جستجوی مقالات مرتبط با کلیدواژه "5" در نشریات گروه "ریاضی"
تکرار جستجوی کلیدواژه «5» در نشریات گروه «علوم پایه»-
Journal of Computational Algorithms and Numerical Dimensions, Volume:4 Issue: 1, Winter 2025, PP 18 -33An implicit Superclass of non-block Extended Backward Differentiation Formulae (SEBDF) for the numerical integration of first-order stiff system of Ordinary Differential Equations (ODEs) in Initial Value Problems (IVPs) with optimal stability properties is presented. The stability and convergence properties of the SEBDF schemes show that the methods are consistent, zero stable and convergent. The plotted Region of Absolute Stability (RAS) of the methods using boundary locus shows that the methods are A-stable of order up to order 5 and A(α)-stable of order up to 9. The algorithm is described whereby the required approximate solution is predicted using classical explicit Euler’s method and conventional Backward Differentiation Formula (BDF) schemes of order k and then corrected using a Super class of Extended Backward Differentiation Formula (SEBDF) schemes of higher orders k+1. The SEBDF schemes are implemented using a Modified Newton iteration algorithm iterated to convergence in which some selected systems of first-order stiff IVPs are solved, and the numerical results obtained for the proposed methods are often better than the existing BDF and SBDF methods for solving stiff IVPs.Keywords: Stiff, Backward Differentiation Formula, Extended Backward Differentiation Formula, A-Stability, Convergence, Consistency
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Let $r\geq 2$. A subset $S$ of vertices of a graph $G$ is a $r$-hop independent dominating set if every vertex outside $S$ is at distance $r$ from a vertex of $S$, and for any pair $v, w\in S$, $d(v, w)\neq r$. A $r$-hop Roman dominating function ($r$HRDF) is a function $f$ on $V(G)$ with values $0,1$ and $2$ having the property that for every vertex $v \in V$ with $f(v) = 0$ there is a vertex $u$ with $f(u)=2$ and $d(u,v)=r$. A $r$-step Roman dominating function ($r$SRDF) is a function $f$ on $V(G)$ with values $0,1$ and $2$ having the property that for every vertex $v$ with $f(v)=0$ or $2$, there is a vertex $u$ with $f(u)=2$ and $d(u,v)=r$. A $r$HRDF $f$ is a $r$-hop Roman independent dominating function if for any pair $v, w$ with non-zero labels under $f$, $d(v, w)\neq r$. We show that the decision problem associated with each of $r$-hop independent domination, $r$-hop Roman domination, $r$-hop Roman independent domination and $r$-step Roman domination is NP-complete even when restricted to planar bipartite graphs or planar chordal graphs.Keywords: Dominating Set, Hop Dominating Set, Step Dominating Set, Hop Independent Set, Hop Roman Dominating Function, Hop Roman Independent Dominating Function, Complexity
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An edge $e$ of a simple graph $G=(V_{G},E_{G})$ is said to ev-dominate a vertex $v\in V_{G}$ if $e$ is incident with $v$ or $e$ is incident with a vertex adjacent to $v$. A subset $D\subseteq E_{G}$ is an edge-vertex dominating set (or an evd-set for short) of $G$ if every vertex of $G$ is ev-dominated by an edge of $D$. The edge-vertex domination number of $G$ is the minimum cardinality of an evd-set of $G$. In this paper, we initiate the study of the graphs with unique minimum evd-sets that we will call UEVD-graphs. We first present some basic properties of UEVD-graphs, and then we characterize UEVD-trees by equivalent conditions as well as by a constructive method.Keywords: Edge-Vertex Domination, Edge-Vertex Domination Number, Trees
