Journal of Mahani Mathematical Research
Volume:13 Issue: 1, Winter and Spring 2024

‎We consider a planar symmetric vector field that undergoes a homoclinic bifurcation‎. ‎In order to study the existence of exterior periodic solutions of the vector field around broken symmetric homoclinic orbits‎, ‎we investigate the existence of fixed points of the exterior Poincare map around these orbits‎. This Poincare map is the result of the combination of flows inside and outside the homoclinic orbits. It shows how ‎a big periodic orbit converts to two small periodic orbits by passing through a double homoclinic structure‎. Finally‎, ‎we use the results to investigate the existence of periodic solutions of the perturbed Duffing equation.

‎In the context of observers‎, ‎any mathematical model according to the viewpoint of an observer is called a relative model‎. ‎The purpose of the present paper is to study the relative model of logical entropy‎. ‎Given an observer ‎, ‎we define the relative logical entropy and relative conditional logical entropy of a sub- -algebra having finitely many atoms on the relative probability ‎‎ measure space and prove the ergodic properties of these measures‎. ‎Finally‎, ‎it is shown that the relative logical entropy is invariant under‎ ‎the relation of equivalence modulo zero.

Today, the great performance of Deep Neural Networks(DNN) has been proven in various fields. One of its most attractive applications is to produce artistic designs. A carpet that is known as a piece of art is one of the most important items in a house, which has many enthusiasts all over the world. The first stage of producing a carpet is to prepare its map, which is a difficult, time-consuming, and expensive task. In this research work, our purpose is to use DNN for generating a Modern Persian Carpet Map. To reach this aim, three different DNN style transfer methods are proposed and compared against each other. In the proposed methods, the Style-Swap method is utilized to create the initial carpet map, and in the following, to generate more diverse designs, methods Clip-Styler, Gatys, and Style-Swap are used separately. In addition, some methods are examined and introduced for coloring the produced carpet maps. The designed maps are evaluated via the results of filled questionnaires where the outcomes of user evaluations confirm the popularity of generated carpet maps. Eventually, for the first time, intelligent methods are used in producing carpet maps, and it reduces human intervention. The proposed methods can successfully produce diverse carpet designs, and at a higher speed than traditional ways.

Inverse data envelopment analysis (InvDEA) is a remarkable and popular management tool. This paper deals with one application of this tool. In fact, the problem of the combination of the units is investigated in the presence of negative data. The problem of combining units refers to the fact that a set of units create a new unit based on synergy to improve their performance. We use multiple objective programming for this purpose and suggest new models based on predetermined conditions for the new unit. The proposed models estimate inputs and outputs simultaneously. Importance advantages of the proposed models are i) We can follow multiple goals in the problem of combining units because multiple objective programming is applied. ii) Models can simultaneously estimate the inputs and outputs of the combined unit. iii) Unlike the existing methods in the InvDEA-based merging literature, the negative data do not need to be transferred to positive data. Finally, a numerical example is used to explain and validate the model proposed in this paper.

By considering a fixed point in the punctured unit disk and using the --derivative, a new subfamily of meromorphic and univalent functions is defined. Also, the first and second order { --derivative} of meromorphic functions are introduced. Coefficient bounds, extreme points, radii of starlikeness and convexity are obtained. Furthermore, the convexity and preserving under convolution with some restrictions on parameters are investigated

The Inverse Gaussian (IG) distribution is widely used to model positively skewed data. In this article, we examine goodness of fit tests for the Inverse Gaussian distribution based on the empirical distribution function. In order to compute the test statistics, parameters of the Inverse Gaussian distribution are estimated by maximum likelihood estimators (MLEs), which are simple explicit estimators. Critical points and the actual sizes of the tests are obtained by Monte Carlo simulation. Through a simulation study, power values of the tests are compared with each other. Finally, an illustrative example is presented and analyzed.

Here, we investigate the existence of solutions for the initial value problem of fractional-order differential inclusion containing a nonlocal infinite-point or Riemann–Stieltjes integral boundary conditions. A sufficient condition for the uniqueness of the solution is given. The continuous dependence of the solution on the set of selections and on some data is studied. At last, examples are designed to illustrate the applicability of the theoretical results.

