Journal of Mahani Mathematical Research
https://jmmrc.uk.ac.ir/
Journal of Mahani Mathematical Researchendaily1Mon, 11 Dec 2023 00:00:00 +0330Mon, 11 Dec 2023 00:00:00 +0330On RM-algebras with an additional condition
https://jmmrc.uk.ac.ir/article_4000.html
In this paper, we apply a new condition to RM-algebras. We obtain some relations among this condition with another axioms in some algebras of logic and some examples are given to illustrate them. %It is proved We prove that the relation derived from this new algebra is a partial ordering. It is proved that RM-algebras with condition (I) are abelian group. Also, we present that the BI-algebras, BCK-algebras, L-algebras, KL-algebras CL-algebras and BE-algebras satisfying (I) are trivial.Distributional Nikulin-Rao-Robson validity under a novel gamma extension with characterizations and risk assessment
https://jmmrc.uk.ac.ir/article_4215.html
In this work, a novel probability distribution is introduced and studied. Some characterizations are presented. Several financial risk indicators, such as the value-at-risk, tail-valueat-risk, tail variance, tail Mean-Variance, and mean excess loss function are considered under the maximum likelihood estimation, the ordinary least squares, the weighted least squares, and the Anderson Darling estimation methods. These four methods were applied for the actuarial evaluation under a simulation study and under an application to insurance claims data. For distributional validation under the complete data, the well-known Nikulin-Rao-Robson statistic is considered. The Nikulin-Rao-Robson test statistic is assessed under a simulation study and under three complete real data sets. For censored distributional validation, a new version of the Nikulin-Rao-Robson statistic is considered. The new Nikulin-Rao-Robson test statistic is assessed under a comprehensive simulation study and under three censored real data sets.Fraïssé limit via forcing
https://jmmrc.uk.ac.ir/article_4112.html
Suppose $\mathcal{L}$ is a finite relational language and $\mathcal{K}$ is a class of finite $\mathcal{L}$-structures closed under substructures and isomorphisms. It is called aFra\"{i}ss\'{e} class if it satisfies Joint Embedding Property (JEP) and Amalgamation Property (AP). A Fra\"{i}ss\'{e} limit, denoted $Flim(\mathcal{K})$, of aFra\"{i}ss\'{e} class $\mathcal{K}$ is the unique\footnote{The existence and uniqueness follows from Fra\"{i}ss\'{e}'s theorem, See \cite{hodges}.} countable ultrahomogeneous (every isomorphism of finitely-generated substructures extends to an automorphism of $Flim(\mathcal{K})$) structure into which every member of $\mathcal{K}$ embeds.Given a Fra&iuml;ss&eacute; class K and an infinite cardinal &kappa;, we define a forcing notion which adds a structure of size &kappa; using elements of K, which extends the Fra&iuml;ss&eacute; construction in the case &kappa;=&omega;.Commutators-based graph in polygroup
https://jmmrc.uk.ac.ir/article_4113.html
In this paper, first, we study commutators of a polygroup. Then for a finite polygroup $P$ and a fixed element $g \in P$, we introduce the $g$-graph $\Delta_P^g$. In addition, with some additional conditions, we see that it is connected and the diameter is at most $3$. Then, we investigate isomorphic graphs. Specially, we obtain a new isomorphic graph derived from an isomorphic graph and two non-commutative isomorphic polygroups. Also, we show that two polygroups with&nbsp; isomorphic graphs preserve nilpotency.Multipliers in weak Heyting algebras
https://jmmrc.uk.ac.ir/article_4182.html
In this paper, we introduce the notion of multipliers in weak Heyting algebras and investigate some related properties of them. We obtain the relations between multipliers, closure operators, and homomorphisms in weak Heyting algebras. Relations among image sets and fixed point sets of multipliers in weak Heyting algebras are investigated. Also, we study algebraic structures of the set of all multipliers in weak Heyting algebras. Using multipliers, the left and right m-stabilizers in weak Heyting algebras are introduced, and some related properties are given. Also, we obtain conditionssuch that the left and right m-stabilizers form two weak Heyting algebras.Parsimonious mixture of mean-mixture of normal distributions with missing data
https://jmmrc.uk.ac.ir/article_4229.html
Clustering multivariate data based on mixture distributions is a usual method to characterize groups and label data sets. Mixture models have recently been received considerable attention to accommodate asymmetric and missing data via exploiting skewed and heavy-tailed distributions. In this paper, a mixture of multivariate mean-mixture of normal distributions is considered for handling missing data. The EM-type algorithms are carried out to determine maximum likelihood of parameters estimations. We analyzed the real data sets and conducted simulation studies to demonstrate the superiority of the proposed methodology.Generalized total time on test transform for weighted variables, properties and applications
