Free Download (Mathematics n’ Mathematical Physics)

Notes in Pure Mathematics & Mathematical Structures in Physics:
(i) the latest revision is available here: ddos:notes (ddos is for “direct download from the original source”), 12 Nov 2024, PDF file of 755 pages (lxxxv-667 pp., to be precise);
(ii) public repositories: doi:10.5281.10427921 (2023-), or hal-04362941 (2023-);
(iii) please do not download the book from the arXiv repository arXiv:2105.14863 [math-ph] (2021-), Bibcode: 2021arXiv210514863N:
· it is an outdated version (clearly I am talking about the latest version present in this repository, dating back to March 2023),
· the arXiv software is not able to generate the pdfTeX, during the (new) “Submission Processing”: «arXiv’s automated TeX processing has failed to process your source»; «AutoTeX returned error: Unable to suc[c]essfully process tex files», or «Fatal error occurred, no output PDF file produced», to close with the mournful «AutoTeX aborting». It is the same old story every time. And every time, I have to waste a day trying to figure out why their internal LaTeX editor throws a “tantrum”. I am tired of having to deal with an inefficient system, which is managed by a slow-witted staff. Technology must be at the service of man and not the opposite, making ourselves a little more slaves. Sure, my text (the set of files forming the book) makes use of advanced LaTeX codes and tricks, but the crucial point is that, as far as I am concerned, I do not encounter any errors on my computer: I am used to test the .tex files with different LaTeX editors (under texlive 2021-2023), before submitting a new project. So, it is: go to hell.

Appropriately-modified extracta (2022-), with some simplifications, from my Notes, to give an appetizer of the ponderous book:
· Tensor Calculus, Lorentz–Minkowski 4-Manifolds plus Spinor Representation, & Clifford Algebra (40 pages): doi:10.5281.7220175, or ddos:e1 (epitome I),
·The Lagrangian Density Farrago in 3-Interactions of the Standard Quantum Fields (8 pages): doi:10.5281.7220203, or ddos:e2 (epitome II),
· The Ricci Flow, & The Hamilton–Perelman Metric Evolution Machinery (42 pages): doi:10.5281.7220215, or ddos:e3 (epitome III),
· Calabi–Yau Theorem: a Non-linear Complex Equation of Monge–Ampère Type on Compact Kähler Manifolds (12 pages): doi:10.5281.7220232, or ddos:e4 (epitome IV),
· Hölder Continuity of Subspaces in a Map with the Anosov Property (5 pages): doi:10.5281.7220254, or ddos:e5 (epitome V),
· Poincaré Recurrence Theorem plus Symplectic Form & Liouville invariance under the Hamiltonian Flow (9 pages): doi:10.5281.7220280, or ddos:e6 (epitome VI),
· Geometric Multivalence of Ergodicity, and Entropy within the Topological Thermodynamics: at the Frontier of Order & Chaos (27 pages) doi:10.5281.7220292, or ddos:e7 (epitome VII),
· Pullback and Random Attractors & Stochastic Systems (Itô and Stratonovich Calculi) (14 pages): doi:10.5281.7220308, or ddos:e8 (epitome VIII),
· Toroidal Fourier Analysis (7 pages): doi:10.5281.7220320, or ddos:e9 (epitome IX).

Athena leaped from Jupiter’s head (Tum quoque, cùm Pallas cerebro Jovis excidit, aurum), right? This article jumps out of Chap. 10 of the Notes, but develops unpublished ponderationes, and goes its own way:
Lenticular Algebro-geometric Continuous Point-Motion (or Geodetic Line): On the Ricci & Kähler–Ricci Flow Over Time (10 pages): accessible at doi:10.5281.7220346 (2022-), or ddos:lenticular.

A succinct but dense paper in functional analysis (harmonic analysis, to be exact):
Bounded Mean Oscillation: an ℝ-Function with Multi-𝕂₆ Cubes. Dual of the Hardy Space H ¹ and Banach Extent (7 pages): alternatively doi:10.5281.8413243 (2023-), or ddos:bmo; outdated versions: arXiv:2212.00681 [math.FA] (2022-), Bibcode: 2022arXiv221200681N (the arXiv computer program for the pdfTeX processing system is not without flaws).

Spin & Torsion Tensors on Gauge Gravity: a Re-examination of the Einstein–Cartan Spatio-Temporal Theory (28 pages): available at doi:10.5281.7568818 (2023-) or hal-03948127 (2023-); or even ddos:ect.
A grievous corollary. The public is always greedy for anecdotes. Here you are satisfied. This paper was written under opioids—oxycodone and tramadol—to counteract the unbearable pain associated with the onset of a disease affecting the bottom of my feet. Two lines from F. Hölderlin come to mind, extracted from the hymn Patmos (1803): «Wo aber Gefahr ist, wächst / Das Rettende auch» (Wherever there is danger, there grows / salvation too).