In this paper, an attempt has been taken to develop a method to solve the neutrosophic multiobjective linear fractional programming (NMOLFPP) problem. In the first step of our method, the problem is linearized based on some transformations. Then, the linearized model is reduced to a crisp multi-objective programming problem with the help of the accuracy function for each objective. In the following, we extended Zimmerman’s approach to maximize the truth membership and minimize the indeterminacy and falsity membership functions in the solution procedure. Finally, to illustrate the proposed approach, a numerical example is included.

In this paper the meanings of neutrosophic special -dominating set, neutrosophic special -domination number, inverse neutrosophic special domination set (number) and inverse neutrosophic special -domination number are introduced and some of related results are investigated. Finally, an application of inverse neutrosophic special dominating set in decision making under ashy clauses between certainty and uncertainty is provided. In fact, we present a decision-making problem in real-world applied example which discusses the factors influencing a companys efficiency. The presented model is, in fact, a factor-based model wherein the impact score of each factor is divided into two types of direct and indirect influences.

One of the humanities' most basic topics is the response time to creative problem-solving and decision-making in this field. In recent years, response time modeling by fitting an exponentially-modified normal (E-MN) probability distribution and the results obtained from this process have been widely used. The E-MN probability distribution results from the convolution of a normal probability distribution and an exponential probability distribution and contains three parameters. In this paper, a developed Bayesian (DB) estimation method is introduced to estimate the parameters of an E-MN probability distribution. This new estimation method uses the adaptive rejection Metropolis-Hastings (ARM-H) sampling method. The reason for this is that in normal mode and based on the classical Bayesian estimation method, the chosen prior probability density functions (pdfs) lead to posterior pdfs with unknown form and, they are not always logarithmically concave. Also, respectively, simulation and real data sets study have been done to demonstrate the better performance of the DB estimation method than the two other well-known estimation methods used in this context, including the maximum likelihood (ML) estimation method and the quantile maximum likelihood (QML) estimation method. To show the better efficiency of the proposed estimation method compared with the two other estimation methods, the root mean squared error (RMSE) criterion is used.

In this paper, we investigate the normalized Ricci-Bourguignon flow with incomplete initial metric on an open surface. We show that such a flow converges exponentially to a metric with constant Gaussian curvature if the initial metric is suitable. In particular, if the initial metric is complete then the metrics converge to the standard hyperbolic metric.

In this paper, we use new techniques to prove Hyers-Ulam and Hyers-Ulam-Rasiass stability of Deeba, Drygas and logarithmic functional equations in non-Archimedean normed spaces. We generalize some earlier results connected with the stability of these functional equations and inequalities. In addition, we provide some examples to clarify the definitions and theorems.

As the main findings of our research work, we present a novel theorem on the relationship between the number of extrema of compound sinusoidal signals and its high-frequency component. In the case of signals consisting of the sum of two sine signals, if the high-frequency component has a higher product of the frequency and the amplitude, then we prove that the frequency of the high-frequency component is proportional to the number of extrema in a time interval. This theorem justifies some of the experimental results of other researchers on the relevance of extrema to frequency and amplitude. To confirm the theorem, extrema counting was performed on speech signals and compared with Fourier transform. The experimental results show that the average number of extrema of the compound sinusoidal signal or its derivatives over a time interval can be used to estimate the frequency at its highest frequency band. An important application of this research work is the fast calculation of high frequencies of a signal. This theorem also shows that the number of extrema points can be used as a new effective feature for signal processing, especially speech signals.

The main aim of this research is to investigate the stability of a functional equation that maintains the lattice structure in a uniformly complete unital Banach -algebra. Through this inquiry, we can shed light on the behavior of this equation and its relationship with the algebraic properties of a Banach space. This research has both theoretical and practical implications. It contributes to the foundations of functional analysis, lattice theory, operator theory, approximation theory, and various applied mathematical disciplines. The findings from this research can have implications in diverse fields ranging from mathematics and physics to engineering and computer science, offering valuable insights and potential applications.

