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In this work, we introduce a new concept called the tripotent divisor graph of a commutative ring. It is defined with vertices set in a ring R, where distinct vertices r1 and r2 are connected by an edge if their product belongs to the set of all nonunite tripotent in R. We denote this graph as 3I ΓR. We utilize this graph to examine the role of tripotent elements in the structure of rings. Additionally, we provide various findings regarding graph-theoretic characteristics of this graph, including its diameter, vertex degrees, and girth. Furthermore, we investigate the size, central vertices, and distances between vertices for the tripotent divisor graph formed by the direct product of two fields.

Salma M S Ahmad, Hanan Nazar, Md Mizanur Rahman, Radoslaw Stefan Rusyniak, Allal Ouhtit Biological Sciences Program, Department of Biological and Environmental Sciences, College of Arts and Science, Qatar University, Doha, QatarCorrespondence: Allal Ouhtit, Department of Biological and Environmental Sciences, College of Arts and Science, Qatar University, PO Box 2713, Doha, Qatar, Tel +974 4403-7572, Email aouhtit@qu.edu.qaAbstract: Breast cancer (BC) is the most common malignancy worldwide and has a poor prognosis, because it begins in the breast and disseminates to lymph nodes and distant organs. While invading, BC cells acquire aggressive characteristics from the tumor microenvironment through several mechanisms. Thus, understanding the mechanisms underlying the process of BC cell invasion can pave the way towards the development of targeted therapeutics focused on metastasis. We have previously reported that the activation of CD44 receptor with its major ligand hyaluronan (HA) promotes BC metastasis to the liver in vivo. Next, a gene expression profiling microarray analysis was conducted to identify and validate CD44-downstream transcriptional targets mediating its pro-metastatic function from RNA samples collected from Tet CD44-induced versus control MCF7-B5 cells. We have already validated a number of novel CD44-target genes and published their underlying signaling pathways in promoting BC cell invasion. From the same microarray analysis, Integrin subunit beta 1 binding protein 1 (ITGB1BP1) was also identified as a potential CD44-target gene that was upregulated (2-fold) upon HA activation of CD44. This report will review the lines of evidence collected from the literature to support our hypothesis, and further discuss the possible mechanisms linking HA activation of CD44 to its novel potential transcriptional target ITGB1BP1.Keywords: ITGB1BP1, Breast cancer, CD44, Hyaluronan, metastasis

The idempotent divisor graph of a commutative ring R is a graph with vertices set in R* = R-{0}, and any distinct vertices x and y are adjacent if and only if x.y = e, for some non-unit idempotent element e2 = e ? R, and is denoted by ?(R). The purpose of this work is using some properties of ring theory and graph theory to find the clique number, the chromatic number and the region chromatic number for every planar idempotent divisor graphs of commutative rings. Also we show the clique number is equal to the chromatic number for any planar idempotent divisor graph. Among other results we prove that: Let Fq, Fpa are fieldes of orders q and pa respectively, where q=2 or 3, p is a prime number and a Is a positive integer. If a ring R @ Fq x Fpa . Then (?(R))= (?(R)) = *( ?(R)) = 3.

In this work, we study zero-divisor graph of the ring Zpmq2 and give some properties of this graph. Furthermore we find Hosoya polynomial and Wiener index for this graph.

Deviations are the difference between the planning budget and the actual for financial periods and specific financial accounts, and it is the tool that management uses it to control and to know the reality of achieving pre-set plans. The success of the budget and its positive deviation is evidence of achieving the institution’s financial goals, and the negative deviation of the budget is evidence of the failure to achieve the budget, and then the administration must identify the causes of the deviation and address it. The research aims to analyze the results of the balance sheet budget and comparing them with the actual results, and determine the deviations if they are negative or positive for a sample of Iraqi private banks that are Consisting of (Islamic banks and commercial banks). In addition, the study sample consisted of Baghdad Bank, the Middle East Bank, Iraqi Islamic Bank, and National Islamic Bank for the fiscal years 2016 and 2017, as these institutions were chosen because they published discretionary budgets in their financial statements. Furthermore, the SPSS statistical tool was used in the study to analyze the deviation data. Islamic banks are better than commercial banks in terms of the rate of implementation of planning budgets since the majority of their statistical results are positive, which was one of the researchers’ most important findings.