https://jmmrc.uk.ac.ir/article_4307.html
In this article, the generalized &nbsp;total &nbsp;time on test transform and some related transforms for weighted variables are stated. Their characteristics and relationship with each other have been considered and also these transforms have been investigated in the weighted mode from the point of view of stochastic orders. Also, by presenting graphs of generalized total time on test transform &nbsp; for some common weight functions, its behavior with respect to the weighted function is studied. Then the relationship of this transform with its initial state is expressed. In the following, the topic under discussion is explained with some practical examples. Then providing a comprehensive exploration of the applications of the studied transforms within the domains of insurance and reliability. By delving into these practical contexts, we gain valuable insights into how these mathematical tools can be effectively utilized to address complex challenges in risk assessment, decision-making, and resource allocation. Additionally, the examination of the NBU class of distributions offers a deeper understanding of their behavior, shedding light on their relevance and applicability in various statistical analyses.&nbsp; &nbsp; Finally, the article concludes with a detailed discussion of a specific real dataset, offering a concrete demonstration of how the topic under study can be applied in practice.Analyzing skewed financial data using skew scale-shap mixtures of multivariate normal distributions
https://jmmrc.uk.ac.ir/article_4310.html
This paper introduces an innovative family of statistical models called the multivariate skew scale-shape mixtures of normal distributions. These models serve as a versatile tool in statistical analysis by efficiently characterizing the skewed and leptokurtic nature commonly observed in multivariate datasets. Their applicability shines in real-world scenarios where data often deviate from standard statistical assumptions due to the presence of outliers. We present an EM-type algorithm designed for maximizing likelihood estimation and evaluate the model's effectiveness through real-world data applications. Through rigorous testing against various datasets, we assess the performance and practicality of the proposed algorithm in real statistical scenarios. The results demonstrate the remarkable performance of this new family of distributions.On almost sure convergence rates for the kernel estimator of a covariance operator under negative association
https://jmmrc.uk.ac.ir/article_4398.html
&nbsp; &nbsp; It is suppose that $\{X_n,~n\geq 1\}$ is a strictly stationary sequence of negatively associated random variables with continuous distribution function F. The aim of this paper is to estimate the distribution of $(X_1,X_{k+1})$ for $k\in I\!\!N_0$ using kernel type estimators. We also estimate the covariance function of the limit empirical process induced by the sequence $\{X_n,~n\geq 1\}$. Then, we obtain uniform strong convergence rates for the kernel estimator of the distribution function of $(X_1,X_{k+1})$. These rates, which do not require any condition on the covariance structure of the variables, were not already found. Furthermore, we show that the covariance function of the limit empirical process based on kernel type estimators has uniform strong convergence rates assuming a convenient decrease rate of covariances $Cov(X_1,X_{n+1}),~n\geq 1$. Finally, the convergence rates obtained here are empirically compared with corresponding results already achieved by some authors.On the power of Gini index-based goodness-of-fit test for the Inverse Gaussian distribution
https://jmmrc.uk.ac.ir/article_4052.html
The Inverse Gaussian distribution finds application in various fields, such as finance, survival analysis, psychology, engineering, physics, and quality control. Its capability to model skewed distributions and non-constant hazard rates makes it a valuable tool for understanding a wide range of phenomena. In this paper, we present a goodness-of-fit test specifically designed for the Inverse Gaussian distribution. Our test uses an estimate of the Gini index, a statistical measure of inequality. We provide comprehensive details on the exact and asymptotic distributions of the newly developed test statistic. To facilitate the application of the test, we estimate the unknown parameters of the Inverse Gaussian distribution using maximum likelihood estimators. Monte Carlo methods are utilized to determine the critical points and assess the actual sizes of the test. A power comparison study is conducted to evaluate the performance of existing tests. Comparing its powers with those of other tests, we demonstrate that the Gini index-based test performs favorably. Finally, we present a real data analysis for illustrative purposes.Algebra fuzzy norms generated by homomorphisms
