This volume represents a broad survey of current research in the fields of nonlinear analysis and nonlinear differential equations. It is dedicated to Djairo G. de Figueiredo on the occasion of his 70th birthday. The collection of 34 research and survey articles reflects the wide range of interests of Djairo de Figueiredo, including:
- various types of nonlinear partial differential equations and systems, in particular equations of elliptic, parabolic, hyperbolic and mixed type;
- equations of SchrAdinger, Maxwell, Navier-Stokes, Bernoulli-Euler, Seiberg-Witten, Caffarelli-Kohn-Nirenberg;
- existence, uniqueness and multiplicity of solutions;
- critical Sobolev growth and connected phenomena;
- qualitative properties, regularity and shape of solutions;
- inequalities, a-priori estimates and asymptotic behavior;
- various applications to models such as asymptotic membranes, nonlinear plates and inhomogeneous fluids.
The contributions of so many distinguished mathematicians to this volume document the importance and lasting influence of the mathematical research of Djairo de Figueiredo. The book thus is a source of new ideas and results and should appeal to graduate students and mathematicians interested in nonlinear problems.

Validation of computer systems is the process that assures the formal assessment and report of quality and performance measures for all the life-cycle stages of software and system development, its implementation, qualification and acceptance, operation, modification, requalification, maintenance and retirement (PICS CSV PI 011-3). It is a process that demonstrates the compliance of computer systems functional and non-functional requirements, data integrity, regulated company procedures and safety requirements, industry standards, and applicable regulatory authority's requirements. Compliance is a state of being in adherence to application-related standards or conventions or regulations in laws and similar prescriptions. This book, which is relevant to the pharmaceutical and medical devices regulated operations, provides practical information to assist in the computer validation to production systems, while highlighting and efficiently integrating worldwide regulation into the subject. A practical approach is presented to increase efficiency and to ensure that the validation of computer systems is correctly achieved.

Data integrity is fundamental in a pharmaceutical and medical devices quality system. This book provides practical information to enable compliance with data integrity, while highlighting and efficiently integrating worldwide regulation into the subject. The ideas presented in this book are based on many years' experience in regulated industries in various computer systems development, maintenance, and quality functions. In addition to case studies, a practical approach will be presented to increase efficiency and to ensure that the design and testing of the data integrity controls are correctly achieved.

Covering regulatory requirements stipulated by the FDA, this book delineates the organization, planning, verification, and documentation activities and procedural controls required for compliance with worldwide computer systems validation regulations. The author introduces supporting technologies such as encryption and digital signatures and places regulatory compliance within the context of quality assurance. He demonstrates the importance of integrating validation activities into the system lifecycle using a structured top-down approach. He covers practical applications of quality assurance and engineering techniques as they relate to the development of systems fit to meet user and regulatory requirements.

Covering regulatory requirements stipulated by the FDA, this book delineates the organization, planning, verification, and documentation activities and procedural controls required for compliance with worldwide computer systems validation regulations. The author introduces supporting technologies such as encryption and digital signatures and places regulatory compliance within the context of quality assurance. He demonstrates the importance of integrating validation activities into the system lifecycle using a structured top-down approach. He covers practical applications of quality assurance and engineering techniques as they relate to the development of systems fit to meet user and regulatory requirements.

Data integrity is a critical aspect to the design, implementation, and usage of any system which stores, processes, or retrieves data. The overall intent of any data integrity technique is the same: ensure data is recorded exactly as intended and, upon later retrieval, ensure the data is the same as it was when originally recorded. Any alternation to the data is then traced to the person who made the modification. The integrity of data in a patient's electronic health record is critical to ensuring the safety of the patient. This book is relevant to production systems and quality control systems associated with the manufacture of pharmaceuticals and medical device products and updates the practical information to enable better understanding of the controls applicable to e-records. The book highlights the e-records suitability implementation and associated risk-assessed controls, and e-records handling. The book also provides updated regulatory standards from global regulatory organizations such as MHRA, Medicines and Healthcare Products Regulatory Agency (UK); FDA, Food and Drug Administration (US); National Medical Products Association (China); TGA, Therapeutic Goods Administration (Australia); SIMGP, Russia State Institute of Medicines and Good Practices; and the World Health Organization, to name a few.

