and since then, many mathematicians have studied this kind of sequences and obtained some generalized difference sequence spaces. In this paper, using the generalized difference operator, we introduce the concept of the deferred f-statistical convergence of generalized difference sequences of the order $\alpha$ and give some inclusion relations between the deferred f-statistical convergence of generalized difference sequences and deferred f-statistical convergence of generalized difference sequences of the order $\alpha$. Our results are more general than the corresponding results in the existing literature. Full article

The aim of this study was to compare the concentration of phenolic compounds, glucosinolates, proteins, sugars and vitamin C between kohlrabi (Brassica oleracea var. acephala gongylodes), Savoy cabbage (B. oleracea sabauda), Brussels sprouts (B. oleracea gemmifera), cauliflower (B. oleracea botrytis), radish (Raphanus sativus) and garden cress (Lepidium sativum) microgreens for their antioxidant and hypoglycemic potential. In addition, we applied an in vitro-simulated system of human digestion in order to track the bioaccessibility of the selected phenolic representatives, and the stability of the microgreens’ antioxidant and hypoglycemic potential in terms of α-amylase and α-glucosidase inhibition after each digestion phase. Using spectrophotometric and RP-HPLC methods with statistical analyses, we found that garden cress had the lowest soluble sugar content, while Savoy cabbage and Brussels sprouts had the highest glucosinolate levels (76.21 ± 4.17 mg SinE/g dm and 77.73 ± 3.33 mg SinE/g dm, respectively). Brussels sprouts were the most effective at inhibiting protein glycation (37.98 ± 2.30% inhibition). A very high positive correlation (r = 0.830) between antiglycation potential and conjugated sinapic acid was recorded. For the first time, the antidiabetic potential of microgreens after in vitro digestion was studied. Kohlrabi microgreens best inhibited α-amylase in both initial and intestinal digestion (60.51 ± 3.65% inhibition and 62.96 ± 3.39% inhibition, respectively), and also showed the strongest inhibition of α-glucosidase post-digestion (19.22 ± 0.08% inhibition). Brussels sprouts, cauliflower, and radish had less stable α-glucosidase than α-amylase inhibitors during digestion. Kohlrabi, Savoy cabbage, and garden cress retained inhibition of both enzymes after digestion. Kohlrabi antioxidant capacity remained unchanged after digestion. The greatest variability was seen in the original samples, while the intestinal phase resulted in the most convergence, indicating that digestion reduced differences between the samples. In conclusion, this study highlights the potential of various microgreens as sources of bioactive compounds with antidiabetic and antiglycation properties. Notably, kohlrabi microgreens demonstrated significant enzyme inhibition after digestion, suggesting their promise in managing carbohydrate metabolism and supporting metabolic health. Full article

We examine the co-variability between the surface wind divergence and vorticity and how it varies with latitude in the Pacific Ocean using surface vector winds from reanalysis and satellite scatterometer observations. We show a strong correlation between divergence and vorticity throughout the extratropical oceans. From this observation, we develop a dynamical model to explain the first-order dynamics which govern this strong co-variability. Our model exploits the fact that for much of the time, the large-scale surface winds are approximately in a steady-state Ekman balance to first order. An angle ${\alpha }^{\prime }$ is derived from Ekman dynamics by utilizing only the surface divergence and vorticity and is shown to succinctly summarize the co-variability between divergence and vorticity. This approach yields insight into the dynamics that shape the spatial variations in the large-scale surface wind field over the ocean; previous research has focused mainly on explaining variability in the vector winds rather than the derivative wind fields. Our model predicts two steady-state conditions which are easily identifiable as discrete peaks in ${\alpha }^{\prime }$ Probability Distribution Functions (PDFs). In the Northern Hemisphere, steady-state conditions can be either (1) diverging, with negative vorticity, or (2) converging, with positive vorticity. We show that these two states correspond to relative high and low sea-level pressure features, respectively. Southern Hemisphere conditions are similar to those of the Northern Hemisphere, except with the opposite sign of vorticity. This model also predicts the latitudinal variations in the co-variability between divergence and vorticity due to the latitudinal variation in the Coriolis parameter. The main conclusion of this study is that the statistical co-variability between the surface divergence and vorticity over the ocean is consistent with Ekman dynamics and provides perhaps the first dynamical approach for interpreting their statistical distributions. The related ${\alpha }^{\prime }$ PDFs provide a unique method for analyzing air–sea interactions and will likely have applications in evaluating the surface wind fields from scatterometers and weather and reanalysis models. Full article

