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This paper delves into the exploration of extremally disconnected spaces within the context of neutrosophic nano topological space. It introduces a novel space termed neutrosophic nano mixed space, created through the fusion of neutrosophic nano minimal structure and neutrosophic nano topology. The primary objective is to investigate extremal disconnectedness within this new space, shedding light on its properties and implications. Furthermore, the research examines the characterization of various types of open sets within the neutrosophic nano mixed space. As an extension, we gave a bio-mathematical application of neutrosophic nano extremal disconnectedness.

Rice is the most widely consumed staple food for a large part of the world’s human population, especially in Asia. Sheath blight caused by Rhizoctonia solani, is one of the most serious diseases of rice. Research progress is limited due to non availability of absolute resistant sources to sheath blight in rice. A total of 1013 germplasm comprising of mutants, introgression lines from wild species, A, B, R lines, Tropical japonica accessions, land races from north eastern India, wild rice accessions of O. nivara and O. rufipogon and gall midge biotype differentials maintained at ICAR-IIRR were evaluated with artificial inoculation for resistance to sheath blight disease during 2012 under field conditions. The germplasm identified as resistant/moderately resistant were further tested both under glass house and field conditions in the subsequent years (2013 and 2014) and seasons (Both Kharif and Rabi). Based on three years of testing, seven genotypes such as SM 801 (N 22 mutant), 10–3 (Introgression line), Ngnololasha, Wazuhophek, Gumdhan and Phougak (land races from north east) and RP 2068-18-3-5 (gall midge biotype differential) were identified as moderately resistant to sheath blight. Agro-morphological characterization using 62 DUS descriptors for two years (2013 and 2014) revealed that disease resistance positively correlated with stem thickness and negatively with tiller number. No correlation was observed with traits like plant height and heading date with sheath blight resistance. Resistant genotypes with medium to semi dwarf stature should be used in breeding programmes in the development of sheath blight resistant cultivars.

The main idea of this paper is to generate supra and infra topologies from simple undirected graphs. For this, we have introduced two new operators namely supra and infra operators which are defined on the power set of the vertex set of a graph. Moreover, we have also proved that the supra operator satisfying Kuratowski’s closure axiom will yield a topology. Further it was extended to develop the concept of connectedness and separation axioms on G-supra and G-infra spaces.

The main idea of this article is to define a fuzzy crisp set, intuitionistic crisp set and neutrosophic crisp set from simple digraphs. These sets have their own impact to generate the subbasis which in turn yields topological spaces. Moreover, an attempt has been made to extend our concept in induced subgraphs that lead us to relative topology. We have also formalized the structural equivalence of the isomorphic graphs and the topologies induced by them. A comparison between topologies has been made for some types of connected digraphs. Also, we have defined separation axioms on digraphs and related them to the topological separation axioms.

Hand dominance has long been associated with differences in neural control and motor performance, with the dominant hand typically exhibiting better coordination in reaching tasks. However, the extent to which this dominance influences performance in finger force control remains unclear. This study aimed to examine the behavioural and neural features of the dominant and non-dominant hands during grasping and lifting tasks in healthy young adults, focusing on the synergy index, EEG band power, and EEG–EMG coherence as key measures. Twenty right-handed adults participated in this study. Participants engaged in an experimental task where they grasped a handle for the initial 5 s, followed by lifting and holding it for an additional 5 s. There were two task conditions: fixed (thumb platform secured) and free (thumb platform movable). It was hypothesized that the dominant hand would exhibit greater finger force coordination and enhanced neural features, including higher EEG band power and increased EEG–EMG coherence, compared to the non-dominant hand. Contrary to the hypothesis, we found statistical equivalence in the synergy index, EEG band power, and EEG–EMG coherence between the dominant and non-dominant hands across both fixed and free task conditions. These findings suggest that both hands can achieve similar levels of performance in tasks emphasizing steady-state force maintenance, despite the typical advantages of the dominant hand in other motor tasks. However, a significant difference was observed between task conditions, with the fixed condition showing higher values than the free condition in both behavioural (synergy index—η 2  = 0.81, p < 0.0001,) and neural (EEG band power η 2  = 0.37, p < 0.05 and EEG–EMG coherence—η 2  = 0.49, p < 0.0001) features. These differences were likely due to changes in friction, yet the adjustments remained consistent between the dominant and non-dominant hands.

This paper discusses mathematical model of hydrogen evolution via H + and H 2 O reduction at a rotating disc electrode. Rotating disc electrodes are the preferred technology for analysing electrochemical processes in electrically powered cells and another rotating machinery, such as combustion engines, air compressors, gearboxes, and generators. The theory of nonlinear convection–diffusion equations provides the foundation for the model. In the present study, the Akbari-Ganji approach is utilised to solve, concurrently, the mass transport equations of  H + and OH -   in the electrolyte and on the electrode surface under steady-state circumstances. A general and simple analytical expression is obtained for the reactants' hydrogen and hydroxide ion concentrations. Additionally, numerical solutions using non-standard finite difference methods are presented, and compared with the analytical solution. The exact solution for the limiting case results is presented and examined with the general results. Furthermore, the graphs and tables that compare the theoretical and numerical solutions demonstrated the accuracy and dependability of our paradigm.

IntroductionMaintaining fluid intake sufficient to reduce arginine vasopressin (AVP) secretion has been hypothesised to slow kidney cyst growth in autosomal dominant polycystic kidney disease (ADPKD). However, evidence to support this as a clinical practice recommendation is of poor quality. The aim of the present study is to determine the long-term efficacy and safety of prescribed water intake to prevent the progression of height-adjusted total kidney volume (ht-TKV) in patients with chronic kidney disease (stages 1–3) due to ADPKD.Methods and analysisA multicentre, prospective, parallel-group, open-label, randomised controlled trial will be conducted. Patients with ADPKD (n=180; age ≤65 years, estimated glomerular filtration rate (eGFR) ≥30 mL/min/1.73 m2) will be randomised (1:1) to either the control (standard treatment+usual fluid intake) or intervention (standard treatment+prescribed fluid intake) group. Participants in the intervention arm will be prescribed an individualised daily fluid intake to reduce urine osmolality to ≤270 mOsmol/kg, and supported with structured clinic and telephonic dietetic review, self-monitoring of urine-specific gravity, short message service text reminders and internet-based tools. All participants will have 6-monthly follow-up visits, and ht-TKV will be measured by MRI at 0, 18 and 36 months. The primary end point is the annual rate of change in ht-TKV as determined by serial renal MRI in control vs intervention groups, from baseline to 3 years. The secondary end points are differences between the two groups in systemic AVP activity, renal disease (eGFR, blood pressure, renal pain), patient adherence, acceptability and safety.Ethics and disseminationThe trial was approved by the Human Research Ethics Committee, Western Sydney Local Health District. The results will inform clinicians, patients and policy-makers regarding the long-term safety, efficacy and feasibility of prescribed fluid intake as an approach to reduce kidney cyst growth in patients with ADPKD.Trial registration number ANZCTR12614001216606.