Data integrity is a critical aspect to the design, implementation, and usage of any system which stores, processes, or retrieves data. The overall intent of any data integrity technique is the same: ensure data is recorded exactly as intended and, upon later retrieval, ensure the data is the same as it was when originally recorded. Any alternation to the data is then traced to the person who made the modification. The integrity of data in a patient's electronic health record is critical to ensuring the safety of the patient. This book is relevant to production systems and quality control systems associated with the manufacture of pharmaceuticals and medical device products and updates the practical information to enable better understanding of the controls applicable to e-records. The book highlights the e-records suitability implementation and associated risk-assessed controls, and e-records handling. The book also provides updated regulatory standards from global regulatory organizations such as MHRA, Medicines and Healthcare Products Regulatory Agency (UK); FDA, Food and Drug Administration (US); National Medical Products Association (China); TGA, Therapeutic Goods Administration (Australia); SIMGP, Russia State Institute of Medicines and Good Practices; and the World Health Organization, to name a few.

The Latin American School of Mathematics (ELAM) is one of the most important mathematical events in Latin America. It has been held every other year since 1968 in a different country of the region, and its theme varies according to the areas of interest of local research groups. The subject of the 1986 school was Partial Differential Equations with emphasis on Microlocal Analysis, Scattering Theory and the applications of Nonlinear Analysis to Elliptic Equations and Hamiltonian Systems.

Validation of computer systems is the process that assures the formal assessment and report of quality and performance measures for all the life-cycle stages of software and system development, its implementation, qualification and acceptance, operation, modification, requalification, maintenance and retirement (PICS CSV PI 011-3). It is a process that demonstrates the compliance of computer systems functional and non-functional requirements, data integrity, regulated company procedures and safety requirements, industry standards, and applicable regulatory authority's requirements. Compliance is a state of being in adherence to application-related standards or conventions or regulations in laws and similar prescriptions. This book, which is relevant to the pharmaceutical and medical devices regulated operations, provides practical information to assist in the computer validation to production systems, while highlighting and efficiently integrating worldwide regulation into the subject. A practical approach is presented to increase efficiency and to ensure that the validation of computer systems is correctly achieved.

Data integrity is fundamental in a pharmaceutical and medical devices quality system. This book provides practical information to enable compliance with data integrity, while highlighting and efficiently integrating worldwide regulation into the subject. The ideas presented in this book are based on many years' experience in regulated industries in various computer systems development, maintenance, and quality functions. In addition to case studies, a practical approach will be presented to increase efficiency and to ensure that the design and testing of the data integrity controls are correctly achieved.

Good Manufacturing Practice (GMP) ensures medicinal products are produced consistently and controlled to the quality standards appropriate for their intended use and as required by product specifications or marketing authorization. Annex 11 details the European Medicines Agency (EMA) GMP requirements for computer systems. The purpose of Annex 11 is to provide the EMA healthcare industry with consistent criteria for effective implementation, control, and use of computer systems. EU Annex 11 Guide to Computer Validation Compliance for the Worldwide Health Agency GMP supplies practical information to facilitate compliance with computer system GMP requirements, while highlighting and integrating the Annex 11 guidelines into the computer compliance program. The ideas presented in this book are based on the author's 25 years of experience with computer validation in the healthcare industry with various computer systems development, maintenance, and quality functions. The book details a practical approach to increase efficiency and to ensure that software development and maintenance are achieved correctly. Examining the implementation of the computer systems validation entirely based on EU Annex 11, the book includes examples from laboratory, clinical, and manufacturing computer systems. It also discusses electronic record integrity associated with stored information.