Hamde Nazar,1 Gregory Maniatopoulos,2 Efi Mantzourani,3 Neil Watson41School of Pharmacy, Newcastle University, Newcastle upon Tyne, UK; 2Institute of Health and Society, Newcastle University, Newcastle upon Tyne, UK; 3School of Pharmacy and Pharmaceutical Sciences, Cardiff University, Cardiff, Wales, UK; 4Pharmacy Services, Royal Victoria Infirmary NHS Hospital Trust, Newcastle upon Tyne, UK An emerging clinical role for community pharmacists is to become actively involved in the follow-up care of patients who are discharged back into the community (transfer of care services) by promoting better medication adherence and by contributing to the safe, effective, and efficient use of medication.1 Recent research highlights how this extended role of community pharmacists could help to reduce drug-related adverse events, unnecessary health provider visits, hospitalizations, and readmissions while strengthening integrated primary care delivery across the healthcare system.1,2

In this paper, we consider the crossing number and the chromatic number of the zero divisor graph Γ(Z_(2^2 p)) to show that this type of zero divisor graphs is bipartite graph, and the smallest cycle in Γ(Z_(2^2 p)) is of length four this implies that the girth is equal four.

In this paper we construct a star zero divisor graph from the zero divisor graph of the ring Zqp. The star zero divisor graph is obtained by removing some vertices from the zero divisor graph Γ(Zqp), in different ways , but the best way to get star zero divisor graph SΓ(Zqp) is by removing an odd number of zero divisors. Finally the crossing number, the girth and the diameter of this graph is also determined.

Hamde Nazar,1 Mahdi Nazar,2 Charlotte Rothwell,1 Jane Portlock,3 Andrew Chaytor,1 Andrew Husband1 1School of Medicine, Pharmacy and Health, Durham University, UK; 2Cumberland Infirmary, North Cumbria University Hospitals NHS Trust, UK; 3School of Pharmacy and Biomedical Sciences, University of Portsmouth, UK Abstract: Prescribing is a characteristic role of a medical practitioner. On graduating from medical school, students are presumed to have acquired the necessary pharmacology knowledge underpinning the therapeutics and developed their personal skills and behaviors in order to write a safe and effective prescription (The Four Ps). However, there are reports of errors in medical prescribing and dissatisfied feedback from recent graduates, which evidence potential flaws in the current training in the practice of prescribing. We examine the Four Ps from a systems approach and offer scope for educators and curriculum designers to review and reflect on their current undergraduate teaching, learning, and assessment strategies in a similar manner. We also adopt a national framework of common competencies required of all prescribers to remain effective and safe in their area of practice as a more objective layer to the broader learning outcomes of the General Medical Council Tomorrow's Doctors 2009. This exercise demonstrates where standard, recognized competencies for safe prescribing can be accommodated pedagogically within existing medical curricula.Keywords: prescribing, medical curriculum, clinical pharmacology teaching, therapeutics, education

For each commutative ring we associate a graph

Shortage of irrigation water at critical growth stages of maize is limiting its production worldwide. Breeding drought-tolerant cultivars is one possible solution while identification of potential genotypes is crucial for genetic improvement. To assess genetic variation for seedling-stage drought tolerance, we tested 40 inbred lines in a completely randomized design under glasshouse conditions. From these, two contrasting inbred lines were used to develop six basic generations (P1, P2, F1, F2, BC1F1, BC2F2). These populations were then evaluated in a triplicated factorial randomized complete block design under non-stressed and drought-stressed conditions. For statistical analyses, a nested block design was employed to ignore the replication effects. Significant differences (p≤0.01) were recorded among the genotypes for investigated seedling-traits. Absolute values of fresh root length, fresh root weight, and dry root weight lead to select two genotypes, one tolerant (WFTMS) and one susceptible (Q66). Estimates of heritability, genetic advance, and genotypic correlation coefficients were higher and significant for most of the seedling-traits. Generation variance analysis revealed additive gene action. Narrow-sense heritability [F2 ≥ 65; F∞ ≥ 79] revealed the same results. Generation mean analysis signified additive genetic effects in the inheritance of cob girth, non-additive for plant height, grains per ear row and grain yield per plant, and environmental for ear leaf area, cob length, grain rows per ear, biomass per plant, and 100-grain weight under drought-stressed conditions. For conferring drought-tolerance in maize, breeders can adopt the recombinant breeding strategy to pyramid the desirable genes.

