ABSTRACT The article explains and analyzes the conception of rough lacunary ideal statistical convergence on random ‐normed spaces for double sequences. The geometrical and topological results of rough lacunary ideal …
ABSTRACT The article explains and analyzes the conception of rough lacunary ideal statistical convergence on random ‐normed spaces for double sequences. The geometrical and topological results of rough lacunary ideal statistical limit points, rough lacunary ideal cluster points, and rough lacunary ideal boundedness are considered on these spaces. Through an exploration of properties associated with rough lacunary ideal convergence, equivalent conditions establish for set of lacunary ideal statistical limit points in the context of rough lacunary ideal statistically convergent double sequences.
Psoriasis is a long-lasting inflammatory skin condition that impacts millions globally. The occurrence of this disorder differs significantly across various areas, resulting from a complex interplay of genetic and environmental …
Psoriasis is a long-lasting inflammatory skin condition that impacts millions globally. The occurrence of this disorder differs significantly across various areas, resulting from a complex interplay of genetic and environmental influences. In psoriasis, the pathogenesis represents a complex interaction of innate and adaptive immunity that plays a significant role in the disease manifestation process. Many genetic factors predispose to psoriasis, which is considered a polygenic disease. Several genes concerning pathways like NF-κB and PI3K/Akt that modulate the amplification of inflammatory response and keratinocyte dysregulation have been elaborated in the light of their differential expression, susceptibility loci, and polymorphisms. Such genetic insights could open a whole new avenue for precision medicine in which biomarkers and gene-targeting therapies are promising options for personalized treatment. This review emphasizes the need for complex investigations into psoriasis, from molecular mechanisms to clinical manifestations, to bridge the gap between basic research and therapeutic development by furthering the understanding of psoriasis and paving the way for innovative treatments addressing skin lesions and systemic effects.
Abstract Potentially toxic element contamination in water poses a significant environmental concern. Lead in divalent form (Pb 2+ ) is considered as highly toxic due to its wide number of …
Abstract Potentially toxic element contamination in water poses a significant environmental concern. Lead in divalent form (Pb 2+ ) is considered as highly toxic due to its wide number of applications in synthetic paint, metal smelting, and industrial applications and is harmful to the environment and public health. Researchers are exploring biochar production from biomass such as coconut husk biochar (CHBC) to achieve the objectives of sustainable development and circular economy. Thus, in this current study, we focused on the production, effectiveness, and characterization of CHBC as a cost-effective adsorbent for the elimination of Pb 2+ . In this regard, biochar was optimized at different temperatures of 200°C, 400°C and 600°C, and the best yield was obtained at 600°C. Scanning electron microscopy (SEM) and X-ray diffraction (XRD) studies were conducted for further characterization, which showed an increase in the crystallinity of biochar from 56.4% to 64.3%, suggesting that the prepared biochar is highly porous. The prepared biochar was leveraged for the removal of Pb 2+ from water using varying concentrations, temperatures, and pH conditions, and the analysis was carried out using ultraviolet–visible (UV–vis) spectroscopy. The optimal parameters were found to be a molar concentration of 0.0125 M, a catalyst dose of 500 mg, room temperature, and a pH of 6. Adsorption follows Langmuir and Temkin isotherms, which appear to be well suited in the adsorption process based on the correlation coefficient of the linear graph ( R 2 = 0.97 and 0.99) and pseudo-first-order kinetics, with a correlation coefficient of R 2 = 0.546. The empirical results indicate that the usage of a pseudo-first-order kinetics model is well-matched in the adsorption process, and the evaluation was done by using UV–vis spectroscopy, while characterization was carried out using SEM–energy-dispersive X-ray spectroscopy, Fourier transform infrared spectroscopy, and XRD. Thus, the prepared biochar has been demonstrated to be an efficient platform for lead decontamination, paving the way for future researchers to explore and develop more effective techniques. This approach aligns with sustainable development goals and contributes to improved waste management practices.
ABSTRACT The article explains and analyzes the conception of rough lacunary ideal statistical convergence on random ‐normed spaces for double sequences. The geometrical and topological results of rough lacunary ideal …
ABSTRACT The article explains and analyzes the conception of rough lacunary ideal statistical convergence on random ‐normed spaces for double sequences. The geometrical and topological results of rough lacunary ideal statistical limit points, rough lacunary ideal cluster points, and rough lacunary ideal boundedness are considered on these spaces. Through an exploration of properties associated with rough lacunary ideal convergence, equivalent conditions establish for set of lacunary ideal statistical limit points in the context of rough lacunary ideal statistically convergent double sequences.
