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Block circulant MDS matrices are used in the design of linear diffusion layers for lightweight cryptographic applications. Most of the work on construction of block circulant MDS matrices focused either on finite fields or $ GL(m, \mathbb{F}_2) $. The main objective of this paper is to extend the above study of block circulant MDS matrices to finite commutative rings. Additionally, we examine the behavior of the XOR count distribution under different reducible polynomials of equal degree over $ \mathbb{F}_2 $. We show that the determinant of a block circulant matrix over a ring can be expressed in a simple form. We construct $ 4 \times 4 $ and $ 8 \times 8 $ block circulant matrices over a ring. Furthermore, for non-negative integer $ l $, we identify the conditions under which a ring $ \mathfrak{R}_l = \frac{\mathbb{F}_2[x]}{\langle (f(x))^{2^l} \rangle} $, contains a finite field of order $ 2^m $, where $ f(x) $ is an irreducible polynomial of degree $ m $. To facilitate efficient implementation, we analyze XOR distributions within specific rings, such as $ R_1 = \frac{\mathbb{F}_2[x]}{\langle (1+x^2+x^6) \rangle} $ and $ R_2 = \frac{\mathbb{F}_2[x]}{\langle (1+x^4+x^6) \rangle} $. Our calculations reveal distinct XOR distributions when utilizing two reducible polynomials of equal degree, with XOR count distributions 776 and 764, respectively. However, when using irreducible polynomials of the same degree, the XOR count distributions remain the same. This difference is advantageous for applications in lightweight cryptography.

This paper deals with some identities on Banach $ ^* $-algebras that are equipped with linear generalized derivations. As an application of one of our results, we describe the structure of the underlying algebras. Precisely, we prove that for a linear generalized derivation $ F $ on a Banach $ ^* $-algebra $ A $, either we obtain the existence of a central idempotent element $ e\in Q $, for which $ F = 0 $ on $ eQ $ and $ (1-e)Q $ satisfies $ s_{4} $, or the set of elements $ u\in A $ such that the identity $ [F(u)^n, F(u^*)^nF(u)^n]\in Z(A) $ holds for no positive integer $ n $ turns out to be dense. In addition to this we consider an identity satisfied by a semisimple Banach $ ^* $-algebra and look for its commutativity. Moreover, some related results are also established.

Abstract The potential of solid waste as an energy source is clear, owing to its wide availability and renewable properties, which provide a critical answer for energy security. This can be especially effective in reducing the environmental impact of fossil fuels. Countries that rely heavily on coal should examine alternatives such as electricity from solid waste to provide a constant energy supply while also contributing to atmospheric restoration. In this regards, Low Emissions Analysis Platform (LEAP) is used for simulation the entire energy system in Pakistan and forecasted its capital cost and future CO2 emissions in relation to the use of renewable and fossil fuel resources under the different growth rates of solid waste projects like 20%, 30% and 40% for the study period 2023–2053. The results revealed that, 1402.97 TWh units of energy are generated to meet the total energy demand of 1193.93 TWh until 2053. The share of solid waste based electricity in total energy mix is increasing from a mere 0.81% in 2023 to around 9.44% by 2053 under the 20% growth rate, which then increase to 39.67% by 2053 under the 30% growth rate and further increases to 78.33% by 2053 under the 40% growth rate. It is suggested that 40% growth rate for solid waste based electricity projects is suitable for Pakistan until 2053 because under this condition, renewable sources contributes 95.2% and fossil fuels contributed 4.47% in the total energy mix of Pakistan. Hence, CO2 emissions are reduced from 148.26 million metric tons to 35.46 million metric tons until 2053 but capital cost is increased from 13.23 b$ in 2023 to 363.11 b$ by 2053.

Topological indices are numerical parameters that indicate the topology of graphs or hypergraphs. A hypergraph H=(V(H),E(H)) consists of a vertex set V(H) and an edge set E(H), where each edge e∈E(H) is a subset of V(H) with at least two elements. In this paper, our main aim is to introduce a general hypergraph structure for the prime ideal sum (PIS)- graph of a commutative ring. The prime ideal sum hypergraph of a ring R is a hypergraph whose vertices are all non-trivial ideals of R and a subset of vertices Ei with at least two elements is a hyperedge whenever I+J is a prime ideal of R for each non-trivial ideal I, J in Ei and Ei is maximal with respect to this property. Moreover, we also compute some degree-based topological indices (first and second Zagreb indices, forgotten topological index, harmonic index, Randić index, Sombor index) for these hypergraphs. In particular, we describe some degree-based topological indices for the newly defined algebraic hypergraph based on prime ideal sum for Zn where n=pα,pq,p2q,p2q2,pqr,p3q, p2qr,pqrs for the distinct primes p,q,r and s.

