GPH-International Journal of Mathematics

THE RESONANCE - FREQUENCIES IN THE < ENTORHINAL BRAIN - CORTEX STRUCTURE >, FROM THE -- MILD DEMENTIA STAGE -- TO THE -- SEVERE DEMENTIA STAGE -- & The Cancerous Pancreas – Gland

Markos Georgallides — 2026-06-30

a... The Conservation of Energy in Caves and in Atoms Compounds. have been widely Analyzed and Proofed in Prior Articles [106],[118].

b... In Mechanics - Physics is generally followed the Theory of Vibrations for Actions.

THE ATOMS – ACTIONS: {[A]}→{[B]±Eₙ} = C = Eₙ + {[A] ± [B]}, → Eₙ = Eᵢ + E???? ↔

[[A]] = [Atom OR Compound] = The Signalling.(Wc) → The Initial Carrier - Wave,

[[B]] = Any[A- OR -C] ≡ Any Signalling.(w) Wave,

[[C]] = The NEW & Modulated [A] Signal = [MAS] = f^(w+wc)/2 + f^(w−wc)/2,

ANTIDOTE = The Demodulated [MAS] = [DMAS] = f^(w+2wc)/2 + f^(w−2wc)/2,

Atoms Action (1).... [A] → {[B]±Eₙ} ≡ [C] ≡ ± Eₙ + {[B] + [A]}, & [A] ≡ [C] + {Xₙ}

Where ↔ [A] = The Initial-State, [C] = The Final-State, and [Xₙ] = {[B] ± [Eₙ]} ≡
The Antidote.

CONDITIONS UNDER WHICH THE NORM OF AN ELEMENTARY OPERATOR OF LENGTH n ˃2 IS EXPRESSIBLE IN TERMS OF THE NORMS OF ITS COEFFICIENT OPERATORS

ESTHER KAWIRA — 2026-07-13

In the current paper we determine the conditions under which the norm of an elementary operator of finite length is expressible in terms of its coefficient operators using Stampfli’s maximal numerical range.

Advancements in fixed point results for ordered metric space via extended F-weak contraction with applications

Yahaya Jibrin Danjuma — 2026-07-20

Abstract In (Ann. Math. Comp. Sc., 20, 82–97, 2024), Raji and Ibrahim introduced a new class of contractions, termed modified α-F-weak contractions, and established fixed point results in complete metric spaces, thereby extending the classical Banach contraction principle. Building on this, the present paper introduces an extended F-weak contraction mapping in ordered metric spaces and derives corresponding fixed-point results. The theoretical contributions are further illustrated through numerical examples. As an application, we demonstrate the existence and uniqueness of solutions to a first-order ordinary differential equation subject to periodic boundary conditions.

Mathematics subject Classification 47H10; 54H25