scholarly journals Zeros of combinations of Bessel functions and the mean charge of graphene nanodots

2016 ◽  
Vol 187 (1) ◽  
pp. 497-510 ◽  
Author(s):  
C. G. Beneventano ◽  
I. V. Fialkovsky ◽  
E. M. Santangelo
Keyword(s):  
Bessel Functions ◽  
The Mean ◽  
Mean Charge

scholarly journals Limit theorems for hitting times of 1-dimensional generalized diffusions

1998 ◽  
Vol 152 ◽  
pp. 1-37
Author(s):  
Matsuyo Tomisaki ◽  
Makoto Yamazato
Keyword(s):  
Limit Theorems ◽  
Bessel Functions ◽  
Diffusion Processes ◽  
Hitting Times ◽  
Finite Dimensional ◽  
Independent Increments ◽  
Starting Point ◽  
Self Similar ◽  
The Mean ◽  
The One

Abstract.Limit theorems are obtained for suitably normalized hitting times of single points for 1-dimensional generalized diffusion processes as the hitting points tend to boundaries under an assumption which is slightly stronger than that the existence of limits γ + 1 of the ratio of the mean and the variance of the hitting time. Laplace transforms of limit distributions are modifications of Bessel functions. Results are classified by the one parameter {γ}, each of which is the degree of corresponding Bessel function. In case the limit distribution is degenerate to one point, by changing the normalization, we obtain convergence to the normal distribution. Regarding the starting point as a time parameter, we obtain convergence in finite dimensional distributions to self-similar processes with independent increments under slightly stronger assumption.

Material dependence on the mean charge state of light ions in titanium, zirconium and copper

2019 ◽  
Vol 73 (10) ◽  
Author(s):  
Jennifer Schofield ◽  
Jay A. LaVerne ◽  
Daniel Robertson ◽  
Philippe Collon ◽  
Simon M. Pimblott
Keyword(s):  
Charge State ◽  
Light Ions ◽  
The Mean ◽  
Titanium Zirconium ◽  
Mean Charge

Ion behaviour in plant cell walls. III. Measurement of the mean charge separation distance and the linear charge density parameter in delignified Sphagnum russowii cell walls

1990 ◽  
Vol 68 (4) ◽  
pp. 768-772 ◽  
Author(s):  
Conrad Richter ◽  
Jack Dainty
Keyword(s):  
Cell Wall ◽  
Charge Density ◽  
Charge Separation ◽  
Cell Walls ◽  
Separation Distance ◽  
Cation Binding ◽  
Density Parameter ◽  
Linear Charge Density ◽  
The Mean ◽  
Mean Charge

According to the Manning condensation theory, the structure of cation-binding uronates in the cell wall can influence ionic behaviour. Assuming the theory is valid, we measured, in cation-binding experiments, the dimensionless linear charge density parameter and the mean charge separation distance in the fully ionized delignified Sphagnum russowii cell wall. Our charge separation estimate, 1.00 ± 0.02 nm, indicates that approximately 1.3 neutral sugars are interpolated between the uronic acids in the polyuronate chains of the cation exchanger. This compares well with chemical data of isolated wall fractions from another Sphagnum species reported by other workers. The charge density parameter estimate, 0.71 ± 0.02, implies that univalent cations never condense, whereas cations with two or more positive charges condense when the degree of ionization of the fixed (wall) charges is high enough. Key words: ion exchange, cell wall, charge density.

scholarly journals Measurement of stopping power of 240 MeV argon ions in partially ionized helium discharge plasma

2000 ◽  
Vol 18 (4) ◽  
pp. 647-653 ◽  
Author(s):  
M. OGAWA ◽  
U. NEUNER ◽  
H. KOBAYASHI ◽  
Y. NAKAJIMA ◽  
K. NISHIGORI ◽  
...  
Keyword(s):  
Energy Loss ◽  
Electron Density ◽  
Target Thickness ◽  
Stopping Power ◽  
Helium Plasma ◽  
Discharge Ignition ◽  
The Mean ◽  
Argon Ions ◽  
Partially Ionized ◽  
Mean Charge

