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Let S be a ∗-algebra containing the unity and a nontrivial projection. In the present paper, we showthat under certain restrictions if a map Ψ : S → S satisfies Ψ(L ⋄ N • D) = Ψ(L) ⋄ N • D + L ⋄Ψ(N) • D + L ⋄ N • Ψ(D) for all L, N, D ∈ S, then Ψ is an additive ∗-derivation.

In this paper, we apply a rough soft set to a spe-cial algebraic hyperstructure, and give the concept of a rough soft semihypergroup. We propose the notion of lower and upper approximations concerning a special semihypergroup and obtain some properties. Moreover, we consider a connection between the lower(upper) approximation of a special semihypergroup and the lower(upper) approximation of the associated -hypergroupoid. In the last section of this research, we discuss the decision-making algorithm of rough soft semihypergroups. Afterward, we obtain a relation between the decision-making algorithm of rough soft semi-hypergroups and their associated rough soft -hypergroupoids for a special semihypergroup.

In this paper we will extend some results on the commutativity of quotient rings proved in [1] and [11]. However, we will consider endomorphisms instead of derivations and generalized derivations, which is sufficient to obtain good results. We will also show that the conditions imposed in that paper cannot be removed.

Let $R$ be a commutative Noetherian ring and $\mathfrak{a}$ be an ideal of $R$. Suppose $M$ is a finitely generated $R$-module and $N$ is an Artinian $R$-module. We define the concept of filter coregular sequence to determine the infimum of integers $i$ such that the generalized local homology $\textrm{H}^{\mathfrak{a}}_i(M, N)$ is not finitely generated as an $\widehat{R}^{\mathfrak{a}}$-module, where $\widehat{R}^{\mathfrak{a}}$ denotes the $\mathfrak{a}$-adic completion of $R$. In particular, if $R$ is a complete semi-local ring, then $\textrm{H}^{\mathfrak{a}}_i(M, N)$ is a finitely generated $\widehat{R}^{\mathfrak{a}}$-module for all non-negative integers $i$ if and only if $(0:_N\mathfrak{a}+\textrm{Ann}(M))$ has finite length.

In this paper, we present and examine the characteristics of (f, g)-derivations for a residuated lattice. Some relationships between (f, g)-derivationand isotone, contractive and ideal (f, g)-derivations are given. The set of fixedpoint of an (f, g)-derivation is introduced and its structure is studied. More precisely, we show that the set of fixed points is also a residuated lattice.

The concept of actions of a BE-algebra on its subalgebra is introduced and certain properties of these actions are derived. The notion of cut-homomorphisms is introduced in BE-algebras and proved that the class of all cut-homomorphisms forms an ordered BE-algebra. Properties of fixed points of cut-homomorphisms of BE-algebras are investigated and a set of equivalent conditions is given for any two cut-homomorphisms are equal in the sense of mappings.

Recently Rather et al. [18] considered the generalized polar derivative and studied the relative position of zeros of the generalized polar derivative with respect to the zeros of the polynomial. In this paper, by taking into account the size of the constant term and the leading coefficient of the polynomial $P(z)$, we obtain some lower bound estimates for the generalized polar derivative of certain polynomials, which refine and generalize various results due to Aziz and Rather, Malik, Tur\'{a}n, Dubinin, Govil and others.

In our country, management of a large part of the economic resources is the responsibility of the state, and therefore its management has fundamental effects on the nation's fate. Therefore, public sector managers must be accountable to the people and their representatives, and provide the means for this accountability based on valid information. Nevertheless, to achieve adequate and appropriate accountability, the public sector naturally requires performance auditing in various components in addition to investigating financial statements and making statements in the framework of financial auditing principles. Therefore, the present study aims to propose a model to analyze the effects of performance audits on effectiveness to improve the accountability of executive agencies. For this purpose, the research method was correlational and in the form of a survey design with practical objectives. Then, to test the hypothesis (7) and obtain the optimal model, using Pearson correlation, regression, and meaningfulness of structural equations and finally, the path analysis algorithm through SPSS software, was designed and tested. The statistical population included directors, auditors, and experts of the Supreme Audit Court of Iran (SAC) from March 2016 to March 2018. The results of the test of research hypotheses showed that the effectiveness of performance audits through direct and indirect paths affects the improvement of accountability of executive agencies and its seven dimensions. Directly according to the results of the research, the research hypotheses (7) for the indirect effect of the effectiveness performance auditing on organizational, legal, professional, political, financial, moral and cultural accountability rates of 0.077, 0.025, 0.078, 0.093, 0.088, 0.085, and 0.055. The harmonious mean of the composite indexes of meaning as indirect effects of this pattern is estimated at 0.501. Exploratory results, combined with the confirmation of research hypotheses and design of equations and structural regressions, provide an optimal model that accounts for about 50.1\% of the changes in executive accountability responses through the implementation of the audit of effectiveness, indicating that the audit performance of the effectiveness has a significant relation with the improvement Responsible for executing agencies.

