In this paper we study a class of nonlinear integro-differential equations which correspond to a fractional-order time derivative and interpolate nonlinear heat and wave equations. For this purpose we first establish ...
In this paper we study a class of nonlinear integro-differential equations which correspond to a fractional-order time derivative and interpolate nonlinear heat and wave equations. For this purpose we first establish some space-time estimates of the linear flow which is produced by Mittag-Leffler's functions based on Mihlin-Hörmander's multiplier estimates and other harmonic analysis tools. Using these space-time estimates we prove the well-posedness of a local mild solution of the Cauchy problem for the nonlinear integro-differential equation in C([0, T);Lp(Rn)) or Lq(0, T;Lp(Rn)).
We show a new Bell-Clauser-Horne inequality for two entangled three-dimensional quantum systems (so-called qutrits). This inequality is not violated by a maximally entangled state of two qutrits observed through a sym...
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We show a new Bell-Clauser-Horne inequality for two entangled three-dimensional quantum systems (so-called qutrits). This inequality is not violated by a maximally entangled state of two qutrits observed through a symmetric three-input- and three-output-port beam splitter only if the amount of noise in the system is greater than (11−63)/2≈0.308. This result is in a perfect agreement with the previous numerical calculations presented in Kaszlikowski et al. [Phys. Rev. Lett. 85, 4418 (2000)]. Moreover, we prove that for noiseless case, the necessary and sufficient condition for the threshold quantum efficiency of detectors below which there is no violation of local realism for the optimal choice of observables is equal to 6(15−43)/59≈0.821. This efficiency result again agrees with the numerical predictions.
We investigate the effects of thermonuclear reaction rate uncertainties on nova nucleosynthesis. One‐zone nucleosynthesis calculations have been performed by adopting temperature‐density‐time profiles of the hottes...
We investigate the effects of thermonuclear reaction rate uncertainties on nova nucleosynthesis. One‐zone nucleosynthesis calculations have been performed by adopting temperature‐density‐time profiles of the hottest hydrogen‐burning zone (i.e., the region in which most of the nucleosynthesis takes place). We obtain our profiles from 7 different, recently published, hydrodynamic nova simulations covering peak temperatures in the range from Tpeak=0.145–0.418 GK. For each of these profiles, we individually varied the rates of 175 reactions within their associated errors and analyzed the resulting abundance changes of 142 isotopes in the mass range below A=40. In total, we performed ≈7350 nuclear reaction network calculations. We find that present reaction rate estimates are reliable for predictions of Li, Be, C and N abundances in nova nucleosynthesis. However, rate uncertainties of several reactions have to be reduced significantly in order to predict more reliable O, F, Ne, Na, Mg, Al, Si, S, Cl and Ar abundances.
Calculated Hugoniots curves of porous metal Cu, Ni, and Mo are reported using the newly developed classical mean‐field potential approach where both the cold and thermal parts of the Helmholtz free‐energy are derive...
Calculated Hugoniots curves of porous metal Cu, Ni, and Mo are reported using the newly developed classical mean‐field potential approach where both the cold and thermal parts of the Helmholtz free‐energy are derived entirely from the 0‐K total energies and electronic density of states calculated with the full‐potential linearized augmented plane wave method within the generalized gradient approximation. Our approach permits efficient computation and invokes no empirical parameters. The calculation reproduces experimental data both at low and high porosities.
Focuses on a study which explored the numerical solution of delay differential equations. Linear stability of numerical methods; Application of one-leg methods; Error analysis.
Focuses on a study which explored the numerical solution of delay differential equations. Linear stability of numerical methods; Application of one-leg methods; Error analysis.
The Thermal expansion,Hugoniot state and 300 K isotherm of sodium have been calculated on the basis of:(i)the accurate calculations of 0 K total energies with the full-potential linearized augmented plane wave method ...
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The Thermal expansion,Hugoniot state and 300 K isotherm of sodium have been calculated on the basis of:(i)the accurate calculations of 0 K total energies with the full-potential linearized augmented plane wave method within the generalized gradient approximation to exchange-correlational functional and(ii)the newly developed classical mean-field statistics where both the cold and thermal parts of the Helmholtz free-energy are entirely derived from the 0 K total energy.A quite satisfactory agreement between calculation and experiment has been *** approach does not invoke any empirical parameter,which has long been a desirability on the field of material science.
The isotope shifts and hyperfine structures of seven optical transitions for all seven stable isotopes of Nd II were measured by using collinear fast-ion-beam laser *** nuclear parameterλwas obtained from the measure...
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The isotope shifts and hyperfine structures of seven optical transitions for all seven stable isotopes of Nd II were measured by using collinear fast-ion-beam laser *** nuclear parameterλwas obtained from the measured optical isotope shifts for all seven stable isotopes with improved ***λvalues were analysed by using the Fermi distribution for the nuclear charge *** values of δ,δand δwere determined.
Some convergence results are given for A(a)-stable linear multistep methods applied to two classes of two-parameter singular perturbation problems, which extend the existing relevant results about one-parameter proble...
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Some convergence results are given for A(a)-stable linear multistep methods applied to two classes of two-parameter singular perturbation problems, which extend the existing relevant results about one-parameter problems by Lubich~[1]. Some numerical examples confirm our results.
We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove tha...
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We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove that the scattering operator carries a band in Hs into Hs.
In the present paper we study the long time behavior of solutions to the Davey-Stewartson system in the Banach spaces. We make use of the properties of the semigroup generated by the linear principal operator in Lp() ...
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In the present paper we study the long time behavior of solutions to the Davey-Stewartson system in the Banach spaces. We make use of the properties of the semigroup generated by the linear principal operator in Lp() and prove that the Davey-Stewartson system possesses a compact global attractor Ap in Lp(). Furthermore, one show that the attractor is in fact independent of p and prove the attractor has finite Hausdorff and fractal dimensions.
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