https://jmmrc.uk.ac.ir/article_4179.html
&lrm;&lrm;&lrm;As a new approach, for a nonzero normed algebra $A$, we will define some different classes of algebra fuzzy norms on $A$ generated by homomorphisms and continuous homomorphisms. Also as a source of examples and counterexamples in the field of fuzzy normed algebras, separate continuity of the elements within each class are investigated.A novel method for solving fuzzy parabolic PDE by using the SG-Hukuhara differentiability
https://jmmrc.uk.ac.ir/article_4253.html
In this paper, the method of Crank-Nicolson is proposed for approximating the solution of &nbsp;a fuzzy parabolic PDE by applying the subject of &nbsp;SG-Hukuhara differentiability where the initial and boundary conditions are fuzzy numbers. The consistency and stability of this method are investigated and finally, &nbsp;a non-trivial example is given by this method.A new entropy estimator and its application to goodness of fit test for Weibull distribution
https://jmmrc.uk.ac.ir/article_4255.html
In this article, we introduce a new estimator of entropy of continuous random variable. Bias, variance and the mean squared error of the new estimator are obtained and compared with the other existing estimators. The results show that the proposed estimator has a lower mean squared error than its competitors. Then, we propose some goodness of fit tests for Weibull distribution based on the entropy estimators. To assess the effectiveness of the proposed tests, we utilize Monte Carlo simulation to evaluate their power against eighteen different alternatives with varying sample sizes. The results show that the tests are powerful and we can use them in practice. Finally, two real datasets are considered and modeled by the Weibull distribution.The evolution of binary system from predynastic Egypt to Leibniz era
https://jmmrc.uk.ac.ir/article_4266.html
Egyptians of the predynastic era had a good decimal number system for counting and addition. Although, up to some times, they had problem in counting beyond a million, by the dawn of their history, Narmer, the founder of the first Egyptian dynasty had accountants that could record 400,000 cows and 1,422,000 goats of a war booty. Except for some ambiguities in the case of Mayan number system, specialists in the history of mathematics can guess that &nbsp;how the counting system of the various civilizations evolved into one of the number systems in base 10, 20, 60, etc. There is a puzzle in the mixture of the &nbsp;Egyptian decimal and binary number systems which we are going to discuss and present a justification for it. The novelty of the present paper is the study of the evolution of the binary number system from the predynastic Egypt down to the Leibniz era who, by the benefit of &nbsp;Khwarazmi's &nbsp;"Indian Arithmetics," &nbsp;completed this evolution by representing integers in $0-1$ forms and performing the hybrid decimal/binary Egyptian arithmetic operations purely inside the $0-1$ system. The second author is pleased to dedicate his share of this paper to &nbsp;Esfandiar Eslami &nbsp;showing &nbsp;his love and appreciation for decades of his friendship and collaboration (since 1967) and, of course, the young coauthor joins the joy of this dedication to her former professor.Equalizer in the Kleisli category of the $n$-fuzzy powerset monad
https://jmmrc.uk.ac.ir/article_4320.html
In this article, we first consider the $L$-fuzzy powerset monad on a completely distributive lattice $L$. Then for $L=[n]$, we investigate the fuzzy powerset monad on $[n]$ and we introduce simple, subsimple and quasisimple $L$-fuzzy sets. Finally, we provide necessary and sufficient conditions for the existence of an equalizer of a given pair of morphisms in the Kleisli category associated to this monad. Several illustrative examples are also provided.Nonparametric estimators for varextropy under $\alpha$-mixing condition with appliction in exponential AR(1) model
https://jmmrc.uk.ac.ir/article_4353.html
The goal of this paper is to study the problem of estimation of varextropy function under $\alpha$-mixing dependence condition. We propose nonparametric estimators for varextropy, residual varextropy and &nbsp;past varextropy. Asymptotic properties of the proposed estimators&nbsp; are investigated under regularity conditions. Moreover, the comparison of the proposed estimators for varextropy in terms of the bias and mean squared error has been done by Monte Carlo method. Furthermore, a real data example is presented.Some properties of finite generalized-groups
https://jmmrc.uk.ac.ir/article_4396.html