Let $ s \geq 1 $ be a fixed integer. In this paper, we focus on generating cyclic codes over the ring $ \mathcal{R}(\alpha_1, \alpha_2, \ldots, \alpha_s) $, where $ \alpha_i \in \mathbb{F}_q\backslash \{0\} $, $ 1 \leq i \leq s $, by using the Gray map that is defined by the idempotents. Moreover, we describe the process to generate an idempotent by using the formula (2.1). As applications, we obtain both optimal and new quantum codes. Additionally, we solve the DNA reversibility problem by introducing $ \mathbb{F}_q $ reversibility. The aim to introduce the $ \mathbb{F}_q $ reversibility is to describe IUPAC nucleotide codes, and consequently, 5 IUPAC DNA bases are considered instead of 4 DNA bases $ (A, \; T, \; G, \; C) $.

This paper focuses on examining a new type of n-additive map called the symmetric reverse n-derivation. As implied by its name, it combines the ideas of n-additive maps and reverse derivations, with a 1-reverse derivation being the ordinary reverse derivation. We explore several findings that expand our knowledge of these maps, particularly their presence in semiprime rings and the way rings respond to specific functional identities involving elements of ideals. Also, we provide examples to help clarify the concept of symmetric reverse n-derivations. This study aims to deepen our understanding of these symmetric maps and their properties within mathematical structures.

For a left module MR over a non-commutative ring R, the notion for the class of nilpotent elements (nilR(M)) was first introduced and studied by Sevviiri and Groenewald in 2014 (Commun. Algebra, 42, 571–577). Moreover, Armendariz and semicommutative modules are generalizations of reduced modules and nilR(M)=0 in the case of reduced modules. Thus, the nilpotent class plays a vital role in these modules. Motivated by this, we present the concept of nil-Armendariz modules as a generalization of reduced modules and a refinement of Armendariz modules, focusing on the class of nilpotent elements. Further, we demonstrate that the quotient module M/N is nil-Armendariz if and only if N is within the nilpotent class of MR. Additionally, we establish that the matrix module Mn(M) is nil-Armendariz over Mn(R) and explore conditions under which nilpotent classes form submodules. Finally, we prove that nil-Armendariz modules remain closed under localization.

Let $ n \geq 1 $ be a fixed integer. Within this study, we present a novel approach for discovering reversible codes over rings, leveraging the concept of $ r $-glifted polynomials. This technique allows us to achieve optimal reversible codes. As we extend our methodology to the domain of DNA codes, we establish a correspondence between $ 4t $-bases of DNA and elements within the ring $ R_{2t} = F_{4^{2t}}[u]/(u^{2}-1) $. By employing a variant of $ r $-glifted polynomials, we successfully address the challenges of reversibility and complementarity in DNA codes over this specific ring. Moreover, we are able to generate reversible and reversible-complement DNA codes that transcend the limitations of being linear cyclic codes generated by a factor of $ x^n-1 $.

Let $ \mathfrak{S} $ be a ring. The main objective of this paper is to analyze the structure of quotient rings, which are represented as $ \mathfrak{S}/\mathfrak{P} $, where $ \mathfrak{S} $ is an arbitrary ring and $ \mathfrak{P} $ is a prime ideal of $ \mathfrak{S} $. The paper aims to establish a link between the structure of these rings and the behaviour of traces of symmetric $ n $-derivations satisfying some algebraic identities involving prime ideals of an arbitrary ring $ \mathfrak{S} $. Moreover, as an application of the main result, we investigate the structure of the quotient ring $ \mathfrak{S}/\mathfrak{P} $ and traces of symmetric $ n $-derivations.

Orb web spiders are common and highly diversified animals found in almost all habitats. They have remarkable plasticity against biotic and abiotic factors, making them excellent indicators of environmental health. The web creation behavior of spiders is influenced by disturbances in the environment. The aim of this research was to observe the alteration in the web-building behavior of Neoscona vigilans caused by human activities, specifically traffic disturbances. Spider webs were located and photographed at nighttime along the roadside, and their web characteristics were calculated. Spiders were captured from webs for their body measurements. Spider fourth leg length, carapace width, and body length had a significant association with web size and diameter, CTL, capture area, and mesh size. The quantity of trapped prey, the height of the plant, and the foliage radius increased with the distance from the road. Conversely, anchor points and web elevation from the ground dropped. The highest and lowest proportions of anomalies (modifications/defects) were recorded as holes (52.7%) in 105 webs (100%) and supernumerary (0.7%) in 55 webs (52.4%), respectively. Road disturbance had a negative influence on the spider’s behavior as the webs formed in close proximity to the road had a higher frequency of anomalies, with a gradual decrease distantly. We can gain further insight into how different environmental changes, disruptions, and pollutants lead to this imperfection in the otherwise flawless perfect structure of spider webs.

