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Journal articles on the topic 'Lp-balls'

Author: Grafiati

Published: 6 September 2023

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1

Globevnik, Josip. "Holomorphic maps of discs into balls of lp-spaces." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 1 (January 1986): 123–33. http://dx.doi.org/10.1017/s030500410006401x.

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2

Jeng, M., and O. Knill. "Billiards in the lp unit balls of the plane." Chaos, Solitons & Fractals 7, no. 4 (April 1996): 543–54. http://dx.doi.org/10.1016/0960-0779(95)00080-1.

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3

Koldobsky, Alexander, and Marisa Zymonopoulou. "Extremal sections of complex lp-balls, 0 < p ≤2." Studia Mathematica 159, no. 2 (2003): 185–94. http://dx.doi.org/10.4064/sm159-2-2.

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4

Guseinov, Kh G., and A. S. Nazlipinar. "On the continuity property of Lp balls and an application." Journal of Mathematical Analysis and Applications 335, no. 2 (November 2007): 1347–59. http://dx.doi.org/10.1016/j.jmaa.2007.01.109.

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5

Li, Pengtao, and Zhichun Zhai. "Application of Capacities to Space-Time Fractional Dissipative Equations II: Carleson Measure Characterization for Lq(ℝ+n+1,μ) L^q (\mathbb{R}_ + ^{n + 1} ,\mu ) −Extension." Advances in Nonlinear Analysis 11, no. 1 (January 1, 2022): 850–87. http://dx.doi.org/10.1515/anona-2021-0232.

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Abstract This paper provides the Carleson characterization of the extension of fractional Sobolev spaces and Lebesgue spaces to L q ( ℝ + n + 1 , μ ) L^q (\mathbb{R}_ + ^{n + 1} ,\mu ) via space-time fractional equations. For the extension of fractional Sobolev spaces, preliminary results including estimates, involving the fractional capacity, measures, the non-tangential maximal function, and an estimate of the Riesz integral of the space-time fractional heat kernel, are provided. For the extension of Lebesgue spaces, a new Lp –capacity associated to the spatial-time fractional equations is introduced. Then, some basic properties of the Lp –capacity, including its dual form, the Lp –capacity of fractional parabolic balls, strong and weak type inequalities, are established.

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6

Koldobsky, A., A. Pajor, and V. Yaskin. "Inequalities of the Kahane–Khinchin type and sections of Lp-balls." Studia Mathematica 184, no. 3 (2008): 217–31. http://dx.doi.org/10.4064/sm184-3-2.

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7

Jiang, Tiefeng. "Distributions of eigenvalues of large Euclidean matrices generated from lp balls and spheres." Linear Algebra and its Applications 473 (May 2015): 14–36. http://dx.doi.org/10.1016/j.laa.2013.09.048.

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8

P�rez, F., C. Abdallah, and D. Docampo. "Robustness analysis of polynomials with linearly correlated uncertain coefficients in lp-normed balls." Circuits Systems and Signal Processing 15, no. 4 (July 1996): 543–54. http://dx.doi.org/10.1007/bf01183161.

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9

Kalton, N. J., A. Koldobsky, V. Yaskin, and M. Yaskina. "The Geometry of L0." Canadian Journal of Mathematics 59, no. 5 (October 1, 2007): 1029–49. http://dx.doi.org/10.4153/cjm-2007-044-0.

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AbstractSuppose that we have the unit Euclidean ball in ℝn and construct new bodies using three operations — linear transformations, closure in the radial metric, and multiplicative summation defined by We prove that in dimension 3 this procedure gives all origin-symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of a normed space in L0 that naturally extends the corresponding properties of Lp-spaces with p ≠ 0, and show that the procedure described above gives exactly the unit balls of subspaces of L0 in every dimension. We provide Fourier analytic and geometric characterizations of spaces embedding in L0, and prove several facts confirming the place of L0 in the scale of Lp-spaces.

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10

Lacko, Vladimír, and Radoslav Harman. "A conditional distribution approach to uniform sampling on spheres and balls in Lp spaces." Metrika 75, no. 7 (June 16, 2011): 939–51. http://dx.doi.org/10.1007/s00184-011-0360-x.

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11

Cao, Kaikai, and Xiaochen Zeng. "Adaptive Wavelet Estimations in the Convolution Structure Density Model." Mathematics 8, no. 9 (August 19, 2020): 1391. http://dx.doi.org/10.3390/math8091391.

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Using kernel methods, Lepski and Willer study a convolution structure density model and establish adaptive and optimal Lp risk estimations over an anisotropic Nikol’skii space (Lepski, O.; Willer, T. Oracle inequalities and adaptive estimation in the convolution structure density model. Ann. Stat.2019, 47, 233–287). Motivated by their work, we consider the same problem over Besov balls by wavelets in this paper and first provide a linear wavelet estimate. Subsequently, a non-linear wavelet estimator is introduced for adaptivity, which attains nearly-optimal convergence rates in some cases.