In this article, we discuss&nbsp; the concept of completely simple-semigroups, which serves as a natural extension of the group structures. These semigroups, also known as generalized-groups, provide an interesting generalization beyond the realm of the groups. Many scientists have investigated various applications of generalized-groups. Notably, this algebraic structure has connections to the unified gauge theory. In this article, we investigate the structures and properties of generalized-groups, providing examples and results within this fascinating subject. Specially, we show that the generalized Lagrange Theorem may not be true for generalized-groups.Zip and weak zip algebras in a congruence-modular variety
https://jmmrc.uk.ac.ir/article_4410.html
The zip (commutative) rings, introduced by Faith and Zelmanowitz, generated a fruitful line of investigation in ring theory. Recently, Dube, Blose and Taherifar developed an abstract theory of zippedness by means of frames. Starting from some ideas contained in their papers, we define and study the zip and weak zip algebras in a semidegenerate congruence-modular variety $\mathcal{V}$. We obtain generalizations of some results existing in the literature of zip rings and zipped frames. For example, we prove that a neo-commutative algebra $A\in \mathcal{V}$ is a weak zip algebra if and only if the frame $RCon(A)$ of radical congruences of $A$ is a zipped frame (in the sense of Dube and Blose). We study the way in which the reticulation functor preserves the &nbsp;zippedness property. Using the reticulation and a Hochster's theorem we prove that &nbsp;a neo-commutative algebra $A\in \mathcal{V}$ is a weak zip algebra if and only if the minimal prime spectrum $Min(A)$ of $A$ is a finite space.Superderivations and Jordan superderivations of generalized quaternion algebras
https://jmmrc.uk.ac.ir/article_4411.html
Let $H_{\alpha,\beta}$ be the generalized quaternion algebra over a unitary commutative ring. This paper aims to consider superderivations and Jordan superderivations of $H_{\alpha,\beta}$ and hence to obtain the superalgebra $Der_{s} (H_{\alpha,\beta})$ of superderivations and $Der_{Js} (H_{\alpha,\beta})$ of Jordan superderivations of $H_{\alpha,\beta}$. It turns out that on generalized quaternion algebras, any superderivation is inner. &nbsp;In particular, there exist Jordan superderivations that are not superderivations.Strongly regular relations on regular hypergroups
https://jmmrc.uk.ac.ir/article_4413.html
Hypergroups that have at least one identity element and where each element has at least one inverse are called regular hypergroup. In this regards, for a regular hypergroup $H$, it is shown that there exists a correspondence between the set of all strongly regular relations on $H$ and the set of all normal subhypergroups of $H$ containing $S_{\beta}$. More precisely, it has been proven that for every strongly regular relation $\rho$ on $H$, there exists a unique normal subhypergroup of $H$ containing $S_{\beta}$, such that its quotient is a group, isomorphic to $H/\rho$. Furthermore, this correspondence is extended to a lattice isomorphism between them.On derivations of pseudo L-algebras
https://jmmrc.uk.ac.ir/article_4414.html
In this article, the focus is on the study of derivations on two types of algebraic structures: pseudo L-algebras and pseudo CKL-algebras. For pseudo L-algebras, the notions of left and right derivations are introduced. These derivations are characterized and equivalent characterizations are given. Additionally, the concepts of identity and ideal derivations are defined based on the notion of derivations in pseudo L-algebras. It is proven that any identity derivation is also an ideal derivation. However, an example is provided to demonstrate that not all ideal derivations are identity derivations. Moreover, it is shown that ideal left derivations in pseudo L-algebras are idempotent. The article also introduces the notion of fixed point sets in pseudo L-algebras and investigates some properties associated with them. Moving on to pseudo CKL-algebras, various properties of derivations in these structures are studied. The relationship between pseudo CKL-algebras and pseudo BCK-algebras is established, and it is proven that any pseudo CKL-algebra is also a pseudo BCK-algebra. Conversely, an example is provided to show that not all pseudo BCK-algebras are pseudo CKL-algebras. Additionally, it is demonstrated that the contractive derivation of a pseudo CKL-algebra is an identity derivation. We introduce the definition of a pre-ideal and also introduce the definition of a non-empty subset I in pseudo L-algebra, which is d-invariant, and prove that every pre-ideal I in pseudo CKL-algebra is d-invariant, where d is a derivation. Overall, the article explores derivations in pseudo L-algebras and pseudo CKL-algebras, providing definitions, characterizations, and examples to illustrate various properties and relationships between these algebraic structures.Weighted differentiation composition operators on the $Q_K(p,q)$ spaces and their essential norms
https://jmmrc.uk.ac.ir/article_4415.html