Einstein–Cartan Theory: Retrospective and Novelties (32 pages): doi:10.5281.10641153 (2024) or ddos:ect_intentio. This article takes up a previous writing by integrating it with an introductory part. I made some small variations in the technical-mathematical part. It shall be published in a special issue of a review, Intentio (based in Toulon), which intends to investigate the concept of knowledge—ἐπιστήμη, ah, an unknown word nowadays—in the old way, ou seja, in a universal manner, according to its multiple ramifications.

Stochastic Covariant Derivatives in a (Curved) Space-Time: a Glimpse into the Fractoid Spaces (23 pages): ddos:scd; alternatively hal-04081660 (2023-), doi:10.5281.8413143 (2023-); outdated versions: arXiv:2303.10177 [math.PR] (2023), Bibcode: 2023arXiv230310177N.

Linear System with Time-Dependent Square (n × n)-Matrix: a Brief Remark on Spectral Theory of Ordinary Differential Equations (7 pages): doi:10.5281.7861531 (2023-), or ddos:lsm.

Spinoriality: From Projections in a Flat Set of Paths to Elements in Curved Space(-Times) (14 pages): doi:10.5281.7958256 (2023-); alternatively hal-04102963 (2023-), or even ddos:spinoriality.

Gelfand Type Elliptic Boundary Problems: a Synoptic Novel Codification of Solutions & Non-Solutions (23 pages): hal-04219781 (2023-), doi:10.5281.8399005 (2023-), or even ddos:gp.

Q&A on the Continuous Spectrality and a Related Equation (4 pages): doi:10.5281.10057580 (2023-); alternatively ddos:cs. This is not an article. It is a private text. But it nevertheless has its public interest (it is simply a behind the scenes piece that refers to a back-and-forth).

Fourier Transform: Some Progress of a Chameleonic Math-Object (15 pages): doi:10.5281.10475724 (2024-), hal-04375757 (2024-), or ddos:ft.

Navier–Stokes Equations. Mathematics of Fluids in 2- and 3-Space: Dirichlet Boundary Conditions plus Asymptotic Analysis (14 pages): doi:10.5281.12734649 (2024-), then hal-04646969, or ddos:ns.

On Some Applications of Absolute Differential Calculus to the Theory of Binary Quadratic Differential Forms and Systems in Two Variables (15 pages): hal-04776516, doi:10.5281.14070306, or ddos:grc. This translation dates back to the second half of the decade in the 2010s. I am making it available after several years in LaTeX.

Be warned
(α) The management of the interline spacing, and letter spacing, performed (obligatorily) by the arXiv software for the automatic TeX processing script—from my .tex source—is pitiful, and sometimes ugly things pop up. But there is more (an epiphany for fearless hearts, like me). What about the cojonerìa of those who manage the arXiv policies, and the dust stirring in the cranium of arXiv moderators? They take actually functions of censoring, for the simple fact that they understand nothing about mathematics. If one says something that goes against the main thread, if one tries to raise criticisms of the imposed n’ wrong model of today’s mathematics, one must be ready for clashes. This condition is true in general; and this explains all the rubbish that is published. In the meantime the load of sheep (pecoròni) increases. It is enough to reverse Wilde’s phrase to understand what I mean: «whenever people agree with me, I always feel I must be wrong», from Lady Windermere’s Fan, in Id., The Complete Plays, Poems, Novels and Stories of Oscar Wilde, Parragon, London, 1995, p. 401.
(α.1) An excess of specialization ineluctably leads to sterility, which then equals the most farcical obtuseness; and that is what happened to arXiv in recent years, not to mention many other repositories that host scientific articles, or the vast majority of peer-reviewed journals covering mathematics. The lack of a propaedeutical culture, without disturbing the encyclopedic one, among the arXiv moderators (LOL) is bloodcurdling. These are miserable people who cannot see beyond their own nose—or, if you prefer: “When the sage points at the Moon, the fool looks at the finger”. They are duller than the Laputans, the inhabitants of the flying island (see J. Swift, Travels into Several Remote Nations of the World. In Four Parts. By Lemuel Gulliver, First a Surgeon, and then a Captain of Several Ships, Part Three: A Voyage to Laputa, B. Motte, London, MDCCXXVI · 1726). This is a further sign of the decline of contemporary mathematical knowledge, devoured by the worm of sightless hyperspecialization in watertight compartments. This abysmal ignorance is a recent novelty in the Ivy League (more accurately, for some years now; consider that I am writing this annotation on October 18, 2023). I am speaking from direct experience; besides, I am very familiar with the history of mathematics & related physics, and its thousand anecdotes.
Here is the thing: the specialist ends up with a double inability to understand, c’est-à-dire he no longer understands what he is doing, because he is no longer able to connect his discipline (which in the meantime has turned into a sub-specialization of a sub-specialization...) to a network of parallel and broader knowledge to which his pediculous “specialism” is linked umbilically.
(β) Stay away from INSPIRE-HEP (High Energy Physics) library because it automatically adds links in my references that are not present in my book: the INSPIRE system for automatic reading-indexing documents is ad mentulam canis.