Journal articles: 'Spherical maximal functions'

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Lacey, Michael T. "Sparse bounds for spherical maximal functions." Journal d'Analyse Mathématique 139, no. 2 (October 2019): 613–35. http://dx.doi.org/10.1007/s11854-019-0070-2.

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Seeger, Andreas, Stephen Wainger, and James Wright. "Spherical Maximal Operators on Radial Functions." Mathematische Nachrichten 187, no. 1 (1997): 241–65. http://dx.doi.org/10.1002/mana.19971870112.

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Duoandikoetxea, Javier, Adela Moyua, and Osane Oruetxebarria. "The spherical maximal operator on radial functions." Journal of Mathematical Analysis and Applications 387, no. 2 (March 2012): 655–66. http://dx.doi.org/10.1016/j.jmaa.2011.09.028.

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Kajima, Yasuhiro. "Spherical functions on orthogonal groups." Nagoya Mathematical Journal 141 (March 1996): 157–82. http://dx.doi.org/10.1017/s0027763000005572.

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Let G be a p-adic connected reductive algebraic group and K a maximal compact subgroup of G. In [4], Casselman obtained the explicit formula of zonal spherical functions on G with respect to K on the assumption that K is special. It is known (Bruhat and Tits [3]) that the affine root system of algebraic group which has good but not special maximal compact subgroup is A1 C2, or Bn (n > 3), and all Bn-types can be realized by orthogonal groups. Here the assumption “good” is necessary for the Satake’s theory of spherical functions.

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Kesler, Robert, Michael T. Lacey, and Darío Mena. "Sparse bounds for the discrete spherical maximal functions." Pure and Applied Analysis 2, no. 1 (January 1, 2020): 75–92. http://dx.doi.org/10.2140/paa.2020.2.75.

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Gauthier, P. M., and J. Xiao. "Functions of bounded expansion: normal and Bloch functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 66, no. 2 (April 1999): 168–88. http://dx.doi.org/10.1017/s144678870003929x.

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AbstractNormal functions and Bloch functions are respectively functions of bounded spherical expansion and bounded Euclidean expansion. In this paper we discuss the behaviour of normal functions and of Bloch functions in terms of the maximal ideal space of H∞, the Bergman projection and the Ahlfors-Shimizu characteristic.

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Roos, Joris, and Andreas Seeger. "Spherical maximal functions and fractal dimensions of dilation sets." American Journal of Mathematics 145, no. 4 (August 2023): 1077–110. http://dx.doi.org/10.1353/ajm.2023.a902955.

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abstract: For the spherical mean operators $\scr{A}_t$ in $\Bbb{R}^d$, $d\ge 2$, we consider the maximal functions $M_Ef=\sup_{t\in E}|\scr{A}_t f|$, with dilation sets $E\subset [1,2]$. In this paper we give a surprising characterization of the closed convex sets which can occur as closure of the sharp $L^p$ improving region of $M_E$ for some $E$. This region depends on the Minkowski dimension of $E$, but also other properties of the fractal geometry such as the Assouad spectrum of $E$ and subsets of $E$. A key ingredient is an essentially sharp result on $M_E$ for a class of sets called (quasi-)Assouad regular which is new in two dimensions.

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Anderson, Theresa C., and Eyvindur Ari Palsson. "Bounds for discrete multilinear spherical maximal functions in higher dimensions." Bulletin of the London Mathematical Society 53, no. 3 (January 22, 2021): 855–60. http://dx.doi.org/10.1112/blms.12465.

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Dosidis, Georgios, and Loukas Grafakos. "On families between the Hardy–Littlewood and spherical maximal functions." Arkiv för Matematik 59, no. 2 (2021): 323–43. http://dx.doi.org/10.4310/arkiv.2021.v59.n2.a4.

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Leckband, Mark. "A note on the spherical maximal operator for radial functions." Proceedings of the American Mathematical Society 100, no. 4 (April 1, 1987): 635. http://dx.doi.org/10.1090/s0002-9939-1987-0894429-9.

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Cowling, Michael, José García-Cuerva, and Hendra Gunawan. "Weighted estimates for fractional maximal functions related to spherical means." Bulletin of the Australian Mathematical Society 66, no. 1 (August 2002): 75–90. http://dx.doi.org/10.1017/s0004972700020694.

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We prove weighted Lp-Lq estimates for the maximal operators ℳα, given by , where μt denotes the normalised surface measure on the sphere of centre 0 and radius t in Rd. The techniques used involve interpolation and the Mellin transform. To do this, we also prove weighted Lp-Lq estimates for the operators of convolution with the kernels |·|−α−iη.

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Ho, Kwok-Pun. "Spherical maximal functions, variation and oscillation inequalities on Herz spaces." Arab Journal of Basic and Applied Sciences 26, no. 1 (January 2, 2019): 72–77. http://dx.doi.org/10.1080/25765299.2018.1554201.

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Hughes, Kevin. "Restricted weak-type endpoint estimates for k-spherical maximal functions." Mathematische Zeitschrift 286, no. 3-4 (January 7, 2017): 1303–21. http://dx.doi.org/10.1007/s00209-016-1802-y.