In the present investigation, we report a new one phase, one pot method for synthesis of 3.5 ± 0.7 nm average sized gelatin capped gold nano particles (Gel-AuNPs) using strong reductant NaBH4 in aqueous system at room temperature. Size controlled Gel-AuNPs were characterized by UV-Visible, STEM, XRD, DLS and FT-IR. Spherical Gel-AuNPs showed excellent catalytic activity for reduction of three differently charged dyes eosin B (EB), methylene blue (MB) and rose bengal (RB) in the presence of NaBH4. The study revealed that 100% reduction of EB, MB and RB dyes was carried out in just 150 sec. The developed catalyst was easy to recover and capable to be reused three times. The process of reduction rate and kinetics of dyes was monitored using UV-Visible spectrophotometer. A plot of lnC Vs time (sec) showed that reaction follows the first order kinetics. Rate constant (K) was determined for EB, MB and RB reduction at 10 μM, which was found as 2.735 x10-2 sec-1, 2.738 x 10-2 sec-1 and 2.55 x 10-2 sec-1, respectively. The study revealed that catalytic reduction of dyes by Gel-AuNPs in aqueous medium is environmental friendly in terms of recovery of catalyst, is exceptionally fast and hence extremely economical.

This paper discusses steady state analysis and performance characteristics of three-phase self excited induction generators operating in parallel arvd supplying a balanced load. It is shown that induction machines with similar or different parameters and speeds can be operated in parallel and their steady state performance characteristics can be accurately predicted using the proposed method. The performance characteristics of such machines are influenced by the excitation capacitance, load resistance as well as speeds and parameters of the individual machines. Typical cases have been investigated for a number of test machines operating in parallel. Predictions of the proposed method have been verified experimentally.

The aim of this outline is to investigate the consequences of viscous dissipative self-gravitational collapse in non-static spherically symmetric geometry by adopting a Misner-Sharp approach in the context of f(R) metric formalism. In this outline, we propose a viable f(R) model for the physical significance of a self-gravitating system. We determine the junction conditions between interior and exterior space-times. Furthermore, we extend our work for the dissipative dark source case in both forms of heat transformation and free radiation streaming. Finally, the dissipative variables such as heat flux, bulk, and shear viscosity are evaluated in the dynamical equation and then coupled with full causal transport equations in the background of the Israel-Stewart notion. The present analysis discusses the whole study of self-gravitational collapse and recognizes the form of a reduced collapse due to decreasing gravitational mass density, which depends on thermodynamical collapsing variables. Key words: self-gravitating system, dynamical equations, transport equations, f(R) gravity model. Notre but est l'examen des consequences de l'effondrement autogravitationnel dissipatif et visqueux dans une geometrie spheriquement symetrique en adoptant l'approche de Misner-Sharp dans le contexte d'une formalisme metrique f(R). De facon plus precise, nous proposons un modele f(R) viable pour decrire physiquement le systeme autogravitationnel. Nous determinons les conditions de jonction entre les espaces-temps interieur et exterieur. Nous etendons aussi notre etude au cas d'une source sombre dissipative sous les deux formes, de transformation de chaleur et de diffusion libre de radiation en continu. Les equations dynamiques permettent d'evaluer les variables dissipatives, comme le flux d'energie, la viscosite volumique et de cisaillement, couplees ensuite avec les equations causales de transport suivant l'approche d'Israel-Stewart. Notre analyse discute l'ensemble de l'effondrement autogravitant, reconnu comme un effondrement reduit suite a la diminution de la densite de masse gravitationnelle qui depend des variables thermodynamiques d'effondrement. [Traduit par la Redaction] Mots-cles: systeme autogravitant, equations dynamiques, equations de transport, modele de gravite f(R)., 1. Introduction Currently, the theory of general relativity has an immense impact on astronomical, self-gravitational, cosmological, and relativistic physics. Current astrophysical observations such as type Ia supernovae and their cross-association [...]

