The dielectric properties of the nematic mesophase, p-methoxy benzylidene p-decyl aniline(MBDA), measured in planar geometry with a function of frequency and temperature are investigated in detail. The complex dielect...The dielectric properties of the nematic mesophase, p-methoxy benzylidene p-decyl aniline(MBDA), measured in planar geometry with a function of frequency and temperature are investigated in detail. The complex dielectric permittivity(ε' and ε'') is also studied at a bias voltage of 10 V for planar aligned sample cell of nematic mesophase. The dielectric permittivity with bias voltage attains a higher(> 2 times) value than that without bias voltage at a temperature of 56℃,which is due to the fact that the linking group of nematic molecules is internally interacted with an applied bias voltage.This is supported by observing an enhanced dielectric permittivity of nematic liquid crystal(LC) in the presence of bias voltage, which can be fully explained as the increasing of the corresponding dipole moment. The dielectric relaxation behaviors of nematic LC are also demonstrated for planar aligned sample cell. The remarkable results are observed that the relaxation frequency shifts into low frequency region with the increase of the bias voltage applied to the planar aligned sample cells. The dielectric relaxation spectra are fitted by Cole–Cole nonlinear curve fitting for nematic mesophase in order to determine the dielectric strength.展开更多
In this paper, we mainly aim to compute the optimal inventory in the phase wise supply chain for queued customers in the interval of lower and upper bounds with particular life of the items. Important performance meas...In this paper, we mainly aim to compute the optimal inventory in the phase wise supply chain for queued customers in the interval of lower and upper bounds with particular life of the items. Important performance measures such as total optimal cost of the system and total expected delivery have also been computed by applying the dynamic programming and Drichlet theorem. Finally, numerical demonstration and sensitivity analysis have also been presented to gain the better perspective of the model.展开更多
Various investigators such as Khan ([1-4]), Khan and Ram [5], Chandra [6,7], Leindler [8], Mishra et al. [9], Mishra [10], Mittal et al. [11], Mittal, Rhoades and Mishra [12], Mittal and Mishra [13], Rhoades et al. [1...Various investigators such as Khan ([1-4]), Khan and Ram [5], Chandra [6,7], Leindler [8], Mishra et al. [9], Mishra [10], Mittal et al. [11], Mittal, Rhoades and Mishra [12], Mittal and Mishra [13], Rhoades et al. [14] have determined the degree of approximation of 2π-periodic signals (functions) belonging to various classes Lipα, Lip(α,r), Lip(ξ(t),r) and W(Lr,ζ(t)) of functions through trigonometric Fourier approximation (TFA) using different summability matrices with monotone rows. Recently, Mittal et al. [15], Mishra and Mishra [16], Mishra [17] have obtained the degree of approximation of signals belonging to -class by general summability matrix, which generalizes the results of Leindler [8] and some of the results of Chandra [7] by dropping monotonicity on the elements of the matrix rows (that is, weakening the conditions on the filter, we improve the quality of digital filter). In this paper, a theorem concerning the degree of approximation of the conjugate of a signal (function) f belonging to Lip(ξ(t),r) class by (E,q) summability of conjugate series of its Fourier series has been established which in turn generalizes the results of Chandra [7] and Shukla [18].展开更多
文摘The dielectric properties of the nematic mesophase, p-methoxy benzylidene p-decyl aniline(MBDA), measured in planar geometry with a function of frequency and temperature are investigated in detail. The complex dielectric permittivity(ε' and ε'') is also studied at a bias voltage of 10 V for planar aligned sample cell of nematic mesophase. The dielectric permittivity with bias voltage attains a higher(> 2 times) value than that without bias voltage at a temperature of 56℃,which is due to the fact that the linking group of nematic molecules is internally interacted with an applied bias voltage.This is supported by observing an enhanced dielectric permittivity of nematic liquid crystal(LC) in the presence of bias voltage, which can be fully explained as the increasing of the corresponding dipole moment. The dielectric relaxation behaviors of nematic LC are also demonstrated for planar aligned sample cell. The remarkable results are observed that the relaxation frequency shifts into low frequency region with the increase of the bias voltage applied to the planar aligned sample cells. The dielectric relaxation spectra are fitted by Cole–Cole nonlinear curve fitting for nematic mesophase in order to determine the dielectric strength.
文摘In this paper, we mainly aim to compute the optimal inventory in the phase wise supply chain for queued customers in the interval of lower and upper bounds with particular life of the items. Important performance measures such as total optimal cost of the system and total expected delivery have also been computed by applying the dynamic programming and Drichlet theorem. Finally, numerical demonstration and sensitivity analysis have also been presented to gain the better perspective of the model.
文摘Various investigators such as Khan ([1-4]), Khan and Ram [5], Chandra [6,7], Leindler [8], Mishra et al. [9], Mishra [10], Mittal et al. [11], Mittal, Rhoades and Mishra [12], Mittal and Mishra [13], Rhoades et al. [14] have determined the degree of approximation of 2π-periodic signals (functions) belonging to various classes Lipα, Lip(α,r), Lip(ξ(t),r) and W(Lr,ζ(t)) of functions through trigonometric Fourier approximation (TFA) using different summability matrices with monotone rows. Recently, Mittal et al. [15], Mishra and Mishra [16], Mishra [17] have obtained the degree of approximation of signals belonging to -class by general summability matrix, which generalizes the results of Leindler [8] and some of the results of Chandra [7] by dropping monotonicity on the elements of the matrix rows (that is, weakening the conditions on the filter, we improve the quality of digital filter). In this paper, a theorem concerning the degree of approximation of the conjugate of a signal (function) f belonging to Lip(ξ(t),r) class by (E,q) summability of conjugate series of its Fourier series has been established which in turn generalizes the results of Chandra [7] and Shukla [18].