This paper discusses a hybrid grey wolf optimizer utilizing a clone selection algorithm (pGWO-CSA) to overcome the disadvantages of a standard grey wolf optimizer (GWO), such as slow convergence speed, low accuracy in the single-peak function, and easily falling into local optimum in the multi-peak function and complex problems. The modifications of the proposed pGWO-CSA could be classified into the following three aspects. Firstly, a nonlinear function is used instead of a linear function for adjusting the iterative attenuation of the convergence factor to balance exploitation and exploration automatically. Then, an optimal α wolf is designed which will not be affected by the wolves β and δ with poor fitness in the position updating strategy; the second-best β wolf is designed, which will be affected by the low fitness value of the δ wolf. Finally, the cloning and super-mutation of the clonal selection algorithm (CSA) are introduced into GWO to enhance the ability to jump out of the local optimum. In the experimental part, 15 benchmark functions are selected to perform the function optimization tasks to reveal the performance of pGWO-CSA further. Due to the statistical analysis of the obtained experimental data, the pGWO-CSA is superior to these classical swarm intelligence algorithms, GWO, and related variants. Furthermore, in order to verify the applicability of the algorithm, it was applied to the robot path-planning problem and obtained excellent results. Full article

Objectives: psychological flexibility is a crucial construct highly correlated with psychological wellness. There is a need for a tool to measure psychological flexibility in order to accurately ascertain the effects of treatment. The existing industry standard, the Acceptance and Action Questionnaire-II (AAQ-II), has issues with conflating psychological flexibility with distress; moreover, it does not cover the hexaflexes. The 23-item CompACT was designed to surmount these limitations. Methods: the classical test theory (CTT) and Rasch measurement theory (RMT) were used to check the validity and reliability of the Malay version of the CompACT Scale. Cronbach’s α, McDonald’s Ω, and greatest lower bound were used to measure internal consistency. A Pearson’s correlation test was used to measure test–retest reliability of the Malay versus the original English version. For validity, convergent validity was established by using the Malay AAQ-7 Scale. The dimensionality of the Malay version of the CompACT Scale was explored using exploratory factor analysis. For the RMT, weighted fit statistics (infit) and outlier sensitive fit statistic (outfit) mean square (MnSq) values were used at the item level, while item and person separation reliability values and item and person separation indices were applied at the scale level. Results: the internal consistency measures, including Cronbach α and McDonald’s Ω, passed the suggested cutoff points. Convergent validity with the AAQ-II was 0.693. The quality of the Malay version of the CompACT Scale was also satisfactory, as all item and person reliability values and indices exceeded the suggested cut-off points. Conclusions: the Malay CompACT is a psychometrically sound instrument to assess psychological flexibility in both clinical and research settings. Full article

Numerical solution and parameter estimation for a type of fractional diffusion equation are considered. Firstly, the symmetrical compact difference scheme is applied to solve the forward problem of the fractional diffusion equation. The stability and convergence of the symmetrical difference scheme are presented. Then, the Bayesian method is considered to estimate the unknown fractional order $\alpha$ of the fractional diffusion equation model. To validate the efficiency of the symmetrical numerical scheme and the estimation method, some simulation tests are considered. The simulation results demonstrate the accuracy of the compact difference scheme and show that the proposed estimation algorithm can provide effective statistical characteristics of the parameter. Full article

The aim of the present work is to introduce notions of statistical convergence, strongly p-Cesàro summability and the statistically Cauchy sequence of order $\alpha$ in paranormed spaces. Some certain topological properties of these new concepts are examined. Furthermore, we introduce the some inclusion relations among them. Full article

Our goal in this work is to introduce the notion $\left[V,,,\lambda \right]{\left(\mathcal{I}\right)}_2$ -summability and ideal λ-double statistical convergence of order α with respect to the intuitionistic fuzzy norm $\left(\mu ,,,v\right)$ . We also make some observations about these spaces and prove some inclusion relations. Full article