Prime Index Research Articles

A Study on the Classification of All Simple Commutative Near-Rings upto Isomorphism

This research paper aims to classify all simple commutative Near-Rings up to isomorphism, which are rings with no zero divisors and no ideals containing a nonzero element that is not prime ideal. The authors use various techniques from algebraic number theory and representation theory of semi simple algebras to construct representations of these rings over the integers or rational numbers. They also provide examples showing how these classes can be distinguished by their algebraic properties, such as whether they are PID (prime idempotent domain), zero-divisorless, or have ideals containing elements with prime index. The study contributes new results and insights into the classification of near-rings, which has implications for other areas of abstract algebra and number theory.

On Finite Groups with Three Supersolvable Subgroups of Pairwise Relatively Prime Indices

Let G be a finite group. In this paper, we obtain some new conditions for supersolvability of G with three supersolvable subgroups of pairwise relatively prime indices in G. Our main results improve and extend some known results in the literature.

On Edge Prime Index of a Graph

Relatively Prime Edge labeling extends the notion of prime labeling by considering edges. Prime labeling requires adjacent vertices to possess relatively prime labels, while relatively prime edge labeling requires adjacent edges to have relatively prime labels. The transformation of a coprime edge-labeled graph into a relatively prime edge-labeled graph introduces the concept of Edge Prime Index (or Relatively Prime Index). This study focuses on cases where a coprime edge-labeled graph can be converted into a relatively prime edge-labeled graph by removing certain edges from graph G, thereby establishing the concept of Edge Prime Index. Finally, the Edge Prime Index of some graphs are found.

A mathematical approach to optimizing brand school placement via intuitionistic Sombor indices

The property of fuzziness is advantageous for any setting where a problem prediction and solution are intended. In comparison to the classical approach (crisp set), fuzzy graphs are beneficial as they provide greater precision and flexibility. Intuitionistic fuzzy graphs (IFGs) are generalizations of fuzzy graphs, in which each vertex is allocated an ordered pair whose first coordinate represents the membership value and whose second coordinate gives the non-membership value. Sombor indices are recently invented indices and are prime indices in describing the topology of a graph. They have demonstrated strong prediction ability in mathematical chemistry. The main aim of this research draft is to define two milestones, the fifth and sixth versions of Sombor indices in an intuitionistic fuzzy environment, IFGs are much more generalized and universal as compared to crisp graph theory, so we converted these two topological indices in this environment and then formulae for some fundamental families of graphs such as path graph, cycle graph, complete graph etc. are being derived. Our manuscript presents a novel application of opening a chain of schools of a popular brand in a certain vicinity, including the cluster center of the chain and applying intuitionistic fuzzy-based topological indices to assess their performance. With the help of this application, we highlight the practical implications and benefits of employing intuitionistic fuzzy-based techniques on the performance of schools through a comparative analysis. We checked the importance of intuitionistic fuzzy Sombor indices by presenting the application and concluded these indices can be applied to decision-making problems. With the help of the application, the efficiency of both of the intuitionistic fuzzy Sombor indices is also characterized, which must be a future efficacious tool in decision-making issues.

A note on Huppert's theorem and Chen's theorem

Let G be a finite group. We prove that every maximal subgroup of G has prime index if and only if every maximal subgroup of G that contains the normalizer of some Sylow subgroup has prime index, which implies that the hypothesis in Huppert's theorem and the hypothesis in Chen's theorem are actually equivalent. Moreover, we prove that the hypothesis in a theorem of Shao and Beltrán and the hypothesis in a theorem of Li et al. are also equivalent.

Graceful Labeling of Prime Index Graph of Group Zp × Zpn

The prime index graph π(G) of a finite group G is a special type of undirected simple graph whose vertex set is set of subgroups of G, in which two distinct vertices are adjacent if one has prime index in the other. Let p and q be distinct primes. In this paper, we establish that prime index graph of a finite cyclic p-group Zpn, a finite abelian group Zpn × Zq and a finite abelian p-group Zp × Zpn always have graceful labeling without any condition on n using the concept of path graph or p-layer ladder graph of size n + 1.

Evaluation and analysis of India's energy security: A policy perspective

This research aims to determine the prime energy security criteria and indices in the case of India. The energy security indices are determined through literature review and energy portfolio experts. This study explores five new perspectives about India's energy security; energy flow risk, operational risk, financial risk, strategic risk, and environmental risk. The study uses integrated methodology hesitant fuzzy set and regret set theory for energy security indices evaluation and selection. This integrated approach emphasizes the psychological characteristics of experts and the variation in decision making. The study reveals that Government has to focus on alternative fuel selection (wj = 0.1077), geopolitical risk (wj = 0.1042), and less capacity of strategic reservoir (wj = 0.0987). Further, the results show that for long term energy security India have to focus on the strategic risk; policies formulation for new fuels, more strategic reservoir, and diversity their energy sources.

