Many people are facing life-threatening diseases, terminal illness, and the long-term care of elderly parents, but have few resources to rely on in these difficult times. They often keep their challenges private only to suffer in silence with no real support system. This book delivers practical solutions to the problems everyone must deal with when they are experiencing the degradation of the quality of their life or the potential loss of a loved one. Based on experiences derived from 25 years of prayer ministry, Bertram’s Hidden Treasures provides insight and guidance to equip patients, family members, and friends to walk through these challenging times with foresight, looking for and expecting to see God at work in many miraculous ways. It offers sound advice grounded in the truths found in Scripture and the wisdom revealed through real-life stories and case studies. This book helps those who have ever wondered . . . If God is good, why are we going through this? What will our family do during this crisis? How do we fight the fear that is trying to consume us? How can we encourage reconciliation in our family? Where can we find peace in the journey? What happens when we die? Is there life after death? What is heaven like? Hidden Treasures will inspire, motivate, and encourage loved ones to begin to walk the road to heaven without the fear and anxiety associated with death and dying. They’ll discover that the Word of God has answers to the questions that seem to have no answer; and that comfort awaits as they begin to view their situation from a heavenly perspective. Ultimately, it reveals that hope is available, death with dignity is possible, and there are hidden treasures to embrace along the way.
Nearly 200 problems, each with a detailed, worked-out solution, deal with the properties and applications of the gamma and beta functions, Legendre polynomials, and Bessel functions. 1971 edition.
Since the appearance of Banach algebra theory, the interaction between the theories ofBanach algebras with involution and that of bounded linear operators on a Hilbert space hasbeen extensively developed. The connections of Banach algebras with the theory ofbounded linear operators on a Hilbert space have also evolved, and Calkin Algebras andAlgebras of Operators on Banach Spaces provides an introduction to this set of ideas.The book begins with a treatment of the classical Riesz-Schauder theory which takesadvantage of the most recent developments-some of this material appears here for the firsttime. Although the reader should be familiar with the basics of functional analysis, anintroductory chapter on Banach algebras has been included. Other topics dealt with includeFredholm operators, semi-Fredholm operators, Riesz operators. and Calkin algebras.This volume will be of direct interest to both graduate students and research mathematicians.
How is art both distinct and different from the rest of human life, while also mattering in and for it? This central yet overlooked question in contemporary philosophy of art is at the heart of Georg Bertram's new aesthetic. Drawing on the resources of diverse philosophical traditions – analytic philosophy, French philosophy, and German post-Kantian philosophy – his book offers a systematic account of art as a human practice. One that remains connected to the whole of life.
Commences with the historical development of fractional calculus, its mathematical theory—particularly the Riemann-Liouville version. Numerous examples and theoretical applications of the theory are presented. Features topics associated with fractional differential equations. Discusses Weyl fractional calculus and some of its uses. Includes selected physical problems which lead to fractional differential or integral equations.
Forest mensuration – the science of measurement applied to forest vegetation and forest products – holds value for basic ecology as well as sustainable forest management. As demands on the world’s forests have grown, scientists and professionals are increasingly called on to quantify forest composition, structure, and the goods and services forests provide. Grounded in geometry, sampling theory, and ecology as well as practical field experience, forest mensuration offers opportunities for creative problem solving and critical thinking. This fifth edition of the classic volume, Forest Mensuration, includes coverage of traditional and emerging topics, with attention to SI and Imperial units throughout. The book has been reorganised from the fourth edition to better integrate non-timber and ecological aspects of forest mensuration at the tree, stand, forest, and landscape scales throughout. The new edition includes new chapters that specifically address the integration of remotely sensed data in the forest inventory process, and inventory methods for dead and downed wood. One unifying theme, not only for traditional forestry but for the non-timber inventory and for remote sensing, is the use of covariates to make sampling more efficient and spatially explicit. This is introduced in the introductory chapter on statistics and the chapter on sampling designs has been restructured to highlight this approach and lay the foundation for further learning. New examples will be developed throughout the textbook with an emphasis on current issues and international practice. Students in applied forestry programs will find ample coverage of forest products and timber inventory, while expanded material on biodiversity, biomass and carbon inventory, downed dead wood, and the growing role of remote sensing in forest assessment will be valuable to a broader audience in applied ecology.
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