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For $n \ge 2t+1$ where $t \ge 1$, the circulant graph $C_n (1, 2, \dots , t)$ consists of the vertices $v_0, v_1, v_2, \dots , v_{n-1}$ and the edges $v_i v_{i+1}$, $v_i v_{i+2}, \dots , v_i v_{i + t}$, where $i = 0, 1, 2, \dots , n-1$, and the subscripts are taken modulo $n$. We prove that the metric dimension ${\rm dim} (C_n (1, 2, \dots , t)) \ge \left\lceil \frac{2t}{3} \right\rceil + 1$ for $t \ge 5$, where the equality holds if and only if $t = 5$ and $n = 13$. Thus ${\rm dim} (C_n (1, 2, \dots , t)) \ge \left\lceil \frac{2t}{3} \right\rceil + 2$ for $t \ge 6$. This bound is sharp for every $t \ge 6$.Keywords: Cayley Graph, Distance, Resolving Set
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A vertex $u$ of a graph $G=(V,E)$ ve-dominates every edge incident to $u$ as well as every edge adjacent to these incident edges. A set $S\subseteq V$ is a vertex-edge dominating set (or a ved-set for short) if every edge of $E$ is ve-dominated by at least one vertex in $S$. A ved-set is independent if its vertices are pairwise non-adjacent. The independent ve-domination number $i_{ve}(G)$ is the minimum cardinality of an independent ved-set and the upper independent ve-domination number $\beta_{ve}(G)$ is the maximum cardinality of a minimal independent ved-set of $G$. In this paper, we are interesting in graphs $G$ such that $i_{ve}(G)=\beta_{ve}(G)$, which we call well ve-covered graphs. We show that recognizing well ve-covered graphs is co-NP-complete, and we present a constructive characterization of well ve-covered trees.Keywords: Vertex-Edge Domination, Independent Vertex-Edge Domination, Well Ve-Covered Graphs, Trees
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In 2020, mathematical chemist, Ivan Gutman, introduced a new vertex-degree-based topological index called the Sombor Index, denoted by $SO(G)$, where $G$ is a simple, connected, finite, graph. This paper aims to present some novel formulas, along with some upper and lower bounds on the Sombor Index of generalized Sierpi\'nski graphs; originally defined by Klav\v{z}ar and Milutinovi\'c by replacing the complete graph appearing in $S(n,k)$ with any graph and exactly replicating the same graph, yielding self-similar graphs of fractal nature; and on the Sombor Index of the $m$-Mycielskian or the generalized Mycielski graph; formed from an interesting construction given by Jan Mycielski (1955); of some simple graphs such as \(K_n\), \(C_n^2\), \(C_n\), and \(P_n\). We also provide Python codes to verify the results for the \(SO\left(S\left(n,K_m\right)\right)\) and \(SO\left(\mu_m\left(K_n\right)\right)\).Keywords: Topological Index, Sombor Index, Bounds, Sierpiński Graphs, Mycielskian Graphs
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For any graph, Weisfeiler and Leman assigned the smallest matrix algebra which contains the adjacency matrix of the graph. The coherent configuration underlying this algebra for a graph $\Gamma$ is called the coherent configuration of $\Gamma$, denoted by $\mathcal{X}(\Gamma)$. In this paper, we study the coherent configuration of circular-arc graphs. We give a characterization of the circular-arc graphs $\Gamma$, where $\mathcal{X}(\Gamma)$ is a homogeneous coherent configuration. Moreover, all homogeneous coherent configurations which are obtained in this way are characterized as a subclass of Schurian coherent configurations.Keywords: Coherent Configuration, Homogeneous, Circular-Arc Graph, Wreath Product
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This insightful article examines the $\lambda$-statistical convergence of function sequences within neutrosophic norm spaces. It introduces novel concepts such as $\lambda$-statistical pointwise convergence and $\lambda$-statistical uniform convergence specifically tailored for neutrosophic norm spaces, representing a notable advancement in the field. The article elucidates the foundational properties of these innovative concepts, offering valuable insights into their theoretical foundations and practical applications.Keywords: Neutrosophic Normed Space (NNS), Neutrosophic Equicontinuity, T-Norm, T-Conorm, ~$, Lambda$-Statistical Convergence, Pointwise, Uniform Convergence