Psoriasis is a long-lasting inflammatory skin condition that impacts millions globally. The occurrence of this disorder differs significantly across various areas, resulting from a complex interplay of genetic and environmental …
Psoriasis is a long-lasting inflammatory skin condition that impacts millions globally. The occurrence of this disorder differs significantly across various areas, resulting from a complex interplay of genetic and environmental influences. In psoriasis, the pathogenesis represents a complex interaction of innate and adaptive immunity that plays a significant role in the disease manifestation process. Many genetic factors predispose to psoriasis, which is considered a polygenic disease. Several genes concerning pathways like NF-κB and PI3K/Akt that modulate the amplification of inflammatory response and keratinocyte dysregulation have been elaborated in the light of their differential expression, susceptibility loci, and polymorphisms. Such genetic insights could open a whole new avenue for precision medicine in which biomarkers and gene-targeting therapies are promising options for personalized treatment. This review emphasizes the need for complex investigations into psoriasis, from molecular mechanisms to clinical manifestations, to bridge the gap between basic research and therapeutic development by furthering the understanding of psoriasis and paving the way for innovative treatments addressing skin lesions and systemic effects.
Abstract Potentially toxic element contamination in water poses a significant environmental concern. Lead in divalent form (Pb 2+ ) is considered as highly toxic due to its wide number of …
Abstract Potentially toxic element contamination in water poses a significant environmental concern. Lead in divalent form (Pb 2+ ) is considered as highly toxic due to its wide number of applications in synthetic paint, metal smelting, and industrial applications and is harmful to the environment and public health. Researchers are exploring biochar production from biomass such as coconut husk biochar (CHBC) to achieve the objectives of sustainable development and circular economy. Thus, in this current study, we focused on the production, effectiveness, and characterization of CHBC as a cost-effective adsorbent for the elimination of Pb 2+ . In this regard, biochar was optimized at different temperatures of 200°C, 400°C and 600°C, and the best yield was obtained at 600°C. Scanning electron microscopy (SEM) and X-ray diffraction (XRD) studies were conducted for further characterization, which showed an increase in the crystallinity of biochar from 56.4% to 64.3%, suggesting that the prepared biochar is highly porous. The prepared biochar was leveraged for the removal of Pb 2+ from water using varying concentrations, temperatures, and pH conditions, and the analysis was carried out using ultraviolet–visible (UV–vis) spectroscopy. The optimal parameters were found to be a molar concentration of 0.0125 M, a catalyst dose of 500 mg, room temperature, and a pH of 6. Adsorption follows Langmuir and Temkin isotherms, which appear to be well suited in the adsorption process based on the correlation coefficient of the linear graph ( R 2 = 0.97 and 0.99) and pseudo-first-order kinetics, with a correlation coefficient of R 2 = 0.546. The empirical results indicate that the usage of a pseudo-first-order kinetics model is well-matched in the adsorption process, and the evaluation was done by using UV–vis spectroscopy, while characterization was carried out using SEM–energy-dispersive X-ray spectroscopy, Fourier transform infrared spectroscopy, and XRD. Thus, the prepared biochar has been demonstrated to be an efficient platform for lead decontamination, paving the way for future researchers to explore and develop more effective techniques. This approach aligns with sustainable development goals and contributes to improved waste management practices.
In this article we introduce the notion of I-convergent and I-Cauchy double sequences in a fuzzy normed linear space and establish some basic results related to these notions. Further, we …
In this article we introduce the notion of I-convergent and I-Cauchy double sequences in a fuzzy normed linear space and establish some basic results related to these notions. Further, we define I-limit points and I-cluster points of a double sequenc
We introduce the notions of lacunary -convergence and lacunary -Cauchy in the topology induced by random -normed spaces and prove some important results.
We introduce the notions of lacunary -convergence and lacunary -Cauchy in the topology induced by random -normed spaces and prove some important results.
x * ∈ X is said to be an r-limit point of a sequence (xi ) in some normed linear space (X,∥ · ∥) if (r ≥ 0). The set …
x * ∈ X is said to be an r-limit point of a sequence (xi ) in some normed linear space (X,∥ · ∥) if (r ≥ 0). The set of all r-limit points of (xi , denoted by LIM r x i , is bounded closed and convex. Further properties, in particular the relation between this rough convergence and other convergence notions, and the dependence of LIM r x i on the roughness degree r, are investigated. For instance, the set-valued mapping r ↦ LIM r x i is strictly increasing and continuous on (), where . For a so-called ρ-Cauchy sequence (xi ) satisfying it is shown in case X = R n that r = (n/(n + 1))ρ (or for Euclidean space) is the best convergence degree such that LIM r x i ≠ Ø.
