Interpolation function of the genocchi type polynomials

The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary positive real parameters. We prove multiplication theorem of these polynomials. Furthermore, we give some identities and applications associated with these numbers, polynomials and their interpolation functions.Comment: 14 page

On Expectations-Driven Business Cycles in Economies with Production Externalities: A Comment

Eusepi (2009, International Journal of Economic Theory 5, pp. 9-23) analytically finds that a one-sector real business cycle model may exhibit positive co-movement between consumption and investment when the equilibrium wage-hours locus is positively-sloped and steeper than the household's labor supply curve. However, we show that this condition does not imply expectations-driven business cycles will emerge in Eusepi's model. Specifically, a positive news shock about future productivity improvement leads to an aggregate recession whereby output, employment, consumption and investment all fall in the announcement period.Expectations-Driven Business Cycles; Production Externalities.

Development of code evaluation criteria for assessing predictive capability and performance

Computational Fluid Dynamics (CFD), because of its unique ability to predict complex three-dimensional flows, is being applied with increasing frequency in the aerospace industry. Currently, no consistent code validation procedure is applied within the industry. Such a procedure is needed to increase confidence in CFD and reduce risk in the use of these codes as a design and analysis tool. This final contract report defines classifications for three levels of code validation, directly relating the use of CFD codes to the engineering design cycle. Evaluation criteria by which codes are measured and classified are recommended and discussed. Criteria for selecting experimental data against which CFD results can be compared are outlined. A four phase CFD code validation procedure is described in detail. Finally, the code validation procedure is demonstrated through application of the REACT CFD code to a series of cases culminating in a code to data comparison on the Space Shuttle Main Engine High Pressure Fuel Turbopump Impeller

Putative spin liquid in the triangle-based iridate Ba3_3IrTi2_2O9_9

We report on thermodynamic, magnetization, and muon spin relaxation measurements of the strong spin-orbit coupled iridate Ba$_3$IrTi$_2$O$_9$, which constitutes a new frustration motif made up a mixture of edge- and corner-sharing triangles. In spite of strong antiferromagnetic exchange interaction of the order of 100~K, we find no hint for long-range magnetic order down to 23 mK. The magnetic specific heat data unveil the $T$-linear and -squared dependences at low temperatures below 1~K. At the respective temperatures, the zero-field muon spin relaxation features a persistent spin dynamics, indicative of unconventional low-energy excitations. A comparison to the $4d$ isostructural compound Ba$_3$RuTi$_2$O$_9$ suggests that a concerted interplay of compass-like magnetic interactions and frustrated geometry promotes a dynamically fluctuating state in a triangle-based iridate.Comment: Physical Review B accepte

Hamiltonian Analysis of Poincar\'e Gauge Theory: Higher Spin Modes

We examine several higher spin modes of the Poincar\'e gauge theory (PGT) of gravity using the Hamiltonian analysis. The appearance of certain undesirable effects due to non-linear constraints in the Hamiltonian analysis are used as a test. We find that the phenomena of field activation and constraint bifurcation both exist in the pure spin 1 and the pure spin 2 modes. The coupled spin-$0^-$ and spin-$2^-$ modes also fail our test due to the appearance of constraint bifurcation. The ``promising'' case in the linearized theory of PGT given by Kuhfuss and Nitsch (KRNJ86) likewise does not pass. From this analysis of these specific PGT modes we conclude that an examination of such nonlinear constraint effects shows great promise as a strong test for this and other alternate theories of gravity.Comment: 30 pages, submitted to Int. J. Mod. Phys.