Sharing confidential information is a critical concern in today’s world. Secret sharing schemes facilitate the sharing of secrets in a way that ensures only authorized participants (shareholders) can access the secret using their allocated shares. Hierarchical secret sharing schemes (HSSSs) build upon Shamir’s scheme by organizing participants into different levels based on priority. Within HSSS, participants at each level can reconstruct the secret if a specified number, denoted as the threshold value (t), or more of them are present. Each level has a predetermined threshold value. If the number of participants falls below the threshold at any level, higher-level participants must be involved in reconstructing the secret at lower levels. Our paper proposes schemes that implement hierarchical access structures and enable the sharing of multiple secrets. Additionally, our proposed scheme includes share verification. We have analyzed potential attacks and demonstrated the scheme’s resistance against them. Through security analysis and comparison with existing schemes, we highlight the novelty and superiority of our proposed approach, contributing to advancements in secure information-sharing practices.

Let n and m be fixed positive integers. In this paper, we establish some structural properties of prime rings equipped with higher derivations. Motivated by the works of Herstein and Bell-Daif, we characterize rings with higher derivations D=dii∈N satisfying (i) dnx,dmy∈ZR for all x,y∈R and (ii) dnx,y∈ZR for all x,y∈R.

Let $R$ be a prime ring, $\alpha$ an automorphism of $R$ and $b$ an element of $Q$, the maximal right ring of quotients of $R$. The main purpose of this paper is to characterize skew $b$-derivations in prime rings which satisfy various differential identities. Further, we provide an example to show that the assumed restrictions cannot be relaxed.

Let $ \mathcal{A} $ be a Banach algebra and $ n > 1 $, a fixed integer. The main objective of this paper is to talk about the commutativity of Banach algebras via its projections. Precisely, we prove that if $ \mathcal{A} $ is a prime Banach algebra admitting a continuous projection $ \mathcal{P} $ with image in $ \mathcal{Z}(\mathcal{A}) $ such that $ \mathcal{P}(a^n) = a^n\; \text{for all} \; a \in \mathcal{G} $, the nonvoid open subset of $ \mathcal{A} $, then $ \mathcal{A} $ is commutative and $ \mathcal{P} $ is the identity mapping on $ \mathcal{A} $. Apart from proving some other results, as an application we prove that, a normed algebra is commutative iff the interior of its center is non-empty. Furthermore, we provide some examples to show that the assumed restrictions cannot be relaxed. Finally, we conclude our paper with a direction for further research.

The present paper aims to investigate the containment of nonzero central ideal in a ring $ \mathcal{R} $ when the trace of symmetric $ n $-derivations satisfies some differential identities. Lastly, we prove that in a prime ring $ \mathcal{R} $ of suitable torsion restriction, if $ \mathfrak{D}, \mathcal{G} : \mathcal{R}^n \rightarrow \mathcal{R} $ are two nonzero symmetric $ n $-derivations such that $ \mathcal{f}(\vartheta)\vartheta +\vartheta\mathcal{g}(\vartheta) = 0 $ holds $ \forall \; \vartheta \in \mathcal{W} $, a nonzero left ideal of $ \mathcal{R} $ where $ \mathcal{f} $ and $ \mathcal{g} $ are the traces of $ \mathfrak{D} $ and $ \mathcal{G} $, respectively, then either $ \mathcal{R} $ is commutative or $ \mathcal{G} $ acts as a left $ n $-multiplier. Finally, we characterize symmetric $ n $-derivations in terms of left $ n $-multipliers.

The Government of Pakistan has established clean energy transition goals in the national Alternative and Renewable Energy (ARE) Policy. The goal of this policy is to increase the 30% capacity of green energy in total energy mix by 2030. In this regard, the aim of this study is to develop a de-carbonization plan for achieving net zero emissions through the deployment of a green energy system for the period 2021 to 2040 by incorporating the ARE policy targets. The Low Emissions Analysis Platform (LEAP®) software is used for finding the unidirectional causality among gross domestic product, population within the country, energy demand, renewable energy production and CO2 emissions for Pakistan. The results revealed that energy production of 564.16 TWh is enough to meet the energy demand of 480.10 TWh with CO2 emissions of 22.19 million metric tons, having a population of 242.1 million people and GDP growth rate of 5.8%, in the year 2040 in Pakistan. The share of green energy production is 535.07 TWh, which can be utilized fully for meeting energy demand in the country, and almost zero emissions will produce till 2040. CO2 emissions produced by burning natural gas were 20.64 million metric tons in 2020, which then reduced to 3.25 million metric tons in 2040. CO2 emissions produced by burning furnace oil are also reduced from 4.19 million metric tons in 2020 to 2.06 million metric tons in 2040. CO2 emissions produced by burning coal were 24.85 million metric tons in 2020, which then reduced to 16.88 million metric tons in 2040. Energy demand is directly related to the population and GDP of the country, while renewable utilization is inversely proportional to carbon emissions. The declining trend of carbon emissions in Pakistan would help to achieve net zero emissions targets by mid-century. This technique would bring prosperity in the development of a clean, green and sustainable environment.