The concept of (quasi) superhypergraphs as a generalization of graphs makes a relation between some sets of elements in detail and in general (in the form of parts to parts, parts to whole, and whole to whole elements of sets) and is very useful in the real world. This paper considers the novel concept of (quasi) superhypergraphs and introduces the notation of dominating set and domination number of (quasi) superhypergraphs. Especially, we have analyzed the domination number of uniform (quasi) superhypergraphs and computed their domination number on different cases. The flows (from right to left, from left to right, and two-sided) as maps play a main role in (quasi) superhypergraphs and it is proved that domination numbers of (quasi) superhypergraphs are dependent on the flows. We define the valued-star (quasi) superhypergraphs for the design of hypernetworks and compute their domination numbers. We have shown that the domination numbers of valued-star (quasi) superhypergraphs are distinct in different flow states. In final, we introduce some applications of dominating sets of (quasi) superhypergraphs in hypernetwork as computer networks and treatment networks with the optimal application.

The generalization of asymmetric Laplace (AL) distribution has recently received considerable attention in dealing with skewed and long-tailed data. In this article, we introduce a new family of distributions based on the location mixture of asymmetric Laplace (LM-AL) distribution. Some properties of this family, such as expressions for mean, variance, skewness and kurtosis coefficients and characteristic function, are derived. We show that this family of distributions is quite flexible because it has wider ranges of skewness and kurtosis than the other skew distributions introduced in the literature. We also introduce a family of weighted distributions based on the survival function of the exponential distribution and will show that truncated LM-AL distribution in zero which can be used in survival analysis, belongs to this family. In order to compute the maximum likelihood (ML) estimation of the parameters in the location mixture of AL distribution, an EM-type algorithm is developed and the estimation of parameters of model in survival analysis performed using a maximization algorithm, due to the problem complexity. Finally, the performance and applicability of the truncated LM-AL model in survival analysis is illustrated through analyzing a simulation study and two real data set. This family of distributions represent a suitable alternative to existing models such as Weibull, log-normal, log-logistic, gamma and Lindley distributions.

The aim of this paper is to construct fraction of a Γ-module over a commutative Γ-ring. There should be an appropriate set S of elements in a Γ-ring R to be used as a Γ-module of fractions. Then we study the homomorphisms of a Γ-module which can lead to related basic results. We show that for every Γ-module M, S−1 (0 :R M) = (0 :S−1R S−1M). Also, if M is a finitely generated RΓ-module, then S−1M is finitely generated

For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W) := (d(v, w1), d(v, w2), . . . , d(v, wk)) is called the (metric) representation of v with respect to W, where d(x, y) is the distance between the vertices x and y. The set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W. The minimum cardinality of a resolving set for G is its metric dimension. In this paper, we investigate the metric dimension of the lexicographic product of graphs G and H, G[H], for some known graphs.

The Aichi biodiversity targets were established by the UN convention of biological Diversity and consist of 20 specific targets to address and mitigate biodiversity loss across the globe. We determine how well OECD countries are achieving the Aichi targets. We use the Sustainable Development Goals to make the determination. The Biodiversity and Habitat issue category assesses countries’ actions toward retaining natural ecosystems and protecting the full range of biodiversity within their borders. It consists of seven indicators: terrestorial biome protection (weighted for national and global rarity of biomes), marine protected areas, Protected Areas Representativeness Index, Species Habitat Index, Species Protection Index, and Biodiversiy Index, [4]. We determine the similarity between the rankings determined by the weighted average values and the Environmental Performance Index (EPI) scores

Data dimensions and networks have grown exponentially with the Internet and communications. The challenge of high-dimensional data is increasing for machine learning and data science. This paper presents a hybrid filter-wrapper feature selection method based on Equilibrium Optimization (EO) and Simulated Annealing (SA). The proposed algorithm is named Filter-Wrapper Binary Equilibrium Optimizer Simulated Annealing (FWBEOSA). We used SA to solve the local optimal problem so that EO could be more accurate and better able to select the best subset of features. FWBEOSA utilizes a filtering phase that increases accuracy as well as reduces the number of selected features. The proposed method is evaluated on 17 standard UCI datasets using Support Vector Machine (SVM) and K-Nearest Neighbors (KNN) classifiers and compared with ten state-of-the-art algorithms (i.e., Binary Equilibrium Optimizer (BEO), Binary Gray Wolf Optimization (BGWO), Binary Swarm Slap Algorithm (BSSA), Binary Genetic Algorithm (BGA), Binary Particle Swarm Optimization (BPSO), Binary Social Mimic Optimization (BSMO), Binary Atom Search Optimization (BASO), Modified Flower Pollination Algorithm (MFPA), Bar Bones Particle Swarm Optimization (BBPSO) and Two-phase Mutation Gray Wolf Optimization (TMGWO)). Based on the results of the SVM classification, the highest level of accuracy was achieved in 13 out of 17 data sets (76%), and the lowest number of selected features was achieved in 15 out of 17 data sets (88%). Furthermore, the proposed algorithm using class KNN achieved the highest accuracy rate in 14 datasets (82%) and the lowest selective feature rate in 13 datasets (76%).

