Factor Price Equalization : Geometrical Conditions

This paper presents a geometrical approach to the univalence problem for a system of cost functions. We present a natural (almost tautological) extension of a geometrical theorem due to McKenzie: our sufficient condition is related to the non-separability of two cones formed by convex combinations of the rows of the Jacobian matrix. This means that the cones spanned by the rows of Jacobian matrix (i.e., production coefficients) do not move wildly so that the two cones corresponding to the two end points (i.e., factor price vectors) cannot be separated by the hyperplane orthogonal to the vector of changes in factor prices. Unlike most ofthe previous propositions, our condition can naturally include as a special case such linear systems as having a non-singular matrix. We also give an alternative condition employing the concept of monotone functions. Dual to the above result is one more condition, which is shown to be closely connected with Kuhn's WARP-like requirement when the given functions are concave as well as homogeneous of degree one

A Note on Qualitative Economics for Univalence of Nonlinear Mappings

This note is aimed at presenting an easy and simple proposition on the univalence of a given nonlinear differentiable mapping whose Jacobian matrix has sign-regularity. First the notion of sign-regularity of Jacobian matrix on a domain is defined. We classifY the sign patterns into four categories: plus, minus, zero, and the rest. The plus sign is given to the (i, j) entry of the Jacobian matrix when the i-th component function is always increasing with respect to the j-th coordinate variable, the negative sign when the function is always decreasing, and the sign of zero when the function does not include the j-th coordinate variable. Otherwise, the sign is set as an asterisk *. Our proof is simple and elementary by use ofthe mean value theorem. In the final section, we give a list of our future research topics, some of which are under way. Especially a generalization to discontinuous mappings should be interesting

Gas–liquid flow in stirred reactors: Trailing vortices and gas accumulation behind impeller blades

In a gas–liquid stirred reactor, gas tends to accumulate in low-pressure regions behind the impeller blades. Such gas accumulation significantly alters impeller performance characteristics. We have computationally investigated gas–liquid flow generated by a Rushton (disc) turbine. Rotating Rushton turbine generates trailing vortices behind the blades, which influence the gas accumulation in the impeller region. Characteristics of these trailing vortices were first investigated by considering a model problem of flow over a single impeller blade. Predicted results were compared with the published experimental data. Circulation velocity and turbulent kinetic energy of the trailing vortices were found to scale with blade tip velocity. Several numerical experiments were carried out to understand interaction of gas bubbles and trailing vortices. Gas–liquid flow in stirred vessel was then simulated by extending the computational snapshot approach of Ranade and Dometti (Chem. Engng Res. Des., 74, 476–484, 1996). The approach was able to capture the main features of gas–liquid flow in stirred vessels. The detailed analysis of predicted results with reference to experimental data and the results obtained for flow over a single impeller blade will be useful for extending the scope of computational fluid dynamics (CFD) based tools for engineering gas–liquid stirred reactors

Evolution of Sonar Survey Systems for Sea Floor Studies

Approximately 71% of our planet is covered with oceans. It is also known that oceans are the last frontiers for the mankind’s survival and therefore it becomes pertinent that they are studied in great details. It has been found that the exploration of the oceans can be done more precisely using acoustics as one of the methods, as the acoustic waves can propagate over large distances and also using a broad spectrum of frequencies various issues of the ocean studies can be addressed more effectively than many of the other methods, both in terms resolution (using high frequency components) of measuring parameters and over large ranges (using low to very low frequency components). Currently with the technological advancement and improved computing algorithms, we have state of art systems for ocean exploration, which can provide information about the sea floor, sub-surface including ocean floor classification. These could be projected in 2-D and 3-D visualization to a great accuracy. Also available are acoustical methods wherein one can obtain an extremely important information about water column properties (both in terms of bioinformation and physical properties), and has great importance as this water column is the medium for transmission of all kind of energies(acoustic for short, medium and long ranges and some time light source for exploration over a very short distance) that are used for exploration on the oceans. It will therefore be interesting to understand the progress of underwater acoustics from its very primitive stage, where acoustic transmission through water medium was used for first time to the present day highly complex but very advanced acoustic sea-floor surveying systems. It will also be interesting to know, with a very old maritime history of using seas for transportation, as to what were the methods used by early time seafarers to understand depths of the oceans they were sailing. It has taken almost a century in developing an acoustic system to arrive at the present day advancement. An attempt has been made to present a perspective of evolution and advancement in underwater acoustics and related electronic, material and computational advancement, starting from the early attempts to the modern day acoustic equipments

Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture

We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an irreducible characteristic polynomial that has a given Fibonacci index. For dimensions of the form 2^(2^k) we present a solution that shows an analogy to an open conjecture of Wiedemann in finite field theory. Finally, we discuss the equivalence of mutually unbiased bases.Comment: 11 pages, added chapter on equivalenc

Flow generated by radial flow impellers: PIV measurements and CFD simulations

Particle image velocimetry (PIV) and computational fluid dynamics (CFD) have been used to investigate the single phase and gas-liquid flow generated by a Scaba SRGT turbine. The key details of the trailing vortices, the turbulent flow around the impeller blades and the accumulation of gas have been studied by using PIV measurements and CFD simulations. Both the experimental and numerical results show that the flow and the trailing vortices are not altered significantly upon gassing. The simulated results are generally in good agreement with the experimental findings. The CFD simulations also show that only small low-pressure regions exist behind the blades of the Scaba turbine compared with the very large lowpressure zones formed by the Rushton turbine. These results enable better understanding of the improved performance of the Scaba turbine for gas-liquid dispersions compared with the Rushton turbine

Semi-Insulating Polysilicon Hetero- and Isotype Junctions on Silicon

The effects of nitrogen trifluorideinthe gas stream during deposition of semi-insulating polysilicon (SIPOS) on the electrical characteristics of undoped (SIPSO)/p-Si, and n+-SIPOS/n-Si isotype junctions were investigated. The current-voltage characteristics of undoped SIPOS/p-Si heterojunctions exhibit a strong dependence on the oxygen content of the SIPOS film and depart from a hyperbolic sine behavior as the refractive index of the SIPOS increases.. The addition of nitrogen trifluoride decreases the current density of these undoped SIPOS/p-Si heterojunctions due presumably to the oxidation/hydrolysis of SiF species intoSiO2. The n+-SIPOS formed a rectifying isotype junction o n-Si. The forward current voltage characteristics exhibit two distinct activation energies separated by a kink in the forward semi-logarithmic characteristics; one below the cut-in voltage and one above the cut-in voltage. The two activation energies result from the presence of interface states in the structures. However, the forward current-voltage characteristics of the fluorinated SIPOS isotype junctions exhibit no kink and only a single activation energy due, presumably, to hydrogen passivating the interfacial traps during the hydrolysis process