A study of the q-analogue of the paranormed Cesàro sequence spaces
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In this article, we introduce and investigate the q-Ces?ro matrix C(q) = (cq uv) with q ? (0, 1) for which we have cq uv ={qv/[u + 1]q (0 ? v ? u) 0 (v > u), where the q-number [?]q is given, as usual in the q-theory, by [?]q := {1 ? q?/1 ? q (? ? C) ?n?1 k=0 qk = 1 + q + q2 + ....+ qn?1 (? = n ? N), C and N being the sets of complex numbers and positive integers, respectively. The q-Ces?ro matrix C(q) is a q-analogue of the Ces?ro matrix C1. We study the sequence spaces Xq(p), Xq 0(p), Xq c (p) and Xq ?(p), which are obtained by the domain of the matrix C(q) in the Maddox spaces ?(p), c0(p), c(p) and ??(p), respectively. We derive the Schauder basis and the alpha-, beta- and gamma-duals of these newly-defined spaces. Moreover, we state and prove several theorems characterizing matrix transformation from the spaces Xq(p),Xq 0(p),Xq c(p) and Xq ?(p) to anyone of the spaces c0, c or ??.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it