In this manuscript, we consider an extended version of biconservativity condition (namely, -biconservativity) on the Riemannian hypersurfaces of Lorentzian standard 4-space forms. This new condition is obtained by substituting the Cheng-Yau operator instead of the Laplace operator . We show that every -biconservative Riemannian hypersurface of a Lorentzian 4-space form with constant mean curvature has constant scalar curvature.

Let R be a commutative ring with identity and R(RM) denote the bounded lattice of radical submodules of an R-module M. We say that M is a radical distributive module, if R(RM) is a distributive lattice. It is shown that the class of radical distributive modules contains the classes of multiplication modules and finitely generated distributive modules properly. Also, it is shown that if M is a radical distributive semisimple R-module and for any radical submodule N of M with direct sum complement N˜, the complementary operation on R(RM) is defined by N0 := N˜ + rad{0}, then R(RM) with this unary operation forms a Boolean algebra. In particular, if M is a multiplication module over a semisimple ring R, then R(RM) is a Boolean algebra, which is also a homomorphic image of R(RR)

The aim of this manuscript is to introduce and analyze a stochastic finite difference scheme for Ito stochastic partial differential equations. We also discuss the consistency, stability, and convergence for the stochastic finite difference scheme. The numerical simulations obtained from the proposed stochastic finite difference scheme show the efficiency of the suggested stochastic finite difference scheme.

In this note, we obtain a reverse version of the Haagerup Theorem. In particular, if A ∈ Mn has a 2 × 2− principal submatrix as  1 α β 1  with β 6= ¯α, then kSAk > 1 where the operator SA : Mn −→ Mn is defined by SA(B) := A ◦ B where ” ◦ ” stands for Schur product

One of the alternative versions of Shannon entropy is a measure of information which is called exponential entropy. Shannon and exponential entropies depend only on the event probabilities. These measures have also been extended to incorporate a set of weights associated with the events. Such weights may reflect some additional characteristics of the events such as their relative importance. In this paper, Axiomatic derivations and properties of weighted exponential entropy parallel to those achieved for weighted entropy are investigated. The relation between weighted exponential entropy of X and a strictly monotone and nonnegative function of X has obtained. The generalized weighted entropy and the generalized weighted exponential entropy for continuous random variable have been presented.

. There exists a one to one correspondence between higher derivations {dn}∞n=0 on an algebra A and the family of sequences of derivations {δn}∞n=1 on A. In this paper, we obtain a relation that calculates each derivation δn(n ∈ N) directly as a linear combination of products of terms of the corresponding higher derivation {dn}∞n=0. Also, we find the general form of the family of inner derivations corresponding to an inner higher derivation. We show that for every two higher derivations on an algebra A, the product of them is a higher derivation on A. Also, we prove that the product of two inner higher derivations is an inner higher derivation.

In recent years, data mining and machine learning methods in the medical field have received much attention and have optimized many complex issues in the medical field. One of the problems facing researchers is the appropriate dataset, and the suitable dataset on which different methods of data mining and machine learning can be applied is rarely found. One of the most reliable and appropriate datasets in the field of diabetes diagnosis is the Indian Survey Database. In this article, we have tried to review the methods that have been implemented in recent years using machine learning classification algorithms on this data set and compare these methods in terms of evaluation criteria and feature selection methods. After comparing these methods, it was found that models that used feature selection methods were more accurate than other approaches.

