WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7150
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Article Mock Alexander Polynomials(Australian National University, 2025) Gügümcü, Neslihan; Kauffman, L.H.In this paper, we construct Mock Alexander polynomials for starred links and linkoids in surfaces. These polynomials are defined as state summations on link or linkoid diagrams that satisfy f = n, where f denotes the number of regions and n denotes the number of crossings of diagrams. These new invariants are chirality and reversibility sensitive. © The authors.Article Citation - WoS: 5Citation - Scopus: 5Mechanical Behaviour of Photopolymer Cell-Size Graded Triply Periodic Minimal Surface Structures at Different Deformation Rates(Mdpi, 2024) Yilmaz, Yunus Emre; Novak, Nejc; Al-Ketan, Oraib; Erten, Hacer Irem; Yaman, Ulas; Mauko, Anja; Ren, ZoranThis study investigates how varying cell size affects the mechanical behaviour of photopolymer Triply Periodic Minimal Surfaces (TPMS) under different deformation rates. Diamond, Gyroid, and Primitive TPMS structures with spatially graded cell sizes were tested. Quasi-static experiments measured boundary forces, representing material behaviour, inertia, and deformation mechanisms. Separate studies explored the base material's behaviour and its response to strain rate, revealing a strength increase with rising strain rate. Ten compression tests identified a critical strain rate of 0.7 s-1 for "Grey Pro" material, indicating a shift in failure susceptibility. X-ray tomography, camera recording, and image correlation techniques observed cell connectivity and non-uniform deformation in TPMS structures. Regions exceeding the critical rate fractured earlier. In Primitive structures, stiffness differences caused collapse after densification of smaller cells at lower rates. The study found increasing collapse initiation stress, plateau stress, densification strain, and specific energy absorption with higher deformation rates below the critical rate for all TPMS structures. However, cell-size graded Primitive structures showed a significant reduction in plateau and specific energy absorption at a 500 mm/min rate.Article Citation - Scopus: 2Analysis of the Logistic Growth Model With Taylor Matrix and Collocation Method(Etamaths Publishing, 2023) Çelik, Elçin; Uçar, DenizEarly analysis of infectious diseases is very important in the spread of the disease. The main aim of this study is to make important predictions and inferences for Covid 19, which is the current epidemic disease, with mathematical modeling and numerical solution methods. So we deal with the logistic growth model. We obtain carrying capacity and growth rate with Turkey epidemic data. The obtained growth rate and carrying capacity is used in the Taylor collocation method. With this method, we estimate and making predictions close to reality with Maple. We also show the estimates made with the help of graphics and tables. © 2023 the author(s).Article Citation - WoS: 20Citation - Scopus: 25Vertex-Decomposable Graphs, Codismantlability, Cohen-Macaulayness, and Castelnuoco-Mumford Regularity(Electronic Journal of Combinatorics, 2014) Biyikoglu, Turker; Civan, YusufWe call a vertex x of a graph G = (V, E) a codominated vertex if N-G[y] subset of N-G[x] for some vertex y is an element of V \{x}, and a graph G is called codismantlable if either it is an edgeless graph or it contains a codominated vertex x such that G - x is codismantlable. We show that (C-4, C-5)-free vertex-decomposable graphs are codismantlable, and prove that if G is a (C-4, C-5, C-7)-free well-covered graph, then vertex-decomposability, codismantlability and Cohen-Macaulayness for G are all equivalent. These results complement and unify many of the earlier results on bipartite, chordal and very well-covered graphs. We also study the Castelnuovo-Mumford regularity reg(G) of such graphs, and show that reg(G) = im(G) whenever G is a (C-4, C-5)-free vertex-decomposable graph, where im(G) is the induced matching number of G. Furthermore, we prove that H must be a codismantlable graph if im(H) = reg(H) = m(H), where m(H) is the matching number of H. We further describe an operation on digraphs that creates a vertex-decomposable and codismantlable graph from any acyclic digraph. By way of application, we provide an infinite family H-n (n >= 4) of sequentially Cohen-Macaulay graphs whose vertex cover numbers are half of their orders, while containing no vertex of degree-one such that they are vertex-decomposable, and reg(H-n) = im(H-n) if n >= 6. This answers a recent question of Mahmoudi, et al [12].Article Citation - WoS: 14Citation - Scopus: 11Extensions of Weakly Supplemented Modules(Mathematica Scandinavica, 2008) Alizade, Rafail; Büyükaşık, EnginIt is shown that weakly supplemented modules need not be closed under extension (i.e. if U and M/U are weakly supplemented then M need not be weakly supplemented). We prove that, if U has a weak supplement in M then M is weakly supplemented. For a commutative ring R, we prove that R is semilocal if and only if every direct product of simple R-modules is weakly supplemented.Article Citation - WoS: 16Citation - Scopus: 14Rings Whose Modules Are Weakly Supplemented Are Perfect. Applications To Certain Ring Extensions(Mathematica Scandinavica, 2009) Büyükaşık, Engin; Lomp, ChristianIn this note we show that a ring R is left perfect if and only if every left R-module is weakly supplemented if and only if R is semilocal and the radical of the countably infinite free left R-module has a weak supplement.