**[1] The Log of Gravity**

Although economists have long been aware of Jensen’s inequality, many econometric applications have neglected an important implication of it: under heteroskedasticity, the parameters of log-linearized models estimated by OLS lead to biased estimates of the true elasticities. We explain why this problem arises and propose an appropriate estimator. Our criticism of conventional practices and the proposed solution extend to a broad range of applications where log-linearized equations are estimated. We develop the argument using one particular illustration, the gravity equation for trade. We find significant differences between estimates obtained with the proposed estimator and those obtained with the traditional method.

**[2] Gravity concentration technology**

This book is devoted to gravity concentration technology for over a half a century. It provides coverage of the entire subject and contains information on both new and classical methods of gravity concentration. Contents: I. Laboratory Techniques and Theoretical Aspects. 1. An Introduction to Gravity Concentration. 2. Development of the Gravity Concentration Flowsheet. 3. Mineralogical Aspects of Gravity Concentration. 4. Heavy Liquid Separation for Specific Gravity Fractionation. 5. Theory of Heavy Medium Separation. 6. Theory of Gravity Concentration. II. Unit Processes. 7. The Unit Processes of Gravity Concentration. 8. Feed Preparation. 9. Heavy Medium Separation. 10. Jigging. 11. Sluice Boxes and Palongs. 12. Pinched Sluice Concentration. 13. Spiral Concentration. 14. The Shaking Table. 15. The Recovery of Fines. 16. Dry Gravity Concentration. 17. Miscellaneous Methods of Concentration. III. Plant Practice. 18. Gravity Concentration in Operation. 19. Coal Preparation in Great Britain. 20. Canadian Coal Preparation: A Growing Resource. 21. Processing of Iron Ore. 22. Industrial Minerals: Processing by Gravity Concentration. 23. Mineral Sands. 24. Gravity Concentration of Gold. 25. Technical Aspects of the Concentration of the Metal Oxides. 26. Cornish Tin Processing. 27. Alluvial Tin Processing in South East Asia. 28. The Treatment of Tungsten Ore. 29. Tantalum Processing. 30. Miscellaneous Minerals. Appendices: Symbols Used in Plant Flowsheets. Author Index. Subject Index.

**[3] The Gravity Model**

Gravity has long been one of the most successful empirical models in economics. Incorporating deeper theoretical foundations of gravity into recent practice has led to a richer and more accurate estimation and interpretation of the spatial relations described by gravity. Wider acceptance has followed. Recent developments are reviewed here, and suggestions are made for promising future research.

**[4] Quantum Gravity and the Holographic Mass**

We find an exact quantized expression of the Schwarzschild solution to Einstein’s field equations utilizing spherical Planck units in a generalized holographic approach. We consider vacuum fluctuations within volumes as well as on horizon surfaces, generating a discrete spacetime quantization and a novel quantized approach to gravitation. When applied at the quantum scale, utilizing the charge radius of the proton, we find values for the rest mass of the proton within of the CODATA value and when the 2010 muonic proton charge radius measurement is utilized we find a deviation of from the proton rest mass. We identify a fundamental mass ratio between the vacuum oscillations on the surface horizon and the oscillations within the volume of a proton and find a solution for the gravitational coupling constant to the strong interaction. We derive the energy, angular frequency, and period for such a system and determine its gravitational potential considering mass dilation. We find the force range to be closely correlated with the Yukawa potential typically utilized to illustrate the exponential drop-off of the confining force. Zero free parameters or hidden variables are utilized.

**[5] The Effect of Gravity Loads on Seismic Lateral Displacements of R.C. Frames**

This paper includes an analytical study for an investigation of the gravity load effect on the seismic lateral displacements of a R.C. building located in Khartoum city (which lies in zone 2, of zone factor, z = 0.1), Sudan. The R.C. building used in this study is a 6-storey residential building with 3-bays in each direction. Two selected frames of the building were analyzed using STAAD-III software, linear static and dynamic analysis software, one in N-S direction and the other in E-W direction. The analysis was performed for two types of restraints: fixed and pinned, for both frames under the same loading. Four cases of damping ratios (0%, 5%, 10% and 20%) were used in the analysis. These ratios were taken as percentages of the critical damping. The software used the Dynamic Response Spectrum method (DRS) to solve the dynamic equilibrium equations of motion. The recorded ground motions of the 1940 El Centro earthquake were selected to be used as input data to calculate the seismic lateral displacements. Regardless of values of damping ratios and types of restraints used, it was found that the gravity load contributed in reducing the lateral displacements by an average amount of 25%. In other words, the lateral displacements caused by the combination of (gravity +seismic) loads are less than those caused by the seismic load only.

**Reference**

**[1] **Silva, J.S. and Tenreyro, S., 2006. The log of gravity. *The Review of Economics and statistics*, *88*(4), pp.641-658.

**[2] **Burt, R.O., 1984. Gravity concentration technology.

**[3] **Anderson, J.E., 2011. The gravity model. *Annu. Rev. Econ.*, *3*(1), pp.133-160.

**[4] **Haramein, N., 2013. Quantum gravity and the holographic mass. *Physical Science International Journal*, pp.270-292.

**[5] **Hassaballa, A.E., 2016. The Effect of Gravity Loads on Seismic Lateral Displacements of RC Frames. *Current Journal of Applied Science and Technology*, pp.1-9.