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Deleaval, Luc. "On the boundedness of the Dunkl spherical maximal operator." Journal of Topology and Analysis 08, no. 03 (June 8, 2016): 475–95. http://dx.doi.org/10.1142/s1793525316500163.

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In this paper, we introduce a Dunkl-type spherical maximal operator associated with a finite reflection group and study its boundedness. In view of this study, we give some results on suitable square functions and maximal multiplier operators in the Dunkl setting.

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Flicker, Yuval Z. "Stable base change for spherical functions." Nagoya Mathematical Journal 106 (June 1987): 121–42. http://dx.doi.org/10.1017/s0027763000000921.

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Let E/F be an unramified cyclic extension of local non-archimedean fields, G a connected reductive group over F, K(F) (resp. K(E)) a hyper-special maximal compact subgroup of G(F) (resp. G(E)), and H(F) (resp. H(E)) the Hecke convolution algebra of compactly-supported complex-valued K(F) (resp. G(E))-biinvariant functions on G(F) (resp. G(E)). Then the theory of the Satake transform defines (see § 2) a natural homomorphism H(E) → H(F), θ→f. There is a norm map N from the set of stable twisted conjugacy classes in G(E) to the set of stable conjugacy classes in G(F); it is an injection (see [Ko]). Let Ω‱(x, f) denote the stable orbital integral of f in H(F) at the class x, and Ω‱(y, θ) the stable twisted orbital integral of θ in H(E) at the class y.

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Ciaurri, Óscar, Adam Nowak, and Luz Roncal. "Maximal estimates for a generalized spherical mean Radon transform acting on radial functions." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 4 (November 26, 2019): 1597–619. http://dx.doi.org/10.1007/s10231-019-00933-x.

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Romera, Elena, and Fernando Soria. "Endpoint estimates for the maximal operator associated to spherical partial sums on radial functions." Proceedings of the American Mathematical Society 111, no. 4 (April 1, 1991): 1015. http://dx.doi.org/10.1090/s0002-9939-1991-1068130-6.

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LARSEN, NADIA S., and RUI PALMA. "Positive definite *-spherical functions, property (T) and C*-completions of Gelfand pairs." Mathematical Proceedings of the Cambridge Philosophical Society 160, no. 1 (October 26, 2015): 77–93. http://dx.doi.org/10.1017/s0305004115000559.

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AbstractThe study of existence of a universal C*-completion of the *-algebra canonically associated to a Hecke pair was initiated by Hall, who proved that the Hecke algebra associated to (SL2($\mathbb{Q}$p), SL2($\mathbb{Z}$p)) does not admit a universal C*-completion. Kaliszewski, Landstad and Quigg studied the problem by placing it in the framework of Fell–Rieffel equivalence, and highlighted the role of other C*-completions. In the case of the pair (SLn($\mathbb{Q}$p), SLn($\mathbb{Z}$p)) for n ⩾ 3 we show, invoking property (T) of SLn($\mathbb{Q}$p), that the C*-completion of the L1-Banach algebra and the corner of C*(SLn($\mathbb{Q}$p)) determined by the subgroup are distinct. In fact, we prove a more general result valid for a simple algebraic group of rank at least 2 over a $\mathfrak{p}$-adic field with a good choice of a maximal compact open subgroup.

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Andersen, Kenneth F. "Weighted inequalities for the Stieltjes transform and the maximal spherical partial sum operator on radial functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 1 (1995): 195–204. http://dx.doi.org/10.1017/s0308210500030833.

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If TRf(x) is the spherical partial sum of the Fourier transform of f and T*f(x) = SUPR > 0 | TRf(x)|, sufficient conditions are given on the non-negative weight function ω(x) which ensure that T* restricted to radial functionsis bounded on the Lorentz space Lp,s(Rn,ω) into Lp,q(Rn, ω) For power weights, these conditions are also necessary. The weight pairs (u,v) for which the generalised Stieltjes transform Sλ is bounded from LP,S(R+, v)into Lp,q(R+, u)are also characterised. These are an essential ingredient for the study of T*.

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20

Cartwright, Donald I., and Wojciech MŁotkowski. "Harmonic analysis for groups acting on triangle buildings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 56, no. 3 (June 1994): 345–83. http://dx.doi.org/10.1017/s1446788700035540.

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AbstractLet Δ be a thick building of type Ã2, and let be its set of vertices. We study a commutative algebra of ‘averaging’ operators acting on the space of complex valued functions on . This algebra may be identified with a space of ‘biradial functions’ on , or with a convolution algebra of bi-K-invariant functions on G, if G is a sufficiently large group of ‘type-rotating’ automorphisms of Δ, and K is the subgroup of G fixing a given vertex. We describe the multiplicative functionals on and the corresponding spherical functions. We consider the C*-algebra induced by on l2, find its spectrum Σ, prove positive definiteness of a kernel kz for each z ∈ Σ, find explicity the spherical Plancherel formula for any group G of type rotating automorphisms, and discuss the irreducibility of the unitary representations appearing therein. For the class of buildings ΔJ arising from the groups ΓJ introduced in [2], this involves proving that the weak closure of is maximal abelian in the von Neumann algebra generated by the left regular representation of ΓJ.

