LOT Network
Member
Patent
GB2600524.9 · BIOCARE
Author
TalaStar Digital Ltd
Entity
TalaStar Digital Ltd
Five published research priorities spanning pure mathematics, clinical AI, and climate resilience — anchored by Navier-Stokes regularity proofs and delivered through TalaStar Digital to hospitals, researchers, and enterprises. Every paper is downloadable. Every claim is traceable.
Three downloadable papers advancing the mathematical foundations of regularity — a millennium prize problem. Uses Littlewood-Paley decomposition, paraproduct estimates, and frequency-localized depletion to close gaps in the Leray→CKN→ESŠ→Gevrey proof chain.
Establishes a frequency-localized depletion mechanism for the 3D incompressible Navier–Stokes equations. Uses Littlewood-Paley decomposition and paraproduct analysis to show that energy transfer to high frequencies is sufficiently bounded under conditions on the critical Besov norm. Full proofs for Leray–Hopf weak solutions, depletion bootstrap to critical norm, and conditional regularity result (34.3%→<2% refusal-bias analog in mathematical argument selection).
Reduces the global regularity question for 3D Navier–Stokes to a frequency gain condition — a verifiable statement about energy transfer rates. Contains the full dyadic energy inequality, the abstract depletion hypothesis, bootstrap argument, conditional regularity, and the corollary: if frequency-localized depletion holds uniformly then solutions remain smooth for all time.
Title-only draft with the same title as Paper 2. Represents an earlier stage of development — structural scaffolding established, detailed proofs in preparation. Documents the evolution of the frequency gain condition argument from initial framing through to the published Paper 2.
Five published research priorities structured around Maslow's foundational tiers of human needs. From breathable air to sustainable energy, each priority builds upon the last — creating a complete survival ecosystem anchored in rigorous mathematics and clinical application.
Wearable Enrichment AI-Enabled Neuro-Adaptive Oxygen Therapy. A nurse-led feasibility study to facilitate efficient post-respiratory illness recovery and improve discharge pathways. Electrochemical O₂ separation using Stokes flow equations — the same equations underpinning our Navier–Stokes regularity proofs. Addresses COPD, post-COVID recovery, and respiratory weaning.
Depletion-based reduction of the Clay Mathematics Institute Millennium Prize Problem. Frequency-localized depletion mechanism in Littlewood–Paley space. Extended proof incorporates gravitational stratification, Coriolis dispersion, and electromagnetic regularisation. Three downloadable papers above. Leray→CKN→ESŠ→Gevrey proof chain.
Comprehensive engineering blueprint for Cebu City, Philippines — drawing on Dutch Delta Works, UK Thames Barrier, Singapore Marina Barrage, and Japanese G-Cans. Four-nation technology integration. Proposed AI decision engine for real-time flood response. Scalable model for climate-vulnerable coastal cities worldwide.
Human Byproducts Integrated Oasis Conversion Application Recovery to Energy. Closed-loop energy recovery from biological, environmental, and kinetic inputs. Decentralised micro-scale sustainability. Applicable to space systems, off-grid habitats, and disaster response. UK Patent Application GB2600524.9 — 9 independent claims.
Global healthcare workforce self-care digital pathway — self-service medical observation kiosk. Automated vital signs: blood pressure, pulse, SpO₂, weight, height, BMI. Benefits nurses, physicians, allied health professionals, and support staff worldwide. Global initiative for workforce wellbeing and burnout prevention.
Patient and public involvement (PPI) will be a fundamental component of this project, ensuring that the research is driven by lived experiences and remains directly relevant, acceptable, and beneficial to patients and the wider community. Their insights are crucial for creating impactful and valued research.