Displaying similar documents to “Pressure and recurrence”

Some remarks on descriptive characterizations of the strong McShane integral

Sokol Bush Kaliaj (2019)

Mathematica Bohemica

Similarity:

We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function f : W X defined on a non-degenerate closed subinterval W of m in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure V F generated by the primitive F : W X of f , where W is the family of all closed non-degenerate subintervals of W .

Equilibrium states for interval maps: the potential - t log | D f |

Henk Bruin, Mike Todd (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let f : I I be a C 2 multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium states for the potential φ t : x - t log | D f ( x ) | for t close to 1 , and also that the pressure function t P ( φ t ) is analytic on an appropriate interval near t = 1 .

Partitioning planar graph of girth 5 into two forests with maximum degree 4

Min Chen, André Raspaud, Weifan Wang, Weiqiang Yu (2024)

Czechoslovak Mathematical Journal

Similarity:

Given a graph G = ( V , E ) , if we can partition the vertex set V into two nonempty subsets V 1 and V 2 which satisfy Δ ( G [ V 1 ] ) d 1 and Δ ( G [ V 2 ] ) d 2 , then we say G has a ( Δ d 1 , Δ d 2 ) -partition. And we say G admits an ( F d 1 , F d 2 ) -partition if G [ V 1 ] and G [ V 2 ] are both forests whose maximum degree is at most d 1 and d 2 , respectively. We show that every planar graph with girth at least 5 has an ( F 4 , F 4 ) -partition.

A note on representation functions with different weights

Zhenhua Qu (2016)

Colloquium Mathematicae

Similarity:

For any positive integer k and any set A of nonnegative integers, let r 1 , k ( A , n ) denote the number of solutions (a₁,a₂) of the equation n = a₁ + ka₂ with a₁,a₂ ∈ A. Let k,l ≥ 2 be two distinct integers. We prove that there exists a set A ⊆ ℕ such that both r 1 , k ( A , n ) = r 1 , k ( A , n ) and r 1 , l ( A , n ) = r 1 , l ( A , n ) hold for all n ≥ n₀ if and only if log k/log l = a/b for some odd positive integers a,b, disproving a conjecture of Yang. We also show that for any set A ⊆ ℕ satisfying r 1 , k ( A , n ) = r 1 , k ( A , n ) for all n ≥ n₀, we have r 1 , k ( A , n ) as n → ∞.

On a magnetic characterization of spectral minimal partitions

Bernard Helffer, Thomas Hoffmann-Ostenhof (2013)

Journal of the European Mathematical Society

Similarity:

Given a bounded open set Ω in n (or in a Riemannian manifold) and a partition of Ω by k open sets D j , we consider the quantity 𝚖𝚊𝚡 j λ ( D j ) where λ ( D j ) is the ground state energy of the Dirichlet realization of the Laplacian in D j . If we denote by k ( Ω ) the infimum over all the k -partitions of 𝚖𝚊𝚡 j λ ( D j ) , a minimal k -partition is then a partition which realizes the infimum. When k = 2 , we find the two nodal domains of a second eigenfunction, but the analysis of higher k ’s is non trivial and quite interesting. In this...

Dimension of weakly expanding points for quadratic maps

Samuel Senti (2003)

Bulletin de la Société Mathématique de France

Similarity:

For the real quadratic map P a ( x ) = x 2 + a and a given ϵ > 0 a point x has good expansion properties if any interval containing x also contains a neighborhood  J of x with P a n | J univalent, with bounded distortion and B ( 0 , ϵ ) P a n ( J ) for some n . The ϵ -weakly expanding set is the set of points which do not have good expansion properties. Let α denote the negative fixed point and M the first return time of the critical orbit to [ α , - α ] . We show there is a set of parameters with positive Lebesgue measure for which the Hausdorff...

Extension of point-finite partitions of unity

Haruto Ohta, Kaori Yamazaki (2006)

Fundamenta Mathematicae

Similarity:

A subspace A of a topological space X is said to be P γ -embedded ( P γ (point-finite)-embedded) in X if every (point-finite) partition of unity α on A with |α| ≤ γ extends to a (point-finite) partition of unity on X. The main results are: (Theorem A) A subspace A of X is P γ (point-finite)-embedded in X iff it is P γ -embedded and every countable intersection B of cozero-sets in X with B ∩ A = ∅ can be separated from A by a cozero-set in X. (Theorem B) The product A × [0,1] is P γ (point-finite)-embedded...

Sum-product theorems and incidence geometry

Mei-Chu Chang, Jozsef Solymosi (2007)

Journal of the European Mathematical Society

Similarity:

In this paper we prove the following theorems in incidence geometry. 1. There is δ > 0 such that for any P 1 , , P 4 , and Q 1 , , Q n 2 , if there are n ( 1 + δ ) / 2 many distinct lines between P i and Q j for all i , j , then P 1 , , P 4 are collinear. If the number of the distinct lines is < c n 1 / 2 then the cross ratio of the four points is algebraic. 2. Given c > 0 , there is δ > 0 such that for any P 1 , P 2 , P 3 2 noncollinear, and Q 1 , , Q n 2 , if there are c n 1 / 2 many distinct lines between P i and Q j for all i , j , then for any P 2 { P 1 , P 2 , P 3 } , we have δ n distinct lines between P and Q j . 3. Given...