Due to the recent climate change, organizations all over the globe are developing plans for reducing carbon emissions by developing clean energy technologies and energy efficient devices. However, the path for transition to green energy system is still unclear and in general, the representation of green energy supply for transition pathways is limited. Therefore, this study outlines a plan for getting Swedish energy sector completely carbon neutral by 2050. The approach can also be applicable to the majority of nations worldwide. Computer based simulations are performed on Energy PLAN software for making clean, green and sustainable energy system that can balance every component of entire energy system during the study period 2022 to 2050. This study takes into account the sustainable use of renewable sources for all economic sectors as well as the interchange of energy with nearby nations under the two scenarios. Additionally, the energy system works in tandem with other industries to create a fully carbon-free environment. The results revealed that, 50% de-carbonization is possible till 2035 and 100% de-carbonization is possible till 2050. This enables a discussion of how ambitious 10-year goals might serve as a first step toward the mid-century elimination of fossil fuels from the energy sector.

Let n≥2 be a fixed integer and A be a C∗-algebra. A permuting n-linear map G:An→A is known to be symmetric generalized n-derivation if there exists a symmetric n-derivation D:An→A such that Gς1,ς2,…,ςiςi′,…,ςn=Gς1,ς2,…,ςi,…,ςnςi′+ςiD(ς1,ς2,…,ςi′,…,ςn) holds ∀ςi,ςi′∈A. In this paper, we investigate the structure of C∗-algebras involving generalized linear n-derivations. Moreover, we describe the forms of traces of linear n-derivations satisfying certain functional identity.

Let n≥1 be a fixed integer. The main objective of this paper is to compute some topological indices and coindices that are related to the graph complement of the prime ideal sum (PIS) graph of Zn, where n=pα,p2q,p2q2,pqr,p3q,p2qr, and pqrs for the different prime integers p,q,r, and s. Moreover, we construct M-polynomials and CoM-polynomials using the PIS-graph structure of Zn to avoid the difficulty of computing the descriptors via formulas directly. Furthermore, we present a geometric comparison for representations of each surface obtained by M-polynomials and CoM-polynomials. Finally, we discuss the applicability of algebraic graphs to chemical graph theory.

Let m and n be fixed positive integers. Suppose that A is a von Neumann algebra with no central summands of type I1, and Lm:A→A is a Lie-type higher derivation. In continuation of the rigorous and versatile framework for investigating the structure and properties of operators on Hilbert spaces, more facts are needed to characterize Lie-type higher derivations of von Neumann algebras with local actions. In the present paper, our main aim is to characterize Lie-type higher derivations on von Neumann algebras and prove that in cases of zero products, there exists an additive higher derivation ϕm:A→A and an additive higher map ζm:A→Z(A), which annihilates every (n−1)th commutator pn(S1,S2,⋯,Sn) with S1S2=0 such that Lm(S)=ϕm(S)+ζm(S)forallS∈A. We also demonstrate that the result holds true for the case of the projection product. Further, we discuss some more related results.

The key motive of this paper is to study symmetric additive mappings and discuss their applications. The study of these symmetric mappings makes it possible to characterize symmetric n-derivations and describe the structure of the quotient ring S/P, where S is any ring and P is a prime ideal of S. The symmetricity of additive mappings allows us to transfer ring theory results to functional analyses, particularly to C∗-algebras. Precisely, we describe the structures of C∗-algebras via symmetric additive mappings.

Alkylating agents pose the biggest threat to the genomic integrity of cells by damaging DNA bases through regular alkylation. Such damages are repaired by several automated types of machinery inside the cell. O6-alkylguanine-DNA alkyltransferase (AGT) is an enzyme that performs the direct repair of an alkylated guanine base by transferring the alkyl group to a cysteine residue. In the present study, using extensive MD simulations and hybrid QM/MM calculations, we have investigated the key interactions between the DNA lesion and the hAGT enzyme and elucidated the mechanisms of the demethylation of the guanine base. Our simulation shows that the DNA lesion is electrostatically stabilized by the enzyme and the Arg135 of hAGT enzyme provides the main driving force to flip the damaged base into the enzyme. The QM/MM calculations show demethylation of the damaged base as a three-step process in a thermodynamically feasible and irreversible manner. Our calculations show that the final product forms via Tyr114 in a facile way in contrast to the previously proposed Lys-mediated route.

The key objective of this paper is to study the cyclic codes over mixed alphabets on the structure of FqPQ, where P=Fq[v]⟨v3−α22v⟩ and Q=Fq[u,v]⟨u2−α12,v3−α22v⟩ are nonchain finite rings and αi is in Fq/{0} for i∈{1,2}, where q=pm with m≥1 is a positive integer and p is an odd prime. Moreover, with the applications, we obtain better and new quantum error-correcting (QEC) codes. For another application over the ring P, we obtain several optimal codes with the help of the Gray image of cyclic codes.

