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"A need for a deeper understanding of the convergence properties of augmented Lagrangian algorithms and of their relationship to operator-splitting methods such as alternating-methods direction and the development of more efficient algorithms prompted the authors to write this book. The volume is oriented to applications in continuum mechanics. This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods (coupled to finite-element approximations). It begins with a description of the mechanical and mathematical frameworks of the considered applications as well as a general analysis of the basic numerical methods additionally used to study them. These ideas are then applied to specific classes of mechanical problems."

"Kompaktifikasi dimensi ekstra 5D dengan suku kinetik hukum pangkat (power law), telah berhasil menggulung satu dimensi ekstra, serta memperoleh informasi radius dan kestabilannya. Namun dari kajian tersebut didapatkan kompaktifikasi yang bersifat anti-de sitter (Ads) pada empat dimensi. Hal yan menunjukkan bahwa lagrangian yang dipilih belum sesuai dengan lagrangian alam semesta tempat kita berada yang mengharuskan bersifat de sitter (dS).

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The 5D extra dimension compatibility with the power law kinetic terms, has succeeded in rolling an extra dimension, and obtained information on its radius and stability. However, from this study, it was found that anti-de sitter compactification (Ads) in four dimensions was obtained. This shows that the selected lagrangian does not match the universe we are in, which requires it to be de sitter (dS)."

"This monograph gives a modern account of the application of critical point theory, and more specifically Morse theory, to Lagrangian dynamics, with particular emphasis toward existence and multiplicity of periodic orbits of non-autonomous and time-periodic systems."

"This book describes the current state of the art in damage mechanics, applying theory to typical damage and fracture problems encountered in various fields of current engineering."

"This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear, quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited."