Robustness of the partitions in grouping multi-item inventories

A recent work obtained closed-form solutions to the.problem of optimally grouping a multi-item inventory into subgroups with a common order cycle per group, when the distribution by value of the inventory could be described by a Pareto function. This paper studies the sensitivity of the optimal subgroup boundaries so obtained. Closed-form expressions have been developed to find intervals for the subgroup boundaries for any given level of suboptimality. Graphs have been provided to aid the user in selecting a cost-effective level of aggregation and choosing appropriate subgroup boundaries for a whole range of inventory distributions. The results of sensitivity analyses demonstrate the availability of flexibility in the partition boundaries and the cost-effectiveness of any stock control system through three groups, and thus also provide a theoretical support to the intuitive ABC system of classifying the items.

Effectiveness factor for zeroth-order catalytic reactions with volume change and nonuniform catalyst activity profiles

Analytical solutions are presented for the effectiveness factor of a zeroth-order reaction with volume change and nonuniform catalyst activity profile in slab, cylinder and spherical pellets. The possibility of shape normalization is considered for a variety of activity profiles and pellet shapes. When the catalyst activity at the external surface of the pellet is non-zero, shape normalization is obtained, which makes the asymptotic behavior of the effectiveness factor identical for small and large values of Thiele modulus, however, the normalization can lead to significant errors, particularly for the case of activity profiles decreasing towards the outer surface of the catalyst.

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

Pressure-induced first-order transition in layered crystalline semiconductor GeSe to a metallic phase

The electrical resistivity of layerd crystalline GeSe has been investigated up to a pressure of 100 kbar and down to liquid-nitrogen temperature by use of a Bridgman anvil device. A pressure-induced first-order phase transition has been observed in single-crystal GeSe near 6 GPa. The high-pressure phase is found to be quenchable and an x-ray diffraction study of the quenched material reveals that it has the face-centered-cubic structure. Resistivity measurements as a function of pressure and temperature suggest that the high-pressure phase is metallic.

Realization of first order optical systems using thin lensest

A first order optical system is investigated in full generality within the context of wave optics. The problem is reduced to a study of the ray transfer matrices. The simplest such systems correspond to axially symmetric propagation. Realization of such systems by centrally located lenses separated by finite distances is studied. It is shown that, contrary to the commonly held view, the set of first order systems that can be realized using axially symmetric thin lenses exhausts the entire SL(2, R) group; at most three lenses are needed to realize any element of this group. In particular, the inverse of free propagation can be so realized. Among anisotropic systems it is again shown that every element of the lens group Sp(4, R) can be realized using a finite number of thin lenses.

Ultrafast Switching Time and Third Order Nonlinear Coefficients of Microwave Treated Single Walled Carbon Nanotube Suspensions

Microwave treated water soluble and amide functionalized single walled carbon nanotubes have been investigated using femtosecond degenerate pump-probe and nonlinear transmission experiments. The time resolved differential transmission using 75 femtosecond pulse with the central wavelength of 790 nm shows a bi-exponential ultrafast photo-bleaching with time constants of 160 fs (130 fs) and 920 fs (300 fs) for water soluble (amide functionalized) nanotubes. Open and closed aperture z-scans show saturation absorption and positive (negative) nonlinear refraction for water soluble (amide functionalized) nanotubes. Two photon absorption coefficient, beta(0) similar to 250 cm/GW (650 cm/GW) and nonlinear index, gamma similar to 15 cm(2)/pW (-30 cm(2)/pW) are obtained from the theoretical fit in the saturation limit to the data for two types of nanotubes.

Determination of integral fringe order in photoelasticity

The paper describes a method to determine the integral fringe order associated with a fractional fringe value that is measured using Tardy or other similar compensators. The method makes use of two different wavelengths of light to determine the fractional fringe values. Further, it does not assume the independence of the material fringe constant on the wavelength of light used. From these measured fractional fringe values, the associated integral fringe order is determined. A method to construct a ready-reckoner table is also described which helps to identify the integral fringe order from any two measured fractional fringe values.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Fracture Behavior of Multidirectional DCB Specimen: Higher-Order Beam Theories

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

Random vibration of a second order non-linear elastic system

A method is presented for obtaining, approximately, the response covariance and probability distribution of a non-linear oscillator under a Gaussian excitation. The method has similarities with the hierarchy closure and the equivalent linearization approaches, but is different. A Gaussianization technique is used to arrive at the output autocorrelation and the input-output cross-correlation. This along with an energy equivalence criterion is used to estimate the response distribution function. The method is applicable in both the transient and steady state response analysis under either stationary or non-stationary excitations. Good comparison has been observed between the predicted and the exact steady state probability distribution of a Duffing oscillator under a white noise input.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.