A well-known result of Posner’s second theorem states that if the commutator of each element in a prime ring and its image under a nonzero derivation are central, then the ring is commutative. In the present paper, we extended this bluestocking theorem to an arbitrary ring with involution involving prime ideals. Further, apart from proving several other interesting and exciting results, we established the ∗-version of Vukman’s theorem. Precisely, we describe the structure of quotient ring A/L, where A is an arbitrary ring and L is a prime ideal of A. Further, by taking advantage of the ∗-version of Vukman’s theorem, we show that if a 2-torsion free semiprime A with involution admits a nonzero ∗-centralizing derivation, then A contains a nonzero central ideal. This result is in the spirit of the classical result due to Bell and Martindale (Theorem 3). As the applications, we extended and unified several classical theorems. Finally, we conclude our paper with a direction for further research.

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Let Fq be a field of order q, where q is a power of an odd prime p, and α and β are two non-zero elements of Fq. The primary goal of this article is to study the structural properties of cyclic codes over a finite ring R=Fq[u1,u2]/⟨u12−α2,u22−β2,u1u2−u2u1⟩. We decompose the ring R by using orthogonal idempotents Δ1,Δ2,Δ3, and Δ4 as R=Δ1R⊕Δ2R⊕Δ3R⊕Δ4R, and to construct quantum-error-correcting (QEC) codes over R. As an application, we construct some optimal LCD codes.

Ravine and gully formations are both spectacular and also the worst forms of water-induced soil erosion and have in situ and ex situ impact on geomorphology, hydrology, productivity and environmental security, and they are the root causes of degradation of marginal and adjacent land along with reduced production potential. A long-term (2011–2019) study was conducted on marginal land of the Chambal ravine to assess the impact of six land uses, i.e., Agriculture (T1—Rainfed Soybean), Agri-horticulture (T2—Soybean + Manilkara achras), Horti-Pastoral (T3—Emblica officinalis + Cenchurus ciliaris), Pasture (T4—C. ciliaris), Silviculture (T5—Acacia nilotica) and Silvi-pasture (T6—A. nilotica + C. Ciliaris) on soil properties, runoff interception, sediment trapping and soil loss reduction. The lowest average annual soil loss (4.83 ton ha−1 year−1) and runoff (109.52 mm) were recorded under T4, while the highest sediment loss (8.09 ton ha−1 year−1) and runoff (136.07 mm), respectively, were under T5. The runoff coefficient of land uses was in the order of T3 (20.30%) < T4 (20.56%) < T1 (21.95%) < T2 (22.26%) < T6 (22.83%) < T5 (25.54%). The C. ciliaris improved bulk density and recorded lowest in horti-pasture (1.63 ± 0.04 g cm−3) followed by pasture (1.66 ± 0.03 g cm−3) land use system. The active SOC content in pasture, horti-pasture and silvi-pasture was 0.95, 0.87 and 0.64 times higher, respectively, than agriculture land use. Under pure C. ciliaris cover, resistance to penetration varied from 0.68 to 1.97 MPa, while in silviculture land use, it ranges from 1.19 to 2.90 Mpa. Grass cover had substantial impact on soil loss and runoff reduction, SOC content, soil aggregation and resistance to penetration. In degraded ecosystems, Cenchrus ciliaris can be used alone and in combination with plants for protection of natural resources from water-induced soil erosion, runoff conservation, soil quality improvement and maximization of precipitation water use.

Let k,m be positive integers and F2m be a finite field of order 2m of characteristic 2. The primary goal of this paper is to study the structural properties of cyclic codes over the ring Sk=F2m[v1,v2,…,vk]⟨vi2−αivi,vivj−vjvi⟩, for i,j=1,2,3,…,k, where αi is the non-zero element of F2m. As an application, we obtain better quantum error correcting codes over the ring S1 (for k=1). Moreover, we acquire optimal linear codes with the help of the Gray image of cyclic codes. Finally, we present methods for reversible DNA codes.

ABSTRACT Diagnosis of latent tuberculosis infection (LTBI) using biomarkers in order to identify the risk of progressing to active TB and therefore predicting a preventive therapy has been the main bottleneck in eradication of tuberculosis. We compared two assays for the diagnosis of LTBI: transcript signatures and interferon gamma release assay (IGRA), among household contacts (HHCs) in a high tuberculosis-burden population. HHCs of active TB cases were recruited for our study; these were confirmed to be clinically negative for active TB disease. Eighty HHCs were screened by IGRA using QuantiFERON-TB Gold Plus (QFT-Plus) to identify LTBI and uninfected cohorts; further, quantitative levels of transcript for selected six genes (TNFRSF10C, ASUN, NEMF, FCGR1B, GBP1, and GBP5) were determined. Machine learning (ML) was used to construct models of different gene combinations, with a view to identify hidden but significant underlying patterns of their transcript levels. Forty-three HHCs were found to be IGRA positive (LTBI) and thirty-seven were IGRA negative (uninfected). FCGR1B, GBP1, and GBP5 transcripts differentiated LTBI from uninfected among HHCs using Livak method. ML and ROC (Receiver Operator Characteristic) analysis validated this transcript signature to have a specificity of 72.7%. In this study, we compared a quantitative transcript signature with IGRA to assess the diagnostic ability of the two, for detection of LTBI cases among HHCs of a high-TB burden population; we concluded that a three gene (FCGR1B, GBP1, and GBP5) transcript signature can be used as a biomarker for rapid screening. IMPORTANCE The study compares potential of transcript signature and IGRA to diagnose LTBI. It is first of its kind study to screen household contacts (HHCs) in high TB burden area of India. A transcript signature (FCGR1B, GBP1, & GBP5) is identified as potential biomarker for LTBI. These results can lead to development of point-of-care (POC) like device for LTBI screening in a high TB burdened area.