An energy loss of 240 MeV argon ions in a Z-pinch helium plasma has been for the first time observed throughout the entire pinching process. Standard Stark broadening analysis gives an electron density ranging from 4 to 6 × 1017 cm−3 during the pinch. To deduce stopping power from the energy loss, the target thickness of the helium plasma has been evaluated assuming the mean charge of helium based on thermal equilibrium. The observed electron density and the mean charge of helium give a target thickness of 30 ± 3 μg cm−2 from 1 μs to 1.8 μs after the discharge ignition. The measured stopping power exceeds a tabulated value for cold helium gas by a factor of 2 to 3 around the time of the first pinch. The experimental stopping power is compared with theoretical values calculated using an equation of stopping power for a partially ionized plasma.

The mean charge multiplicity for pp and $$p\bar p$$ collisionscollisions

1983 ◽  
Vol 38 (6) ◽  
pp. 189-200
Author(s):  
Chien-er Lee ◽  
Yeou Wei Yang ◽  
Lai Kin Hung
Keyword(s):  
The Mean ◽  
Charge Multiplicity ◽  
Mean Charge

Under non-denaturing solvent conditions, the mean charge state of a multiply charged protein ion formed by electrospray is linearly correlated with the macromolecular surface

2004 ◽  
Vol 231 (2-3) ◽  
pp. 131-137 ◽  
Author(s):  
Mélanie Hautreux ◽  
Nathalie Hue ◽  
Alexis Du Fou de Kerdaniel ◽  
Abdelattif Zahir ◽  
Valérie Malec ◽  
...  
Keyword(s):  
Charge State ◽  
Multiply Charged ◽  
The Mean ◽  
Mean Charge

QUASI-NONUNIQUENESS IN THE SCATTERED FIELD OF A DIELECTRIC CIRCULAR CYLINDER

2010 ◽  
Vol 08 (01) ◽  
pp. 63-83 ◽  
Author(s):  
T. M. DUNSTER
Keyword(s):  
Dielectric Constant ◽  
Circular Cylinder ◽  
Scattered Field ◽  
Bessel Functions ◽  
Hankel Functions ◽  
Plane Wave Incident ◽  
The Mean ◽  
The Difference ◽  
Scattered Fields ◽  
Uniform Asymptotic Expansions

It is well known that the scattered field of a z polarized plane wave incident on a dielectric circular cylinder can be expanded as an infinite series involving Hankel functions. From numerical calculations of this expansion, Lam and Yedlin [5] observed that the mean square measure, over all space, of the difference of the scattered fields from two or more distinct values of the dielectric constant of the cylinder can take very small values, thereby almost contradicting the uniqueness property. We investigate this phenomenon rigorously using uniform asymptotic expansions of Bessel functions, and from our analysis we determine the spurious values of the dielectric constant which lead to this quasi-nonuniqueness.

Particle-size distribution, cation exchange capacity and charge density of deferrated montmorillonites

Clay Minerals ◽  
1982 ◽  
Vol 17 (2) ◽  
pp. 209-216 ◽  
Author(s):  
M. S. Stul ◽  
L. Van Leemput
Keyword(s):  
Charge Density ◽  
Cation Exchange Capacity ◽  
Exchange Capacity ◽  
Particle Sizes ◽  
Citrate Solution ◽  
Interlayer Cation ◽  
The Mean ◽  
Mean Charge ◽  
Wyoming Bentonite ◽  
By Products

AbstractDifferent montmorillonites (Otay, Chambers, Marnia, Camp Berteau, Moosburg, Greek White, Wyoming bentonite were deferrated with a dithionite/citrate solution; iron sulphide by-products were eliminated with an HCl washing and citrates with an H2O2 oxidation. The smaller CEC after deferration could not be assigned to either (i) the occurrence of a positive correlation between CEC and particle sizes smaller than 0.2 µm or (ii) to the mean charge density of these sub-fractions. All sub-fractions had a heterogeneous interlayer cation density distribution.

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