This book focuses on the latest approaches and methods in fundamental mathematics and mechanics, and discusses the practical application of abstract mathematical approaches, such as differential geometry, and differential and difference equations in solid mechanics, hydrodynamics, aerodynamics, optimization, decision-making theory and control theory. Featuring selected contributions to the open seminar series of Lomonosov Moscow State University and Igor Sikorsky Kyiv Polytechnic Institute by mathematicians from China, Germany, France, Italy, Spain, Russia, Ukraine and the USA, the book will appeal to mathematicians and engineers working at the interface of these fields

Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms.- Reduction of the Lame Tensor Equations to the System ofNon-Coupled Tetraharmonic Equations.- Junction Flow around Cylinder Group on Flat Platee.- Accounting for Shear Deformation in the Problem of Vibrations and Dissipative Heating of Flexible Viscoelastic Structural Element with Piezoelectric Sensor and Actuator.- A Stochastic Theory of Scale-Structural Fatigue and Structure Durability at Operational Loading.- On Tikhonov Regularization of Optimal Distributed Control Problem for an Ill-Posed Elliptic Equation with p-Laplace Operator and L1-type of Non-Linearity.- Symmetries and Conservation Laws of the Equations of Two-Dimensional Shallow Water over Uneven Bottom.- xistence and Stability Analysis of Solutions for an Ultradian Glucocorticoid Rhythmicity and Acute Stress Model.- Mixed Dirichlet-Transmission Problems in Non-Smooth Domains.