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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6

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Quartile: search.filters.quartile.Q3Subject: search.filters.subject.Mathematics

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Now showing 1 - 10 of 29
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    PublicationOpen Access
    On the distributions of sigma(N)/N and N/Phi(N)
    (Rocky Mountain Mathematics Consortium, 2013) Department of Mathematics; Alkan, Emre; Faculty Member; Department of Mathematics; College of Sciences; 32803
    We prove that the distribution functions of sigma(n)/n and n/phi(n) both have super-exponential asymptotic decay when n ranges over certain subsets of integers, which, in particular, can be taken as the set of l-free integers not divisible by a thin subset of primes.
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    PublicationOpen Access
    The intersection problem for PBD(5*,3)s
    (Elsevier, 2008) Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252
    For every v equivalent to 5 (mod 6) there exists a pairwise balanced design (PBD) of order v with exactly one block of size 5 and the rest of size 3. We will refer to such a PBD as a PBD(5*, 3). A flower in a PBD(5*, 3) is the set of all blocks containing a given point. If (S, B) is a PBD(5*, 3) and F is a flower, we will write F* to indicate that F contains the block of size 5. The intersection problem for PBD(5*, 3)s is the determination of all pairs (v, k) such that there exists a pair of PBD(5*, 3)s (S, B-1) and (S, B-2) of order v containing the same block b of size 5 such that vertical bar(B-1\b) boolean AND (B-2\b)vertical bar = k. The flower intersection problem for PBD(5*, 3)s is the determination of all pairs (v, k) such that there exists a pair of PBD(5*, 3)s (S, B-1) and (S, B-2) of order v having a common flower F* such that vertical bar(B-1\F*) boolean AND (B-2\F*)vertical bar = k. In this paper we give a complete solution of both problems.
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    PublicationOpen Access
    Embedding partial Latin squares in Latin squares with many mutually orthogonal mates
    (Elsevier, 2020) Donovan, Diane; Grannell, Mike; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432
    In this paper it is shown that any partial Latin square of order n can be embedded in a Latin square of order at most 16n2 which has at least 2n mutually orthogonal mates. Further, for any t⩾2, it is shown that a pair of orthogonal partial Latin squares of order n can be embedded in a set of t mutually orthogonal Latin squares (MOLS) of order a polynomial with respect to n. A consequence of the constructions is that, if N(n) denotes the size of the largest set of MOLS of order n, then N(n2)⩾N(n)+2. In particular, it follows that N(576)⩾9, improving the previously known lower bound N(576)⩾8.
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    PublicationOpen Access
    Symplectic and lagrangian surfaces in 4-Manifolds
    (Rocky Mountain Mathematics Consortium, 2008) Department of Mathematics; Etgü, Tolga; Faculty Member; Department of Mathematics; College of Sciences; 16206
    This is a brief summary of recent examples of isotopically different symplectic and Lagrangian surfaces representing a fixed homology class in a simply-connected symplectic 4-manifold.
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    PublicationOpen Access
    Embeddings of P-3-designs into bowtie and almost bowtie systems
    (Elsevier, 2009) Lindner, Curt; Quattrocchi, Gaetano; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252
    This paper determines for each admissible w, the set of all n such that every P-3-design of order w can be embedded in an (almost) bowtie system of order n.
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    PublicationOpen Access
    Erratum: Geometric phase, bundle classification, and group representation
    (American Institute of Physics (AIP) Publishing, 1999) Department of Mathematics; Department of Physics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; Department of Physics; College of Sciences; 4231
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    PublicationOpen Access
    Cyclotomic p-adic multi-zeta values
    (Elsevier, 2019) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    The cyclotomic p-adic multi-zeta values are the p-adic periods of pi(uni)(1)(G(m) \ mu M,(.)), the unipotent fundamental group of the multiplicative group minus the M-th roots of unity. In this paper, we compute the cyclotomic p-adic multi-zeta values at all depths. This paper generalizes the results in [9] and [10]. Since the main result gives quite explicit formulas we expect it to be useful in proving non-vanishing and transcendence results for these p-adic periods and also, through the use of p-adic Hodge theory, in proving non-triviality results for the corresponding p-adic Galois representations.
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    PublicationOpen Access
    Geometric phase for non-Hermitian Hamiltonians and its holonomy interpretation
    (American Institute of Physics (AIP) Publishing, 2008) Mehri-Dehnavi, Hossein; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    For an arbitrary possibly non-Hermitian matrix Hamiltonian H that might involve exceptional points, we construct an appropriate parameter space m and line bundle L-n over m such that the adiabatic geometric phases associated with the eigenstates of the initial Hamiltonian coincide with the holonomies of L-n. We examine the case of 2 X 2 matrix Hamiltonians in detail and show that, contrary to claims made in some recent publications, geometric phases arising from encircling exceptional points are generally geometrical and not topological in nature.
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    PublicationOpen Access
    Biembeddings of cycle systems using integer Heffter arrays
    (Wiley, 2020) Cavenagh, Nicholas J.; Donovan, Diane M.; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432
    In this paper, we use constructions of Heffter arrays to verify the existence of face 2-colorable embeddings of cycle decompositions of the complete graph. Specifically, forn degrees 1(mod 4)andk degrees 3(mod4),n >> k > 7and whenn degrees 0(mod 3)thenk degrees 7(mod 12), there exist face 2-colorable embeddings of the complete graphK2nk+1onto an orientable surface where each face is a cycle of a fixed lengthk. In these embeddings the vertices ofK2nk+1will be labeled with the elements ofZ2nk+1in such a way that the group,(Z2nk+1,+)acts sharply transitively on the vertices of the embedding. This result is achieved by verifying the existence of nonequivalent Heffter arrays,H(n;k), which satisfy the conditions: (1) for each row and each column the sequential partial sums determined by the natural ordering must be distinct modulo2nk+1; (2) the composition of the natural orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. The existence of Heffter arraysH(n;k)that satisfy condition (1) was established earlier in Burrage et al. and in this current paper, we vary this construction and show, fork > 11, that there are at least(n-2)[((k-11)/4)!/e]2such nonequivalentH(n;k)that satisfy both conditions (1) and (2).
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    PublicationOpen Access
    Divisor function and bounds in domains with enough primes
    (Hacettepe Üniversitesi, 2019) Department of Mathematics; Göral, Haydar; Master Student; Department of Mathematics; College of Sciences
    In this note, first we show that there is no uniform divisor bound for the Bezout identity using Dirichlet's theorem on arithmetic progressions. Then, we discuss for which rings the absolute value bound for the Bezout identity is not trivial and the answer depends on the number of small primes in the ring.