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Garrigós, Gustavo, and Andreas Seeger. "On plate decompositions of cone multipliers." Proceedings of the Edinburgh Mathematical Society 52, no. 3 (September 23, 2009): 631–51. http://dx.doi.org/10.1017/s001309150700048x.

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AbstractAn important inequality due to Wolff on plate decompositions of cone multipliers is known to have consequences for sharp Lp results on cone multipliers, local smoothing for the wave equation, convolutions with radial kernels, Bergman projections in tubes over cones, averages over finite-type curves in ℝ3 and associated maximal functions. We observe that the range of p in Wolff's inequality, for the conic and the spherical versions, can be improved by using bilinear restriction results. We also use this inequality to give some improved estimates on square functions associated to decompositions of cone multipliers in low dimensions. This gives a new L4 bound for the cone multiplier operator in ℝ3.

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Benavides-Bravo, Francisco Gerardo, Roberto Soto-Villalobos, José Roberto Cantú-González, Mario A. Aguirre-López, and Ángela Gabriela Benavides-Ríos. "A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series." Mathematics 9, no. 19 (October 3, 2021): 2466. http://dx.doi.org/10.3390/math9192466.

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Variogram models are a valuable tool used to analyze the variability of a time series; such variability usually entails a spherical or exponential behavior, and so, models based on such functions are commonly used to fit and explain a time series. Variograms have a quasi-periodic structure for rainfall cases, and some extra steps are required to analyze their entire behavior. In this work, we detailed a procedure for a complete analysis of rainfall time series, from the construction of the experimental variogram to curve fitting with well-known spherical and exponential models, and finally proposed a novel model: quadratic–exponential. Our model was developed based on the analysis of 6 out of 30 rainfall stations from our case study: the Río Bravo–San Juan basin, and was constructed from the exponential model while introducing a quadratic behavior near to the origin and taking into account the fact that the maximal variability of the process is known. Considering a sample with diverse Hurst exponents, the stations were selected. The results obtained show robustness in our proposed model, reaching a good fit with and without the nugget effect for different Hurst exponents. This contrasts to previous models, which show good outcomes only without the nugget effect.

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Mason-Brown, Lucas. "Regular Functions on the 𝐾-nilpotent cone." Representation Theory of the American Mathematical Society 26, no. 33 (October 5, 2022): 1047–62. http://dx.doi.org/10.1090/ert/629.

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Let G G be a complex reductive algebraic group with Lie algebra g \mathfrak {g} and let G R G_{\mathbb {R}} be a real form of G G with maximal compact subgroup K R K_{\mathbb {R}} . Associated to G R G_{\mathbb {R}} is a K × C × K \times \mathbb {C}^{\times } -invariant subvariety N θ \mathcal {N}_{\theta } of the (usual) nilpotent cone N ⊂ g ∗ \mathcal {N} \subset \mathfrak {g}^* . In this article, we will derive a formula for the ring of regular functions C [ N θ ] \mathbb {C}[\mathcal {N}_{\theta }] as a representation of K × C × K \times \mathbb {C}^{\times } . Some motivation comes from Hodge theory. In [Hodge theory and unitary representations of reductive Lie groups, Frontiers of Mathematical Sciences, Int. Press, Somerville, MA, 2011, pp. 397–420], Schmid and Vilonen use ideas from Saito’s theory of mixed Hodge modules to define canonical good filtrations on many Harish-Chandra modules (including all standard and irreducible Harish-Chandra modules). Using these filtrations, they formulate a conjectural description of the unitary dual. If G R G_{\mathbb {R}} is split, and X X is the spherical principal series representation of infinitesimal character 0 0 , then conjecturally g r ( X ) ≃ C [ N θ ] gr(X) \simeq \mathbb {C}[\mathcal {N}_{\theta }] as representations of K × C × K \times \mathbb {C}^{\times } . So a formula for C [ N θ ] \mathbb {C}[\mathcal {N}_{\theta }] is an essential ingredient for computing Hodge filtrations.

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Lakzian, Sajjad, and Michael Munn. "On Weak Super Ricci Flow through Neckpinch." Analysis and Geometry in Metric Spaces 9, no. 1 (January 1, 2021): 120–59. http://dx.doi.org/10.1515/agms-2020-0123.

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Abstract In this article, we study the Ricci flow neckpinch in the context of metric measure spaces. We introduce the notion of a Ricci flow metric measure spacetime and of a weak (refined) super Ricci flow associated to convex cost functions (cost functions which are increasing convex functions of the distance function). Our definition of a weak super Ricci flow is based on the coupled contraction property for suitably defined diffusions on maximal diffusion subspaces. In our main theorem, we show that if a non-degenerate spherical neckpinch can be continued beyond the singular time by a smooth forward evolution then the corresponding Ricci flow metric measure spacetime through the singularity is a weak super Ricci flow for a (and therefore for all) convex cost functions if and only if the single point pinching phenomenon holds at singular times; i.e., if singularities form on a finite number of totally geodesic hypersurfaces of the form {x} × 𝕊 n . We also show the spacetime is a refined weak super Ricci flow if and only if the flow is a smooth Ricci flow with possibly singular final time.