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A g-phase retrievable frame is a $\lambda$-phase retrievable frame in finite dimensional Hilbert space $\mathcal{H}_n$, where $\lambda$ is an special function, which is called phase coefficient function. In this paper we study the Lipschitz analysis of the nonlinear map $\alpha_{\lambda,{\mathcal{F}}}:\widehat{\mathcal{H}_n}\longrightarrow\mathbb{F}^m, \ \ \ \alpha_{\lambda,{\mathcal{F}}}(\hat{x}):=\begin{bmatrix}\lambda\left( \left\langle {x,f_k}\right\rangle\right)\end{bmatrix}_{1\leq k\leq m}$, where $\widehat{\mathcal{H}_n}$ is the quotient space corresponding to a special equivalence relation on $\mathcal{H}_n$ with respect to phase coefficient function $\lambda$, $\mathcal{F}=\{f_k\}_{k=1}^m$ is a $\lambda$-phase retrievable frame for $\mathcal{H}_n$, $\mathbb{F}=\mathbb{R}$ for real Hilbert space $\mathcal{H}_n$ and $\mathbb{F}=\mathbb{C}$ for complex Hilbert space $\mathcal{H}_n$.Keywords: Frame, Phase Coefficient Function, Phase Retrievable Frame, $, Lambda$-Phase Retrievable Frame, G-Phase Retrievable Frame, Lipschitz Continuous Function
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For $\alpha>0$, the growth space $\mathcal{A}^{-\alpha}$ is the space of all function $f\in H(\DD)$ such that $$\left\|f\right\|_{\mathcal{A}^{-\alpha}}=\sup_{z\in\DD}\left(1-\left|z\right|^2\right)^\alpha \left|f(z)\right|<\infty.$$In this work, we obtain exact formula for the norm of weighted composition operators from $\mathcal{A}^{-\alpha}$ into $\mathcal{A}^{-\beta}$. Especially, we show that\begin{align*}\left\|uC_\varphi\right\|_{ \mathcal{A}^{-\alpha}\rightarrow \mathcal{A}^{-\beta}}= \sup_{z\in\mathbb{D}}\frac{\left(1-\left |z \right|^2\right)^\beta \left|u(z)\right|}{\left(1-\left |\varphi(z) \right|^2 \right)^\alpha}.\end{align*}As a corollary, we show that $C_\varphi: \mathcal{A}^{-\alpha}\rightarrow \mathcal{A}^{-\alpha}$ is isometry if and only if $\f$ is rotation. Then the exact formula for the essential norm $uC_\varphi: \mathcal{A}^{-\alpha}\rightarrow \mathcal{A}^{-\beta}$ is given as follow$$\left\|uC_\varphi\right\|_{e, \mathcal{A}^{-\alpha}\rightarrow \mathcal{A}^{-\beta}}= \left(\frac{e}{2\alpha}\right)^\alpha \limsup n^\alpha \left\|u\varphi^{n-1}\right\|_{\mathcal{A}^{-\beta}}.$$Also, some equivalence conditions for compactness of such operators operator between difference growth spaces are given.Keywords: Essential Norm, Growth Space, Isometry, Norm
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In this paper, we define a modified version of frame in quaternionic Hilbert spaces (QHS) and give a necessary condition for a block Bessel sequence in terms of a bounded right linear operator. Also, a necessary and sufficient condition for a sequence to be a block Bessel sequence is given. Further, a method to construct a desired block frame using a given block frame is discussed. Finally, a characterization of block frame in terms of a right linear operator is given.Keywords: Frames, Block Frames, Quaterninic Hilbert Space
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A mapping $ f$ from a bitopological space $(X, \tau_{1}, \tau_{2})$ into a bitopological space $(Y, \tau^{'}_{1}, \tau^{'}_{2}) $ is said to be a pair-homeomorphism if and only if the induced functions $ f_1: (X, \tau_{1})\rightarrow(Y, \tau^{'}_{1}) $ and $ f_2: (X, \tau_{2})\rightarrow(Y, \tau^{'}_{2}) $ are homeomorphisms. The {deck} of a bitopological space $(X, \tau_{1}, \tau_{2})$ is the set $\mathscr{D}(X)=\{[X_{x}]:x\in X\},$ where $[Z]$ denotes the pair-homeomorphism class of $Z$. A bitopological space $X$ is {reconstructible} if whenever $\mathscr{D}(X)=\mathscr{D}(Y)$ then $(X, \tau_{1}, \tau_{2})$ is pair-homeomorphic to $(Y, \tau^{'}_{1}, \tau^{'}_{2})$. A property $\mathscr{P}$ of a bitopological space $ X $ is {recognizable} if $\mathscr{D}(X)=\mathscr{D}(Y)$ implies \textquotedblleft$X$ has $\mathscr{P}$ if and only if $Y$ has $\mathscr{P}$\textquotedblright. It is shown that every finite bitopological space, with a unique isolated point and at most two non pair-homeomorphic cards, are recognizable.Keywords: Reconstruction, Bitopological Space, Isolated Point, Pair-Homeomorphism