A localization property for B p q s and F p q s spaces

Hans Triebel (1994)

Studia Mathematica

Similarity:

Let f j = k a k f ( 2 j + 1 x - 2 k ) , where the sum is taken over the lattice of all points k in n having integer-valued components, j∈ℕ and a k . Let A p q s be either B p q s or F p q s (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on n . The aim of the paper is to clarify under what conditions f j | A p q s is equivalent to 2 j ( s - n / p ) ( k | a k | p ) 1 / p f | A p q s .

Limits of log canonical thresholds

Tommaso de Fernex, Mircea Mustață (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let 𝒯 n denote the set of log canonical thresholds of pairs ( X , Y ) , with X a nonsingular variety of dimension n , and Y a nonempty closed subscheme of X . Using non-standard methods, we show that every limit of a decreasing sequence in 𝒯 n lies in 𝒯 n - 1 , proving in this setting a conjecture of Kollár. We also show that 𝒯 n is closed in 𝐑 ; in particular, every limit of log canonical thresholds on smooth varieties of fixed dimension is a rational number. As a consequence of this property, we see that in...

Σ s -products revisited

Reynaldo Rojas-Hernández (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show that any Σ s -product of at most 𝔠 -many L Σ ( ω ) -spaces has the L Σ ( ω ) -property. This result generalizes some known results about L Σ ( ω ) -spaces. On the other hand, we prove that every Σ s -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every Σ s -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...

C * -points vs P -points and P -points

Jorge Martinez, Warren Wm. McGovern (2022)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In a Tychonoff space X , the point p X is called a C * -point if every real-valued continuous function on C { p } can be extended continuously to p . Every point in an extremally disconnected space is a C * -point. A classic example is the space 𝐖 * = ω 1 + 1 consisting of the countable ordinals together with ω 1 . The point ω 1 is known to be a C * -point as well as a P -point. We supply a characterization of C * -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space...

On sum-product representations in q

Mei-Chu Chang (2006)

Journal of the European Mathematical Society

Similarity:

The purpose of this paper is to investigate efficient representations of the residue classes modulo q , by performing sum and product set operations starting from a given subset A of q . We consider the case of very small sets A and composite q for which not much seemed known (nontrivial results were recently obtained when q is prime or when log | A | log q ). Roughly speaking we show that all residue classes are obtained from a k -fold sum of an r -fold product set of A , where r log q and log k log q , provided the...

Generalized versions of Ilmanen lemma: Insertion of C 1 , ω or C loc 1 , ω functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We prove that for a normed linear space X , if f 1 : X is continuous and semiconvex with modulus ω , f 2 : X is continuous and semiconcave with modulus ω and f 1 f 2 , then there exists f C 1 , ω ( X ) such that f 1 f f 2 . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ω ( t ) = t ) to the case of an arbitrary nontrivial modulus ω . This generalization (where a C l o c 1 , ω function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.

Convolution operators with anisotropically homogeneous measures on 2 n with n-dimensional support

E. Ferreyra, T. Godoy, M. Urciuolo (2002)

Colloquium Mathematicae

Similarity:

Let α i , β i > 0 , 1 ≤ i ≤ n, and for t > 0 and x = (x₁,...,xₙ) ∈ ℝⁿ, let t x = ( t α x , . . . , t α x ) , t x = ( t β x , . . . , t β x ) and | | x | | = i = 1 n | x i | 1 / α i . Let φ₁,...,φₙ be real functions in C ( - 0 ) such that φ = (φ₁,..., φₙ) satisfies φ(t • x) = t ∘ φ(x). Let γ > 0 and let μ be the Borel measure on 2 n given by μ ( E ) = χ E ( x , φ ( x ) ) | | x | | γ - α d x , where α = i = 1 n α i and dx denotes the Lebesgue measure on ℝⁿ. Let T μ f = μ f and let | | T μ | | p , q be the operator norm of T μ from L p ( 2 n ) into L q ( 2 n ) , where the L p spaces are taken with respect to the Lebesgue measure. The type set E μ is defined by E μ = ( 1 / p , 1 / q ) : | | T μ | | p , q < , 1 p , q . In the case α i β k for 1 ≤ i,k ≤ n we characterize the...

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

Similarity:

Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...

Cobham's theorem for substitutions

Fabien Durand (2011)

Journal of the European Mathematical Society

Similarity:

The seminal theorem of Cobham has given rise during the last 40 years to a lot of work about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let α and β be two multiplicatively independent Perron numbers. Then a sequence x A , where A is a finite alphabet, is both α -substitutive and β -substitutive if and only if x is ultimately...

Theoretical analysis for 1 - 2 minimization with partial support information

Haifeng Li, Leiyan Guo (2025)

Applications of Mathematics

Similarity:

We investigate the recovery of k -sparse signals using the 1 - 2 minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume k -sparse signals 𝐱 with the prior support T which is composed of g true indices and b wrong...