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Ahrens, Cory, and Gregory Beylkin. "Rotationally invariant quadratures for the sphere." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2110 (July 29, 2009): 3103–25. http://dx.doi.org/10.1098/rspa.2009.0104.

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We construct near-optimal quadratures for the sphere that are invariant under the icosahedral rotation group. These quadratures integrate all ( N +1) 2 linearly independent functions in a rotationally invariant subspace of maximal order and degree N . The nodes of these quadratures are nearly uniformly distributed, and the number of nodes is only marginally more than the optimal ( N +1) 2 /3 nodes. Using these quadratures, we discretize the reproducing kernel on a rotationally invariant subspace to construct an analogue of Lagrange interpolation on the sphere. This representation uses function values at the quadrature nodes. In addition, the representation yields an expansion that uses a single function centred and mostly concentrated at nodes of the quadrature, thus providing a much better localization than spherical harmonic expansions. We show that this representation may be localized even further. We also describe two algorithms of complexity for using these grids and representations. Finally, we note that our approach is also applicable to other discrete rotation groups.

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Lemaire, Bertrand, and Manish Mishra. "Matching of orbital integrals (transfer) and Roche Hecke algebra isomorphisms." Compositio Mathematica 156, no. 3 (January 21, 2020): 533–603. http://dx.doi.org/10.1112/s0010437x19007838.

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Let $F$ be a non-Archimedean local field, $G$ a connected reductive group defined and split over $F$, and $T$ a maximal $F$-split torus in $G$. Let $\unicode[STIX]{x1D712}_{0}$ be a depth-zero character of the maximal compact subgroup $T$ of $T(F)$. This gives by inflation a character $\unicode[STIX]{x1D70C}$ of an Iwahori subgroup $\unicode[STIX]{x2110}\subset T$ of $G(F)$. From Roche [Types and Hecke algebras for principal series representations of split reductive$p$-adic groups, Ann. Sci. Éc. Norm. Supér. (4) 31 (1998), 361–413], $\unicode[STIX]{x1D712}_{0}$ defines a reductive $F$-split group $\widetilde{G}^{\prime }$ whose connected component $G^{\prime }$ is an endoscopic group of $G$, and there is an isomorphism of $\mathbb{C}$-algebras $\unicode[STIX]{x210B}(G(F),\unicode[STIX]{x1D70C})\rightarrow \unicode[STIX]{x210B}(\widetilde{G}^{\prime }(F),1_{\unicode[STIX]{x2110}^{\prime }})$ where $\unicode[STIX]{x210B}(G(F),\unicode[STIX]{x1D70C})$ is the Hecke algebra of compactly supported $\unicode[STIX]{x1D70C}^{-1}$-spherical functions on $G(F)$ and $\unicode[STIX]{x2110}^{\prime }$ is an Iwahori subgroup of $G^{\prime }(F)$. This isomorphism gives by restriction an injective morphism $\unicode[STIX]{x1D701}:Z(G(F),\unicode[STIX]{x1D70C})\rightarrow Z(G^{\prime }(F),1_{\unicode[STIX]{x2110}^{\prime }})$ between the centers of the Hecke algebras. We prove here that a certain linear combination of morphisms analogous to $\unicode[STIX]{x1D701}$ realizes the transfer (matching of strongly $G$-regular semi-simple orbital integrals). If $\operatorname{char}(F)=p>0$, our result is unconditional only if $p$ is large enough.

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Kulikov, A. N., E. V. Kudryashova, P. P. Mikhailov, and A. R. Suleimanova. "Intrastromal keratoplasty with intracorneal ring segments implantation as an independent method of visual rehabilitation in patients with keratoconus." Modern technologies in ophtalmology, no. 5 (October 20, 2021): 137–42. http://dx.doi.org/10.25276/2312-4911-2021-5-137-142.

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Purpose. To assess the possibility of using intrastromal keratoplasty with intracorneal ring segments implantation as an independent technique to achieve visual rehabilitation in patients with keratoconus of the stages I and II. Material and methods. There were examined and operated 14 eyes (10 patients) with keratoconus of the stages I and II (classification by Izmailova SB, 2014). Patients were divided into two groups depending on the keratoconus stage. All patients underwent intrastromal keratoplasty with intracorneal ring segments implantation using the femtosecond technology. The on average follow-up was 5.7 months. Results. In the first group: the average UCVA value increased with from 0.31±0.21 to 0.81±0.31 (p<0.05); the BCVA increased from 0.89±0.08 to 0.94±0.10 (p>0.05); the spherical component of refraction decreased from 0.96±1.25 to 0.08±0.20 (p<0.05); the cylindrical component of refraction decreased from 4.25±1.73 to 0.50±1.22 (p<0.05). In the second group: UCVA increased from 0.51±0.40 to 0.61±0.28 (p<0.05); the BCVA increased from 0.70±0.17 to 0.81±0.26 (p>0.05); the spherical component of refraction decreased from 4.88±2,61±0.53±0.63 (p<0.05); the cylindrical component of refraction decreased from 2.69±1.65 to 1.41±1.02 (p<0.05). Conclusion. 1. After implantation of intracorneal ring segments, both in patients with I and in patients with the II stage of keratoconus, there was an increase in the UCVA and BCVA, as well as a significant reduction in maximal keratometry and coma, which provides the improving of the quality of vision. 2. In all cases the UCVA and BCVA that were obtained after the treatment reached a sufficiently high level to ensure the possibility of performing their professional functions, without resorting to additional surgical treatment techniques. That characterizes this method as an independent and sufficient to achieve high visual acuity in patients with I and II stages of keratoconus. Key words: keratoconus, corneal intrastromal segments, femtosecond laser, visual rehabilitation.

