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Filling metric spaces [article]

Yevgeny Liokumovich, Boris Lishak, Alexander Nabutovsky, Regina Rotman
2021 arXiv   pre-print
Moreover, one can find F with a nearly minimal HC_m+1 such that its image lies in the C(m)HC_m(f(Y))^1 m-neighbourhood of f(Y) with the exception of a subset with zero (m+1)-dimensional Hausdorff measure  ...  We prove a new version of isoperimetric inequality: Given a positive real m, a Banach space B, a closed subset Y of metric space X and a continuous map f:Y → B with f(Y) compact inf_FHC_m+1(F(X))≤ c(m)  ...  A part of this work was done during the authors' visit to the Research Institute for Mathematical Studies, Kyoto University, in July, 2018.  ... 
arXiv:1905.06522v2 fatcat:itk4ifvkh5gddm6tqnqkz55qpi

Variations on the Boman covering lemma [article]

J. M. Aldaz
2018 arXiv   pre-print
We prove that the strong type (q,q) of the uncentered maximal operator, by itself, implies certain generalizations of the Boman covering lemma for the exponent p, and in turn, these generalizations entail  ...  We explore some variants of the Boman covering lemma, and their relationship to the boundedness properties of the maximal operator. Let 1 < p < ∞ and let q be its conjugate exponent.  ...  The generalized weak p-Boman covering property is defined analogously, with sets of positive measure contained in the smaller balls replacing the latter. Theorem 4.5.  ... 
arXiv:1812.01876v1 fatcat:5za7ul6kbbdvzcvkz3fggdblri

The Influence of location of balls and ball diameter difference in rolling bearings on the nonrepetitive runout (NRRO) of retainer revolution

Shoji Noguchi, Kentaro Hiruma, Hiroyuki Kawa, Tohru Kanada
2005 Precision engineering  
Consequently, it is clarified that the mean value of the retainer revolution component calculated in all locations of balls decreased with increasing number of balls in a rolling bearing.  ...  The nonrepetitive runout (NRRO) value of retainer revolution is caused mainly by the diameter differences of balls mounted in a bearing.  ...  , (r 0 , a rn , φ rn ), (R 0 , a Rn , φ Rn ) and (r bk0 , a bkn , φ bkn ) are coefficients in the Fourier series expansion.  ... 
doi:10.1016/j.precisioneng.2004.03.003 fatcat:w5j3m6oy2ve5vaz3uiao4txcnu

Hausdorff dimension of limsup sets of random rectangles in products of regular spaces [article]

Fredrik Ekström, Esa Järvenpää, Maarit Järvenpää, Ville Suomala
2017 arXiv   pre-print
The almost sure Hausdorff dimension of the limsup set of randomly distributed rectangles in a product of Ahlfors regular metric spaces is computed in terms of the singular value function of the rectangles  ...  Let X be a (c, s)-regular space and let r and R be positive numbers such that r ≤ 2R. Let B be a closed ball of radius R in X. Then B can be covered by 4 s c 2 (R/r) s closed balls of radius r.  ...  The upper bound for f µ is obtained in a standard way by showing that each rectangle R (x n , r n ) has a cover by balls whose contribution to the sum in the definition of the t-dimensional Hausdorff measure  ... 
arXiv:1705.02616v2 fatcat:xfah2qs45bdebnouf2ydhqxnl4

Hausdorff dimension of limsup sets of random rectangles in products of regular spaces

Fredrik Ekström, Esa Järvenpää, Maarit Järvenpää, Ville Suomala
2018 Proceedings of the American Mathematical Society  
The almost sure Hausdorff dimension of the limsup set of randomly distributed rectangles in a product of Ahlfors regular metric spaces is computed in terms of the singular value function of the rectangles  ...  Let X be a (c, s)-regular space and let r and R be positive numbers such that r ≤ 2R. Let B be a closed ball of radius R in X. Then B can be covered by 4 s c 2 (R/r) s closed balls of radius r.  ...  The upper bound for f µ is obtained in a standard way by showing that each rectangle R (x n , r n ) has a cover by balls whose contribution to the sum in the definition of the t-dimensional Hausdorff measure  ... 
doi:10.1090/proc/13920 fatcat:4knffqrc3fapzg5kspn5nybgjy

Contact distribution in a thinned Boolean model with power-law radii

Yinghua Dong, Gennady Samorodnitsky
2017 Journal of Applied Probability  
We consider a weighted stationary spherical Boolean model in ℝ d to which a Matérn-type thinning is applied.  ...  Assuming that the radii of the balls in the Boolean model have regularly varying tails, we establish the asymptotic behavior of the tail of the contact distribution of the thinned germ–grain model under  ...  With this choice of G, balls with a smaller radius have a larger weight.  ... 
doi:10.1017/jpr.2017.26 fatcat:s4wyvou2czbuhgy6l27up3f4yq

Subspaces of Small Codimension of Finite-Dimensional Banach Spaces

Alain Pajor, Nicole Tomczak-Jaegermann
1986 Proceedings of the American Mathematical Society  
Then for an operator taking values in a Hubert space, we deduce an inequality for entropy numbers of the operator and its dual.  ...  Given a finite-dimensional Banach space E and a Euclidean norm on E, we study relations between the norm and the Euclidean norm on subspaces of E of small codimension.  ...  Fix 0 < A < l. Let j be the smaller integer larger than or equal to (1 -A)n. Set V -(diy/l -X/M*)Be, where a constant 0 < di < 1 will be defined later, W = (s/T^X/M*)BE D B2.  ... 
doi:10.2307/2045920 fatcat:q3zlbxapljchvhnugmq4djlusi