In this paper, firstly we obtain characterization for boundedness of the weighted differentiation composition operator &nbsp;from $Q_K(p,q) $ space into weighted Zygmund space. Then we give an estimation for the essential norm of such an operator on the mentioned spaces. &nbsp;As an application, we present a characterization for the compactness of the above operator.Interval shrinkage estimation of two-parameter exponential distribution with random censored data
https://jmmrc.uk.ac.ir/article_4428.html
The use of the two-parameter exponential distribution model in fitting survival and reliability analysis data in the presence of censored random data has recently attracted the attention of a large number of authors. Considering the importance of the model, its parameter estimation is discussed using the method of moment, maximum likelihood and shrinkage estimation. To present the interval shrinkage estimator, it is first proved that the moment estimators are asymptotically unbiased and the interval shrinkage estimator performs better compared to other estimators. Finally, using two real data sets and statistical criteria, the goodness of fit of the model is compared with censored random data based on parameter estimation methods.Some inequalities for eigenvalues of an elliptic differential operator
https://jmmrc.uk.ac.ir/article_4429.html
&lrm;In the present paper, we investigate &nbsp;the eigenvalues of an elliptic differential operator on compact Riemannian manifolds with boundary and derive a general inequality for these eigenvalues. Applying this inequality, we give universal estimates &nbsp;for eigenvalues on compact domains of &nbsp;complete submanifolds in an Euclidean space, and of complete manifolds admitting special functions. Finally, we find universal bounds on &nbsp;the $(k+1)$-th eigenvalue on such objects in terms of the first $k$ eigenvalues independent of &nbsp;the domains.Solvable intransitive permutation groups with constant movement
https://jmmrc.uk.ac.ir/article_4438.html
In this paper, all solvable intransitive permutation groups with constant movement are classified and we show that they are one of the following groups: a cyclic $p$-group, an elementary abelian $p$-group, a Frobenius group of order 12 or a Frobenius group of order $pq$, where $p$ and $q$ are primes such that $p=q(q-1)+1.$Fuzzy modeling using the similarity-based approximate reasoning system
https://jmmrc.uk.ac.ir/article_4439.html
Just as we humans use many different types of inferential procedures to help us understand things or to make decisions,&nbsp; there are many different fuzzy logic inferential procedures, including similarity-based approaches. Similarity measures can be seen not only as a general notion but also as a particular family of fuzzy relations which play &nbsp;crucial roles for the motivation and the whole design of similarity-based reasoning. In the context of similarity-based reasoning, several issues merit concern. One is the representation of implication relation and two is the composition of a fuzzy implication relation with an observed system fact. The others are&nbsp; continuity and robustness of these systems which are the soul that must be inherited in the newly setup frameworks. Therefore, the purpose of this study is to introduce a new similarity-based approximate reasoning system which is based on introducing a new class of similarity measure on the space of $LR$-fuzzy numbers. Therefore, &nbsp;first, a new class of similarity measures is introduced between fuzzy sets. The similarity measure is needed in order to activate rules which are in terms of linguistic variables. Second, &nbsp;it is proved that the proposed measures satisfy the properties of the axiomatic definition as well as the other properties by a theorem. Next, &nbsp;we validate the effectiveness of the &nbsp; proposed similarity measure in a bidirectional approximate reasoning system in order to provide a &nbsp;nonlinear mapping of fuzzy &nbsp;input data into fuzzy output data. Finally, &nbsp;using existing experimental data from Uniaxial Compressive Strength (UCS) testing, &nbsp;the fuzzy inference system constitutive model is produced to describe the influence of joint geometry (joint location, trace length and orientation) on the UCS of rock. The numerical results will show that the proposed model based on similarity-based approximate reasoning systems has better performance compared with the Mamdani fuzzy inference systems and the &nbsp;multivariate regression.Numerical solutions for fractional optimal control problems using Müntz-Legendre polynomials
https://jmmrc.uk.ac.ir/article_4440.html
This study introduces a novel method using the M&uuml;ntz-Legendre polynomials for numerically solving fractional optimal control problems. Utilizing the unique properties of M&uuml;ntz-Legendre polynomials when dealing with fractional operators, these polynomials are used to approximate the state and control variables in the considered problems. Consequently, the fractional optimal control problem is transformed into a nonlinear programming problem through collocation points, yielding unknown coefficients. To achieve this, stable and efficient methods for calculating the fractional integral and derivative operators of M&uuml;ntz-Legendre functions based on three-term recurrence formulas and Jacobi-Gauss quadrature rules are presented. A thorough convergence analysis, along with error estimates, is provided. Several numerical examples are included to demonstrate the efficiency and accuracy of the proposed method.Best states for women to work: Analysis using mathematics of uncertainly
