Current Issue : July-September Volume : 2025 Issue Number : 3 Articles : 5 Articles
It is common sense to assume, under the influence of modified Hooke law, that a spring-mass system should oscillate. A systematic numeric analysis proves otherwise. We have proven that the mentioned modified force subject to k xn for even n integers fails to produce oscillations. In contrast, the same format for odd n integers is conducive to harmonic oscillations. For the latter case, the impact of the chosen odd n values on the oscillation periods is mathematically identified. For selected cases, the corresponding oscillations are graphed. The analysis is based on applying a Computer Algebra System (CAS), Mathematica [1]-[3]....
As an appendix of [Gao et al . Sharp isolated toughness bound for fractional (k,m) -deleted graphs, Acta Mathematicae Applicatae Sinica, English Series, 2025, 41(1): 252-269], the detailed proof of Theorem 4.1 in this work is presented....
Let X ⊂ Pn, where 3 ≤ n ≤ 5, be an irreducible hypersurface of degree d ≥ 2. Fix an integer t ≥ 3. If n = 5, assume t ≥ 4 and (t, d) ̸= (4, 2). Using the Differential Horace Lemma, we prove that OX(t) is not secant defective. For a fixed X, our proof uses induction on the integer t. The key points of our method are that for a fixed X, we only need the case of general linear hyperplane sections of X in lower-dimension projective spaces and that we do not use induction on d, allowing an interested reader to tackle a specific X for n > 5. We discuss (as open questions) possible extensions of some weaker forms of the theorem to the case where n > 5....
In this paper, we focus on the parameter estimations and some related issues of a class of fractional uncertain differential equations. We obtain the parameter estimations of the considered equations by using rectangular and trapezoidal algorithms for numerical approximation of optimal problems. Subsequently, by taking the trapezoidal method as an example, the predicted variable–corrected variable method is used to solve fractionalorder uncertain differential equations, and numerical solutions were demonstrated by using different α-paths. Finally, by using the trapezoidal algorithm, we predicted the closing prices of Tencent Holdings for the entire year of 2023 and compared them with actual historical values, showcasing the applicability and effectiveness of this method in practical applications....
Let S be a numerical semigroup with multiplicity m(S). Then, S is called a second-level numerical semigroup if x + y + z − m(S) ∈ S for every {x, y, z} ⊆ S \ {0}. In this paper, we present some algorithms to compute all the second-level numerical semigroups with multiplicity, genus, and a Frobenius fixed number. For m and r, which are positive integers, such that m < r and gcd(m, r) = 1, we show that there exists the minimal second-level numerical semigroup with multiplicity m containing r. We solve the Frobenius problem for these semigroups and show that they satisfy Wilf’s conjecture....
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