A note on finite groups in which every non-nilpotent maximal subgroup has prime index

Let [Formula: see text] be a finite group in which every non-nilpotent maximal subgroup has prime index and [Formula: see text] the largest prime divisor of [Formula: see text], without using the solvability of [Formula: see text] we prove that either the Sylow [Formula: see text]-subgroup of [Formula: see text] is normal or [Formula: see text] has a normal [Formula: see text]-complement.

Effect of weak alternating magnetic fields on neutrophilic granulocytes. An analytical review

The article discusses the main achievements in recent years in studying the biological effects of weak and superweak low-frequency magnetic fields, either variable or combined with constant ones. Considered are neutrophil granulocytes activated by chemical stimulants or intact when the magnetic fields affect isolated cells, blood, and whole organisms. The methods include recording changes in ROS concentration levels (the most noticeable effect of exposure to a weak magnetic field), priming index, calcium homeostasis, proliferative activity, immune status, as well as the influence of various chemical agents on these indicators. The leading methods in this field are fluorescence spectrometry and chemiluminescence analysis. The experimental results indicate the biological effectiveness of this physical factor, the specific effect of which depends on the type of biosystem, its functional status, the environment, and the parameters of the fields themselves. The data obtained can have applied significance in magnetotherapy, immune response optimization in various diseases, acceleration of tissue regeneration and repair, and increasing the body's resistance to infections. They also can have academic significance since they help to identify the primary field acceptors and magnetic targets and their localization in the cell, study relationships with signal cascades, build models of biological signal amplification pathways, and find biologically significant frequencies and field amplitudes.

Prime index elements graph of a group

For a group G, we define the (directed and undirected) prime index elements graph of G. We study some interplay between the algebraic properties of a group and the graph theoretic properties of its (directed and undirected) prime index elements graphs. Also we describe some relationships of this graph with the power graph and the reduced power graph of a group.

The changing economic relationship between some of the major COVID-19 impacted countries with prominent wealth: a comparative study from the view point of stock markets.

In the present work, a study has been made over the prime stock indices of some fiscally prominent countries impacted by COVID-19. The countries are separated in two ways: (1) considering gross total number of infected cases—here seven mostly impacted countries with certain global economic influence are selected; (2) considering the concentration of the infected cases—here six major impacted countries with considerable influence are selected. This sort of categorization is itself a novel strategy which is capable of including some less populated, but severely impacted countries of economic importance. The objective of the present analysis is to comprehend the impact of COVID-19 on these markets and to recognize the effect of COVID-19 on mutual association and dependence between these markets. To add more flavour of reliability, we have taken a new and fresh strategy of fixing the time frames under consideration before and during COVID-19 pandemic as uniform. We have used both linear and nonlinear Granger causality analysis and employed generalized forecast error variance decomposition analysis to review the exogeneity and endogeneity of the individual markets. The present study shows that this pandemic has changed the underlying relationship: some exogenous stock markets have become endogenous and vice versa in the pandemic. Linear relationship has been reduced radically, whereas nonlinear relationship has been improved during the COVID-affected period. TASE, the highest returned and significantly uncorrelated index, emerged as the most exogenous market in the pre-COVID period, though it is nonlinearly endogenous in the long term, in the COVD-affected period. CAC 40 is the most endogenous market for the short term in both pre-COVID and COVID-affected period. B3 and NYSE, exogenous in the pre-COVID period, turned out to be linearly endogenous in the COVID-affected duration, whereas BIST 100 and BSE SENSEX are found to be exogenous markets in the COVID-affected period according to both linear and nonlinear causal analysis. They were also exogenous in the pre-COVID era for the short-term period, with BSE SENSEX exhibiting exogeneity anti-persistently for the COVID-affected period too. Association among the markets is more in long term rather than short term. A possible conclusion is also that the markets may regain long-term association once the effect of COVID would fade away.

Research on Medical Multi-Source Data Fusion Based on Big Data

Objectives: The uniform data standard system is built to realize the interconnection between the heterogenous information systems in hospitals and to solve the problem of data island. Methods: The establishment of the integration platform is started from the aspects such as establishment of integration platform model, design of platform architecture and data interaction process, promotion of standardization of the data format and prime index construction for patients. Results: The ESB (Enterprise Service Bus) and the SOA (Service Oriented Architecture) are used to achieve the medical multi-source data fusion through the integration platform with two interface methods of MQ (Message Queue) and Web Service. Conclusion: The intelligent decision support system established on the integration platform is used to provide powerful data support to improve data utilization, regulate medical behaviors, advance medical quality and enhance management efficiency.

