Review of Quaternion Differential Equations: Historical Development, Applications, and Future Direction

Terrain Analysis: Historical Perspective and Future Direction

THE SOIL AND WATER ASSESSMENT TOOL : HISTORICAL DEVELOPMENT , APPLICATIONS , AND FUTURE RESEARCH DIRECTIONS Invited Review Series

The Soil and Water Assessment Tool (SWAT) model is a continuation of nearly 30 years of modeling efforts conducted by the USDA Agricultural Research Service (ARS). SWAT has gained international acceptance as a robust interdisciplinary watershed modeling tool as evidenced by international SWAT conferences, hundreds of SWAT‐related papers presented at numerous other scientific meetings, and dozen...

Ranks of the common solution to some quaternion matrix equations with applications

We derive the formulas of the maximal andminimal ranks of four real matrices $X_{1},X_{2},X_{3}$ and $X_{4}$in common solution $X=X_{1}+X_{2}i+X_{3}j+X_{4}k$ to quaternionmatrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3}$. Asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. We give the exp...

Recent Development in Partial Differential Equations and Their Applications

In recent years, the partial differential equations, both fractional and integer orders, have been recognized as a powerful modelingmethodology.They are inspired by problemswhich arise in diverse fields such as biology, fluid dynamics, physics, differential geometry, control theory, materials science, and engineering. The purpose of this special issue is to report and review some recent develop...

APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS IN STABILITY INDEX AND CRITICAL LENGTH IN AVALANCHE DYNAMICS

In this study, Stability analysis of snow slab which is under detonation has developed in the present model. The model has been studied by using the basic concepts of non-detonation model and concepts of underwater explosions with appropriate modifications to the present studies. The studies have also been extended to account the effect of critical length variations at the time of detonation an...