Abstract In this work, using the concept of natural density, we introduce the notion of rough statistical convergence. We define the set of rough statistical limit points of a sequence …
Abstract In this work, using the concept of natural density, we introduce the notion of rough statistical convergence. We define the set of rough statistical limit points of a sequence and obtain two statistical convergence criteria associated with this set. Later, we prove that this set is closed and convex. Finally, we examine the relations between the set of statistical cluster points and the set of rough statistical limit points of a sequence. Keywords: Natural densityRough convergenceStatistical convergenceAMS Subject Classification: 40A05 ACKNOWLEDGMENTS The author is grateful to the referees and the editor in chief for their corrections and suggestions, which have greatly improved the readability of the paper.
Abstract For given r, ρ ≥ 0, a sequence (xi ) in some normed linear space X is said to be r-convergent if the r-limit set defined by is nonempty, …
Abstract For given r, ρ ≥ 0, a sequence (xi ) in some normed linear space X is said to be r-convergent if the r-limit set defined by is nonempty, and it is called a ρ-Cauchy sequence if This article investigates different aspects of this rough convergence, especially in infinite dimensional spaces, such as analytical properties of r-limit set, relation to other convergence notions, and the dependence of the r-limit set on the roughness degree r. Moreover, by using the Jung constant we find the minimal value of r such that an arbitrary ρ-Cauchy sequence in X is certainly r-convergent.
Given an n ‐normed space with n ≥ 2, we offer a simple way to derive an ( n − 1)‐norm from the n ‐norm and realize that any n …
Given an n ‐normed space with n ≥ 2, we offer a simple way to derive an ( n − 1)‐norm from the n ‐norm and realize that any n ‐normed space is an ( n − 1)‐normed space. We also show that, in certain cases, the ( n − 1)‐norm can be derived from the n ‐norm in such a way that the convergence and completeness in the n ‐norm is equivalent to those in the derived ( n − 1)‐norm. Using this fact, we prove a fixed point theorem for some n ‐Banach spaces.
In this paper we extend the notion of rough convergence using theconcept of ideals which automatically extends the earlier notions ofrough convergence and rough statistical convergence. We define the setof …
In this paper we extend the notion of rough convergence using theconcept of ideals which automatically extends the earlier notions ofrough convergence and rough statistical convergence. We define the setof rough ideal limit points and prove several results associated with thisset.
In (16) K. Menger proposed the probabilistic concept of distance by replacing the number d(p,q), as the distance between points p,q, by a distribution function Fp,q. This idea led to …
In (16) K. Menger proposed the probabilistic concept of distance by replacing the number d(p,q), as the distance between points p,q, by a distribution function Fp,q. This idea led to development of probabilistic analysis (3), (11) (18). In this paper, generalized probabilistic 2-normed spaces are studied and topological properties of these spaces are given. As an example, a space of random variables is considered, connections with the generalized deterministic 2-normed spaces studied in (14) being also given.
In this paper, we introduce and study the notion of rough I2 -lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I2 …
In this paper, we introduce and study the notion of rough I2 -lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I2 -lacunary statistical limit set of a double sequence and discuss some properties of this set.
The main purpose of this work is to define rough statistical convergence in probabilistic normed spaces. We have proved some basic properties as well as some examples which shows this …
The main purpose of this work is to define rough statistical convergence in probabilistic normed spaces. We have proved some basic properties as well as some examples which shows this idea of convergence in probabilistic normed spaces is more generalized as compared to the rough statistical convergence in normed linear spaces. Further, we have shown the results on sets of statistical limit points and sets of cluster points of rough statistically convergent sequences in these spaces.
In this paper we introduce and study the concept of ${\cal I}$-convergence of sequences in metric spaces, where ${\cal I}$ is an ideal of subsets of the set $\N$ of …
In this paper we introduce and study the concept of ${\cal I}$-convergence of sequences in metric spaces, where ${\cal I}$ is an ideal of subsets of the set $\N$ of positive integers. We extend this concept to ${\cal I}$-convergence of sequence of real functions defined on a metric space and prove some basic properties of these concepts.