Let R be a *-ring. For any x,y∈R, we denote the skew Lie product of x and y by ▿[x,y]=xy-yx∗. An additive mapping F:R→R is called a generalized derivation if there exists a derivation d such that F(xy)=F(x)y+xd(y) for all x,y∈R. The objective of this paper is to chracterize generalized derivations and to describe the structure of prime rings with involution * involving skew Lie product. In particular, we prove that if R is a 2-torsion free prime ring with involution * of the second kind and admits a generalized derivation (F,d) such that ▿[x,F(x∗)]±▿[x,x∗]∈Z(R) for all x∈R, then R is commutative or F=∓IR, where IR is the identity mapping of R. Moreover, some related results are also obtained. Finally, we provide two examples to prove that the assumed restrictions on our main results are not superfluous.

Let $\mathcal{R}$ be a prime ring with involution $'*'$ and $\psi: \mathcal{R} \rightarrow \mathcal{R}$ be an endomorphism on $\mathcal{R}$. In this article, we study the action of involution $'*',$ and the effect of endomorphism $\psi$ satisfying $[\psi(x),\psi(x^*)]-[x,x^*]\in \mathcal{Z}(\mathcal{R})$ for all $x\in \mathcal{R}$. In particular, we prove that any centralizing involution on prime rings with involution of characteristic different from two is of the first kind or $\mathcal{R}$ satisfies $s_4$, the standard polynomial identity in four variables. Further, we establish that if a prime ring $\mathcal{R}$ with involution of characteristic different from two admits a non-trivial endomorphism $\psi$ such that $[\psi(x),\psi(x^*)]-[x,x^*]\in \mathcal{Z}(\mathcal{R})$ for all $x\in \mathcal{R}$, then the involution is of the first kind or $\mathcal{R}$ satisfies $s_4$ and $[\psi(x), x]=0$ for all $x\in \mathcal{R}$.

Diabetes mellitus is a metabolic disease largely due to lifestyle and nutritional imbalance, resulting in insulin resistance, hyperglycemia and vascular complications. Diabetic kidney disease (DKD) is a major cause of end-stage renal failure contributing to morbidity and mortality worldwide. Therapeutic options to prevent or reverse DKD progression are limited. Endothelial and glomerular filtration barrier (GFB) dysfunction and sterile inflammation are associated with DKD. Neutrophil extracellular traps (NETs), originally identified as an innate immune mechanism to combat infection, have been implicated in sterile inflammatory responses in non-communicable diseases. However, the contribution of NETs in DKD remains unknown. Here, we show that biomarkers of NETs are increased in diabetic mice and diabetic patients and that these changes correlate with DKD severity. Mechanistically, NETs promote NLRP3 inflammasome activation and glomerular endothelial dysfunction under high glucose stress in vitro and in vivo. Inhibition of NETs (PAD4 inhibitor) ameliorate endothelial dysfunction and renal injury in DKD. Taken together, NET-induced sterile inflammation promotes diabetes-associated endothelial dysfunction, identifying a new pathomechanism contributing to DKD. Inhibition of NETs may be a promising therapeutic strategy in DKD.

The presence of elevated nitrate (NO3-) and nitrite (NO2-) concentration in drinking water higher than the standard limits could endanger the health of consumers. For this data article, concentration of NO3- and NO2- was measured in 118 samples collected from 59 active rural wells in Divandarreh County and the non-carcinogenic risk in the adults and children was estimated by Monte Carlo simulation (MCS). The obtained data showed that the average concentration of NO3- and NO2- was ranges from 31.37 ± 18.87 mg/L and 1.45 ± 0.90 mg/L respectively. Based on acquired data, NO3- concentrations were 37 times higher than NO2- with significant p value of < 0.05. The average concentration of NO3- and NO2- was lower than the national standard with p value < 0.05. However, the concentration of NO3- and NO2- in 23.7% and 13.5% of wells was higher than the national standard of Iran. Total target hazard quotient (TTHQ) in the adults and children was 1.78 and 1.54, respectively. Although, the average concentration of NO3- and NO2- in drinking water was lower than the national standard limits, but the non-carcinogenic risk assessment showed that the children and adults are at a significant risk via nitrate and nitrite in the rural Divandarreh County (TTHQ > 1). Keywords: Nitrate, Nitrite, Groundwater contamination, Risk assessment, Rural Iran, Divandarreh County