Subspaces of small codimension of finite-dimensional Banach spaces

Alain Pajor, Nicole Tomczak-Jaegermann
1986 Proceedings of the American Mathematical Society  
Then for an operator taking values in a Hubert space, we deduce an inequality for entropy numbers of the operator and its dual.  ...  Given a finite-dimensional Banach space E and a Euclidean norm on E, we study relations between the norm and the Euclidean norm on subspaces of E of small codimension.  ...  Fix 0 < A < l. Let j be the smaller integer larger than or equal to (1 -A)n. Set V -(diy/l -X/M*)Be, where a constant 0 < di < 1 will be defined later, W = (s/T^X/M*)BE D B2.  ... 
doi:10.1090/s0002-9939-1986-0845980-8 fatcat:44dxdyw7effzpe5gxdbk4y3ati

Self-Stabilizing Repeated Balls-into-Bins

LucaBecchetti Becchetti, Andrea Clementi, Emanuele Natale, Francesco Pasquale, Gustavo Posta
2015 Proceedings of the 27th ACM on Symposium on Parallelism in Algorithms and Architectures - SPAA '15  
We study the following synchronous process that we call repeated balls-into-bins. The process is started by assigning n balls to n bins in an arbitrary way.  ...  This process corresponds to a non-reversible Markov chain and our aim is to study its self-stabilization properties with respect to the maximum (bin) load and some related performance measures.  ...  a much smaller bound on the maximum load than that in [5] .  ... 
doi:10.1145/2755573.2755584 dblp:conf/spaa/BecchettiCNPP15 fatcat:tq2atreyovcuvlzybcwnq2vmne

Self-stabilizing repeated balls-into-bins

L. Becchetti, A. Clementi, E. Natale, F. Pasquale, G. Posta
2017 Distributed computing  
We study the following synchronous process that we call repeated balls-into-bins. The process is started by assigning n balls to n bins in an arbitrary way.  ...  This process corresponds to a non-reversible Markov chain and our aim is to study its self-stabilization properties with respect to the maximum (bin) load and some related performance measures.  ...  a much smaller bound on the maximum load than that in [5] .  ... 
doi:10.1007/s00446-017-0320-4 fatcat:3db3zbpmunen3ivllreulgxwyy

Page 4391 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
that such a set can be covered by six smaller homothetic copies of itself.  ...  4391 52A General convexity ering] of a half-open d-cube (0, 1)’ by translates of e[0,1)4 (0 < € < 1) can be replaced by a lattice packing [lattice covering] that is not smaller [not larger] than the original  ... 

Self-Stabilizing Repeated Balls-into-Bins [article]

Luca Becchetti, Andrea Clementi, Emanuele Natale, Francesco Pasquale, Gustavo Posta
2016 arXiv   pre-print
by any polynomial in n, with high probability (w.h.p.).  ...  We study the following synchronous process that we call "repeated balls-into-bins". The process is started by assigning n balls to n bins in an arbitrary way.  ...  From any initial configuration, in the Tetris process every bin will be empty at least once within 5n rounds, w.h.p. Proof. Let u P rns be a bin with k ď n balls in the initial configuration.  ... 
arXiv:1501.04822v3 fatcat:7wuz2jbnz5eupi64hn5jrttpxi

The dynamical Borel-Cantelli lemma and the waiting time problems

Stefano Galatolo, Dong Han Kim
2007 Indagationes mathematicae  
We prove that if a system has the dynamical Borel~antelli property, then the time needed to enter for the first time in a sequence of small balls scales as the inverse of the measure of the balls.  ...  This allows to obtain Borel-Cantelli like results in systems like axiom A and generic interval exchanges.  ...  It is clear that in an ergodic system (when A has positive measure) ra(X) is almost everywhere finite. Intuitively, when A is smaller and smaller, then rA(X) is bigger and bigger.  ... 
doi:10.1016/s0019-3577(07)80031-0 fatcat:4aagtu4vwng5nmam7fhhmroudu

Squiggle Ball Capture: A Simple, Visual Kinetic Theory Experiment

Tim Gfroerer, Ken Rathbun
2007 The Physics Teacher  
Simov and Blair Reynolds for performing the trap density-dependent capture time experiment, Professor Mario Belloni for reviewing the manuscript, and Instrumentation Specialist Jerry Snead for assistance with  ...  In reality, the interaction of a ball with the edge of a hole is complex, as has been shown for putting in the game of golf. 6 With Squiggle Balls, the situation is compounded by the fact that the center  ...  In recent years Squiggle Balls have been used to connect random macroscopic particle motion with a wide variety of thermal phenomena.  ... 
doi:10.1119/1.2768689 fatcat:adv7hvk2vvaplkbmirbzwqh4su

Concordance inertia groups

James R Munkres
1970 Advances in Mathematics  
itself that may be extended to a diffeomorphism of M with Mz#Zof : Use u and ux' as coordinate systems covering U(P) in M and M # Z,,, , respectively; and note that (ux')-'fu is the identity on P-i.  ...  Let h' : K + M # Zq be another PD triangulation that equals the identity outside the ball u(P). Choose a combinatorial ball D in K containing this topological ball.  ... 
doi:10.1016/0001-8708(70)90024-1 fatcat:vntvbpe4vnckti3g4d7wmw3wau
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