Displaying similar documents to “ 2 - ( n 2 , 2 n , 2 n - 1 ) designs obtained from affine planes”

Some Additive 2 - ( v , 5 , λ ) Designs

Andrea Caggegi (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica


Given a finite additive abelian group G and an integer k , with 3 k | G | , denote by 𝒟 k ( G ) the simple incidence structure whose point-set is G and whose blocks are the k -subsets C = { c 1 , c 2 , , c k } of G such that c 1 + c 2 + + c k = 0 . It is known (see [Caggegi, A., Di Bartolo, A., Falcone, G.: Boolean 2-designs and the embedding of a 2-design in a group arxiv 0806.3433v2, (2008), 1–8.]) that 𝒟 k ( G ) is a 2-design, if G is an elementary abelian p -group with p a prime divisor of k . From [Caggegi, A., Falcone, G., Pavone, M.: On the additivity...

The natural operators of general affine connections into general affine connections

Jan Kurek, Włodzimierz M. Mikulski (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica


We reduce the problem of describing all f m -natural operators  transforming general affine connections on m -manifolds into general affine ones to the known description of all G L ( 𝐑 m ) -invariant maps 𝐑 m * 𝐑 m k 𝐑 m * k 𝐑 m for k = 1 , 3 .

Construction of Mendelsohn designs by using quasigroups of ( 2 , q ) -varieties

Lidija Goračinova-Ilieva, Smile Markovski (2016)

Commentationes Mathematicae Universitatis Carolinae


Let q be a positive integer. An algebra is said to have the property ( 2 , q ) if all of its subalgebras generated by two distinct elements have exactly q elements. A variety 𝒱 of algebras is a variety with the property ( 2 , q ) if every member of 𝒱 has the property ( 2 , q ) . Such varieties exist only in the case of q prime power. By taking the universes of the subalgebras of any finite algebra of a variety with the property ( 2 , q ) , 2 < q , blocks of Steiner system of type ( 2 , q ) are obtained. The stated correspondence...

Uniqueness of Cartesian Products of Compact Convex Sets

Zbigniew Lipecki, Viktor Losert, Jiří Spurný (2011)

Bulletin of the Polish Academy of Sciences. Mathematics


Let X i , i∈ I, and Y j , j∈ J, be compact convex sets whose sets of extreme points are affinely independent and let φ be an affine homeomorphism of i I X i onto j J Y j . We show that there exists a bijection b: I → J such that φ is the product of affine homeomorphisms of X i onto Y b ( i ) , i∈ I.

Multidimensional self-affine sets: non-empty interior and the set of uniqueness

Kevin G. Hare, Nikita Sidorov (2015)

Studia Mathematica


Let M be a d × d real contracting matrix. We consider the self-affine iterated function system Mv-u, Mv+u, where u is a cyclic vector. Our main result is as follows: if | d e t M | 2 - 1 / d , then the attractor A M has non-empty interior. We also consider the set M of points in A M which have a unique address. We show that unless M belongs to a very special (non-generic) class, the Hausdorff dimension of M is positive. For this special class the full description of M is given as well. This paper continues our...

Leaps: an approach to the block structure of a graph

Henry Martyn Mulder, Ladislav Nebeský (2006)

Discussiones Mathematicae Graph Theory


To study the block structure of a connected graph G = (V,E), we introduce two algebraic approaches that reflect this structure: a binary operation + called a leap operation and a ternary relation L called a leap system, both on a finite, nonempty set V. These algebraic structures are easily studied by considering their underlying graphs, which turn out to be block graphs. Conversely, we define the operation + G as well as the set of leaps L G of the connected graph G. The underlying graph...

Finite projective planes, Fermat curves, and Gaussian periods

Koen Thas, Don Zagier (2008)

Journal of the European Mathematical Society


One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences...

On the Hausdorff dimension of certain self-affine sets

Abercrombie Alex G.., Nair R. (2002)

Studia Mathematica


A subset E of ℝⁿ is called self-affine with respect to a collection ϕ₁,...,ϕₜ of affinities if E is the union of the sets ϕ₁(E),...,ϕₜ(E). For S ⊂ ℝⁿ let Φ ( S ) = 1 j t ϕ j ( S ) . If Φ(S) ⊂ S let E Φ ( S ) denote k 0 Φ k ( S ) . For given Φ consisting of contracting “pseudo-dilations” (affinities which preserve the directions of the coordinate axes) and subject to further mild technical restrictions we show that there exist self-affine sets E Φ ( S ) of each Hausdorff dimension between zero and a positive number depending on Φ. We also...

