in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...

In this current work, we generalize the recent Pathwise Optimization approach of Desai et al. [11] to Multiple stopping problems. The approach also minimizes the dual bound as in Desai et al. [11] to find the best approximation architecture for the Multiple stopping problem. Though, we establish the convexity of the dual operator, in this setting as well, we cannot directly take advantage of th...

abstract some issues such as dehydration, local and chronological disproportion of rainfall, low productivity of water in agricultural sector, increasing demand for agricultural products due to increase in population participate with doughtiness are the most challenges of agricultural water. these factors caused water to be as one of the important and scarce inputs is agricultural products. the...