Solution of an Algebraic Linear System of Equations Using Fixed Point Results in C∗-Algebra Valued Extended Branciari Sb-Metric Spaces
Bibliographic record
Abstract
This study explores the realm of metric spaces, advancing beyond conventional boundaries by introducing two innovative types of metrics known as generalized Branciari-type metrics. Through exacting examination and exemplification, we shed light on the intricacies of these newly defined metric spaces and their extended versions. By drawing parallels with established theorems such as Banach and Kannan, we unveil corollaries that establish necessary symmetric conditions for the existence and uniqueness of fixed points concerning self-operators within these spaces. The inclusion of illustrative examples not only bolsters our theoretical framework but also underscores the practical relevance of our findings. Furthermore, we utilize our research to address real-world applications, showcasing how our results can be employed to determine the existence of unique solutions for algebraic systems of linear equations, thereby bridging the theoretical and applied aspects of mathematical exploration. Through these interventions, our study significantly contributes to the comprehensive understanding and utilization of all the properties in metric spaces within diverse mathematical contexts.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".