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Goldshtein, A., M. SHAPIRO, and C. Gutfinger. "Mechanics of collisional motion of granular materials. Part 3. Self-similar shock wave propagation." Journal of Fluid Mechanics 316 (June 10, 1996): 29–51. http://dx.doi.org/10.1017/s0022112096000432.

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Shock wave propagation arising from steady one-dimensional motion of a piston in a granular gas composed of inelastically colliding particles is treated theoretically. A self-similar long-time solution is obtained in the strong shock wave approximation for all values of the upstream gas volumetric concentration v0. Closed form expressions for the long-time shock wave speed and the granular pressure on the piston are obtained. These quantities are shown to be independent of the particle collisional properties, provided their impacts are accompanied by kinetic energy losses. The shock wave speed of such non-conservative gases is shown to be less than that for molecular gases by a factor of about 2.The effect of particle kinetic energy dissipation is to form a stagnant layer (solid block), on the surface of the moving piston, with density equal to the maximal packing density, vM. The thickness of this densely packed layer increases indefinitely with time. The layer is separated from the shock front by a fluidized region of agitated (chaotically moving) particles. The (long-time, constant) thickness of this layer, as well as the kinetic energy (granular temperature) distribution within it are calculated for various values of particle restitution and surface roughness coefficients. The asymptotic cases of dilute (v0 [Lt ] 1) and dense (v0 ∼ vM) granular gases are treated analytically, using the corresponding expressions for the equilibrium radial distribution functions and the pertinent equations of state. The thickness of the fluidized region is shown to be independent of the piston velocity.The calculated results are discussed in relation to the problem of vibrofluidized granular layers, wherein shock and expansion waves were registered. The average granular kinetic energy in the fluidized region behind the shock front calculated here compared favourably with that measured and calculated (Goldshtein et al. 1995) for vibrofluidized layers of spherical granules.

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Bain, Gregory, Tom McNaughton, Ruth Williams, and Simon MacLean. "Microstructure of the Distal Radius and Its Relevance to Distal Radius Fractures." Journal of Wrist Surgery 06, no. 04 (May 10, 2017): 307–15. http://dx.doi.org/10.1055/s-0037-1602849.

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Background There is a paucity of information on the microstructure of the distal radius, and how this relates to its morphology and function. Purpose This study aims to assess the microanatomical structure of the distal radius, and relate this to its morphology, function, and modes of failure. Methods Six dry adult skeletal distal radii were examined with microcomputed tomography scan and analyzed with specialist computer software. From 3D and 2D images, the subchondral, cortical, and medullary trabecular were assessed and interpreted based on the overall morphology of the radius. Results The expanded distal radial metaphysis provides a wide articular surface for distributing the articular load. The extrinsic wrist ligaments are positioned around the articular perimeter, except on the dorsal radial corner. The subchondral bone plate is a 2 mm multilaminar lattice structure, which is thicker below the areas of the maximal articular load. There are spherical voids distally, which become ovoid proximally, which assist in absorbing articular impact. It does not have Haversian canals. From the volar aspect of the lunate facet, there are thick trabecular columns that insert into the volar cortex of the radius at the metaphyseal–diaphyseal junction. For the remainder of the subchondral bone plate, there is an intermediate trabecular network, which transmits the load to the intermediate trabeculae and then to the trabecular arches. The arches pass proximally and coalesce with the ridges of the diaphyseal cortex. Conclusion The distal radius morphology is similar to an arch bridge. The subchondral bone plate resembles the smooth deck of the bridge that interacts with the mobile load. The load is transmitted to the rim, intermediate struts, and arches. The metaphyseal arches allow the joint loading forces to be transmitted proximally and laterally, providing compression at all levels and avoiding tension. The arches have a natural ability to absorb the impact which protects the articular surface. The distal radius absorbs and transmits the articular impact to the medullary cortex and intermediate trabeculae. The medullary arches are positioned to transmit the load from the intermediate trabeculae to the diaphysis. Clinical Relevance The microstructure of the distal radius is likely to be important for physiological loading of the radius. The subchondral bone plate is a unique structure that is different to the cancellous and cortical bone. All three bone types have different functions. The unique morphology and microstructure of the distal radius allow it to transmit load and protect the articular cartilage.

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Escassut, Alain. "The Ultrametric Corona Problem and spherically complete fields." Proceedings of the Edinburgh Mathematical Society 53, no. 2 (April 30, 2010): 353–71. http://dx.doi.org/10.1017/s0013091508000837.