Soy consumption in human diet has been linked to decreased incidence of a variety of cancers, suggesting a potential role of soy products in cancer prevention and control. Furthermore, a substantial body of evidence in the literature suggests that soy supplementation may improve the efficacy and prevent the adverse effects of cancer chemotherapy and radiation therapy. Isoflavones constitute the predominant anticancer bioactive compounds in soy. Genistein, which is the most abundant and active isoflavone in soy, has a multitude of effects on cancer cells, including inhibition of NF-κB activation and DNA methylation, enhancement of histone acetylation, inhibition of cell growth and metastasis, and antiangiogenic, anti-inflammatory, and anti-oxidant effects. Isoflavones are orally bioavailable, easily metabolized, and usually considered safe. In this article, we review in vitro and in vivo evidence as well as the results of clinical and epidemiological studies on the effects of soy isoflavones, with a focus on sensitization of cancer cells to chemotherapy and radiation while at the same time protecting normal cells from the harmful effects of these treatments.

The objective of this paper is to study Jordan ∗-mappings in rings with involution ∗. In particular, we prove that if R is a prime ring with involution ∗, of characteristic different from 2 and D is a nonzero Jordan ∗-derivation of R such that [D(x),x]=0, for all x∈R and S(R)∩Z(R)≠(0), then R is commutative. Further, we also prove a similar result in the setting of Jordan left ∗-derivation. Finally, we prove that any symmetric Jordan triple ∗-biderivation on a 2-torsion free semiprime ring with involution ∗ is a symmetric Jordan ∗-biderivation.

Let R be an associative ring. An additive mapping d:R→R is called a Jordan derivation if d(x2)=d(x)x+xd(x) holds for all x∈R. The objective of the present paper is to characterize a prime ring R which admits Jordan derivations d and g such that [d(xm),g(yn)]=0 for all x,y∈R or d(xm)∘g(yn)=0 for all x,y∈R, where m⩾1 and n⩾1 are some fixed integers. This partially extended Herstein’s result in [6, Theorem 2], to the case of (semi)prime ring involving pair of Jordan derivations. Finally, we apply these purely algebraic results to obtain a range inclusion result of continuous linear Jordan derivations on Banach algebras.

Candida albicans utilizes arachidonic acid (AA) released during the course of infection (Candidiasis) from phospholipids of infected host cell membranes and synthesizes extracellular prostaglandin(s) which play an important role in hyphae formation and host cell damage. C. albicans biofilms secrete significantly more prostaglandin(s) and evidence suggests that Candida biofilms have dramatically reduced susceptibility to majority of antifungal drugs. AA influences the saturation level of lipids and fluidity of yeast cell membranes. Therefore the aim of this study was to evaluate the effect of AA alone or in combination with antifungal agents on biofilm formation and production of prostaglandin (PGE2) in C. albicans, C. parapsilosis, C. glabrata, C. tropicalis, and C. albicans amphotericin B resistant strain (AmBR). Maximum biofilm formation was found to be in the case of C. albicans compared to C. non-albicans species. However, among the non-albicans species C. tropicalis exhibited highest biofilm formation. Treatment with AA in combination with subinhibitory concentrations of fluconazole and terbinafine separately exhibited significant (p

Chemical mediators of inflammation (CMI) are important in host defense against infection. The reduced capacity of host to induce the secretion of these mediators following infection is one of the factors in host susceptibility to infection. Boron, which has been suggested for its role in infection, is reported in this study to increase lymphocyte proliferation and the secretion of CMI by the lipopolysaccharide (LPS)-stimulated peritoneal macrophages in BALB/c mice. Boron was administered to mice orally as borax at different doses for 10 consecutive days, followed by the stimulation of animals with ovalbumin and isolation of splenocytes for proliferation assay. The lymphocyte subsets were determined by flow cytometry in spleen cell suspension. The mediators of inflammation, TNF-α, IL-6, IL-1β and nitric oxide (NO), were measured in culture supernatant of LPS-primed macrophages isolated from borax treated mice. TNF and ILs were measured by ELISA. NO was determined by Griess test. The expression of inducible nitric oxide synthase (iNOS) in macrophages was studied by confocal microscopy. Results showed a significant increase in T and B cell populations, as indicated by an increase in CD4 and CD19, but not CD8, cells. Boron further stimulated the secretion of TNF-α, IL-6, IL-1β, NO and the expression of iNOS by the LPS-primed macrophages. The effect was dose dependent and most significant at a dose level of 4.6 mg/kg b. wt. Taken together, the study concludes that boron at physiological concentration induces lymphocyte proliferation and increases the synthesis and secretion of pro-inflammatory mediators by the LPS-primed macrophages, more specifically the M1 macrophages, possibly acting through Toll-like receptor. The study implicates boron as a regulator of the immune and inflammatory reactions and macrophage polarization, thus playing an important role in augmenting host defense against infection, with possible role in cancer and other diseases.

