On the Best Constant Problem for a Class of Mixed-Norm Hardy Inequalities

AbstractIn this paper, we obtain the best constant and the equality condition for a class of mixed-norm Hardy inequalities when the weight is a power function. By building and solving the corresponding Euler equation, we look for the best constant and the optimal function. One of the main ingredients is to introduce two key auxiliary functions so that the corresponding equalities are derived.

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Mixed Norm Type Hardy Inequalities

Canadian Mathematical Bulletin ◽

10.4153/cmb-2011-022-0 ◽

2011 ◽

Vol 54 (4) ◽

pp. 630-644 ◽

Cited By ~ 4

Author(s):

Alberto Fiorenza ◽

Babita Gupta ◽

Pankaj Jain

Keyword(s):

Integral Operators ◽

Mixed Norm ◽

Hardy Inequalities ◽

Higher Dimensional ◽

Lower Dimensional

AbstractHigher dimensional mixed norm type inequalities involving certain integral operators are characterized in terms of the corresponding lower dimensional inequalities.

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REFINED GEOMETRIC Lp HARDY INEQUALITIES

Communications in Contemporary Mathematics ◽

10.1142/s0219199703001166 ◽

2003 ◽

Vol 05 (06) ◽

pp. 869-881 ◽

Cited By ~ 6

Author(s):

G. BARBATIS ◽

S. FILIPPAS ◽

A. TERTIKAS

Keyword(s):

Finite Number ◽

Convex Domain ◽

Hardy Potential ◽

Hardy Inequalities ◽

Best Constant ◽

Bounded Convex Domain ◽

Logarithmic Corrections ◽

Bounded Convex ◽

Distance To The Boundary

For a bounded convex domain Ω in RN we prove refined Hardy inequalities that involve the Hardy potential corresponding to the distance to the boundary of Ω, the volume of Ω, as well as a finite number of sharp logarithmic corrections. We also discuss the best constant of these inequalities.

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XRF and PIXE Analysis of light and Dark Adapted Ocular Tissue

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100053619 ◽

1982 ◽

Vol 40 ◽

pp. 190-191

Author(s):

B. J. Panessa ◽

H. W. Kraner ◽

J. B. Warren ◽

K. W. Jones

Keyword(s):

Trace Metals ◽

Pigment Epithelium ◽

Nerve Impulse ◽

Light Response ◽

Ocular Tissue ◽

Emission Spectrometry ◽

Retinol Dehydrogenase ◽

Pixe Analysis ◽

X Ray ◽

Optimal Function

During photoexcitation the retina requires specific electrolytes and trace metals for optimal function (Na, Mg, Cl, K, Ca, S, P, Cu and Zn). According to Hagins (1981), photoexcitation and generation of a nerve impulse involves the movement of Ca from the rhodopsin-ladened membranes of the rod outer segment (ROS) to the plasmalemma, which in turn decreases the in-flow of Na into the photoreceptor, resulting in hyperpolarization. In toad isolated retinas, the presence of Ba has been found to increase the amplitude and prolong the delay of the light response (Brown and Flaming, 1978). Trace metals such as Cu, Zn and Se are essential for the activity of the metalloenzymes of the retina and retina pigment epithelium (RPE) (i.e. carbonic anhydrase, retinol dehydrogenase, tyrosinase, glutathione peroxidase, superoxide dismutase...). Therefore the content and fluctuations of these elements in the retina and choroid are of fundamental importance for the maintenance of vision. This paper presents elemental data from light and dark adapted frog ocular tissues examined by electron beam induced x-ray microanalysis, x-ray fluorescence spectrometry (XRF) and proton induced x-ray emission spectrometry (PIXE).

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Tables for the Power Function of Roy's Two Sided Test for Testing Hypothesis Σ = I in the Bivariate Case

Communications in Statistics - Simulation and Computation ◽

10.1080/03610917308548253 ◽

1973 ◽

Vol 1 (3) ◽

pp. 271-280

Author(s):

F. J. Schuurmann ◽

V. B. Waikar

Keyword(s):

Power Function ◽

Testing Hypothesis ◽

Bivariate Case

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Shift in Stimulus Range and the Exponent of the Power Function for Loudness

PsycEXTRA Dataset ◽

10.1037/e576282009-001 ◽

1987 ◽

Author(s):

Richard Ahlstrom ◽

John C. Baird

Keyword(s):

Power Function ◽

Stimulus Range

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Pediatric Replantation after Traumatic Amputation at the Distal Forearm: Rehabilitation Protocol and Outcomes

Journal of Hand and Microsurgery ◽

10.1055/s-0040-1703096 ◽

2020 ◽

Author(s):

Nicholas C. Oleck ◽

Radhika Malhotra ◽

Haripriya S. Ayyala ◽

Ramazi O. Datiashvili

Keyword(s):

Operating Room ◽

Multidisciplinary Team ◽

Distal Forearm ◽

Left Forearm ◽

Traumatic Amputation ◽

Postoperative Rehabilitation ◽

Rehabilitation Protocol ◽

Microsurgical Technique ◽

Optimal Function ◽

And Function

AbstractMajor limb replantation is a formidable task, especially in the pediatric setting. While meticulous microsurgical technique is required in the operating room, the authors aim to highlight the importance of postoperative rehabilitation therapy for optimal function. We highlight the case of a 12-year-old boy who suffered complete traumatic amputation through the distal left forearm. The limb was successfully replanted with successful restoration of sensation and function with the aid of intensive postoperative occupational therapy. A multidisciplinary team is of paramount importance to maximize function of a replanted upper extremity.

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