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AbstractLet K be a complete ultrametric algebraically closed field and let A be the Banach K-algebra of bounded analytic functions in the ‘open’ unit disc D of K provided with the Gauss norm. Let Mult(A,‖ · ‖) be the set of continuous multiplicative semi-norms of A provided with the topology of simple convergence, let Multm(A, ‖ · ‖) be the subset of the φ ∈ Mult(A, ‖ · ‖) whose kernel is a maximal ideal and let Multa(A, ‖ · ‖) be the subset of the φ ∈ Mult(A, ‖ · ‖) whose kernel is a maximal ideal of the form (x − a)A with a ∈ D. We complete the characterization of continuous multiplicative norms of A by proving that the Gauss norm defined on polynomials has a unique continuation to A as a norm: the Gauss norm again. But we find prime closed ideals that are neither maximal nor null. The Corona Problem on A lies in two questions: is Multa(A, ‖ · ‖) dense in Multm(A, ‖ · ‖)? Is it dense in Multm(A, ‖ · ‖)? In a previous paper, Mainetti and Escassut showed that if each maximal ideal of A is the kernel of a unique φ ∈ Mult(m(A, ‖ · ‖), then the answer to the first question is affirmative. In particular, the authors showed that when K is strongly valued each maximal ideal of A is the kernel of a unique φ ∈ Mult(m(A, ‖ · ‖). Here we prove that this uniqueness also holds when K is spherically complete, and therefore so does the density of Multa(A, ‖ · ‖) in Multm(A, ‖ · ‖).

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Noda, Yohei, Satoshi Koizumi, Tomomi Masui, Ryo Mashita, Hiroyuki Kishimoto, Daisuke Yamaguchi, Takayuki Kumada, Shin-ichi Takata, Kazuki Ohishi, and Jun-ichi Suzuki. "Contrast variation by dynamic nuclear polarization and time-of-flight small-angle neutron scattering. I. Application to industrial multi-component nanocomposites." Journal of Applied Crystallography 49, no. 6 (November 8, 2016): 2036–45. http://dx.doi.org/10.1107/s1600576716016472.

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Dynamic nuclear polarization (DNP) at low temperature (1.2 K) and high magnetic field (3.3 T) was applied to a contrast variation study in small-angle neutron scattering (SANS) focusing on industrial rubber materials. By varying the scattering contrast by DNP, time-of-flight SANS profiles were obtained at the pulsed neutron source of the Japan Proton Accelerator Research Complex (J-PARC). The concentration of a small organic molecule, (2,2,6,6-tetramethylpiperidine-1-yl)oxy (TEMPO), was carefully controlled by a doping method using vapour sorption into the rubber specimens. With the assistance of microwave irradiation (94 GHz), almost full polarization of the paramagnetic electronic spin of TEMPO was transferred to the spin state of hydrogen (protons) in the rubber materials to obtain a high proton spin polarization (PH). The following samples were prepared: (i) a binary mixture of styrene–butadiene random copolymer (SBR) with silica particles (SBR/SP); and (ii) a ternary mixture of SBR with silica and carbon black particles (SBR/SP/CP). For the binary mixture (SBR/SP), the intensity of SANS significantly increased or decreased while keeping itsqdependence forPH= −35% orPH= 40%, respectively. Theqbehaviour of SANS for the SBR/SP mixture can be reproduced using the form factor of a spherical particle. The intensity at lowq(∼0.01 Å−1) varied as a quadratic function ofPHand indicated a minimum value atPH= 30%, which can be explained by the scattering contrast between SP and SBR. The scattering intensity at highq(∼0.3 Å−1) decreased with increasingPH, which is attributed to the incoherent scattering from hydrogen. For the ternary mixture (SBR/SP/CP), theqbehaviour of SANS was varied by changingPH. AtPH= −35%, the scattering maxima originating from the form factor of SP prevailed, whereas atPH= 29% andPH= 38%, the scattering maxima disappeared. After decomposition of the total SANS according to inverse matrix calculations, the partial scattering functions were obtained. The partial scattering function obtained for SP was well reproduced by a spherical form factor and matched the SANS profile for the SBR/SP mixture. The partial scattering function for CP exhibited surface fractal behaviour according toq−3.6, which is consistent with the results for the SBR/CP mixture.

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Roncal, Luz, Saurabh Shrivastava, and Kalachand Shuin. "Bilinear Spherical Maximal Functions of Product Type." Journal of Fourier Analysis and Applications 27, no. 4 (August 2021). http://dx.doi.org/10.1007/s00041-021-09877-4.

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Anderson, Theresa C., and Eyvindur Ari Palsson. "Bounds for discrete multilinear spherical maximal functions." Collectanea Mathematica, January 3, 2021. http://dx.doi.org/10.1007/s13348-020-00308-z.

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Anderson, Theresa C., Brian Cook, Kevin Hughes, and Angel Kumchev. "Improved ℓp -Boundedness for Integral k -Spherical Maximal Functions." Discrete Analysis, May 29, 2018. http://dx.doi.org/10.19086/da.3675.