Some generalizations of Shao and Beltrán’s theorem

Let G and A be finite groups of relative coprime orders and A act on G via automorphisms. In this paper, we prove that when every maximal A-invariant subgroup of G that contains the normalizer of some Sylow subgroup has prime index, then G is supersolvable; if every non-nilpotent maximal A-invariant subgroup of G has prime index or is normal in G, then G is a Sylow tower group.

Sex Moderates The Associations Of Accelerometer-measured Physical Activity Intensity To Executive Functions Among Older Adolescents

Physical activity (PA) of sufficient intensity to improve aerobic fitness is associated with enhanced executive functions (EFs) in preadolescents. However, the relationship between PA intensity and EFs among older adolescents and the effect of sex on these associations remain poorly understood. PURPOSE: To examine the moderating effects of sex on the relationship between accelerometer-measured PA (volume, intensity) and EFs (inhibitory control, working memory) in 15-18 years old adolescents. METHODS: We analyzed baseline data from 417 participants (210 [50%] females, Mage = 16.5 ± 0.40 yrs, BMI = 23.2 ± 4.30 kg/m2) from the Burn 2 Learn cluster randomized controlled trial. Adolescents wore Actigraph GT9X Link accelerometers on their non-dominant wrist for 7 days, 24-h·d-1. Accelerometer metrics included average raw accelerations over 5 s epochs (AvgAcc), intensity gradient (IG; the slope of the log-log regression line of intensity over time; higher IG indicates higher intensity), and moderate-to-vigorous PA (MVPA) using Hildebrand youth cut-points. Inhibitory control was expressed as accuracy, reaction time (RT), and variability of the RT (standard deviation; SDRT) on incongruent trials of a modified Eriksen flanker task. Working memory (WM) was expressed as a d prime (d’) index on the 2-back task (z-scoretarget accuracy - z-scorefalse alarms). Multi-level random intercept models, accounting for clustering within schools, were used to test the moderating effects of sex on the PA-EF relationship, adjusting for age, BMI, and aerobic fitness. RESULTS: Sex moderated the relationship between IG and incongruent SDRT (b = 0.16, 95% CI: 0.04, 0.28, P = 0.01), and IG and the d’ index (b = -0.29, 95% CI: -0.47, -0.11, P = 0.002) even after controlling for AvgAcc. Girls with higher IG showed less variability in incongruent RT (b = -0.16, 95% CI: -0.25, -0.06; boys: Ps ≥ 0.68) and higher d’ index (b = 0.25, 95% CI: 0.11, 0.40; boys: Ps ≥ 0.21). In contrast, AvgAcc was not related to inhibitory control (Ps ≥ 0.06) or WM (Ps ≥ 0.21) after adjusting for IG. MVPA was not related to inhibitory control or WM (Ps ≥ 0.20). CONCLUSIONS: Our findings reveal a novel selective association between PA intensity and EFs among older adolescent girls. Girls with higher intensity profiles showed superior performance across two EF tasks.

Subnormal subgroups and self-invariant maximal subfields in division rings

A maximal subfield of a division ring is said to be self-invariant if it is its own normalizer. Subfields of this kind are important because they have a strong connection with Albert's conjecture on the cyclicity of division rings of prime index. We show that every maximal subfield of the Mal'cev-Neumann division ring, which is of infinite dimension, is self-invariant. We also apply the Mal'cev-Neumann structure to refute the conjecture that every noncentral subnormal subgroup of the multiplicative group of a division ring must contain a noncentral normal subgroup. Finally, among other things, we rely on self-invariant subfields to present a criterion for a division ring to have a finite-dimensional subdivision rings.

An Inquiry into the Persistence of Holiday Effect on Stock Markets in India: Insights and Perspectives on a Seasonal Anomaly

Asset pricing is a key area of literature in analysing and evaluating the stock market efficiency. Though various pricing models made efforts to explain the behaviour of the stocks, the existence of seasonal anomalies in the stock markets creates an opportunity for the investors to generate abnormal returns. The present article emphasizes one of such market anomalies namely, the holiday effect using indices belonging to Indian stock exchanges. Thorough research is performed by including all the prime market-capital and sectoral indices of the National Stock Exchange and the Bombay Stock Exchange. The ARIMAX methodology is adopted to observe the anomaly by considering exogenous variables representing the trading days before the exchange-mandated holidays. Further, the strength of the anomaly is analysed with the incorporation of various stock market reforms and observed to be significantly persistent among most of the Indian market indices (including both the sectoral and the market-capital based indices).