https://jmmrc.uk.ac.ir/article_4445.html
In this paper, we determine the fuzzy similarity measure between the ranking of states with respect to best the states for work for women and work in general. We break the states into regions and determine the same fuzzy similarity measures for each region. We find that the fuzzy similarity measures range from high to very high. We develop new fuzzy similaritymeasures to be used in rankings.Extension of stabilizers on subtraction algebras
https://jmmrc.uk.ac.ir/article_4449.html
This paper explores the intersection between the class of bounded subtraction algebras and the class of Boolean algebras, demonstrating their equivalence. It introduces the concepts of stabilizers for subsets and the stabilizers of one subset with respect to another within subtraction algebras. The study reveals that both the stabilizer of a subset and the stabilizer of an ideal with respect to another ideal are, in fact, ideals themselves. Investigating the impact of stabilizers on product and quotient subtraction algebras is a focal point. Additionally, a novel concept termed the &rdquo;stabilizer operation&rdquo; is defined, and it is proven that the collection of ideals endowed with a binary stabilizer operator forms a bounded Hilbert algebra.Some results on semi maximal filters in BL−algebras
https://jmmrc.uk.ac.ir/article_4466.html
In this article, we present an equivalent definition for the concept of the semi maximal filter in $BL-$algebras and some of their properties are studied. At first, we focus on elucidating the relationship between semi maximal filters and minimal prime filters. By conducting this analysis, some classifications for semi maximal filters are given.Investigating modules with partial endomorphisms having μ-small kernels
https://jmmrc.uk.ac.ir/article_4467.html
In this paper, we introduce and study the concept of generalized monoform modules ($G-M$ modules, for short) which is a proper generalization of that of monoform modules. We present some of their examples, properties and characterizations. It is shown that over a commutative ring $R$, the properties monoform, small monoform, $G-M$, compressible, uniform and weakly co-Hopfian are all equivalent. Moreover, we demonstrate that a ring $R$ is an injective semisimple ring iff any $R$-module is $G-M$. Further, we prove a similar theorem to Hilbert's basis theorem for monoform, small monoform and $G-M$ modules.Characterization of n-Jordan multipliers on rings
https://jmmrc.uk.ac.ir/article_4470.html
&lrm;Our main result states that every Jordan multiplier $T$ from a commutative ring $\mathcal{R}$ into a faithful $\mathcal{R}$-bimodule $M$ with characteristic different from $2$&lrm;, &lrm;is a multiplier. &lrm;We also generalize this result for all $n\geq 2$ with a suitable condition&lrm;. &lrm;Furthermore&lrm;, &lrm;we investigate some illuminating properties of such maps&lrm;. &lrm;The prime spectrum of a BCI-algebra
https://jmmrc.uk.ac.ir/article_4471.html
The aim of the present paper is to define the prime spectrum of a BCI-algebra as a generalization of prime spectrum BCK-algebras with respect to prime ideals. The notions of prime spectrum BCI-algebras using prime ideals, and some properties of these concepts are studied. Finally, we attempt to generalize some useful theorems about prime spectra in BCI-algebras instead of commutative BCK-algebras.A study of new fixed point results via hybrid contractions
https://jmmrc.uk.ac.ir/article_4477.html
The available literature shows that the ideas of admissible mappings and that of Suzuki-type contractions on metric spaces have been well-investigated. However, a hybrid version of these results in connection with $\theta$-contraction has not been adequately examined. On this basis therefore, the aim of this paper is to introduce a new concept under the name an admissible Jaggi-Suzuki-type hybrid ($\theta$-$\phi$)-contraction and to study new conditions for the existence of fixed point for this class of contractions on generalized or rectangular metric space. Applications and examples are provided to support the assumptions of our &nbsp;presented theorems. The results established herein extend some existing ideas in the corresponding literature. A few of these special cases are highlighted and discussed as corollaries.Ensemble of semi-supervised feature selection algorithms to reinforce heuristic function in ant colony optimization
https://jmmrc.uk.ac.ir/article_4480.html