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35

Roos, Joris, Andreas Seeger, and Rajula Srivastava. "Lebesgue Space Estimates for Spherical Maximal Functions on Heisenberg Groups." International Mathematics Research Notices, September 11, 2021. http://dx.doi.org/10.1093/imrn/rnab246.

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Abstract We prove $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups; these are sharp up to two endpoints. The results can be applied to improve currently known bounds on sparse domination for global maximal operators. We also consider lacunary variants and extensions to Métivier groups.

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36

Nowak, Adam, Luz Roncal, and Tomasz Z. Szarek. "Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions." Communications on Pure and Applied Analysis, 2023, 0. http://dx.doi.org/10.3934/cpaa.2023065.

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Makinde, Olusola S. "Depth classification based on affine-invariant, weighted and kernel-based spatial depth functions." Kuwait Journal of Science 48, no. 2 (April 5, 2021). http://dx.doi.org/10.48129/kjs.v48i2.8693.

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Several multivariate depth functions have been proposed in the literature, of which some satisfy all the conditions for statistical depth functions while some do not. Spatial depth is known to be invariant to spherical and shift transformations. In this paper, the possibility of using different versions of spatial depth in classification is considered. The covariance-adjusted, weighted, and kernel-based versions of spatial depth functions are presented to classify multivariate outcomes. We extend the maximal depth classification notions for the covariance-adjusted, weighted, and kernel-based spatial depth versions. The classifiers' performance is considered and compared with some existing classification methods using simulated and real datasets.

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Zienkiewicz-Strzałka, Małgorzata, Anna Deryło-Marczewska, and Stanisław Pikus. "The synthesis and nanostructure investigation of noble metal-based nanocomposite materials." Journal of Materials Science, May 6, 2021. http://dx.doi.org/10.1007/s10853-021-06127-2.

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AbstractThe presented work follows the theme of applied chemistry toward nanomaterials and multiphase functional systems of practical importance. Structural studies of nanocomposite materials are important due to the correlation between physicochemical/structural properties and their application potential. In this work, we report the fabrication and structural characterization of nanocomposite materials constituting noble metal (plasmonic) nanoparticles (AgNP and AuNP) dispersed on selected types of nanostructured solid hosts (nonporous silica, microporous activated carbon, chitosan biopolymer, and ordered mesoporous silica). The ability to maintain a dispersed state of colloidal precursors throughout their deposition on solid hosts was assessed. The influence of the carrier role in the formation and stabilization of nanometallic phases was evaluated taking into account the physicochemical and textural properties of the support surfaces. The size and shape of nanoobjects, clustering effects, interfacial properties, and stability of the immobilized nanophase were implemented by analyzing relevant parameters of SAXS analysis. The dimensional characteristic of the scatterers was evaluated by volume-weighted particle size distribution Dv(R). The detailed overall shape and maximal particle dimension were described by the analysis of pair distance distribution functions (PDDFs). The radius of gyration (Rg) from PDDF and Guinier approximation was calculated for illustrating the dimension of scattered heterogeneities in the investigated solids. The asymptotic behavior of a scattering curve and Porod theory were applied for determining the diffusion and quality of the interfacial surfaces. The size and morphology of nanoparticles in colloidal precursor solutions have been defined as spherical and bimodal in size (~ 6 nm and 20 nm). It was observed that the spherical shape and dispersed state of nanoparticles were achieved for all systems after deposition. However, the morphology of their final form was conditioned by the solid matrices. The particle properties from SAXS were correlated with properties determined by TEM and low-temperature nitrogen sorption analysis. Obtained results suggest good compatibility and correctness of SAXS data reading of nanocomposite systems and can be successfully applied for quick, nondestructive, and effective evaluation of structural properties of complex systems. Graphical abstract

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39

Dalal, Kesha, Venkatesh Katari, Sailaja Paruchuri, and Charles Thodeti. "Regulation of endothelial cell mitochondrial phenotype by mechanosensitive ion channel TRPV4." Physiology 38, S1 (May 2023). http://dx.doi.org/10.1152/physiol.2023.38.s1.5732666.

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Transient receptor potential vanilloid type 4 (TRPV4) is a mechanosensor that regulates endothelial cell (EC) proliferation, migration, and angiogenesis. However, the molecular mechanisms by which TRPV4 regulates EC functions are not well understood. In this study, we investigated if TRPV4 regulates EC function via modulation of mitochondria by employing three types of EC expressing different levels of TRPV4, normal (NEC), TRPV4-deficienct (TEC), and TRPV4 knockout (KOEC). First, we confirmed the functional expression of TRPV4 in these EC using qPCR and calcium imaging. Confocal images upon MitoTracker staining revealed spherical and/or round shaped mitochondria with a perinuclear localization in NEC while in TEC and KOEC the mitochondrial network was elongated and rod shaped with a whole cell distribution. Furthermore, Transmission Electron Microscopy confirmed the presence of clear round mitochondria in NEC compared to elongated mitochondria with distinct cristae in TEC and KOEC. These results indicate increased fusion in TRPV4 deficiency or deletion. When cultured on ECM gels of varying stiffness that mimic stiffness of matrix in pathophysiological conditions such as tumor or heart failure (0.2, 8, and 50 kPa), we found increased distribution of mitochondria in EC with increasing stiffness. Moreover, western blot analysis showed increased expression of a fusion/fission protein ratio (Optic Atrophy 1 (OPA1)/mitochondrial fission factor (MFF)), in TEC and KOEC. Further, uncoupling mitochondrial function by mitochondrial stressors (Oligomycin, FCCP, and Rot/AA) significantly increased basal oxygen consumption rate (OCR), maximal OCR, ATP-linked OCR, and spare capacity in TEC and KOEC than NEC. Finally, a small molecule inhibitor of OPA1, MYLS22, attenuated/normalized the mitochondrial energy metabolism to that of NEC but did not affect NEC. These findings suggest that mechanosensitive TRPV4 channels regulate EC mitochondrial morphology and function through increased OPA1. National Institutes of Health (R15CA202847, R01HL119705, and R01HL148585) to CKT This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

