Latest preprints

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Hening Huang

Teledyne Technologies (United States), United States

Feb 24, 2025
Research Article

Statistics Reform: Practitioner’s Perspective

It is widely believed that one of the main causes of the replication crisis in scientific research is some of the most commonly used statistical methods, such as null hypothesis significance testing (NHST). This has prompted many scientists to call for statistics reform. As a practitioner in hydraulics and measurement science, the author extensively used statistical methods in environmental engineering and hydrological survey projects. The author strongly concurs with the need for statistics reform. This paper offers a practitioner’s perspective on statistics reform. In the author’s view, some statistical methods are good and should withstand statistics reform, while others are flawed and should be abandoned and removed from textbooks and software packages. This paper focuses on two methods derived from the t-distribution: the two-sample t-test and the t-interval method for calculating measurement uncertainty. We demonstrate why both methods should be abandoned. We recommend using advanced estimation statistics in place of the two-sample t-test and an unbiased estimation method in place of the t-interval method. Two examples are presented to illustrate the recommended approaches.
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HH
Hening Huang

Independent researcher

Feb 13, 2025
Commentary

Why Should P-Values Be Abandoned in Scientific Research?

This paper provides a comprehensive analysis of the two-sample one-tailed z-test and the p-value it generates. We reveal the true p-value and its meaning, demonstrate that the usual p-value (i.e. the p-value we obtain in practice) is merely an estimate of the true p-value, and derive the theoretical distribution and coverage interval of the usual p-value. Our findings highlight the inherent limitations of p-values and support the argument that their use should be abandoned in scientific research.

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ME
Mark Edelman

Yeshiva University, United States

Feb 10, 2025
Research Article

Asymptotically Periodic and Bifurcation Points in Fractional Difference Maps

The first step in investigating fractional difference maps, which do not have periodic points except fixed points, is to find asymptotically periodic points and bifurcation points and draw asymptotic bifurcation diagrams. Recently derived equations that allow calculations of asymptotically periodic and bifurcation points contain coefficients defined as slowly converging infinite sums. In this paper we derive analytic expressions for coefficients of the equations that allow calculations of asymptotically periodic and bifurcation points in fractional difference maps.

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3.40

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Ilse De Boeck et al.

Thomas More University of Applied Sciences, Belgium

Jan 31, 2025
Research Article

Patterns of Squares Around an Arbitrary Triangle

H. Ebisui and J.C.G. Notrott studied patterns of squares around respectively a right and an arbitrary triangle, thus generalizing the Pythagorean theorem. We construct a new pattern of squares around an arbitrary triangle, based on the four (hinged) squares theorem, using simple vector constructions to avoid trigonometric calculations. This gives rise to some known or unknown number sequences, with new applications on a geometric pattern of squares.

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3.71

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P. Díaz et al.

Universidad de Zaragoza, Spain

Jan 30, 2025
Research Article

Cauchy-Type Identities Through Collocation Matrices

We present a broader framework for the Cauchy identity derived from the determinant expansion of collocation matrices. This approach yields an infinite family of identities, where the original Cauchy identity stands as a particular case. To illustrate the versatility and depth of this approach, we provide a range of compelling examples, showcasing the connections and applications of these novel identities.

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4.00

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357

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ME
Miklós Erdélyi-Szabó

Alfréd Rényi Institute of Mathematics, Hungary

Jan 28, 2025
Research Article

Encoding Sequences in Intuitionistic Real Algebra

We show that in the presence of random Kripke’s schema choice sequences can be recursively encoded in intuitionistic real algebra.

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2.50

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372

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Antonio J. Pan-Collantes

Universidad de Cádiz, Spain

Jan 24, 2025
Research Article

First Integrals Without Integrating Factors or Symmetries

A new method to find first integrals of ordinary differential equations (ODEs) is presented. The approach is based on the complete integrability of the Pfaffian system associated with the ODE, and it does not require the use of symmetries or integrating factors. Examples of second-, third-, and fourth-order ODEs are provided to illustrate the method, including cases where classical approaches fail. This work extends the range of tools available for the analysis and solution of ODEs.

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C. C. Hsu et al.

Independent researcher

Dec 24, 2024
Short Communication

Generalized Inverse Preservers of Hadamard Circulant Majorization

Let $T:M_n \to M_n$ preserve Hadamard circulant majorization. In this note, we show that this property is inherited by the three most popular generalized inverses, viz. the Moore-Penrose inverse, the group inverse and the Drazin inverse.

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3.86

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426

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