Feature selection (FS) is a well-known dimensionality reduction method that chooses a hopeful subset of the original feature collection to diminish the influence the curse of dimensionality phenomenon. FS improves learning performance by removing irrelevant and redundant features. The significance of semi-supervised learning becomes obvious when labeled instances are not always accessible; however, labeling such data may be costly or time-consuming. Many of the samples in semi-supervised learning are unlabeled. Semi-supervised FS techniques overcome this problem, simultaneously utilizing information from labeled and unlabeled data. This article presents a new semi-supervised FS method called ESACO. ESACO uses a combination of ACO algorithm and a set of heuristics to select the best features. Ant colony optimization algorithm (ACO) is a metaheuristic method for solving optimization problems. Heuristic selection is a significant part of the ACO algorithm that can influence the movements of ants. Utilizing numerous heuristics rather than a single one can improve the performance of the ACO algorithm. However, using multiple heuristics investigates other aspects to attain optimal and better solutions in ACO and provides us with more information. Thus, in the ESACO, we have utilized the ensemble of heuristic functions by integrating them into Multi-Criteria Decision-Making (MCDM) procedure. So far, the utilization of multiple heuristics in ACO has not been studied in semi-supervised FS. We have compared the performance of the ESACO using the KNN classifier with variant experiments with eight semi-supervised FS techniques and 15 datasets. Considering the obtained results, the efficiency of the presented method is significantly better than the competing methods. The article's code link on GitHub can also be found at the following: https://github.com/frshkara/ESACO.Some properties of Camina and $n$-Baer Lie algebras
https://jmmrc.uk.ac.ir/article_4485.html
Let $I$ be a non-zero proper ideal of a Lie algebra $L$. Then $(L, I)$ is called a Camina pair if $I \subseteq [x,L]$, for all $x \in L\setminus I$. Also, $L$ is called a Camina Lie algebra if $(L, L^2)$ is a Camina pair. We first give some properties of Camina Lie algebras, and then show that all Camina Lie algebras are soluble. Also, a new notion of $n$-Baer Lie algebras is introduced, and we investigate some of its properties, for $n=1, 2$. A Lie algebra $L$ is said to be $2$-Baer if for any one dimensional subalgebra $K$ of $L$, there exists an ideal $I$ of $L$ such that $K$ is an ideal of $I$. Finally, we study three classes of Lie algebras with $2$-subideal subalgebras and give some relations among them.The small condition for modules with Noetherian dimension
https://jmmrc.uk.ac.ir/article_4486.html
A module $M$ with Noetherian dimension is said to satisfy the small condition, if for any small submodule $S$ of $M$ the Noetherian dimension of $S$ is strictly less than the Noetherian dimension of $M$. For an Artinian &nbsp;module $M$, this is equivalent to that $M$ is semisimple. In this article, we introduce &nbsp;and study this concept and observe some basic facts for modules with this condition. As a main result, it is shown that if $M$ is a &nbsp;module with &nbsp;finite hollow dimension which satisfies the &nbsp;small condition, then $\alpha \leq n-dim\, M\leq \alpha+1$, where &nbsp;$\alpha=\sup\{ n-dim\,S: S\ll M\}$. Furthermore, if $M$ is a &nbsp;module with Krull dimension and finite hollow dimension, then $\alpha \leq k-dim\, M\leq \alpha+1$, where &nbsp;$\alpha=\sup\{ k-dim\,S: S\ll M\}$. &nbsp;Also, we study the projective cover of modules satisfying the small condition or with finite hollow dimensionA new model for lung cancer prediction based on differential evolution algorithm and effective feature selection
https://jmmrc.uk.ac.ir/article_4488.html
Lung cancer is one of the most dangerous and fatal diseases worldwide. By using advanced machine learning techniques and optimization algorithms, early prediction and diagnosis of this disease can be achieved. Early identification of lung cancer is an important approach that can increase the survival rate of patients. In this paper, a novel method for lung cancer prediction is proposed, which combines two important techniques: Support Vector Machine (SVM) and Differential Evolution (DE) algorithm. Firstly, using the differential evolution algorithm, important and suitable features for lung cancer prediction are extracted. Then, using the SVM classifier, a classification model is built for prediction. The proposed approach is implemented on two lung cancer databases and achieves a good level of accuracy, which is compared with four other methods: C4.5 decision tree, neural network, Naive Bayes classifier, and logistic regression. The proposed model, with high accuracy and generalization power, is a suitable model for lung cancer detection and can serve as a strong decision support system alongside medical professionals.