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Conservation Laws and Particular Solutions for a Keller-Segel Model: 《Advances in Pure Mathematics》2025年第2期107-118,共12页Luyun Chen Jie Lou; This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that...; 关键词：Keller-Segel Model Conservation Laws Mixed Method Exact Solutions

Asymptotic Behaviors of Hankel Determinants Whose Entries Involve Regularly- or Rapidly-Varying Functions. Part II*: 《Advances in Pure Mathematics》2025年第2期119-144,共26页Antonio Granata; Here we complete our work on the asymptotics of Hankel determinants studying the case wherein the entries are “ultrarapidly”-varying functions in the sense that their logarithms are rapidly varying. Moreover, the la...; 关键词：Asymptotic Behaviors of Hankel Determinants Asymptotic Expansions in the Real Domain Regularly- Rapidly- and Exponentially-Varying Functions of Higher Order Algebraic Identities for Hankelians

The SYZ Conjecture through Computational Equivalence: 《Advances in Pure Mathematics》2025年第2期145-181,共37页Logan Nye; We present a proof of the Strominger-Yau-Zaslow (SYZ) conjecture by demonstrating that mirror symmetry fundamentally represents an equivalence of computational structures between Calabi-Yau manifolds. Through developm...; 关键词：Mirror Symmetry Calabi-Yau Manifolds SYZ Conjecture Quantum Complexity Special Lagrangian Fibration

On Algebraic Methods for the Riemann Hypothesis: 《Advances in Pure Mathematics》2025年第1期1-35,共35页Michael Mark Anthony; Properties of the gamma function are examined with implications for the Riemann hypothesis. Some new relations are obtained for the roots of the Zeta function using the properties of the Gamma function, the Bernoulli ...; 关键词：Gamma Function Zeta Function Bernoulli Numbers Robin Inequality Twin Primes PRIMES

Consequences of Invariant Functions for the Riemann Hypothesis: 《Advances in Pure Mathematics》2025年第1期36-72,共37页Michael Mark Anthony; This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specific...; 关键词：LambertW Function Principal Branch Riemann Hypothesis ITERATIONS Robin Inequality Robin Integers INVARIANCE Gauss Gamma Function Li-Function Prime Counting Function Sums of Divisors INVARIANCE PRIMES Twin Primes

Countability of Infinite Paths in the Infinity Tree: Proof of the Continuum Hypothesis in a Non-Cantorian Infinity Theory: 《Advances in Pure Mathematics》2025年第1期73-90,共18页Philip C. Jackson; A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This p...; 关键词：INFINITY Countable UNCOUNTABLE Diagonalization Real Numbers Infinity Tree Continuum Hypothesis Turing Machine Infinite Time Turing Machine Non-Cantorian

Multiplication with the Factor One, a Rare Mathematic Tool for Simplification and Unrevised DIN-ISO-ASTM-14577: 《Advances in Pure Mathematics》2025年第1期91-105,共15页Gerd Kaupp; The search for mechanical properties of materials reached a highly acclaimed level, when indentations could be analysed on the basis of elastic theory for hardness and elastic modulus. The mathematical formulas proved...; 关键词：Instrumental Indentation One-Point Spherical Arithmetic Formulas Reformulation Factor One Twinning Standards Zerodur Undue Fittings Erroneous Standards DIN-ISO-ASTM-14577 Revision Petition Energy-Law-Violation Faked Data

Some Inequalities Involving the Exponential Transform: 《Advances in Pure Mathematics》2024年第12期859-872,共14页Alex Kyriakis Marios Kyriakis; The exponential transform or modified Fourier transform is an integral transform where the Kernel function is Ka(ξ,t)=a−iξt, and a∈] 1,+∞ [. This is a general case of the Fourier transform where the Kernel functio...; 关键词：Modified Fourier Transform INEQUALITIES Riemann Zeta Function Euler-Mascheroni Constant

Completion of the Proof of the Contradiction of Set Theory: 《Advances in Pure Mathematics》2024年第11期807-816,共10页Yury M. Volin; The article is devoted to completing the proof of the inconsistency of set theory. In this article and in the two preceding ones, all steps of the proof are based on generally accepted informal set-theoretic reasoning...; 关键词：Set Theory Inconsistency TREE Strange Tree Through Way Almost through Way ISOMORPHISM Almost Isomorphism Isomorphism Tree Place Plane Superposition (Imposition) of Trees on the Place Plane Disposition of Trees on the Place Plane

Asymptotic Behaviors of Hankelians, Whose Entries Involve Regularly- or Rapidly-Varying Functions, as the Variable Tends to +∞. Part I: 《Advances in Pure Mathematics》2024年第11期817-858,共42页Antonio Granata; The rich literature concerning “asymptotic behavior of Hankel determinants” concerns the behavior, as the order n tends to ∞, of Hankel determinants whose entries are numbers, e.g., with a combinatorial interest or...; 关键词：Asymptotic Behaviors of Hankelians Asymptotic Expansions in the Real Domain Regularly- Rapidly- and Exponentially-Varying Functions of Higher Order

《Advances in Pure Mathematics》