Displaying similar documents to “Characterizations of some bitopological separation axioms in terms of i j - θ - closure operator”

On geodesics of phyllotaxis

Roland Bacher (2014)

Confluentes Mathematici

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Seeds of sunflowers are often modelled by n ⟼ ϕ θ ( n ) = n e 2 i π n θ leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance 2 π θ for θ the golden ratio. We associate to such a map ϕ θ a geodesic path γ θ : ℝ > 0 ⟶ PSL 2 ( ℤ ) ∖ ℍ of the modular curve and use it for local descriptions of the image ϕ θ ( ℕ ) of the phyllotactic map ϕ θ .

Some remarks on the interpolation spaces A θ , A θ

Mohammad Daher (2016)

Commentationes Mathematicae Universitatis Carolinae

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Let ( A 0 , A 1 ) be a regular interpolation couple. Under several different assumptions on a fixed A β , we show that A θ = A θ for every θ ∈ ( 0 , 1 ) . We also deal with assumptions on A ¯ β , the closure of A β in the dual of ( A 0 * , A 1 * ) β .

Linear extenders and the Axiom of Choice

Marianne Morillon (2017)

Commentationes Mathematicae Universitatis Carolinae

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In set theory without the Axiom of Choice ZF, we prove that for every commutative field 𝕂 , the following statement 𝐃 𝕂 : “On every non null 𝕂 -vector space, there exists a non null linear form” implies the existence of a “ 𝕂 -linear extender” on every vector subspace of a 𝕂 -vector space. This solves a question raised in Morillon M., Linear forms and axioms of choice, Comment. Math. Univ. Carolin. 50 (2009), no. 3, 421-431. In the second part of the paper, we generalize our results in the case...

Axiom T D and the Simmons sublocale theorem

Jorge Picado, Aleš Pultr (2019)

Commentationes Mathematicae Universitatis Carolinae

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More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom T D for the relation of certain degrees of scatteredness but did not emphasize its role in the relation between sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons’ result....

On the cardinality of Urysohn spaces and weakly H -closed spaces

Fortunata Aurora Basile, Nathan Carlson (2019)

Mathematica Bohemica

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We introduce the cardinal invariant θ - a L ' ( X ) , related to θ - a L ( X ) , and show that if X is Urysohn, then | X | ≤ 2 θ - a L ' ( X ) χ ( X ) . As θ - a L ' ( X ) ≤ a L ( X ) , this represents an improvement of the Bella-Cammaroto inequality. We also introduce the classes of firmly Urysohn spaces, related to Urysohn spaces, strongly semiregular spaces, related to semiregular spaces, and weakly H -closed spaces, related to H -closed spaces.

The Massera-Schäffer problem for a first order linear differential equation

Nina A. Chernyavskaya, Leonid A. Shuster (2022)

Czechoslovak Mathematical Journal

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We consider the Massera-Schäffer problem for the equation - y ' ( x ) + q ( x ) y ( x ) = f ( x ) , x ∈ ℝ , where f ∈ L p loc ( ℝ ) , p ∈ [ 1 , ∞ ) and 0 ≤ q ∈ L 1 loc ( ℝ ) . By a solution of the problem we mean any function y , absolutely continuous and satisfying the above equation almost everywhere in ℝ . Let positive and continuous functions μ ( x ) and θ ( x ) for x ∈ ℝ be given. Let us introduce the spaces L p ( ℝ , μ ) = f ∈ L p loc ( ℝ ) : ∥ f ∥ L p ( ℝ , μ ) p = ∫ - ∞ ∞ | μ ( x ) f ( x ) | p d x < ∞ , L p ( ℝ , θ ) = f ∈ L p loc ( ℝ ) : ∥ f ∥ L p ( ℝ , θ ) p = ∫ - ∞ ∞ | θ ( x ) f ( x ) | p d x < ∞ . We obtain requirements to the functions μ , θ and q under which (1) for every function f ∈ L p ( ℝ , θ ) there exists a unique solution y ∈ L p ( ℝ , μ ) of the above equation; (2) there is an absolute constant...

