scholarly journals Smooth and Rough Positive Currents

2018 ◽  
Vol 68 (7) ◽  
pp. 2981-2999
Author(s):  
Simion Filip ◽  
Valentino Tosatti
Keyword(s):  
Positive Currents

scholarly journals Relative non-pluripolar product of currents

2021 ◽  
Author(s):  
Duc-Viet Vu
Keyword(s):  
Kähler Manifold ◽  
Monotonicity Property ◽  
Necessary Condition ◽  
Positive Current ◽  
Lelong Numbers ◽  
Kahler Manifold ◽  
Closed Positive Current ◽  
Positive Currents ◽  
Compact Kähler Manifold

AbstractLet X be a compact Kähler manifold. Let $$T_1, \ldots , T_m$$ T 1 , … , T m be closed positive currents of bi-degree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the non-pluripolar product relative to T of $$T_1, \ldots , T_m$$ T 1 , … , T m . We recover the well-known non-pluripolar product of $$T_1, \ldots , T_m$$ T 1 , … , T m when T is the current of integration along X. Our main results are a monotonicity property of relative non-pluripolar products, a necessary condition for currents to be of relative full mass intersection in terms of Lelong numbers, and the convexity of weighted classes of currents of relative full mass intersection. The former two results are new even when T is the current of integration along X.

scholarly journals Polynomial hulls and positive currents

2003 ◽  
Vol 12 (3) ◽  
pp. 317-334 ◽  
Author(s):  
Tien-Cuong Dinh ◽  
Mark G. Lawrence
Keyword(s):  
Positive Currents ◽  
Polynomial Hulls

scholarly journals Dimension of ergodic measures and currents on

2019 ◽  
Vol 40 (8) ◽  
pp. 2131-2155
Author(s):  
CHRISTOPHE DUPONT ◽  
AXEL ROGUE
Keyword(s):  
Upper Bound ◽  
Equilibrium Measure ◽  
Pointwise Dimension ◽  
Ergodic Measures ◽  
Positive Currents ◽  
Green Current

Let $f$ be a holomorphic endomorphism of $\mathbb{P}^{2}$ of degree $d\geq 2$. We estimate the local directional dimensions of closed positive currents $S$ with respect to ergodic dilating measures $\unicode[STIX]{x1D708}$. We infer several applications. The first one is an upper bound for the lower pointwise dimension of the equilibrium measure, towards a Binder–DeMarco’s formula for this dimension. The second one shows that every current $S$ containing a measure of entropy $h_{\unicode[STIX]{x1D708}}>\log d$ has a directional dimension ${>}2$, which answers a question of de Thélin–Vigny in a directional way. The last one estimates the dimensions of the Green current of Dujardin’s semi-extremal endomorphisms.

Electrical Stimulation of the Ear: Clinical Applications

1983 ◽  
Vol 92 (6) ◽  
pp. 621-622 ◽  
Author(s):  
M. Portmann ◽  
J.-M. Aran ◽  
M. Nègrevergne ◽  
Y. Cazals
Keyword(s):  
Electrical Stimulation ◽  
Round Window ◽  
Clinical Applications ◽  
Positive Currents ◽  
Stimulation Of

Electrical stimulation of the ear in humans was performed with an extracochlear electrode on the round window. With positive currents, suppression of tinnitus could be induced. With negative currents, auditory sensations were evoked. Since electrical stimulation with DC currents may be hazardous in the long term, it cannot yet be proposed for the suppression of tinnitus. However, electrically evoked hearing sensations with AC currents seem to be of definite interest for some totally deaf patients.

scholarly journals Regional distribution of the Na+ and K+currents around the crystalline lens of rabbit

2002 ◽  
Vol 282 (2) ◽  
pp. C252-C262 ◽  
Author(s):  
Oscar A. Candia ◽  
Aldo C. Zamudio
Keyword(s):  
Polar Region ◽  
Regional Distribution ◽  
Crystalline Lens ◽  
Theoretical Models ◽  
Vibrating Probe ◽  
Positive Currents ◽  
Posterior Direction ◽  
Net Flows ◽  
Lens Surface ◽  
K Currents

Early studies described asymmetrical electrical properties across the ocular lens in the anterior-to-posterior direction. More recent results obtained with a vibrating probe indicated that currents around the lens surface are not uniform by showing an outwardly directed K+ efflux at the lens equator and Na+ influx at the poles. The latter studies have been used to support theoretical models for fluid recirculation within the avascular lens. However, the existence of a nonuniform current distribution in the lens epithelium from the anterior pole to the equator has never been confirmed. The present work developed a modified short-circuiting technique to examine the net flows of Na+ and K+ across arbitrarily defined lens surface regions. Results indicate that passive inflows of Na+ occur at both the anterior polar region and posterior lens surface, consistent with suggestions derived from the vibrating probe data, whereas K+ efflux plus the Na+-K+ pump-generated current comprise the currents at the equatorial surface and an area anterior to it. Furthermore, Na+-K+ pump activity was absent at the posterior surface and its polar region in all lenses examined, as well as from the anterior polar region in most lenses. The latter unexpected observation suggests that the monolayered epithelium, which is confined to the anterior surface of the lens, does not express an active Na+-K+ pump at its anterior-most aspect. Nevertheless, this report represents the first independent confirmation that positive currents leave the lens around the equator and reenter across the polar and posterior surfaces.

Ionization in flames: current-voltage relationships for the flame ionization detector

1971 ◽  
Vol 321 (1546) ◽  
pp. 361-380 ◽  
Keyword(s):  
Applied Voltage ◽  
Cylindrical Symmetry ◽  
Flame Ionization Detector ◽  
Nitrogen Diffusion ◽  
Ionization Detector ◽  
Basic Form ◽  
Flame Ionization ◽  
Current Voltage ◽  
Positive Currents ◽  
Oxygen Flame

An analysis is made of the ionization current drawn from a flame ionization detector having cylindrical symmetry. An idealized representation of the flame is used which enables a relation to be defined between the applied voltage and the current drawn from the flame, and the expression contains factors dependent on geometry and concentration. Results of experiments confirm the basic form of this expression for both positive and negative currents drawn from a premixed hydrogen + nitrogen + oxygen flame. The expression also holds for positive currents drawn from the hydrogen + nitrogen diffusion flame, but cannot yet satisfactorily account for negative currents at high rates of flow of hydrogen.

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