1,355,552 research outputs found
Faces and Places in Fashion: Diane Von Furstenberg
No full textPart presentation, part Q&A, FIT's "Faces & Places in Fashion" lecture series is an opportunity to connect students and the public alike to the pulse of the fashion industry in an open and conversational setting.Founder and president of Diane von Furstenerg, Inc. Ms. Von Furstenberg shares the story of her personal and professional life through a slideshow of photos from her past
Faces and Places in Fashion: Diane Von Furstenberg
No full textPart presentation, part Q&A, FIT's "Faces & Places in Fashion" lecture series is an opportunity to connect students and the public alike to the pulse of the fashion industry in an open and conversational setting.Founder and president of Diane von Furstenerg, Inc. Ms. Von Furstenberg shares the story of her personal and professional life through a slideshow of photos from her past
New examples of complete sets, with connections to a Diophantine theorem of Furstenberg
No full textA set is called if every sufficiently large integer can be written as the sum of distinct elements of . In this paper we present a new method for proving the completeness of a set, improving results of Cassels ('60), Zannier ('92), Burr, Erd\H{o}s, Graham, and Li ('96), and Hegyv\'ari ('00). We also introduce the somewhat philosophically related notion of a set and refine a theorem of Furstenberg ('67)
Absolutely continuous Furstenberg measures
No full textIn this paper, we provide a sufficient condition for a Furstenberg measure generated by a finitely supported measure to be absolutely continuous. Using this, we give completely explicit examples of absolutely continuous Furstenberg measures including examples which are generated by measures which are not symmetric
Absolutely continuous Furstenberg measures
No full textIn this paper we provide a sufficient condition for a Furstenberg measure
generated by a finitely supported measure to be absolutely continuous. Using
this, we give a very broad class of examples of absolutely continuous
Furstenberg measures including examples generated by measures supported on two
points.Comment: 100 page
Trends in the Economic Independence of Young Adults in the United States: 1973-2007
No full textOne of the major milestones of adulthood is achieving economic independence. Without sufficient income, young people have difficulty leaving their childhood home, establishing a union, or having children-or they do so at great peril. Using the National Longitudinal Survey, this article compares the employment and economic circumstances of young adults aged 22-30 in 1973, 1987, and 2007, and their possible determinants. The results show that achieving economic independence is more difficult now than it was in the late 1980s and especially in the 1970s, even for the older age groups (age 27-28). The deterioration is more evident among men. From the 1970s there has been convergence in the trajectories for the achievement of economic self-sufficiency between men and women, suggesting that the increase in gender parity, especially in education and labor market outcomes, is making their opportunities to be employed and to earn good wages more similar. This convergence also suggests that union formation increasingly may depend on a capacity to combine men's and women's wages
Furstenberg Families and Sensitivity
No full textWe introduce and study some concepts of sensitivity via Furstenberg
families. A dynamical system (X,f) is ℱ-sensitive if there exists a positive ε such that for every x∈X and every open neighborhood U of x there exists y∈U such
that the pair (x,y) is not ℱ-ε-asymptotic; that is, the time set {n:d(fn(x),fn(y))>ε} belongs to ℱ, where ℱ is a Furstenberg family. A dynamical system
(X,f) is (ℱ1, ℱ2)-sensitive if there is a positive ε such that every x∈X is a limit of points y∈X such that the pair (x,y) is ℱ1-proximal but not ℱ2-ε-asymptotic; that is, the time set {n:d(fn(x),fn(y))ε} belongs to ℱ2, where
ℱ1 and ℱ2 are Furstenberg families
Furstenberg systems of pretentious and MRT multiplicative functions
No full text63 pagesInternational audienceWe prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions these systems always have rational discrete spectrum and, as a consequence, zero entropy. We obtain several other refined structural and spectral results, one consequence of which is that the Archimedean characters are the only pretentious multiplicative functions that have Furstenberg systems with trivial rational spectrum, another is that a pretentious multiplicative function has ergodic Furstenberg systems if and only if it pretends to be a Dirichlet character, and a last one is that for any fixed pretentious multiplicative function all its Furstenberg systems are isomorphic. We also study structural properties of Furstenberg systems of a class of multiplicative functions, introduced by Matom\"aki, Radziwill, and Tao, which lie in the intermediate zone between pretentiousness and strong aperiodicity. In a work of the last two authors and Gomilko, several examples of this class with exotic ergodic behavior were identified, and here we complement this study and discover some new unexpected phenomena. Lastly, we prove that Furstenberg systems of general bounded multiplicative functions have divisible spectrum. When these systems are obtained using logarithmic averages, we show that trivial rational spectrum implies a strong dilation invariance property, called strong stationarity, but, quite surprisingly, this property fails when the systems are obtained using Ces\`aro averages
Proximality and equidistribution on the Furstenberg boundary
No full textLet G be a connected semisimple Lie group with finite center and without compact factors, P a minimal parabolic subgroup of G, and Gamma a lattice in G. We prove that every Gamma-orbits in the Furstenberg boundary G/P is equidistributed for the averages over Riemannian balls. The proof is based on the proximality of the action of Gamma on G/P.Let G be a connected semisimple Lie group with finite center and without compact factors, P a minimal parabolic subgroup of G, and Gamma a lattice in G. We prove that every Gamma-orbits in the Furstenberg boundary G/P is equidistributed for the averages over Riemannian balls. The proof is based on the proximality of the action of Gamma on G/P
Furstenberg sets estimate in the plane
No full textWe fully resolve the Furstenberg set conjecture in , that a
-Furstenberg set has Hausdorff dimension . As a result, we obtain an analogue of Elekes' bound for the discretized
sum-product problem and resolve an orthogonal projection question of Oberlin.Comment: 23 pages. v2: fixed small typo in abstract and added more details to
arguments, main results unchange
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