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Displaying similar documents to “Open and solved problems concerning polarized partition relations”

Global analytic and Gevrey surjectivity of the Mizohata operator D 2 + i x 2 2 k D 1

Lamberto Cattabriga, Luisa Zanghirati (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The surjectivity of the operator D 2 + i x 2 2 k D 1 from the Gevrey space E s R 2 , s 1 , onto itself and its non-surjectivity from E s R 3 to E s R 3 is proved.

An empirical almost sure central limit theorem under the weak dependence assumptions and its application to copula processes

Marcin Dudziński (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let: 𝐘 = 𝐘 i , where 𝐘 i = Y i , 1 , . . . , Y i , d , i = 1 , 2 , , be a d -dimensional, identically distributed, stationary, centered process with uniform marginals and a joint cdf F , and F n 𝐱 : = 1 n i = 1 n 𝕀 Y i , 1 x 1 , , Y i , d x d denote the corresponding empirical cdf. In our work, we prove the almost sure central limit theorem for an empirical process B n = n F n - F under some weak dependence conditions due to Doukhan and Louhichi. Some application of the established result to copula processes is also presented.

A partition property of cardinal numbers

N. H. Williams

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CONTENTSIntroduction....................................................................................... 5§ 1. Notation and definitions......................................................... 5§ 2. Negative relations.................................................................... 9§ 3. The Ramification Lemma ..................................................... 10§ 4. The main theorem................................................................... 13§ 5. A result for cardinals...

A note on a property of the Gini coefficient

Marian Genčev (2019)

Communications in Mathematics

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The scope of this note is a self-contained presentation of a mathematical method that enables us to give an absolute upper bound for the difference of the Gini coefficients G ( σ 1 , , σ n ) - G ( γ 1 , , γ n ) , where ( γ 1 , , γ n ) represents the vector of the gross wages and ( σ 1 , , σ n ) represents the vector of the corresponding super-gross wages that is used in the Czech Republic for calculating the net wage. Since (as of June 2019) σ i = 100 · 1 . 34 γ i / 100 , the study of the above difference seems to be somewhat inaccessible for many economists. However, our estimate...

On the gaps between q -binomial coefficients

Florian Luca, Sylvester Manganye (2021)

Communications in Mathematics

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In this note, we estimate the distance between two q -nomial coefficients n k q - n ' k ' q , where ( n , k ) ( n ' , k ' ) and q 2 is an integer.

L p inequalities for the growth of polynomials with restricted zeros

Nisar A. Rather, Suhail Gulzar, Aijaz A. Bhat (2022)

Archivum Mathematicum

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Let P ( z ) = ν = 0 n a ν z ν be a polynomial of degree at most n which does not vanish in the disk | z | < 1 , then for 1 p < and R > 1 , Boas and Rahman proved P ( R z ) p ( R n + z p / 1 + z p ) P p . In this paper, we improve the above inequality for 0 p < by involving some of the coefficients of the polynomial P ( z ) . Analogous result for the class of polynomials P ( z ) having no zero in | z | > 1 is also given.

On the eigenvalues of an elliptic operator a x , H u

Sergio Campanato (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let Ω be a bounded open convex set of class C 2 . Let a x , H u be a non linear operator satisfying the condition (A) (elliptic) with constants α , γ , δ . We prove that a number λ 0 is an eigenvalue for the operator a x , H u if and only if the number α λ is an eigen-value for the operator Δ u . If λ 0 , the two systems a x , H u = λ u and Δ u = α λ u have the same solutions. In particular, also the eventual eigen-values of the operator a x , H u should all be negative. Finally, we obtain a sufficient condition for the existence of solutions u H 2 H 0 1 Ω ...

Partition ideals below ω

P. Dodos, J. Lopez-Abad, S. Todorcevic (2012)

Fundamenta Mathematicae

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Motivated by an application to the unconditional basic sequence problem appearing in our previous paper, we introduce analogues of the Laver ideal on ℵ₂ living on index sets of the form [ k ] ω and use this to refine the well-known high-dimensional polarized partition relation for ω of Shelah.

On the Waring-Goldbach problem for one square and five cubes in short intervals

Fei Xue, Min Zhang, Jinjiang Li (2021)

Czechoslovak Mathematical Journal

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Let N be a sufficiently large integer. We prove that almost all sufficiently large even integers n [ N - 6 U , N + 6 U ] can be represented as n = p 1 2 + p 2 3 + p 3 3 + p 4 3 + p 5 3 + p 6 3 , p 1 2 - N 6 U , p i 3 - N 6 U , i = 2 , 3 , 4 , 5 , 6 , where U = N 1 - δ + ε with δ 8 / 225 .

On the topology of polynomials with bounded integer coefficients

De-Jun Feng (2016)

Journal of the European Mathematical Society

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For a real number q > 1 and a positive integer m , let Y m ( q ) : = i = 0 n ϵ i q i : ϵ i 0 , ± 1 , ... , ± m , n = 0 , 1 , ... . In this paper, we show that Y m ( q ) is dense in if and only if q < m + 1 and q is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].

On the global existence for the Muskat problem

Peter Constantin, Diego Córdoba, Francisco Gancedo, Robert M. Strain (2013)

Journal of the European Mathematical Society

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The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an L 2 ( ) maximum principle, in the form of a new “log” conservation law which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance f 1 1 / 5 . Previous results...