33 papers
This paper presents a novel, computationally efficient integral solution for the mechanical response of a viscoelastic Kelvin-Voigt medium to pulse excitations, offering a simpler alternative to complex inverse Laplace transform methods and enabling straightforward asymptotic analysis.
This paper investigates the asymptotic convergence of partial sums and remainders of the Dirichlet eta function to establish that the continuity of a specific limit ratio within the left half of the critical strip is equivalent to the truth of the Riemann Hypothesis, while also offering insights into the Simple Zeros Conjecture.
Assuming the Riemann hypothesis is false, this paper establishes an asymptotic relation between the residues of a specific series at nontrivial zeros and a continuous function of a rational parameter, offering a new approach to investigating the hypothesis.
This paper explores the geometric structure of the Sieve of Eratosthenes by introducing the concepts of Focals and Extremes to reveal a symmetry in prime distribution and derive a formula for the greatest remainder yielding the same quotient.
This paper claims to prove the union-closed sets conjecture by introducing new concepts of universes, induced communities, and cells to demonstrate that every finite universe contains an element appearing in at least half of the sets within any induced community.
This paper introduces a diagonalization method for functions from natural numbers to real numbers and applies it to prove that the equation has only a finite number of solutions for any fixed natural numbers and .
This paper explores the optimization of unimodular zerofree matrices as a means to find simple and efficient solutions to a matrix equation involving th roots of th powers.
This paper claims to provide an unconditional proof of the Riemann Hypothesis by employing recursive Taylor expansions to analytically continue the zeta function and deriving a contradiction from the assumption of off-critical-line zeros.
This paper presents a systematic bottom-up approach to solving "The Hardest Logic Puzzle Ever" and its generalization, proving that an n-god puzzle is solvable if and only if the number of random gods is less than the number of non-random gods, while also providing an optimized solution for specific variants and an algorithm for finding solutions to the generalized problem.
This paper introduces a micro-agnostic, adaptive geometric framework on cellular spaces where distance is defined by cell-crossing counts, enabling the operational inference of curvature and deformation through unified estimators that bridge discrete measurements to continuum metrics with rigorous stability and convergence guarantees.
This paper investigates the concept of picture fuzzy subgroups by introducing their direct product and establishing several characterizations of this product using -cut sets.
This paper derives a general recursive formula for the Sombor index of multi-level pendant-augmented path trees with nonuniform degree distributions, addressing the lack of closed-form expressions for such complex hierarchical structures.
This paper proposes a likely derivation for Ramanujan's 1927 approximations of an ellipse's perimeter and introduces a new, uniformly more accurate formula based on those insights.