Linearly-invariant families and generalized Meixner–Pollaczek polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The extremal functions  f 0 ( z )   realizing the maxima of some functionals (e.g. max | a 3 | , and  max a r g f ' ( z ) ) within the so-called universal linearly invariant family U α (in the sense of Pommerenke [10]) have such a form that f 0 ' ( z )   looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials P n λ ( x ; θ , ψ ) of a real variable x as coefficients of G λ ( x ; θ , ψ ; z ) = 1 ( 1 - z e i θ ) λ - i x ( 1 - z e i ψ ) λ + i x = ∑ n = 0 ∞ P n λ ( x ; θ , ψ ) z n , | z | < 1 , where the parameters λ , θ , ψ satisfy the conditions:...

Compatibility of the theta correspondence with the Whittaker functors

Vincent Lafforgue, Sergey Lysenko (2011)

Bulletin de la Société Mathématique de France

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We prove that the global geometric theta-lifting functor for the dual pair ( H , G ) is compatible with the Whittaker functors, where ( H , G ) is one of the pairs ( S 𝕆 2 n , 𝕊 p 2 n ) , ( 𝕊 p 2 n , S 𝕆 2 n + 2 ) or ( 𝔾 L n , 𝔾 L n + 1 ) . That is, the composition of the theta-lifting functor from H to G with the Whittaker functor for G is isomorphic to the Whittaker functor for H .

Singularities of 2 Θ -divisors in the jacobian

Christian Pauly, Emma Previato (2001)

Bulletin de la Société Mathématique de France

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We consider the linear system | 2 Θ 0 | of second order theta functions over the Jacobian J C of a non-hyperelliptic curve C . A result by J.Fay says that a divisor D ∈ | 2 Θ 0 | contains the origin 𝒪 ∈ J C with multiplicity 4 if and only if D contains the surface C - C = { 𝒪 ( p - q ) ∣ p , q ∈ C } ⊂ J C . In this paper we generalize Fay’s result and some previous work by R.C.Gunning. More precisely, we describe the relationship between divisors containing 𝒪 with multiplicity 6 , divisors containing the fourfold C 2 - C 2 = { 𝒪 ( p + q - r - s ) ∣ p , q , r , s ∈ C } , and divisors singular along C - C , using...

On the Set-Theoretic Strength of Countable Compactness of the Tychonoff Product 2 ℝ

Eleftherios Tachtsis (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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We work in ZF set theory (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) and show the following: 1. The Axiom of Choice for well-ordered families of non-empty sets ( A C W O ) does not imply “the Tychonoff product 2 ℝ , where 2 is the discrete space 0,1, is countably compact” in ZF. This answers in the negative the following question from Keremedis, Felouzis, and Tachtsis [Bull. Polish Acad. Sci. Math. 55 (2007)]: Does the Countable Axiom of Choice for families of non-empty sets...

Essentially Incomparable Banach Spaces of Continuous Functions

Rogério Augusto dos Santos Fajardo (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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We construct, under Axiom ♢, a family ( C ( K ξ ) ) ξ < 2 ( 2 ω ) of indecomposable Banach spaces with few operators such that every operator from C ( K ξ ) into C ( K η ) is weakly compact, for all ξ ≠ η. In particular, these spaces are pairwise essentially incomparable. Assuming no additional set-theoretic axiom, we obtain this result with size 2 ω instead of 2 ( 2 ω ) .

The local index density of the perturbed de Rham complex

Jesús Álvarez López, Peter B. Gilkey (2021)

Czechoslovak Mathematical Journal

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A perturbation of the de Rham complex was introduced by Witten for an exact 1-form Θ and later extended by Novikov for a closed 1-form on a Riemannian manifold M . We use invariance theory to show that the perturbed index density is independent of Θ ; this result was established previously by J. A. Álvarez López, Y. A. Kordyukov and E. Leichtnam (2020) using other methods. We also show the higher order heat trace asymptotics of the perturbed de Rham complex exhibit nontrivial dependence...