During an epidemic, existing mass media plays a fundamental role in promoting effective, trustworthy and convenient information regarding disease symptoms and prevention measures against the infection. In this research paper, we aim to explore the impact of media awareness projected to a SEIV compartmental model incorporating newly modulated saturated incidence function and discrete-time delay during an epidemic. We considered the time lag in between the process while unaware susceptible individuals would be aware through the campaign media. Sensitivity analysis reveals the influence of the model parameters in the progression of the epidemic. Numerical simulations enable us to visualize the importance of media awareness to convey predictions regarding the mitigation and apparent eradication of the epidemic.

The current research aims to present a financing model through the purchase of debt (factoring) with a risk management approach in listed and non-listed companies. This research was applied in terms of its purpose and descriptive survey in terms of its implementation method. The statistical population includes all managers of listed and non-listed companies. Due to the uncertainty of the number of the population, Cochran's formula was used to determine the sample size and the required sample size was determined to be 384 people. Data collection tools include interpretive structure questionnaires and researcher-made questionnaires. Data analysis was done through interpretive structural software (ISM) and structural equation modelling. The results showed that at the first level,  the factoring selection component was identified as a financial method. Second, two components of communication with factoring companies and interaction with business partners were identified. At the third level, there are financial risk management variables at this level. In fact, this component became a bridge between the second and fourth levels. At the fourth variable level, there are economic and financial factors. Also, the results showed that choosing factoring has a significant effect on communication with companies and interaction with partners. Also, communication with companies and interaction with partners has a significant effect on financial risk management. On the other hand, financial risk management has a significant effect on economic and financial factors. Therefore, the proposed model in this research had good validity.

‎In this paper‎, ‎we investigated boundedness of difference of general polynomial weighted differentiation composition operators from Cauchy transform spaces into function spaces $S=\{f:\ \ f'\in H^1\}$ and $S^2=\{f:\ \ f'\in H^2\}$ with derivative in Hardy spaces‎. ‎‎‎We also obtained an exact formula for the norm of this operator and prove that there is no composition isometry from the Cauchy transform spaces into $S$ and $S^2$ ‎spaces.‎

The problem of characterizing the maximal left algebras of Toeplitz matrices with quaternion entries is a complex as well as a harder problem that has not received much attention until now. In the current paper, we introduce certain families of maximal left algebras of Toeplitz matrices with entries from an algebra of quaternions that cover various classes of the left algebras of quaternion Toeplitz matrices.

Using the Atanassov's intuitionistic fuzzy set, the concept of intuitionistic fuzzy deductive system and intuitionistic fuzzy filter in Sheffer stroke Hilbert algebras is introduced, several properties are investigated.  The conditions under which an intuitionistic fuzzy set can be an intuitionistic fuzzy filter are explored, and  characterizations of an intuitionistic fuzzy filter are considered.  The process of making an intuitionistic fuzzy filter through the collection of filters is displayed, and the union and intersection of intuitionistic fuzzy filters are discussed. Several properties are investigated in relation to the homomorphsm of Sheffer stroke Hilbert algebras, and finally the relationship between an intuitionistic fuzzy filter and an intuitionistic fuzzy deductive system is established.

Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we characterize certain linear maps T : A −→ X by action on zero products. Also we initiate the study of multipliers and Jordan multipliers on standard operator algebras.

This paper investigates norm attainability and modular properties in Orlicz spaces, which generalize $L^p$-spaces and are key in functional analysis and nonlinear problems. It presents theorems on norm attainment, orthogonality, weak compactness, and uniform convexity, and introduces a novel criterion connecting the convexity of the Orlicz function with the smoothness and reflexivity of the space. The research extends classical concepts such as the $\Delta_2$-condition to ensure completeness and separability. The results have practical applications in nonlinear optimization, variational analysis, machine learning, signal processing, image reconstruction, and solving PDEs with nonlinear boundary conditions, providing a strong foundation for future research in these areas.

In this paper, the decomposition of the retro Banach frame (RBF) and operator Banach frame (OBF) into two infinite subsequences has been discussed. In the sequel, we further decompose OBFs into Block sequences and construct OBFs. We demonstrate a result regarding the image of an OBF by a bounded linear operator is also an OBF. Moreover, results related to the perturbation and stability of OBFs have been proved. In the end, we deal with the problem related to the Feichtinger Conjecture as an application.

In this paper, we introduce the new concept of r-efficiency and classify the weakly efficient solutions by this concept, where r = 1, 2, . . . , m and m is the number of objective functions. Afterward, we decompose the multi-objective optimization problem into the collection of subproblems with cardinality r, for two reasons. First, we apply the scalarization techniques for these subproblems to generate r-efficient solutions. Second, in order to present the new mean-equity models for solving the location problem, we employ the mean and inequality measures on these subproblems. Moreover, by introducing the consistency property for the inequality measures and stating the sufficient conditions to maintain this property, we investigate the relationship between r-efficient solutions of the new mean-equity models and efficient solutions of the location problem.