Journal of Prime Research in Mathematics

Abstract: In this paper, we derive an upper bound for the size Ramsey number for a path \(P_3\) versus a friendship graph \(C_{3}^{t}\). Furthermore, some minimal Ramsey graph for a combination \((P_{3}, C_{3}^{t}) \)is presented. We also give an upper bound of the size Ramsey number for \(P_3\) versus \(P_n\).

Abstract: In this paper, we establish weak and strong convergence theorems of the three-step iterative sequences with errors for non-self nonexpansive mappings in uniformly convex Banach spaces. Our results extend and improve the recent ones announced by Naseer Shahzad and some others.

Abstract: The Steenrod algebra can not be realized as an enveloping of any Lie superalgebra. We list several problems that suggest a need to modify the definition of the enveloping algebra, for example, to get rid of certain strange deformations which we qualify as an artifact of the inadequate definition of the enveloping algebra in positive characteristic. P. Deligne appended our paper with his comments, hints and open problems

Abstract: We extend the wavelet estimation method due to Weglein and Secrest [4] to a marine seismic exploration model by taking into account the fluid motion and obtain the wavelet amplitude of the reflected data. This consideration is important for processing marine seismic data and for modeling seismic response. In case of known source location, the method predicts the source spectrum whereas the wave-field is predicted when the source (discrete/continuously distributed) is completely unknown. Moreover, this method is independent of the information about the properties of the earth. We find that the wavelet amplitude tends to zero and as a result, the corresponding reflected waves will be suppressed when the speed of the moving fluid gets closer and closer to the speed of sound. When the speed of the fluid motion is minuscule in comparison with the wave speed in water (Mach number \(M << 1\)), it does not effect the wavelet amplitude and the fluid motion can altogether be ignored which is in accordance with the physical observation.