2,379 research outputs found
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
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
Positive Definite Functions for the Class Lp(G
No full textTitle: Positive Definite Functions for the Class Lp(G), Author: Shaunkat A. Warsi, Location: ThodeThis thesis contains four main theorems on Positive definite functions for the class Lp(G) over compact and locally compact groups. Information as to how the class P(F) varies with F is provided by those theorems. Some topological properties of the set P(Lp) ∩ Lq have been considered. Two results analogous to those of E. Hewitt and H. A. Naimark have also been proved.ThesisMaster of Science (MS
Resolvent Estimates in (weighted) Lp spaces for the Stokes Operator in Lipschitz Domains
No full textRecently, by Z. Shen, resolvent estimates for the Stokes operator were established in Lp(Ω) when Ω is a Lipschitz domain in Rd, with d≥3 and |1/p-1/2|<1/(2d)+ε. This result implies that the Stokes operator generates a bounded analytic semigroup in Lp(Ω) in the case that Ω is a three-dimensional Lipschitz domain and 3/2-ε<p<3+ε. To fully understand the work of Z. Shen, a lot of background information is needed. In this thesis the resolvent estimates are studied in detail in the case d=3. In the end the results of Shen are extended to resolvent estimates in Lp(w,Ω), where Ω is a three-dimensional Lipschitz domain, |1/p-1/2|<1/6, and w∈A2p/3∩RH3/(3-p) is a weight function that belongs to an intersection of a Muckenhoupt weight class and satisfies a reverse Hölder inequality
The Grothendieck property of Weak Lp spaces and Marcinkiewicz spaces
No full textIn this master thesis the proof of Lotz that Weak Lp spaces have the Grothendieck property is studied. The proof is slightly modified to be more explicit and easier to comprehend by introducing lemma’s to better separate different parts of the proof that more clearly reveal its structure. Furthermore, the more general Marcinkiewicz spaces are shown to sometimes have the Grothendieck property, using the sufficient conditions for a Banach lattice to have the Grothendieck property that Lotz derived to prove the Grothendieck property of Weak Lp spaces. For most of these conditions that together are sufficient, proving that Marcinkiewicz spaces satisfy them is done in a way very similar to the case of Weak Lp spaces. However, the proof of the (necessary) condition that the dual sometimes has order continuous norm does not allow for such a simple generalization and requires more work. Finally, by using some more recent results about the existence of symmetric functionals in the dual, the conditions that are given for the Grothendieck property of Marcinkiewicz spaces are shown to be necessary, and we thereby obtain a characterization of the Marcinkiewicz spaces that have the Grothendieck propertyApplied Mathematic
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