Decorrelative Mollifier gravimetry. Basics, ideas, concepts, and examples / Декоррелятивная гравиметрия Моллифера. Основы, идеи, концепции и примеры

An essential objective of mathematics is to create settings and concepts to better understand our world. Mathematics is present in everyday life. Even more, almost all sciences undergo a process of “mathematization” due to increasing technological progress.

What is exactly that enables the mathematicians to provide the transfer from concrete measurements and observables to abstract mathematical formalisms and models? Some programmatic answers should be given at this early stage essentially inspired by the contributions in Freeden (2009, 2015), Freeden et al. (2019):

• The mathematical world of numbers and structures contains efficient tokens by which the rule-like aspect of problems can be described appropriately. This description includes as an essential step a simplification by abstraction. The principal impact of abstraction is to allow the replacement of a continuous signal by a discrete set preferably with minimal loss of any information. So, simplification by abstraction consists of specifying the criteria under which the original continuous signal may be reproduced.

• Essential properties of a problem are separated from unimportant ones, further specified, and afterward included into a solution scheme. The “eye for similarities” often enables mathematicians to recognize a posteriori that an adequately reduced problem may also arise from very different situations in various application areas, so that the resulting solutions may be applicable to multiple settings after an adequate adaptation or concretization. Without this ingredient, the abstraction remains essentially useless.

• The interaction between abstraction and concretization characterizes the history of mathematics and its current development as a common language and an independent standard. A problem reduced by abstraction has to be considered as a new “concrete” problem to be solved within a general framework, that determines the validity of a possible solution <...>