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چالش ریاضی یکی از اجزای اصلی در آموزش ریاضی است که هدف آن تکمیل توانایی یادگیرندگان در زمینه ریاضیات است. همچنین خلاقیت یک ویژگی شخصی و اجتماعی است، که موجب پیشرفت افراد در همه ی سطوح و در تمام مقاطع تاریخی می شود. در واقع به کارگیری اطلاعات و دانسته ها و استفاده از خلاقیت در حل مساله بسیار حائز اهمیت می باشد. در این بین برای یک معلم ریاضیات علاوه بر داشتن روش مناسب و دانش خوب، استفاده از نرم افزار و نظریه های آموزش ریاضی نیز بر شکوفایی استعداد و خلاقیت دانش آموزان موثر بوده و به آنها برای حل یک مساله ی سطح بالاتر کمک می کند. همچنین استفاده از اصول اقلیدس و تسلط بر آن ها، به معلم دیدگاه بهتری برای فرآیند حل مسائل هندسی می دهد. در این مقاله، یک مساله ی هندسی متناسب با سطح کلاس هشتم و نهم برای کلاس هفتم در مدرسه ی سمپاد طرح شده است و ضمن بیان اهمیت اصول اقلیدس، هر دو محیط پویای ریاضیات و محیط کاغذ-مداد، به کار گرفته شده است. با استفاده از نظریه ی آموزش ریاضی فن هیلی، با طراحی یک داربست آموزشی و گفتگوی بین معلم و دانش آموزان و با کمک نظریه ی تنوع، پاسخ مساله توسط چند دانش آموز حدس زده شده است، و یک دانش آموز خلاق به آن پاسخ کامل داده است. در نهایت مساله را به صورت اگر و تنها اگر بیان کردیم. در این میان در محیط پویا و محیط کاغذ-مداد، تجزیه ی ابعادی اشکال نیز به کار برده شد.کلید واژگان: نظریه های آموزش ریاضی, داربست زنی - خلاقیت, نرم افزارهای ریاضی, اگر و تنها اگرMathematical Challenge is one of the main components in mathematics education, which aims to improve the ability of learners in the field of mathematics. Also, creativity is a personal and social characteristic that leads to the development of people at all levels and in all historical periods. In fact, applying information and knowledge and using creativity in solving problems is very important. In between, for a mathematics teacher, in addition to having good techniques and knowledge, the use of software and theories of mathematics education is also effective on the flourishing of students' talent and creativity and helps them to solve a higher-level problem. In geometric concepts, using Euclid's principles and mastering them gives the teacher a better perspective for the problem solving process. In this article, a geometrical problem suitable for the 8th and 9th grade level has been proposed for the 7th grade in Sampad school, and while expressing the importance of Euclid's principles, both the dynamic environment of mathematics and the paper-pencil environment have been used. By using the Van Hiele’s Theory in mathematical education, by designing an educational scaffold and dialogue between the teacher and students and with the help of Variation Theory, the answer of the problem was guessed by several students and a creative student gave a complete answer. Finally, we stated the problem as if and only if. In the meantime, Dimensional Deconstruction of Shapes was also used in the dynamic environment and paper-pencil environment.Keywords: Theories Of Math Education, Scaffolding, Creativity, Math Software, If, Only If
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یک رنگ آمیزی تشخیص از گرافی ساده مانند $G$، عبارت است از یک رنگ آمیزی رئوس $G$ به طوری که تنها خودریختی ای از $G$ که این رنگ آمیزی را حفظ می کند، خودریختی همانی باشد. به عبارت دیگر، این رنگ آمیزی همه ی تقارن های $G$ را «می شکند». عدد تشخیص یک گراف مانند $G$، که با $D (G)$ نمایش داده می شود، کوچک ترین تعداد رنگ مورد نیاز برای یک رنگ آمیزی تشخیص~$G$ است. در این مقاله، علاوه بر مطالعه ی برخی از روابط موجود بین $D (G)$ و پارامترهای مهم گرافی، مفهوم $(D,\alpha) $-عادی بودن یک گراف را تعریف می کنیم که بیانگر مقایسه ی بین $D (G)$ و عدد استقلال $\alpha (G)$ است. سپس طیف وسیعی از گراف ها را از دیدگاه $(D,\alpha) $-عادی بودن مطالعه و رده بندی هایی را برای گراف های دوبخشی، چندبخشی کامل، گراف های جانسون تعمیم یافته و حاصل ضرب های دکارتی و گراف های خط برخی از گراف ها ارائه می کنیم.