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12

Abujalala, Mohammed, and A. Nehir Özden. "Effects of Polishing versus Glazing on Dental Ceramic Wear: A Comparative In Vitro Study." Journal of Medical Imaging and Health Informatics 11, no. 1 (January 1, 2021): 73–79. http://dx.doi.org/10.1166/jmihi.2021.3271.

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This study analyzed the wear behavior caused by steatite antagonists to four dental ceramic materials, comparing this between two surface treatments: polishing and glazing. Methods: Thirty flat samples (10 × 8 × 2 mm) were prepared from each of four ceramics: IPS e. max CAD (IPS), GC Initial LiSi Press (LP), Vita Enamic (VE), and monolithic zirconia (MZ). Subgroups of samples were finished by polishing or glazing or neither (as controls). The samples were subjected to computer-controlled chewing simulation (240,000 cycles of 49 N at 1.6 Hz, with thermocycling at 5/55 C), with steatite balls as antagonists. The samples and antagonists were visualized before and after the test with a laser abrasion measurement system, a CAD/CAM scanner, and electron microscopy scanning, and the volumes lost from the tested samples and antagonists were analyzed. Results: For the MZ samples, the polished samples showed significantly less volume loss than the glazed samples (0.0200 mm3 vs. 0.0305 mm3; p =0.0001), whereas there was significantly greater antagonist volume loss (0.0365 mm3 vs. 0.0240 mm3; p = 0.011). There were no significant differences between the subgroups for IPS, VE, and LP, although antagonist volume losses were non-significantly greater with the glazed samples than with the polished samples. Conclusions: Polishing MZ had adverse effects on the corresponding antagonist wear. Glazed MZ showed the lowest antagonist wear.

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13

Kler, Alexander, Danil Apanovich, and Alexey Maximov. "An effective method for calculating the elements of thermal power plants, which are reduced to solving systems of partial differential equations." E3S Web of Conferences 209 (2020): 03029. http://dx.doi.org/10.1051/e3sconf/202020903029.

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Calculations of dynamic processes in the elements of thermal power plants (TPP) (heat exchangers, combustion chambers, turbomachines, etc.) are necessary to justify permissible and optimal operating modes, the choice of design characteristics elements, assessing their reliability, etc. Such tasks are reduced to solving partial differential equations. At present time for such calculations are mainly used finite-difference method and finite element method. These methods are cumbersome and complex. The article proposes a method, the main idea of which is to reduce the solution of equations to solving linear programming problems (LP) is demonstrated by the example heat exchanger of periodic action. The mathematical description includes the following energy balance equations for gas and ceramics, respectively, on the plane, where - indicates the length of the heat exchanger, and - the operating time. Also provides a more complex model, taking into account the spread of heat inside the balls of the ceramic backfill.

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14

Leung, Denny H. "On Banach spaces with Mazur's property." Glasgow Mathematical Journal 33, no. 1 (January 1991): 51–54. http://dx.doi.org/10.1017/s0017089500008028.

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A Banach space E is said to have Mazur's property if every weak* sequentially continuous functional in E” is weak* continuous, i.e. belongs to E. Such spaces were investigated in [5] and [9] where they were called d-complete and μB-spaces respectively. The class of Banach spaces with Mazur's property includes the WCG spaces and, more generally, the Banach spaces with weak* angelic dual balls [4, p. 564]. Also, it is easy to see that Mazur's property is inherited by closed subspaces. The main goal of this paper is to present generalizations of some results of [5] concerning the stability of Mazur's property with respect to forming some tensor products of Banach spaces. In particular, we show in Sections 2 and 3 that the spaces E ⊗εF and Lp(μ, E) inherit Mazur's property from E andF under some conditions. In Section 4, we will also show the stability of Mazur's property under the formation of Schauder decompositions and some unconditional sums of Banach spaces.

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15

Schlaerth, Jeffrey. "Local and equatorial characterization of unit balls of subspaces of Lp, p>0 and properties of the generalized cosine transform." Journal of Mathematical Analysis and Applications 382, no. 2 (October 2011): 523–33. http://dx.doi.org/10.1016/j.jmaa.2010.09.005.

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16

Savchuk, A. M., and I. V. Sadovnichaya. "Spectral Analysis of One-Dimensional Dirac System with Summable Potential and Sturm- Liouville Operator with Distribution Coefficients." Contemporary Mathematics. Fundamental Directions 66, no. 3 (December 15, 2020): 373–530. http://dx.doi.org/10.22363/2413-3639-2020-66-3-373-530.

