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Publication Metadata only The triangle intersection problem for K4 - E designs(Utilitas Mathematica Publishing Inc., 2007) Billington, Elizabeth J.; Lindner, C. C.; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432An edge-disjoint decomposition of the complete graph Kn into copies of K4 - e, the simple graph with four vertices and five edges, is known to exist if and only if n ≡ 0 or 1 (mod 5) and n ≥ 6 (Bermond and Schönheim, Discrete Math. 19 (1997)). The intersection problem for K4 - e designs has also been solved (Billington, M. Gionfriddo and Lindner, J. Statist. Planning Inference 58 (1997)); this problem finds the number of common K4 - e blocks which two K4 - e designs on the same set may have. Here we answer the question: how many common triangles may two K4 - e designs on the same set have? Since it is possible for two K4 - e designs on the same set to have no common K4 - e blocks and yet some positive number of common triangles, this problem is largely independent of the earlier K4 - e intersection result.Publication Metadata only Z(n)-graded topological generalizations of supersymmetry and orthofermion algebra(Iop Publishing Ltd, 2003) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We review various generalizations of supersymmetry and discuss their relationship. in particular, we show how supersymmetry, parasupersymmetry, fractional supersymmetry, orthosupersymmetry, and the Z(n)-graded topological symmetries are related.Publication Metadata only Exotic stein fillings with arbitrary fundamental group(Springer, 2018) Akhmedov, Anar; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746Let G be a finitely presentable group. We provide an infinite family of homeomorphic but pairwise non-diffeomorphic, symplectic but non-complex closed 4-manifolds with fundamental group G such that each member of the family admits a Lefschetz fibration of the same genus over the two-sphere. As a corollary, we also show the existence of a contact 3-manifold which admits infinitely many homeomorphic but pairwise non-diffeomorphic Stein fillings such that the fundamental group of each filling is isomorphic to G. Moreover, we observe that the contact 3-manifold above is contactomorphic to the link of some isolated complex surface singularity equipped with its canonical contact structure.Publication Metadata only On regular embedding of H-designs into G-designs(Utilitas Mathematica, 2013) Quattrocchi, Gaetano; Department of Mathematics; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Smith, Benjamin R.; Yazıcı, Emine Şule; Faculty Member; Researcher; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 105252; N/A; 27432The graph H is embedded in the graph G, if H is a subgraph of G. An H-design is a decomposition of a complete graph into edge disjoint copies of the graph H, called blocks. An H-i-design with k blocks, say H-1, H-2, ...H-k is embedded in a G-design if for every H-i, there exists a distinct block, say G(i), in the G-design that embeds H-i. If G(i) are all isomorphic for 1 <= i <= k then the embedding is called regular. This paper solves the problem of the regular embedding of H-designs into G-designs when G has at most four vertices and four edges.Publication Metadata only Decomposition of lambda K-nu into kites and 4-cycles(Charles Babbage Research Centre, 2017) Milici, Salvatore; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252Given a collection of graphs H, an H-decomposition of λkv is a decomposition of the edges of λKv into isomorphic copies of graphs in Ti. A kite is a triangle with a tail consisting of a single edge. In this paper we investigate the decomposition problem when H is the set containing a kite and a 4-cycle, that is; this paper gives a complete solution to the problem of decomposing λKv into r kites and s 4-cycles for every admissible values of v, λ, r and s.Publication Metadata only Average r-rank artin conjecture(Polish Acad Sciences Inst Mathematics-IMPAN, 2016) Menici, Lorenzo; Department of Mathematics; Pehlivan, Cihan; Researcher; Department of Mathematics; College of Sciences; N/AN/APublication Metadata only Global attractors and determining modes for the 3D navier-stokes-voight equations(Shanghai Scientific Technology Literature Publishing House, 2009) Titi, Edriss S.; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655The authors investigate the long-term dynamics of the three-dimensional Navier-Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view the authors consider the Navier-Stokes-Voight model as a non-viscous (inviscid) regularization of the three-dimensional Navier-Stokes equations. Furthermore, it is also shown that the weak solutions of the Navier-Stokes-Voight equations converge, in the appropriate norm, to the weak solutions of the inviscid simplified Bardina model, as the viscosity coefficient ν → 0.Publication Metadata only Embedding 4-cycle systems into octagon triple systems(2009) Billington, Elizabeth J.; Lindner, Curt; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Yazıcı, Emine Şule; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; 105252; 27432An octagon triple is the graph consisting of the four triangles (triples) {a, b,c}, {c, d,e}, {e, f,g}, and {g, h,a}, where a,b,c, d,e, f, g and h axe distinct. The 4-cycle (a, c, e, g) is called an inside 4-cycle. An octagon triple system of order n is a pair (X,O), where O is a collection of edge disjoint octagon triples which partitions the edge set of K-n with vertex set X. Let (X, O) be an octagon triple system and let P be the collection of inside 4-cycles. Then (X, P) is a partial 4-cycle system of order n. It is not possible for (X, P) to be a 4-cycle system (not enough 4-cycles). So the problem of determining for each n the smallest octagon triple system whose inside 4-cycles contain a 4-cycle system of order 8n + 1 is immediate. The object of this note is to determine the spectrum for octagon triple systems and to construct for every n a 4-cycle system of order k = 8n + 1 that can be embedded in the inside 4-cycles of some octagon triple system of order approximately 3k. This is probably not the best possible embedding (the best embedding is approximately 2k + 1), but it is a good start.Publication Metadata only The full metamorphosis of lambda-fold block designs with block size four into lambda-fold kite systems(Utilitas Mathematica Publishing, 2013) N/A; Department of Mathematics; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Smith, Benjamin R.; Yazıcı, Emine Şule; Faculty Member; Researcher; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 105252; N/A; 27432Let(X,B)be a λ-fold block design with block size 4. If a path of length two is removed from each block of B the resulting collection of kites K is a partial λ-fold kite system(X,K). If the deleted edges can be arranged into a collection of kites D,then(X,K ∪ D)is a λ-fold kite system [5]. Now for each block 6 ∈ B let {P1(6),P 2(b),P3(b)} be a partition of b into paths of length two and define for each i = 1,2,3, sets Ki and Di as follows: for each b ∈ B,put the kite b\Pi(b)in Ki and the two edges belonging to the path Pi(b)in Di. If the edges in Di can be arranged into a collection of kites Di * then Mi =(X,Ki∪Di *)is a λ-fold kite system,called the ith metamorphosis of(X,B). The full metamorphosis is the set of three metamorphoses {M 1,M2,M3}. We give a complete solution of the following problem: for which n and A does there exist a λ-fold block design with block size 4 having a full metamorphosis into a λ-fold kite system?Publication Metadata only Global behavior of solutions to an inverse problem for semilinear hyperbolic equations(Springer Nature, 2006) Eden, A.; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655This paper is concerned with global in time behavior of solutions for a semilinear, hyperbolic, inverse source problem. We prove two types of results. The first one is a global nonexistence result for smooth solutions when the data is chosen appropriately. The second type of results is the asymptotic stability of solutions when the integral constraint vanishes as t goes to infinity. Bibliography: 22 titles. © 2006 Springer Science+Business Media, Inc.