کلید واژگان: گراف, عدد تشخیص, عدد تثبیت کننده, گراف خط, گراف چندبخشیA distinguishing coloring of a simple graph $G$ is a vertex coloring of $G$ which is preserved only by the identity automorphism of $G$. In other words, this coloring ``breaks'' all symmetries of $G$. The distinguishing number $D(G)$ of a graph $G$ is defined to be the smallest number of colors in a distinguishing coloring of $G$. This concept of “symmetry breaking” was first proposed by Babai in 1977 and after the publication of a seminal paper by Albertson in 1996, it attracted the attention of many mathematicians. In this paper, along with studying some relations between $D(G)$ and some other important graph parameters, we introduce the concept of a $(D,\alpha)$-ordinary graph which displays the comparison between $D(G)$ and the independence number $\alpha(G)$. Then we consider the classification of $(D,\alpha)$-ordinary graphs in various families of graphs such as forests, cycles, generalized Johnson graphs, Cartesian products of graphs and line graphs of connected claw-free graphs. We also propose some conjectures and discuss about some future research directions in this topic.
Keywords: Graph, Distinguishing Number, Independence Number, Line Graph -
این دومین مقاله از یک سه گانه است که به مرور تحولات مهم توپولوژی ابعاد پایین در قرن گذشته می پردازد. با شروع از کارهای پوانکاره در سالهای پایانی قرن نوزدهم و سالهای آغازین قرن بیستم، قدم های اصلی که برای قرار دان خمینه های سه بعدی و توپولوژی جبری مرتبط با آنها در یک چارچوب ریاضی استوار برداشته شد، و قضایای مهمی که فهم این خمینه ها را قوام بخشید را مرور خواهیم کرد. این مرور، با قضایای تجزیه اول خمینه های 3 بعدی و قضیه تجزیه JSJ آغاز می شود. برجسته کردن اهمیت خمینه های 3 بعدی هذلولوی، اثبات قضیه هیولا، و صورت بندی حدس هندسی سازی توسط ترستن نقطه عطف مهمی در مطالعه خمینه های 3 بعدی بوده است. اثبات حدس پوانکاره توسط پرلمان، با استفاده از شار ریچی هامیلتون، این نکته را تایید کرد که گروه بنیادی خمینه های 3 بعدی ناوردایی تقریبا کامل برای این خمینه ها است. با این وجود، مشخص نیست که بسیاری از خصوصیات هندسی خمینه های 3 بعدی چگونه در گروه بنیادی منعکس می شود، و تشخیص این که دو نمایش گروه های بنیادی، گروه هایی یک ریخت را مشخص می کنند یا خیر هم معمولا بسیار دشوار است. راه های موازی برای مطالعه خمینه های 3 بعدی و هم لبگی های 4 بعدی بین آنها با استفاده از ناورداهای آبلی- که کار کردن با آنها ساده تر است- بالاخص شامل نظریه هایی است که در قالب نظریه های توپولوژیک میدان کوانتومی صورت بندی شده اند. چنین نظریه هایی هم در این مقاله مورد اشاره قرار می گیرند. بالاخص، قضیه ای از نویسنده که به توانایی ناورداهای اخیر در تشخیص کره 3 بعدی از سایر خمینه ها می پردازد مورد مطالعه قرار خواهد گرفت.کلید واژگان: خمینه های 3-بعدی, حدس پوانکاره, هندسی سازی, شار ریچی, نظریه های پیمانه ایThis is the second paper from a trio which reviews some of the progress in low dimensional topology in the past century. Starting with the work of Poincare in the last years of 19th century and first few years of 20th century, we review the major steps in putting 3-manifolds and their algebraic topology in a solid mathematical framework, and the important theorems which strengthened the understanding of 3-manifolds, including the prime decomposition theorem and JSJ decomposition of 3-manifolds. Highlighting the significance of hyperbolic 3-manifolds, proving the monster theorem and formulating the geometrization conjecture by Thurston has been a turning point in 3-manifold topology. The proof of geometrization conjecture by Perelman, using Ricci flow of Hamilton, affirmed that the fundamental group is an almost perfect invariant of closed 3-manifolds. Yet, it is not clear how geometric properties are reflected in the fundamental group, and its is difficult to verify whether two group presentations give isomorphic fundamental groups or not. Alternative approaches to the study of 3-manifolds and 4-dimensional cobordisms between them using abelian groups include, in particular, the theories which are formulated as topological quantum field theories (TQFTs). These approaches are also reviewed in the paper. In particular, a theorem of the author which addresses the strength of the later invariants in distinguishing 3-manifolds from the standard 3-sphere is discussed.Keywords: 3-Manifolds, Poincar, ', E Conjecture, Geometrization, Ricci Flow, Gauge Theory
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Structure theory of Clifford-Weyl algebras and representations of ortho-symplectic Lie superalgebras
In this article, the structure of the Clifford-Weyl superalgebras and their associated Lie superalgebras will be investigated. These superalgebras have a natural supersymmetric inner product which is invariant under their Lie superalgebra structures. The Clifford-Weyl superalgebras can be realized as tensor product of the algebra of alternating and symmetric tensors respectively, on the even and odd parts of their underlying superspace. For Physical applications in elementaryparticles, we add star structures to these algebras and investigate the basic relations. Ortho-symplectic Lie algebras are naturally present in these algebras and their representations on these algebras can be described easily.