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We consider one-dimensional Dirac operatorLP,U with Birkhoff regular boundary conditions and summable potential P(x) on[0, ]. We introduce strongly and weakly regular operators. In both cases, asymptotic formulas for eigenvalues are found. In these formulas, we obtain main asymptotic terms and estimates for the second term. We specify these estimates depending on the functional class of the potential: Lp[0,] with p [1,2] and the Besov space Bp,p'[0,] with p [1,2] and (0,1/p). Additionally, we prove that our estimates are uniform on balls Pp,R Then we get asymptotic formulas for normalized eigenfunctions in the strongly regular case with the same residue estimates in uniform metric on x [0,]. In the weakly regular case, the eigenvalues 2n and 2n+1 are asymptotically close and we obtain similar estimates for two-dimensional Riesz projectors. Next, we prove the Riesz basis property in the space (L2[0,])2 for a system of eigenfunctions and associated functions of an arbitrary strongly regular operatorLP,U. In case of weak regularity, the Riesz basicity of two-dimensional subspaces is proved. In parallel with theLP,U operator, we consider the SturmLiouville operator Lq,U generated by the differential -y'' + q(x)y expressionwith distribution potential q of first-order singularity (i.e., we assume that the primitive u = q(1) belongs to L2[0, ]) and Birkhoff-regular boundary conditions. We reduce to this case -(1y')'+i(y)'+iy'+0y, operators of more general form where '1,,0(-1)L2and 10. For operator Lq,U, we get the same results on the asymptotics of eigenvalues, eigenfunctions, and basicity as for operator LP,U . Then, for the Dirac operator LP,U, we prove that the Riesz basis constant is uniform over the ballsPp,R for p1 or 0. The problem of conditional basicity is naturally generalized to the problem of equiconvergence of spectral decompositions in various metrics. We prove the result on equiconvergence by varying three indices: fL[0,] (decomposable function), PL[0,] (potential), and Sm-Sm00,m in L[0,] (equiconvergence of spectral decompositions in the corresponding norm). In conclusion, we prove theorems on conditional and unconditional basicity of the system of eigenfunctions and associated functions of operator LP,U in the spaces L[0,],2, and in various Besov spaces Bp,q[0,].

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17

Kucukaslan, Abdulhamit. "Generalized fractional integrals in the vanishing generalized weighted local and global Morrey spaces." Filomat 37, no. 6 (2023): 1893–905. http://dx.doi.org/10.2298/fil2306893k.

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In this paper, we prove the boundedness of generalized fractional integral operators I? in the vanishing generalized weighted Morrey-type spaces, such as vanishing generalized weighted local Morrey spaces and vanishing generalized weighted global Morrey spaces by using weighted Lp estimates over balls. In more detail, we obtain the Spanne-type boundedness of the generalized fractional integral operators I? in the vanishing generalized weighted local Morrey spaces with wq ? A1+ q/p' for 1 < p < q < ?, and from the vanishing generalized weighted local Morrey spaces to the vanishing generalized weighted weak local Morrey spaces with w A1,q for p = 1, 1 < q < ?. We also prove the Adams-type boundedness of the generalized fractional integral operators I? in the vanishing generalized weighted global Morrey spaces with w Ap,q for 1 < p < q < ? and from the vanishing generalized weighted global Morrey spaces to the vanishing generalized weighted weak global Morrey spaces with w A1,q for p = 1, 1 < q < ?. The our all weight functions belong to Muckenhoupt-Weeden classes Ap,q.

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18

Ronse, Christian, Loic Mazo, and Mohamed Tajine. "Correspondence between Topological and Discrete Connectivities in Hausdorff Discretization." Mathematical Morphology - Theory and Applications 3, no. 1 (January 1, 2019): 1–28. http://dx.doi.org/10.1515/mathm-2019-0001.

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Abstract We consider Hausdorff discretization from a metric space E to a discrete subspace D, which associates to a closed subset F of E any subset S of D minimizing the Hausdorff distance between F and S; this minimum distance, called the Hausdorff radius of F and written rH(F), is bounded by the resolution of D. We call a closed set F separated if it can be partitioned into two non-empty closed subsets F1 and F2 whose mutual distances have a strictly positive lower bound. Assuming some minimal topological properties of E and D (satisfied in ℝn and ℤn), we show that given a non-separated closed subset F of E, for any r > rH(F), every Hausdorff discretization of F is connected for the graph with edges linking pairs of points of D at distance at most 2r. When F is connected, this holds for r = rH(F), and its greatest Hausdorff discretization belongs to the partial connection generated by the traces on D of the balls of radius rH(F). However, when the closed set F is separated, the Hausdorff discretizations are disconnected whenever the resolution of D is small enough. In the particular case where E = ℝn and D = ℤn with norm-based distances, we generalize our previous results for n = 2. For a norm invariant under changes of signs of coordinates, the greatest Hausdorff discretization of a connected closed set is axially connected. For the so-called coordinate-homogeneous norms, which include the Lp norms, we give an adjacency graph for which all Hausdorff discretizations of a connected closed set are connected.

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19

Chidume, C., and E. Chidume. "An Efficient Algorithm for Zeros of Bounded Generalized Ghi-Quasi-Accretive Maps." Proceedings of the Nigerian Academy of Science 6, no. 1 (November 25, 2013). http://dx.doi.org/10.57046/ttzb7886.

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This is a research announcement of the following result. Let E be a real normed linear space in which the single-valued normalized duality map is Holder continuous on balls and let A: E → E be a bounded generalized Φ-quasi-accretive map. A Mann-type iterative sequence is constructed and proved to converge strongly to the unique zero of A. In particular, our Theorems are applicable in real Banach spaces that include the Lp spaces, 1 < p < ∞. The Theorems are stated here without proofs. The full version of this paper, including detailed technical proofs of the Theorems will be published elsewhere.

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