Among the 2-plectic structures on vector spaces, the canonical ones and the 2-plectic structures induced by the Killing form on semisimple Lie algebras are more interesting. In this note, we show that the group of linear preservers of the canonical 2-plectic structure is noncompact and disconnected and its dimension is computed. Also, we show that the group of automorphisms of a compact semisimple Lie algebra preserving its 2-plectic structure, is compact. Furthermore, it is shown that the 2-plectic structure on a semisimple Lie algebra g is canonical if and only if it has an abelian Lie subalgebra whose dimension satisfies in a special condition. As a consequence, we conclude that the 2-plectic structures induced by the

Let G be a finite group. If A ≤ G, recall that A is weakly S-semipermutable in G provided there is K E G such that KA is Spermutable in G, and K ∩ A is S-semipermutable in G. The purpose of this paper is to demonstrate that weakly S-semipermutability of special types of subgroups in a finite group G can help us to determine structural properties of G. For example, given a prime p, a p-soluble finite group G and a Sylow p-subgroup Gp of G, we will show that G is p-supersoluble if the maximal subgroups of Gp are weakly S-semipermutable in G. Moreover, we use the concept of weakly S-semipermutability to prove new criteria for p-nilpotency of finite groups

Feature selection is one of the most important tasks in machine learning. Traditional feature selection methods are inadequate for reducing the dimensionality of online data streams because they assume that the feature space is fixed and every time a feature is added, the algorithm must be executed from the beginning, which in addition to not performing real-time processing, causes many unnecessary calculations and resource consumption. In many real-world applications such as weather forecasting, stock markets, clinical research, natural disasters, and vital-sign monitoring, the feature space changes dynamically, and feature streams are added to the data over time. Existing online streaming feature selection (OSFS) methods suffer from problems such as high computational complexity, long processing time, sensitivity to parameters, and failure to account for redundancy between features. In this paper, the process of OSFS is modeled as a multi-objective optimization problem for the first time. When a feature stream arrives, it is evaluated in the multi-objective space using fuzzy Pareto dominance, where three feature selection methods are considered as our objectives. Features are ranked according to their degree of dominance in the multi-objective space over other features. We proposed an effective method to select a minimum subset of features in a short time. Experiments were conducted using two classifiers and eight OSFS algorithms with real-world datasets. The results show that the proposed method selects a minimal subset of features in a reasonable time for all datasets.

The notion of a (branchwise) commutative BI-algebra is presented, and some related properties are investigated. We show that the class of commutative BH-algebras is broader than the class of commutative BI-algebras. Moreover, we prove every singular BI-algebra is a BH-algebra. Also, we define the commutative ideals in BI-algebras and characterize the commutative BI-algebras in terms of commutative ideals

We use the Key-Moori Method 1 and examine 1-designs and codes from the representations of the alternating group A7. It is shown that a self-dual symmetric 2-(35, 18, 9) design and an optimal even binary [21, 14, 4] LCD code are found such that they are invariant under the full automorphism groups S8 and S7, respectively. Moreover, designs with parameters 1-(21, l, k1,l) and 1-(35, l, k2,l) are obtained, where ω is a codeword, l = wt(ω), k1,l = l|ω S7 |/21 and k2,l = l|ω S7 |/35. It is seen that there exist a 2-(21, 5, 12) design with the full automorphism group S7 among these 1-designs

We introduce the α−higher rank form of the matrix numerical range, which is a special case of the matrix polynomial version of the higher rank numerical range. We also, investigate some algebraic and geometrical properties of this set for general and nilpotent matrices. Some examples to confirm the results are brough

Higher utilization of existing resources and facilities in order to increase efficiency and profitability is always one of the basic challenges for parallel processing systems and environments, and this challenge becomes more complicated when the system resources are heterogeneous. One way to achieve high efficiency and profitability of heterogeneous parallel systems is to schedule tasks optimally. In this paper, an extended tabu search-based scheduling algorithm (ESTS) is presented to improve the profitability of heterogeneous parallel systems, which can achieve suitable solutions in a short computational time. To evaluate the efficiency of the proposed solution, due to the lack of a suitable criterion to evaluate this problem, the obtained results are compared with both the results of an extended scheduling based on a genetic algorithm (ESGA) with a large number of chromosomes and a high number of generations, as well as an extended scheduling based on a simulated annealing algorithm (ESSA) with a linear temperature reduction. The benchmark files of different sizes were tested under the same conditions, and the comparison of results shows the superiority of the proposed solution in terms of profitability and computational time

This paper extends the notion of weak convergence in metric spaces to the case of S-metric spaces. Moreover, some results on the weak convergence of fixed point iterations of Banach’s, Kannan’s, Chatterjea’s, Reich’s, Hardy and Roger’s types of contractions on S-metric spaces are obtained. In addition, an example is presented to demonstrate our primary result