3,434 research outputs found
Estimates For An Integral In Lp Norm Of The (N + 1)-Th Derivative Of Its Integrand
No full textBasing on Taylor’s formula with an integral remaider, an integral is estimated in Lp norm of the (n + 1)-th derivative of its integrand, and the Iyengar’s inequality and many other useful inequalities are generalized
LP Decoding Excess over Symmetric Channels
No full textWe consider the problem of Linear Programming (LP) decoding of binary linear codes. The LP excess lemma was introduced by the first author, B. Ghazi, and R. Urbanke (IEEE Trans. Inf. Th., 2014) as a technique to trade crossover probability for 'LP excess' over the Binary Symmetric Channel. We generalize the LP excess lemma to discrete, binary-input, Memoryless, Symmetric and LLR-Bounded (MSB) channels. As an application, we extend a result by the first author and H. Audah (IEEE Trans. Inf. Th., 2015) on the impact of redundant checks on LP decoding to discrete MSB channels. © 2015 IEEE
A Sobolev estimate for radial lp-multipliers on a class of semi-simple lie groups
No full textLet G be a semi-simple Lie group in the Harish-Chandra class with maximal compact subgroup K. Let ΩK be minus the radial Casimir operator. Let 1 4 dim(G/K) < SG < 1 2 dim(G/K), s ∈ (0, SG] and p ∈ (1,∞) be such that(1 p - 1 2 )< s 2SG . Then, there exists a constant CG,s,p > 0 such that for every m ∈ L∞(G) ∩ L2(G) bi-K-invariant with m ∈ Dom(Ωs K) and Ωs K(m) ∈ L2SG/s(G) we have, (0.1) ∥Tm : Lp(G) → Lp( G)∥ ≤ CG,s,p∥Ωs K(m)∥ L2SG/s(G), where Tm is the Fourier multiplier with symbol m acting on the noncommutative Lp-space of the group von Neumann algebra of G. This gives new examples of Lp-Fourier multipliers with decay rates becoming slower when p approximates 2.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Analysi
Stability properties of stochastic maximal Lp-regularity
No full textIn this paper we consider Lp-regularity estimates for solutions to stochastic evolution equations, which is called stochastic maximal Lp-regularity. Our aim is to find a theory which is analogously to Dore’s theory for deterministic evolution equations. He has shown that maximal Lp-regularity is independent of the length of the time interval, implies analyticity and exponential stability of the semigroup, is stable under perturbation and many more properties. We show that the stochastic versions of these results hold
Dual Lp-Mixed Geominimal Surface Area and Related Inequalities
No full textThe integral formula of dual Lp-geominimal surface area is given and the concept of dual Lp-geominimal surface area is extended to dual Lp-mixed geominimal surface area. Properties for the dual Lp-mixed geominimal surface areas are established. Some inequalities, such as analogues of Alexandrov-Fenchel inequalities, Blaschke-Santaló inequalities, and affine isoperimetric inequalities for dual Lp-mixed geominimal surface areas, are also obtained
Uniqueness When the Lp Curvature is Close to be a Constant for p ∈ [0, 1)
No full textFor fixed positive integer n, p ∈ [0, 1), a ∈ (0, 1), we prove that if a function g : Sn−1 → R is sufficiently close to 1, in the Ca sense, then there exists a unique convex body K whose Lp curvature function equals g. This was previously established for n = 3, p = 0 by Chen, Feng, Liu and in the symmetric case by Chen, Huang, Li, Liu. Related, we show that if p = 0 and n = 4 or n ≤ 3 and p ∈ [0, 1), and the Lp curvature function g of a (sufficiently regular, containing the origin) convex body K satisfies λ−1 ≤ g ≤ λ, for some λ > 1, then maxx∈Sn−1 hK(x) ≤ C(p, λ), for some constant C(p, λ) > 0 that depends only on p and λ. This also extends a result from Chen, Feng, Liu [10]. Along the way, we obtain a result, that might be of independent interest, concerning the question of when the support of the Lp surface area measure is lower dimensional. Finally, we establish a strong non-uniqueness result for the Lp-Minkowksi problem, for −n<p<0
PROPAGATION OF LP//0//1 AND LP//1//1 MODES IN COUPLED OPTICAL FIBERS.
No full textThe author studied the propagation of the fundamental mode, called the LP//0//1 mode, of a single-mode optical fiber and the LP//1//1 mode, the next higher-order mode, in two long lengths of fiber coupled together. This was done by launching light having a wavelength below the cut-off wavelength of the fiber. The effect of lateral misalignment at the coupled junctions was investigated. The results are explained in terms of excitation of the modes at this junction
Life of a Yellow Kid: an audiovisual electro-pop LP
No full textThe basis of this project is to compose, record, produce and mix an eleven song album (LP) with a visualizer, logo and design for each track. The author designed all of the artworks for the songs and LP and produced videos and content for said LP. Also, the author combined all of his influences from electronic music and other genres to create something new to expand the limits of electronic music. This album was influenced by works of artists like Madeon, Porter Robinson, Louis The Child, Urboi, Medasin, Fred Again.. and The Weeknd. Song-writing, recording, sound design, creative production techniques, mixing, graphic design and audiovisual production were the skills and tools necessary for the completion of this LP. The main focus of the LP was to combine different genres of music, like Electro-pop, UK Garage, Pop, House and Drum and Bass. Also this album is about personal experiences of the author and it covers different feelings throughout the LP, creating a sunset literally and figuratively within the album.
This paper was written without any assistance from generative artificial intelligence.https://remix.berklee.edu/graduate-studies-production-technology/1378/thumbnail.jp
Tеорема Литтлвуда - Пелі про простори Lp(t)(ℝⁿ)
No full textWe point out that if the Hardy–Littlewood maximal operator is bounded on the space Lp(t)(ℝ), 1 1 , the Littlewood–Paley operator is bounded on Lp(t) (ℝⁿ), 1 1, оператор Літтлвуда - Пелі обмежений на Lp(t)(Rⁿ),1 < a ≤ p(t) ≤ b<∞,t ∈ R, тоді і тільки тоді, коли p(t)= const.The author was supported by grant GNSF / STO 7 / 3-171
Tеорема Литтлвуда - Пелі про простори Lp(t)(ℝⁿ)
No full textWe point out that if the Hardy–Littlewood maximal operator is bounded on the space Lp(t)(ℝ), 1 1 , the Littlewood–Paley operator is bounded on Lp(t) (ℝⁿ), 1 1, оператор Літтлвуда - Пелі обмежений на Lp(t)(Rⁿ),1 < a ≤ p(t) ≤ b<∞,t ∈ R, тоді і тільки тоді, коли p(t)= const.The author was supported by grant GNSF / STO 7 / 3-171
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