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Bruno, Nicholas. "Ideal structure of rings of analytic functions with non-Archimedean metrics." Journal of Algebra and Its Applications, October 14, 2021. http://dx.doi.org/10.1142/s0219498823500111.

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The work of Helmer [Divisibility properties of integral functions, Duke Math. J. 6(2) (1940) 345–356] applied algebraic methods to the field of complex analysis when he proved the ring of entire functions on the complex plane is a Bezout domain (i.e. all finitely generated ideals are principal). This inspired the work of Henriksen [On the ideal structure of the ring of entire functions, Pacific J. Math. 2(2) (1952) 179–184. On the prime ideals of the ring of entire functions, Pacific J. Math. 3(4) (1953) 711–720] who proved a correspondence between the maximal ideals within the ring of entire functions and ultrafilters on sets of zeroes as well as a correspondence between the prime ideals and growth rates on the multiplicities of zeroes. We prove analogous results on rings of analytic functions in the non-Archimedean context: all finitely generated ideals in the ring of analytic functions on an annulus of a characteristic zero non-Archimedean field are two-generated but not guaranteed to be principal. We also prove the maximal and prime ideal structure in the non-Archimedean context is similar to that of the ordinary complex numbers; however, the methodology has to be significantly altered to account for the failure of Weierstrass factorization on balls of finite radius in fields which are not spherically complete, which was proven by Lazard [Les zeros d’une function analytique d’une variable sur un corps value complet, Publ. Math. l’IHES 14(1) (1942) 47–75].

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Brassel, Byron P., Sunil D. Maharaj, and Rituparno Goswami. "Charged radiation collapse in Einstein–Gauss–Bonnet gravity." European Physical Journal C 82, no. 4 (April 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10334-9.

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AbstractWe generalise the continual gravitational collapse of a spherically symmetric radiation shell of matter in five dimensional Einstein–Gauss–Bonnet gravity to include the electromagnetic field. The presence of charge has a significant effect in the collapse dynamics. We note that there exists a maximal charge contribution for which the metric functions in Einstein–Gauss–Bonnet gravity remain real, which is not the case in general relativity. Beyond this maximal charge the spacetime metric is complex. The final fate of collapse for the uncharged matter field, with positive mass, is an extended, weak and initially naked central conical singularity. With the presence of an electromagnetic field, collapse terminates with the emergence of a branch singularity separating the physical spacetime from the complex region. We show that this marked difference in singularity formation is only prevalent in five dimensions. We extend our analysis to higher dimensions and show that for all dimensions $$N\ge 5$$ N ≥ 5 , charged collapse ceases with the above mentioned branch singularity. This is significantly different than the uncharged scenario where a strong curvature singularity forms post collapse for all $$N\ge 6$$ N ≥ 6 and a weak conical singularity forms when $$N=5$$ N = 5 . A comparison with charged radiation collapse in general relativity is also given.

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42

Brassel, Byron P., Sunil D. Maharaj, and Rituparno Goswami. "Charged radiation collapse in Einstein–Gauss–Bonnet gravity." European Physical Journal C 82, no. 4 (April 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10334-9.

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AbstractWe generalise the continual gravitational collapse of a spherically symmetric radiation shell of matter in five dimensional Einstein–Gauss–Bonnet gravity to include the electromagnetic field. The presence of charge has a significant effect in the collapse dynamics. We note that there exists a maximal charge contribution for which the metric functions in Einstein–Gauss–Bonnet gravity remain real, which is not the case in general relativity. Beyond this maximal charge the spacetime metric is complex. The final fate of collapse for the uncharged matter field, with positive mass, is an extended, weak and initially naked central conical singularity. With the presence of an electromagnetic field, collapse terminates with the emergence of a branch singularity separating the physical spacetime from the complex region. We show that this marked difference in singularity formation is only prevalent in five dimensions. We extend our analysis to higher dimensions and show that for all dimensions $$N\ge 5$$ N ≥ 5 , charged collapse ceases with the above mentioned branch singularity. This is significantly different than the uncharged scenario where a strong curvature singularity forms post collapse for all $$N\ge 6$$ N ≥ 6 and a weak conical singularity forms when $$N=5$$ N = 5 . A comparison with charged radiation collapse in general relativity is also given.

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Journal articles on the topic 'Spherical maximal functions'

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