Computation of Möbius shifts associated with the third-orderand the fourth-order rainbows of a spheroidal droplet

2022 ◽  
Author(s):  
Zhiying Wang ◽  
Haitao Yu ◽  
Jie Yang ◽  
Jianqi Shen
Keyword(s):  
1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.


1979 ◽  
Vol 44 (12) ◽  
pp. 3501-3508 ◽  
Author(s):  
Jan Linek

Isobaric vapour-liquid equilibria in the isobutyl formate-isobutyl alcohol and n-butyl formate-isobutyl alcohol systems have been measured at atmospheric pressure. A modified circulation still of the Gillespie type has been used for the measurements. The experimental data have been correlated by means of the third- and fourth-order Margules equations.


2012 ◽  
Vol 25 (2) ◽  
pp. 161-170 ◽  
Author(s):  
Aleksandar Atanaskovic ◽  
Natasa Males-Ilic ◽  
Bratislav Milovanovic

The linearization effects on two-way Doherty amplifiers are presented in this paper. Symmetrical Doherty amplifier with the additional circuit for linearization has been realized and measurements of the linearization influence on the third- and fifth-order intermodulation products have been carried out. Asymmetrical Doherty amplifier has been designed and effects of the applied linearization technique have been considered through the simulation process. The linearization approach uses the fundamental signals? second harmonics and fourth-order nonlinear signals that are extracted at the output of the peaking cell, adjusted in amplitude and phase and injected at the input and output of the carrier cell in Doherty amplifier.


1972 ◽  
Vol 13 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Don B. Hinton

Numerous formulae have been given which exhibit the asymptotic behaviour as t → ∞solutions ofwhere F(t) is essentially positive and Several of these results have been unified by a theorem of F. V. Atkinson [1]. It is the purpose of this paper to establish results, analogous to the theorem of Atkinson, for the third order equationand for the fourth order equation


2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
S. Z. Ahmad ◽  
F. Ismail ◽  
N. Senu ◽  
M. Suleiman

We constructed three two-step semi-implicit hybrid methods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and zero dissipation. The third is a four-stage fifth-order method with dispersion order eight and dissipation order five. Numerical results show that SIHMs are more accurate as compared to the existing hybrid methods, Runge-Kutta Nyström (RKN) and Runge-Kutta (RK) methods of the same order and Diagonally Implicit Runge-Kutta Nyström (DIRKN) method of the same stage. The intervals of absolute stability or periodicity of SIHM for ODE are also presented.


2019 ◽  
Vol 97 (1) ◽  
pp. 114-116 ◽  
Author(s):  
A. Dwivedi

Expressions have been obtained for the volume derivatives of the Grüneisen parameter, which is directly related to the thermal and elastic properties of materials at high temperatures and high pressures. The higher order Grüneisen parameters are expressed in terms of the volume derivatives, and evaluated in the limit of infinite pressure. The results, that at extreme compression the third-order Grüneisen parameter remains finite and the fourth-order Grüneisen parameter tends to zero, have been used to derive a fundamental theorem according to which the volume derivatives of the Grüneisen parameter of different orders, all become zero in the limit of infinite pressure. However, the ratios of these derivatives remain finite at extreme compression. The formula due to Al’tshuler and used by Dorogokupets and Oganov for interpolating the Grüneisen parameter at intermediate compressions has been found to satisfy the boundary condition at infinite pressure obtained in the present study.


1992 ◽  
Vol 70 (9) ◽  
pp. 745-751
Author(s):  
K. S. Viswanathan ◽  
J. C. Jeeja Ramani

The anomalies of the second-, third-, and fourth-order elastic constants are considered for the phase transition of Hg2X2 type of compounds. Expressions are obtained for the equilibrium values of the order parameters in the ferroelastic phase from the stability conditions. The fluctuation in the order parameter is evaluated from the Landau–Khalatnikov equation. An expression is derived for the shift in the zero-point energy in the low-temperature ferroelastic phase and the specific heat anomaly. It is shown that these are proportional to (T − T)2 and (T − Tc), respectively. All the anomalies of the second-order elastic (SOE) constants are obtained from a single general formula, and relations among them are established. The temperature variation of the SOE constants in the limit [Formula: see text] is discussed. Similarly, expressions are derived for the anomalies of the third- and fourth-order elastic constants. In the limit [Formula: see text] it is shown that these constants diverge as [Formula: see text] and [Formula: see text], respectively.


1973 ◽  
Vol 58 (3) ◽  
pp. 581-593 ◽  
Author(s):  
R. A. Antonia ◽  
J. D. Atkinson

The cumulant-discard approach is used to predict the third- and fourth-order moments and the probability density of turbulent Reynolds shear stress fluctuations uv, the streamwise and normal velocity fluctuations being represented by u and v respectively. Measurements of these quantities in a turbulent boundary layer are presented, with the required statistics of uv obtained by the use of a high-speed digital data-acquisition system. Including correlations between u and u up to the fourth order, the cumulant-discard predictions are in close agreement with the measurements in the inner region of the layer but only qualitatively follow the experimental results in the outer intermittent region. In this latter region, predictions for the third- and fourth-order moments of uv are also obtained by assuming that the properties of both turbulent and irrotational fluctuations are Gaussian and by using some of the available conditional averages of u, v and uv.


2002 ◽  
Vol 17 (35) ◽  
pp. 2317-2325 ◽  
Author(s):  
NIKOLAI URALTSEV

Short-distance expansion of the total semileptonic B widths is reviewed for the OPE-conformable scheme employing low-scale running quark masses. The third- and fourth-order BLM corrections are given and the complete resummation of the BLM series presented. The effect of higher perturbative orders with running quark masses is found to be very small. Numerical consequences for |Vcb| are addressed.


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