One more definition of generalized fG -Mean, in addition to its existing definition, has been framed of for defining average mathematically. This definition can also be suitable for deriving of definitions of different types of average. A number of definitions / formulations of average have been derived from this definition of generalized fG -Mean. This paper is based on the description of this generalized definition of average along with the derivations of some existing definitions / formulations of average from it.

Consider a classical Hardy space on the open unit disk Η², and a toeplitz operator T_φj from Η ² to Η ². We prove that, the inverse Jordan struck problem is always solvable in the class of truncated Toeplitz operator. Also, we prove that, for an inner function Ѳ,A_φj ∈ T_Ѳ, and A*_φj, then .∉ Η ² ∪ Η¯ ^{2   (kindly check the main article)}

Thermal residual stress becomes very important factor to be taken care of during microfabrication process that involves surface micromachining of thin film structures. These microstructures undergo thermal stress due to change in temperatures during the process. Residual stress in thin film causes variations in resonant frequencies and is vital, specifically for beam structures like cantilevers and their arrays. We interpret the challenges involved in microfabrication specifically towards thermal residual stress in the process of crafting thin film structures. We considered the folded cantilever structure and compared with the structure of a flat plate fixed to two cantilever beams on each side forming an array. The substrate was not considered, and uniform temperature is sustained all through in this simulation. COMSOL Multiphysics tool is applied in simulating the effects, with greater insights towards geometries, addressed as the change in resonant frequencies. Taguchi’s orthogonal array method was performed on a set of structure defining parameters and percentage changes in resonant frequencies (very low 0.24-2.75% in folded structure compared to 18-53% in unfolded structures) and change in residual stress (~ 0.07 *10⁷ N/m²  in folded cantilever geometry compared to 2.4 *10⁷ N/m² in unfolded cantilever geometry) . Folded cantilever structures shown to have upper hand over flat beam structures in reducing thermal residual stress. These results are useful for designers to reduce the efforts and time and hence becomes economic advantage to the application developments.

A permutation are the ways of the order of arange of different elements. While a combination is a way of selecting items from a collection.                                    

The wide use of AISI 304 austenitic stainless steel due its special properties increased the interest in studying the behavior of this alloy under different conditions. This study has conducted the effects of cutting speed and feed rate on austenitic stainless steel type AISI 304 during dry turning. Chip thickness, chip curl radius, temperature and hardness were measured at different cutting speeds (67, 96 and 190 m/min) and with different feed rates (0.05, 0.1 and 0.3 mm/rev). Results showed that the best parameter to use during turning this alloy is the use of high speed (190 m/min) with low feed rate which result in lowest temperature generation. Furthermore, the study found that the cutting parameters have not effect on material surface hardness compared with the original material hardness.

In the present paper it is shown that every Near-Ring satisfies some identity properties. Moreover, some examples are given which prove the necessity of identity properties for Near-Rings. 

The purpose of this paper is to unveil the comparative study of some particular near rings like α₁ and β₁ Near-Rings. Moreover, some examples and theorems are given which prove the necessity of the comparative study of Near-Rings.