Solving Equations and the Inverse of Mathematical Operations

1994 ◽  
Vol 94 (3) ◽  
pp. 124-126
Author(s):  
James G. Eberhart
Keyword(s):  
Solving Equations ◽  
Mathematical Operations

scholarly journals Limits of reproducibility and hydrodynamic noise in atmospheric regional modelling

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Beate Geyer ◽  
Thomas Ludwig ◽  
Hans von Storch
Keyword(s):  
Regional Climate Model ◽  
Computer Architecture ◽  
Climate Model ◽  
Initial Conditions ◽  
Regional Climate ◽  
Quality Criterion ◽  
Dynamic State ◽  
Regional Modelling ◽  
Simulation Results ◽  
Mathematical Operations

AbstractReproducibility of research results is a fundamental quality criterion in science; thus, computer architecture effects on simulation results must be determined. Here, we investigate whether an ensemble of runs of a regional climate model with the same code on different computer platforms generates the same sequences of similar and dissimilar weather streams when noise is seeded using different initial states of the atmosphere. Both ensembles were produced using a regional climate model named COSMO-CLM5.0 model with ERA-Interim forcing. Divergent phase timing was dependent on the dynamic state of the atmosphere and was not affected by noise seeded by changing computers or initial model state variations. Bitwise reproducibility of numerical results is possible with such models only if everything is fixed (i.e., computer, compiler, chosen options, boundary values, and initial conditions) and the order of mathematical operations is unchanged between program runs; otherwise, at best, statistically identical simulation results can be expected.

Non-local computing metasurfaces performing mathematical operations

2018 ◽  
Author(s):  
Andrea Cordaro ◽  
Hoyeong Kwon ◽  
Dimitrios Sounas ◽  
Albert Polman ◽  
Andrea Alù
Keyword(s):  
Non Local ◽  
Mathematical Operations

Semi-local convergence of a Newton-like method for solving equations with a singular derivative

2018 ◽  
Vol 27 (1) ◽  
pp. 01-08
Author(s):  
IOANNIS K. ARGYROS ◽  
◽  
GEORGE SANTHOSH ◽  
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Real Line ◽  
Local Convergence ◽  
Approximate Solutions ◽  
Convergence Domain ◽  
Solving Equations ◽  
Solutions Of Equations ◽  
Local Convergence Analysis ◽  
Special Case

We present a semi-local convergence analysis for a Newton-like method to approximate solutions of equations when the derivative is not necessarily non-singular in a Banach space setting. In the special case when the equation is defined on the real line the convergence domain is improved for this method when compared to earlier results. Numerical results where earlier results cannot apply but the new results can apply to solve nonlinear equations are also presented in this study.

Metaphysics of Being of Information

2021 ◽  
pp. 117-125
Author(s):  
Vladimir A. Yakovlev ◽  
Keyword(s):  
Scientific Basis ◽  
Specific Information ◽  
Abstract Concept ◽  
Communicative Practices ◽  
The Subject ◽  
Concept Of Information ◽  
American Physicist ◽  
Mathematical Operations ◽  
Intelligence Theories ◽  
The Universe

In article the metaphysics of being of information is considered and her cat­egorical status. The concept of information plays an especially important role in cognitive disciplines – neurology, cognitive psychology, sociology and arti­ficial intelligence theories altogether forming the scientific basis of new epi­stemology. Information is understood as the objective reality perceived by the subject by means of touch bodies which it fixes and comprehends by means of various semantic pro-positions, logical-mathematical operations and calculations, using it in various communicative practices for achievement of the purposes. On the basis of philosophical traditions of interpretation of cat­egory of life and various interpretations of this abstract concept of modern nat­ural sciences the new understanding of category of life as a basic metaphysical concept of science is offered. The philosophical bases of the theory of creative participation of the person in events of the Universe the famous American physicist-theorist J.A. Wheeler who put forward the thesis “all from Bit” (It from Bit), the information paradigm of the universe developed by the prom­inent modern philosopher L. Floridi. It is demonstrated that the origination and evolution of all objects takes place due to the existence of specific information programs that express the fundamental creativity of the nature. The statement that the category of life in modern interpretation both in natural-science, and in sociocultural aspects expresses life of information, or the information life presented in unity of three spheres of reality – matter, lives and consciousness (reason) is proved.

scholarly journals Learning support pedagogy for children who struggle to develop the concepts underlying the operations of addition and subtraction of numbers: the ‘Calculia’ programme

2014 ◽  
Vol 4 (3) ◽  
pp. 23 ◽  
Author(s):  
Annemarie Fritz-Stratmann ◽  
Antje Ehlert ◽  
Gabriele Klüsener
Keyword(s):  
Student Teachers ◽  
Conceptual Development ◽  
Practical Knowledge ◽  
Individual Development ◽  
Learning Support ◽  
Remediation Strategies ◽  
Teaching Unit ◽  
Addition And Subtraction ◽  
The Individual ◽  
Mathematical Operations

This paper argues for teaching pre-service teachers about remediation strategies for learners who encounter problems in mathematics in the early grades. The premise is that all teachers should be equipped with theory-based practical knowledge to support learning. A few teaching sessions to develop the concepts that underlie the mathematical operations of addition and subtraction are introduced in this paper. An empirically validated, comprehensive model of cumulative arithmetic competence development from the ages of four to eight years forms the basis for the construction of the suggested teaching unit. The model distinguishes five competence levels of arithmetical conceptual development, and proposes that concepts build on one another hierarchically. A ‘part plus part is equivalent to whole’ model was constructed based on this hierarchical structure and the understanding that the concept of addition is a dynamic process. The teaching examples include exercises for all children, not only ones who struggle. Possibilities for adapting the exercises to the individual development level of slower or faster learners are also included. All exercises are accompanied by a reflection on the procedure and strategies applied in order to support meaningful and sustainable learning and to give student teachers the opportunity to use knowledge of mathematical cognition theory during their pre-service years.

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