Keywords: Superspace, Bilinear Form, Exterior Algebra, Symmetric Algebra, Star Structure, Representation -
In recent years, the navigation of mobile robots has been of great interest. One of the important challenges in the navigation of mobile robots is the obstacle avoidance problem so that the robots do not collide with each other and obstacles, during their movement. Hence, for good navigation, a reliable obstacle avoidance methodology is needed. On the other hand, some of the other most important challenges in robot control are in the field of motion planning. The main goal of motion planning is to compile (interpret) high-level languages into a series of primary low-level movements. In this paper, a novel online sensor-based motion planning algorithm that employs the Adaptive Neuro-Fuzzy Inference System (ANFIS) controller is proposed. Also, this algorithm is able to distance the robots from the obstacles (i.e. it provides a solution to the obstacle avoidance problem). In the proposed motion planning algorithm, three distances (i.e. the distance of the robot from the obstacles in three directions: right, left, and front) have been used to prioritize the goal search behavior and obstacle avoidance behavior and to determine the appropriate angle of rotation. Then, for determining the linear velocity, the nearest distance from obstacles and distance from the goal have been used. Theproposed motion planning algorithm has been implemented in the gazebo simulator (by using Turtlebot) and its performance has been evaluated. Finally, to improve the performance of the proposed motion planning algorithm, We have used type-1, interval type-2, and interval type-3 fuzzy sets, then, we have evaluated and compared the efficiency of the proposed algorithm for each of these fuzzy sets under specific criteria.
Keywords: Turtlebot, ANFIS, Fuzzy-Type-2, Fuzzy-Type-3, Tlbo Algorithm -
We first introduce the concept of $C^{*}$-algebra-valued $S_{b}$-metric space, then we prove Banach contraction principle in this space. Finally, existence and uniqueness results for one type of integral equation is discussed.Keywords: Banach Contraction Principle, $B$-Metric Space, $S, {B}$-Metric Space, $C^*$-Algebra, Integral Equation
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This study explores the use of efficient deep learning algorithms for segmenting lower grade gliomas (LGG) in medical images. It evaluates various pre-trained atrous-convolutional architectures and U-Nets, proposing a novel transformer-based approach that surpasses traditional methods. DeepLabV3+ with MobileNetV3 backbone achieved the best results among pre-trained models, but the transformer-based approach excelled with superior segmentation accuracy and efficiency. Transfer learning significantly enhanced model performance on the LGG dataset, even with limited training samples, emphasizing the importance of selecting appropriate pre-trained models. The transformer-based method offers advantages such as efficient memory usage, better generalization, and the ability to process images of arbitrary sizes, making it suitable for clinical applications. These findings suggest that advanced deep learning techniques can improve diagnostic tools for LGG and potentially other cancers, highlighting the transformative impact of deep learning and transfer learning in medical image segmentation.Keywords: Brain Tumor Segmentation, Lower Grade Gliomas, Transformers, Segformer, MRI Images
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Performance measurement is always considered one of the most important tasks of managers. Hence, management knowledge is measurement knowledge and if we cannot measure something, we certainly cannot control it and consequently we cannot manage it. In this paper, we examine data envelopment analysis models for improving inefficient units. In this study, 20 bank branches in Tehran were selected and mathematical models were presented for estimating inputs with interval data. The findings of this research highlight the importance of integrating advanced analytical tools like DEA into management practices. By quantifying inefficiencies and offering clear pathways for improvement, DEA empowers managers to make data-driven decisions that enhance overall performance. This approach is particularly valuable in competitive environments, such as the banking sector, where efficiency and service quality directly impact customer satisfaction and profitability.
Keywords: Data Envelopment Analysis, Interval Data, Estimate, Bank Branch
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