Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Citation - WoS: 5Citation - Scopus: 6Lung Parenchyma Segmentation From Ct Images With a Fully Automatic Method(Springer, 2023) Mousavi Moghaddam, Reza; Aghazadeh, NasserFor the last three years, the world has been facing an infectious disease that primarily affects the human breathing organ. The disease has caused many deaths worldwide so far and has imposed high economic costs on all countries. Therefore, attention to computer-aided detection/diagnosis (CAD) systems to help diagnose and treat diseases related to the human respiratory system should be given more attention so that countries’ health systems can treat patients in epidemics. Considering the importance of CAD systems, we proposed a two-step automatic algorithm. In the first step, we obtain the primary boundary of the lobes in CT lung scan images with the help of some conventional image processing tools. In the second stage, we obtained a more precise boundary of the lung lobes by correcting the unusual dimples and valleys (which are sometimes caused by the presence of juxtapleural nodules). This proposed method has low implementation time. Given that a precise boundary of the pulmonary lobes is essential in the more accurate diagnosis of lung-related diseases, an attempt has been made to ensure that the final segmentation of the lung parenchyma has an acceptable score in terms of evaluation criteria so that the proposed algorithm can be used in the diagnosis procedure. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Article Citation - Scopus: 1Level Set Estimates for the Discrete Frequency Function(Springer Verlag, 2019) Temur, FarukWe introduce the discrete frequency function as a possible new approach to understanding the discrete Hardy-Littlewood maximal function. Considering that the discrete Hardy-Littlewood maximal function is given at each integer by the supremum of averages over intervals of integer length, we define the discrete frequency function at that integer as the value at which the supremum is attained. After verifying that the function is well-defined, we investigate size and smoothness properties of this function.Article On the Structure of Modules Defined by Opposites of Fp Injectivity(Springer Verlag, 2019) Büyükaşık, Engin; Kafkas Demirci, GizemLet R be a ring with unity and let MR and RN be right and left modules,respectively. The module MR is said to be absolutely RN-pure if M circle times NL circle times N is amonomorphism for every extension LR of MR. For a module MR, the subpurity domain of MR is defined to be the collection of all modules RN, such that MR is absolutely RN-pure. Clearly, MR is absolutely RF-pure for every flat module RF and that MR is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, MR is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. We characterize the structure of t.f.b.s. modules over commutative hereditary Noetherian rings. We prove that a module M is t.f.b.s. over a commutative hereditary Noetherian ring if and only if M/Z(M) is t.f.b.s. if and only if Hom(M/Z(M),S)0 for each singular simple module S. Prufer domains are characterized as those domains all of whose nonzero finitely generated ideals are t.f.b.s.Article Citation - WoS: 12Citation - Scopus: 12Stability Analysis by a Nonlinear Upper Bound on the Derivative of Lyapunov Function(Elsevier Ltd., 2020) Şahan, GökhanIn this work, we give results for asymptotic stability of nonlinear time varying systems using Lyapunov-like Functions with indefinite derivative. We put a nonlinear upper bound for the derivation of the Lyapunov Function and relate the asymptotic stability conditions with the coefficients of the terms of this bound. We also present a useful expression for a commonly used integral and this connects the stability problem and Lyapunov Method with the convergency of a series generated by coefficients of upper bound. This generalizes many works in the literature. Numerical examples demonstrate the efficiency of the given approach. © 2020 European Control AssociationArticle 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].