Clear cell type of renal cell carcinoma (RCC) is most common urological malignancy. Several diagnostic challenges arise when it presents as a cutaneous nodule, being an uncommon presentation. Fine needle aspiration cytology (FNAC) of a cutaneous nodule is crucial for distinguishing primary tumours from metastatic tumours because cutaneous metastases represent a terminal stage of illness. Due to considerable overlap of cytomorphological features determination of primary warrants need of detailed clinical history and close inspection of every cytological detail. We report here a case of cutaneous metastasis of RCC on chin in a patient 11 years after nephrectomy. Though there are reports of RCC metastases diagnosed on histology, there are fewer cytology case reports. Cytological differential diagnosis has been discussed for arriving at the final diagnosis in case of clear cell tumours. Early and accurate diagnosis is mandatory for optimal treatment. Cytodiagnosis of cutaneous metastasis of RCC is uncommon due to its low suspicion index in cutaneous nodules. More so, it presents late and an unusual sites due to its resemblance to common dermatological diseases.

Objective: Present study was designed to investigate the effects of altitude mediated acute hypobaric hypoxia on protein turnover in skeletal muscle. Background: Skeletal muscle wasting is considered to be an important factor leading to decrease in physical performance at high altitude. Changes in protein turnover and the mechanism underlying the loss of skeletal muscle mass under these conditions are not very well understood. Method: Male Sprague Dawley rats (n=12 each group) weighing about 180-200 g were exposed to hypobaric hypoxia (9144 m) for six hours. Skeletal muscle homogenates were prepared for carrying out various studies including proteolytic pathways. Result: Acute exposure to hypobaric hypoxia has deleterious effects on skeletal muscle mass which was reflected by one third attenuation in protein synthesis and more than 50 % increase in protein degradation. Hypobaric hypoxia resulted in upregulation of Ub-Proteasome pathway and calpain whereas lysosomal mediated proteolysis remained unchanged. Glutaminase activity, protein carbonyl status, oxidative stress markers were also found to be elevated in hypoxia exposed rats. Conclusion: These results are indicative of excessive protein degradation and decreased protein synthesis during acute hypobaric hypoxia. Moreover increased protein oxidation may also be an important contributor for the skeletal muscle loss.

Let R be a ring and F and G be generalized derivations of R with associated derivations d and g respectively. In the present paper,we shall investigate the commutativity of semiprime ring R admitting generalized derivations F and G satisfying any one of the properties: (i)F(x)x = xG(x), (ii) [F(x), d(y)] = [x,y], (iii) F([x,y]) = [d(x), F(y)], (iv) d(x)F(y) = xy, (v) F(x^2) = x^2, (vi) [F(x),y] = [x,G(y)], (vii) F([x, y]) = [F(x), y] + [d(y), x] and (viii) F(x ◦ y) = F(x) ◦ y −d(y) ◦ x for all x, y in some appropriate subset of R.

This study explores the Whales Optimization Algorithm (WOA)-based PI controller for regulating the voltage and frequency of an inverter-based autonomous microgrid (MG). The MG comprises two 50 kW DGs (solid oxide fuel cells, SOFCs) interfaced using a power electronics-based voltage source inverter (VSI) with a 120-kV conventional grid. Four PI controller schemes for the MG are implemented: (i) stationary PI controller with fixed gain values (Kp and Ki), (ii) PSO tuned PI controller, (iii) GWO tuned PI controller, and (iv) WOA tuned PI controller. The performance of these controllers is evaluated by monitoring the system voltage and frequency during the transition of MG operation mode and changes in the load. The MATLAB/SIMULINK tool is utilised to design the proposed model of grid-tied MG alongside the MATLAB m-file to apply an optimisation technique. The simulation results show that the WOA-based PI controller which optimises the control parameters, achieve 62.7% and 59% better results for voltage and frequency regulation, respectively. The eigenvalue analysis is also provided to check the stability of the proposed controller. Furthermore, the proposed system also satisfies the limits specified in IEEE-1547-2003 for voltage and frequency.

Let R be a ring, and alpha be an endomorphism of R. An additivemapping H: R ightarrow R is called a left alpha-centralizer (resp. Jordan left alpha-centralizer) if H(xy) = H(x)alpha(y) for all x; y in R (resp. H(x^2) = H(x)alpha(x) for all x in R). The purpose of this paper is to prove two results concerning Jordan alpha-centralizers and one result related to generalized Jordan (alpha; eta)-derivations. The result which we referstate as follows: Let R be a 2-torsion-free semiprime ring, and alpha be an automorphism of R. If H: R ightarrow R is an additive mapping such that H(x^2) = H(x)alpha(x) for every x 2 R or H(xyx) = H(x)alpha(yx) for all x; y in R, then H is a left alpha-centralizer on R. Secondly, this result is used to prove that every generalized Jordan (alpha; eta)-derivation on a 2-torsion-free semiprime ring is a generalized (alpha; eta)-derivation. Finally, some examples are given to demonstrate that the restrictions imposed on the hypothesis of the various theorems were not superfluous.