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The mapping class group is generated by two commutators
Baykur, R. Inanc; Korkmaz, Mustafa (2021-05-01)
We show that the mapping class group of any closed connected orientable surface of genus at least five is generated by only two commutators, and if the genus is three or four, by three commutators. (C) 2021 Elsevier Inc. A...
ABSTRACT SIMILARITY, FRACTALS AND CHAOS
Akhmet, Marat; Alejaily, Ejaily Milad (2021-05-01)
A new mathematical concept of abstract similarity is introduced and is illustrated in the space of infinite strings on a finite number of symbols. The problem of chaos presence for the Sierpinski fractals, Koch curve, as w...
Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments
Akhmet, Marat; ARUĞASLAN ÇİNÇİN, Duygu; Tleubergenova, Madina; Nugayeva, Zakhira (2021-03-01)
This is the first time that the method for the investigation of unpredictable solutions of differential equations has been extended to unpredictable oscillations of neural networks with a generalized piecewise constant arg...
Segre Indices and Welschinger Weights as Options for Invariant Count of Real Lines
Finashin, Sergey; Kharlamov, Viatcheslav (2021-03-01)
In our previous paper [5] we have elaborated a certain signed count of real lines on real hypersurfaces of degree 2n - 1 in Pn+1. Contrary to the honest "cardinal" count, it is independent of the choice of a hypersurface a...
Defect-deferred correction method based on a subgrid artificial viscosity model for fluid-fluid interaction
AĞGÜL, MUSTAFA; Kaya Merdan, Songül (Elsevier BV, 2021-02-01)
© 2020 IMACSA defect-deferred correction method, increasing both temporal and spatial accuracy, for fluid-fluid interaction problem with nonlinear interface condition is considered by geometric averaging of the previous tw...
New generalized almost perfect nonlinear functions
Özbudak, Ferruh; Salagean, Ana (2021-02-01)
APN (almost perfect non-linear) functions over finite fields of even characteristic are widely studied due to their applications to the design of symmetric ciphers resistant to differential attacks. This notion was recentl...
Liftable homeomorphisms of cyclic and rank two finite abelian branched covers over the real projective plane
Atalan, Ferihe; Medetogullari, Elif; Ozan, Yıldıray (Elsevier BV, 2021-02-01)
© 2020 Elsevier B.V.In this note, we investigate the property for regular branched finite abelian covers of the real projective plane, where each homeomorphism of the base (preserving the branch locus) lifts to a homeomorp...
Open books decompositions of links of minimally elliptic singularities
Bhupal, Mohan Lal (2021-02-01)
We present an explicit Milnor open book decomposition supporting the canonical contact structure on the link of each minimally elliptic singularity whose fundamental cycle Z satisfies -3 <= Z center dot Z <=-1. For the Mil...
On the performance of curvature stabilization time stepping methods for double-diffusive natural convection flows in the presence of magnetic field
Cibik, Aytekin; Eroglu, Fatma G.; Kaya Merdan, Songül (Springer Science and Business Media LLC, 2021-01-01)
© 2021, Springer Science+Business Media, LLC, part of Springer Nature.This paper considers analytically and numerically the curvature-based stabilization method for double-diffusive natural convection flows in the presence...
Hermitian Rank Metric Codes and Duality
La Cruz, Javier De; Evilla, Jorge Robinson; Özbudak, Ferruh (2021-01-01)
In this paper we define and study rank metric codes endowed with a Hermitian form. We analyze the duality for F-q2-linear matrix codes in the ambient space (F-q2)(n,m) and for both F-q2-additive codes and F-q2m-linear code...
Order compact and unbounded order compact operators
ERKURŞUN ÖZCAN, NAZİFE; Gezer, Niyazi Anıl; Ozdemir, Saziye Ece; Urganci, Irem Mesude (2021-01-01)
We investigate properties of order compact, unbounded order compact and relatively uniformly compact operators acting on vector lattices. An operator is said to be order compact if it maps an arbitrary order bounded net to...
Kapalı eğri üzerine dikdörtgen çizme problemi
Ozan, Yıldıray(2020-12-02)
Düzlemde rastgele basit kapalı bir eğri alalım. Köşeleri bu eğrinin üzerinde olan bir dikdörtgenin var mıdır? Konuşmanın ilk bölümünde bu klasik problemi ele alacağız ve böyle bir dikdörtgenin varlığının gerçel projektif d...
Yüzeylerin Sınıflandırması ve Gauss-Bonnet Teoremi
Ozan, Yıldıray(2020-11-21)
İlk önce yüzeyler ve daha genelde manifold kavramı hakkında konuşacağız. Daha sonra kes-yapıştır tekniğini de vererek yüzeylerin topolojik sınıflandırılması vereceğiz. Euler karakteristiği ve Descartes'ın polihedral yüze...
Liftable homeomorphisms of rank two finite abelian branched covers
Atalan, Ferihe; Medetogullari, Elif; Ozan, Yıldıray (2020-11-01)
We investigate branched regular finite abelian A-covers of the 2-sphere, where every homeomorphism of the base (preserving the branch locus) lifts to a homeomorphism of the covering surface. In this study, we prove that if...
Algebraic Topology (Math 537)
Ozan, Yıldıray(2020-10-13)
Course Content Fundamental group, Van Kampen’s Theorem, covering spaces. Singular homology: Homotopy invariance, homology long exact sequence, Mayer-Vietoris sequence, excision. Cellular homology. Homology with coefficient...
Introduction to Real Analysis (Math 349)
Ozan, Yıldıray(2020-10-13)
Course Content LUB Property of real numbers. Compactness, connectedness, limits and continuity in metric spaces. Sequences and series of scalars, complete metric spaces, limsup. Sequences and series of functions, uniform ...
On the discretization of Darboux Integrable Systems
Zheltukhın, Kostyantyn; ZHELTUKHİNA, NATALYA (Informa UK Limited, 2020-10-01)
We study the discretization of Darboux integrable systems. The discretization is done using x-, y-integrals of the considered continuous systems. New examples of semi-discrete Darboux integrable systems are obtained.
An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows
Demir, Medine; Kaya, Songul (Elsevier BV, 2020-10-01)
This report extends the mathematical support of a subgrid artificial viscosity (SAV) method to simulate the incompressible Navier-Stokes equations to better performing a linearly extrapolated BDF2 (BDF2LE) time discretizat...
Good action on a finite group
Ercan, Gülin; GÜLOĞLU, İSMAİL ŞUAYİP; Jabara, Enrico (Elsevier BV, 2020-10-01)
Let G and A be finite groups with A acting on G by automorphisms. In this paper we introduce the concept of "good action"; namely we say the action of A on G is good, if H = [H, B]C-H (B) for every subgroup B of A and ever...
Shunting inhibitory cellular neural networks with strongly unpredictable oscillations
Akhmet, Marat; Seilova, Roza; Tleubergenova, Madina; Zhamanshin, Akylbek (Elsevier BV, 2020-10-01)
The paper considers a new type of solutions for shunting inhibitory cellular neural networks (SICNNs), strongly unpredictable oscillations. The conditions for the existence, uniqueness and stability of the solutions are de...
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