Temporal variation of solar flare index during solar cycles 21 − 24

The present investigation attempts to quantify the temporal variation of Solar Flare Index (SFI) with other activity indices during solar cycles 21 – 24 by using different techniques such as linear regression, correlation, cross-correlation with phase lag-lead, etc. Different Solar Activity Indices (SAI) considered in this present study are Sunspot Number (SSN), 10.7 cm Solar Radio Flux (F10.7), Coronal Index (CI) and MgII Core-to-Wing Ratio (MgII). The maximum cycle amplitude of SFI and considered SAI has a decreasing trend from solar cycle 22, and cycle 24 is the weakest solar cycle among all other cycles. The SFI with SSN, F10.7, CI and MgII shows hysteresis during all cycles except for solar cycle 22 where both paths for ascending and descending phases are intercepting each other, thereby representing a phase reversal. A positive hysteresis circulation exists between SFI and considered SAI during solar cycles 22 and 23, whereas a negative circulation exists in cycles 21 and 24. SFI has a high positive correlation with coefficient values of 0.92, 0.94, 0.84 and 0.81 for SSN, F10.7, CI and MgII respectively. According to cross-correlation analysis, SFI has a phase lag with considered SAI during an odd-number solar cycle (solar cycles 21 and 23) but no phase lag/lead during an even-numbered solar cycle (solar cycles 22 and 24). However, the entire smoothed monthly average SFI data indicate an in-phase relationship with SSN, F10.7 and MgII, and a one-month phase lag with CI. The presence of those above characteristics strongly confirms the outcomes of different research work with various solar indices and the highest correlation exists between SFI and SSN as well as F10.7 which establishes that SFI may be considered as one of the prime activity indices to interpret the characteristics of the Sun’s active region as well as for more accurate short-range or long-range forecasting of solar events.

The utility of ISSRs for the identification of interspecific hybrids between pearl millet (Pennisetum glaucum [L.] R.Br.) × napier grass (Pennisetum purpureum Schumach)

AbstractInterspecific hybrids between pearl millet (Pennisetum glaucum) and napier grass (Pennisetum purpureum) give rise to perennial fodder crops characterized by high biomass, broad clumps and good palatability. These hybrids are triploid and developed by hand pollination of napier grass pollen on pearl millet panicles. The progeny shows a high percentage of pearl millet genotype due to self-pollination in the female parent. Identification of hybrids at a young stage based on morphological characters is difficult. DNA-based molecular markers have high discriminating power and were used to assess genetic differences between hybrids and their parents. Genetic diversity was studied in 18 pearl millet × napier grass hybrids along with their parents and two released national checks using inter simple sequence repeat (ISSR) markers. Eight ISSR primers gave rise to 125 bands, of which 120 bands were polymorphic. Polymorphic information content and ISSR primer index ranged from 0.40 to 0.49 and 8.88 to 11.14, respectively. The hybrids showed the presence of unique bands, besides those shared with male and female parents. Female (pearl millet) parents formed a separate group in the dendrogram constructed based on ISSR polymorphism. The male (napier grass) parents formed a separate group along with hybrids, indicating a higher similarity of hybrids with the male parents. Principal component analysis and STRUCTURE analyses showed a similar grouping. The close resemblance of hybrids to the male parents confirmed their interspecific origin. The study revealed that ISSR marker analysis could be a quick and reliable method to identify interspecific hybrids at an early stage of growth.

Basic results on an unsolved problem about factorization of finite groups

We deal with an unsolved problem in group theory (question 19.35 of Kourovka Notebook). It asks whether, given a finite group G and a factorization one can always find subsets such that and The case k = 2 is of special interest. We prove that the answer is positive for all finite supersolvable (and so abelian) groups. However, G. Bergman has recently given a counterexample to the question for the case k = 3. Regarding the special case k = 2, at first, we prove that the statement is true for all finite solvable groups, and groups such that for every divisor d of their order, there is a subgroup of order or index d. Thereafter, by proving an extension theorem we show that the answer is positive if it is true for all simple groups with no subgroup of prime index. Also, we give some other theorems and criteria, for checking the property and state a question about some candidates for probable counterexamples. We end by noting some related connections, questions and problems about the topic.

Biological parameters and current status of European eel (Anguilla anguillaLinnaeus, 1758) from Asi River, Northeastern Mediterranean region, Turkey

The biological characteristics of eels from the Asi River, Turkey, were assessed between December 2017 and November 2018. Eels were sampled monthly using fyke nets (operated by professional fishermen), yielding a total of 509 specimens. Total length and weight were measured, sex, age and maturity stages (silver or yellow eel) were determined. Catch Per Unit Effort (CPUE) was calculated for both biomass per unit effort and numbers caught on a monthly and annual basis. The length-weight relationships (LWRs) of silver and yellow eel was W = 0.009*TL3.22 (n = 262) and W = 0.0106*L3.09 (n = 247), respectively. The age of the sampled fish ranged from year class II to VI. Von Bertalanffy growth parameters were estimated as L∞=69.25 cm, K = 0.43 1/year, t0= −0.41 and phi prime index (ǿ)= 3.31 for all samples. The overall eel fishing mortality rate (F) was 0.31 year-1, and the exploitation and survival rates of silver stage eels were estimated with 30% and 39%, respectively.