In this work, we introduce a new concept called the tripotent divisor graph of a commutative ring. It is defined with vertices set in a ring R, where distinct vertices r1 and r2 are connected by an edge if their product belongs to the set of all nonunite tripotent in R. We denote this graph as 3I Γ(R). We utilize this graph to examine the role of tripotent elements in the structure of rings. Additionally, we provide various findings regarding graph‐theoretic characteristics of this graph, including its diameter, vertex degrees, and girth. Furthermore, we investigate the size, central vertices, and distances between vertices for the tripotent divisor graph formed by the direct product of two fields. [ABSTRACT FROM AUTHOR]

Background and objective: Lymphovascular invasion (LVI) is a significant histopathological feature in prostate cancer (PCa) associated with higher risk of biochemical recurrence (BCR) and other adverse outcomes. Our aim was to assess the association of LVI found in radical prostatectomy (RP) specimens with BCR and adverse clinicopathological findings. Methods: A systematic literature search was conducted using the PubMed, Embase, and Web of Science databases in July 2023, with an additional search in May 2024. We included 94 prospective and retrospective studies reporting on LVI in RP specimens and its association with the specified outcomes. Key findings and limitations: Meta-analyses revealed that LVI is significantly associated with higher BCR risk (hazard ratio 1.96, 95% confidence interval [CI] 1.73–2.21), higher pathological tumour stage (odds ratio [OR] 5.77; 95% CI 3.96–8.40), higher Gleason score (OR 5.19, 95% CI 4.12–6.54), lymph node metastasis (OR 11.52, 95% CI 7.65–17.34), distant metastasis (OR 9.10, 95% CI 5.46–15.17), positive surgical margins (OR 2.38, 95% CI 1.83–3.09), extraprostatic extension (OR 5.01, 95% CI 3.11–8.06), seminal vesicle invasion (OR 7.50, 95% CI 3.47–16.23), and perineural invasion (OR 133.71, 95% CI 65.93–271.15). Major limitations of this study include high heterogeneity of the data and the reliance on nonrandomised studies. Conclusions and clinical implications: Our findings reveal that LVI is associated with nearly twofold higher risk of BCR, highlighting its potential role as a critical prognostic marker. Patient summary: We analysed data from multiple studies to understand the impact of the spread of prostate cancer into the lymph or blood vessels, called lymphovascular invasion (LVI). We found that LVI is linked to a higher risk of cancer recurrence after surgery and other negative outcomes. Our findings highlight the importance of considering LVI in treatment decisions for better management of prostate cancer.

A ring R is considered a strongly 2-nil clean ring, or (strongly 2-NC ring for short), if each element in R can be expressed as the sum of a nilpotent and two idempotents that commute with each other. In this paper, further properties of strongly 2-NC rings are given. Furthermore, we introduce and explore a special type of strongly 2-NC ring where every unit is of order 2, which we refer to as a strongly 2-NC rings with U(R) = 2. It was proved that the Jacobson radical over a strongly 2-NC ring is a nil ideal, here, we demonstrated that the Jacobson radical over strongly 2-NC ring with U(R) = 2 is a nil ideal of characteristic 4. We compare this ring with other rings, since every SNC ring is strongly 2-NC, but not every unit of order 2, and if R is a strongly 2-NC with U(R) = 2, then R need not be SNC ring. In order to get N il(R) = 0, we added one more condition involving this ring. [ABSTRACT FROM AUTHOR]

The sine cosine algorithm (SCA), a recently discovered population-based optimization technique, is used to resolve optimization issues. In this research, the study proposes employing the LWSCA (Locally Weighted Sine Cosine Algorithm) as a hybrid approach to enhance the performance of the original SCA (Sine Cosine Algorithm) and mitigate its limitations. These limitations encompass restricted resolution, slow convergence rates, and difficulties in achieving global optimization when dealing with complex, multi-dimensional spaces. The fundamental idea underlying LWSCA is to incorporate the SCA algorithm with the locally weighted (LW) technique and mutation diagram. The hybridization process has two stages: An algorithm is initially changed by altering the fundamental equations to ensure greater effectiveness and accuracy. The second point is that when the LW local approach is used to create a new dependent site, it increases the randomness during the search process. This, in turn, raises the population variance of the optimizer being proposed, ultimately enhancing the overall effectiveness of the global search. The putative method's hybrid architecture is anticipated to significantly increase the potential for exploration and exploitation. By evaluating SCA's performance against IEEE CEC 2017 functions and contrasting it with a variety of different metaheuristic techniques, the usefulness of SCA is investigated. According to the experimental data gathered, the LWSCA's convergence, exploration, and exploitation tendencies have all greatly improved. According to the results, the suggested LWSCA method is a good one that performs better than SCA and other rival algorithms in most functions.