Distortion and spreading models in modified mixed Tsirelson spaces

S. A. Argyros, I. Deliyanni, A. Manoussakis (2003)

Studia Mathematica


The results of the first part concern the existence of higher order ℓ₁ spreading models in asymptotic ℓ₁ Banach spaces. We sketch the proof of the fact that the mixed Tsirelson space T[(ₙ,θₙ)ₙ], θ n + m θ θ and l i m n θ 1 / n = 1 , admits an ω spreading model in every block subspace. We also prove that if X is a Banach space with a basis, with the property that there exists a sequence (θₙ)ₙ ⊂ (0,1) with l i m n θ 1 / n = 1 , such that, for every n ∈ ℕ, | | k = 1 m x k | | θ k = 1 m | | x k | | for every ₙ-admissible block sequence ( x k ) k = 1 m of vectors in X, then there exists c...

A treatment of a determinant inequality of Fiedler and Markham

Minghua Lin (2016)

Czechoslovak Mathematical Journal


Fiedler and Markham (1994) proved det H ^ k k det H , where H = ( H i j ) i , j = 1 n is a positive semidefinite matrix partitioned into n × n blocks with each block k × k and H ^ = ( tr H i j ) i , j = 1 n . We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove det ( I n + H ^ ) det ( I n k + k H ) 1 / k .

The tame automorphism group of an affine quadric threefold acting on a square complex

Cinzia Bisi, Jean-Philippe Furter, Stéphane Lamy (2014)

Journal de l’École polytechnique — Mathématiques


We study the group Tame ( SL 2 ) of tame automorphisms of a smooth affine 3 -dimensional quadric, which we can view as the underlying variety of SL 2 ( ) . We construct a square complex on which the group admits a natural cocompact action, and we prove that the complex is CAT ( 0 ) and hyperbolic. We propose two applications of this construction: We show that any finite subgroup in Tame ( SL 2 ) is linearizable, and that Tame ( SL 2 ) satisfies the Tits alternative.

Centroaffine differential geometry and its relations to horizontal submanifolds

Luc Vrancken (2002)

Banach Center Publications


We relate centroaffine immersions f : M n + 1 to horizontal immersions g of Mⁿ into S n + 1 2 n + 1 ( 1 ) or H n 2 n + 1 ( - 1 ) . We also show that f is an equiaffine sphere, i.e. the centroaffine normal is a constant multiple of the Blaschke normal, if and only if g is minimal.

Self-affine measures and vector-valued representations

Qi-Rong Deng, Xing-Gang He, Ka-Sing Lau (2008)

Studia Mathematica


Let A be a d × d integral expanding matrix and let S j ( x ) = A - 1 ( x + d j ) for some d j d , j = 1,...,m. The iterated function system (IFS) S j j = 1 m generates self-affine measures and scale functions. In general this IFS has overlaps, and it is well known that in many special cases the analysis of such measures or functions is facilitated by expressing them in vector-valued forms with respect to another IFS that satisfies the open set condition. In this paper we prove a general theorem on such representation. The proof...

Integral representations for solutions of exponential Gauß-Manin systems

Marco Hien, Céline Roucairol (2008)

Bulletin de la Société Mathématique de France


Let f , g : U 𝔸 1 be two regular functions from the smooth affine complex variety U to the affine line. The associated exponential Gauß-Manin systems on the affine line are defined to be the cohomology sheaves of the direct image of the exponential differential system 𝒪 U e g with respect to f . We prove that its holomorphic solutions admit representations in terms of period integrals over topological chains with possibly closed support and with rapid decay condition.

Inclusion properties of certain subclasses of analytic functions defined by generalized Salagean operator

M. K. Aouf, A. Shamandy, A. O. Mostafa, S. M. Madian (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica


Let A denote the class of analytic functions with the normalization f ( 0 ) = f ' ( 0 ) - 1 = 0 in the open unit disc U = { z : z < 1 } .  Set f λ n ( z ) = z + k = 2 [ 1 + λ ( k - 1 ) ] n z k ( n N 0 ; λ 0 ; z U ) , and define f λ , μ n in terms of the Hadamard product f λ n ( z ) * f λ , μ n = z ( 1 - z ) μ ( μ > 0 ; z U ) . In this paper, we introduce several subclasses of analytic functions defined by means of the operator I λ , μ n : A A , given by I λ , μ n f ( z ) = f λ , μ n ( z ) * f ( z ) ( f A ; n N 0 ; λ 0 ; μ > 0 ) . Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

On asymptotic behavior of solutions to Emden-Fowler type higher-order differential equations

Irina Astashova (2015)

Mathematica Bohemica


For the equation y ( n ) + | y | k sgn y = 0 , k > 1 , n = 3 , 4 , existence of oscillatory solutions y = ( x * - x ) - α h ( log ( x * - x ) ) , α = n k - 1 , x < x * , is proved, where x * is an arbitrary point and h is a periodic non-constant function on . The result on existence of such solutions with a positive periodic non-constant function h on is formulated for the equation y ( n ) = | y | k sgn y , k > 1 , n = 12 , 13 , 14 .