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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v19

A Complete Proof Of The Riemann Hypothesis Based On A New Expression Of $\xi(s)$

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function

Online: 15 August 2022 (11:18:55 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v8

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Sieve of Eratosthenes; Goldbach conjecture; Polignac conjecture; Twin Prime conjecture

Online: 5 August 2022 (03:41:27 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v7

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Sieve of Eratosthenes; Goldbach conjecture; Polignac conjecture; Twin Prime conjecture

Online: 22 July 2022 (03:38:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v6

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Sieve of Eratosthenes; Goldbach conjecture; Polignac conjecture; Twin Prime conjecture

Online: 11 July 2022 (04:28:25 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v5

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Sieve of Eratosthenes; Goldbach’s conjecture; Polignac’s conjecture; Twin Prime conjecture

Online: 30 June 2022 (03:50:17 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0276.v1

Fermat’s Last Theorem Proved in Hilbert Arithmetic. III. The Quantum-Information Unification of Fermat’s Last Theorem and Gleason’s Theorem

Vasil Penchev

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: completeness; Gleason’s theorem; Fermat’s last theorem; Hilbert arithmetic; idempotency and hi-erarchy; Kochen and Specker theorem; nonstandard bijection; Peano arithmetic; quantum information

Online: 21 June 2022 (03:22:50 CEST)

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The previous two parts of the paper (correspondingly, https://philpapers.org/rec/PENFLT-2 and https://philpapers.org/rec/PENFLT-3) demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart.

Preprint ARTICLE | doi:10.20944/preprints202206.0271.v1

Characterization of a Nonlinear Equality Composed of Multiple Products of Matrices and their Generalized Inverses

Yongge Tian

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: generalized inverse; matrix product; matrix equality; set inclusion; rank equality; block matrix

Online: 20 June 2022 (10:53:30 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0207.v1

Special Spirals are Produced by the ROTASE Galactic Spiral Equations with the Sequential Prime Numbers

Hongjun Pan

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: prime numbers; galactic spiral equations; ROTASE model; phyllotaxis; sunflower seed head

Online: 16 May 2022 (11:04:46 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202202.0021.v3

Examination the Abc Conjecture Using Some Functions

Seiji Fujino

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Number theory; Diophantine equation; abc conjecture

Online: 13 May 2022 (04:17:21 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0112.v1

Fermat’s Last Theorem Proved in Hilbert Arithmetic. II. Its Proof in Hilbert Arithmetic by the Kochen-Specker Theorem With or Without Induction

Vasil Penchev

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: arithmetic mechanics; Gleason’s theorem; Fermat’s last theorem (FLT); Hilbert arithmetic; Kochen and Specker’s theorem; Peano arithmetic; quantum information

Online: 9 May 2022 (09:54:41 CEST)

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The paper is a continuation of another paper (https://philpapers.org/rec/PENFLT-2) published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The relevant mathematical structure is Hilbert arithmetic in a wide sense (https://dx.doi.org/10.2139/ssrn.3656179), in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem.

Preprint ARTICLE | doi:10.20944/preprints202112.0074.v2

Deriving Von Koch's Inequality Without Using the Riemann Hypothesis

Seiji Fujino

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Number theory; Von Koch's inequality; Riemann Hypothesis

Online: 6 May 2022 (12:45:00 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202202.0021.v2

Examination the Abc Conjecture Using Some Functions

Seiji Fujino

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Number theory; Diophantine equation; abc conjecture

Online: 6 May 2022 (05:26:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0176.v1

Series of Floor and Ceiling Function—Part II: Infinite Series

Dhairya Shah, Manoj Sahni, Ritu Sahni, Ernesto León-Castro, Maricruz Olazabal-Lugo

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: ceiling function; floor function; Fibonacci Number; Generalised Dirichlet series; Lerch - Zeta Function; Hurwitz - Zeta function; Polylogarithm; Riemann-Zeta function

Online: 19 April 2022 (06:03:59 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0159.v1

A Modified Piecewise Relaxation Method for Singular Initial Value Problems

Olumuyiwa Otegbeye, Shina Oloniiju, Gerald Marewo

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: relaxation; spectral methods; multi-domain

Online: 18 April 2022 (08:28:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v18

A Complete Proof Of The Riemann Hypothesis Based On A New Expression Of $\xi(s)$

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function

Online: 4 April 2022 (10:55:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202203.0025.v6

A Generalization of the Sum of Divisors Function

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: sum of divisors function; superabundant numbers; colossally abundant numbers; Riemann hypothesis

Online: 25 March 2022 (10:05:06 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0025.v5

A Generalization of the Sum of Divisors Function

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: sum of divisors function; superabundant numbers; colossally abundant numbers; Riemann hypothesis

Online: 18 March 2022 (12:11:02 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0025.v4

A Generalization of the Sum of Divisors Function

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: sum of divisors function; superabundant numbers; colossally abundant numbers; Riemann hypothesis

Online: 17 March 2022 (11:57:24 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0183.v1

Fermat’s Last Theorem Proved in Hilbert Arithmetic. I. From the Proof by Induction to the Viewpoint of Hilbert Arithmetic

Vasil Penchev

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Fermat’s last theorem; Hilbert arithmetic; Kochen and Specker’s theorem; Peano arithmetic; quantum information; qubit Hilbert space

Online: 14 March 2022 (10:54:07 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v17

A Complete Proof Of The Riemann Hypothesis Based On A New Expression Of $\xi(s)$

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function

Online: 8 March 2022 (11:00:07 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0025.v3

A Generalization of the Sum of Divisors Function

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: sum of divisors function; superabundant numbers; colossally abundant numbers; Riemann hypothesis

Online: 7 March 2022 (10:53:32 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0025.v2

A Generalization of the Sum of Divisors Function

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: sum of divisors function; superabundant numbers; colossally abundant numbers; Riemann hypothesis

Online: 3 March 2022 (10:14:28 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0025.v1

A Generalization of the Sum of Divisors Function

Darrell Cox, Eldar Sultanow, Sourangshu Ghosh

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: sum of divisors function; superabundant numbers; colossally abundant numbers; Riemann hypothesis

Online: 1 March 2022 (14:43:37 CET)

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Preprint ARTICLE | doi:10.20944/preprints202105.0499.v3

3x + 1 Problem: Iterative Operations Neither Cause Loops nor Diverge to Infinity

Li Jiang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: 3x + 1 problem; Collatz conjecture; Syracuse problem; iteration

Online: 24 February 2022 (08:38:01 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v16

The Riemann Hypothesis Is True If The Zeros Of $\xi(s)$ Have Strict Increasing Imaginary Parts

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function

Online: 17 February 2022 (09:54:43 CET)

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Preprint ARTICLE | doi:10.20944/preprints202005.0331.v3

Multi-Objective Optimization of Periodical Objectives within a Process

Moses Oyaro Okello

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: optimization; multi-objective optimization; decision making; Time

Online: 3 February 2022 (17:30:32 CET)

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Multi-objective optimization (MOO) is an optimization involving minimization or maximization of several objective functions more than the conventional one objective optimization, which is useful in many fields. Many of the current methodologies addresses challenges and solutions that attempt to solve simultaneously several Objectives with multiple constraints subjoined to each. Often MOO are generally subjected to linear inequality, equality and or bounded constraint that prevent all objectives from being optimized at once. This paper reviews some recent articles in area of MOO and presents deep analysis of Random and Uniform Entry-Exit time of objectives. It further break down process into sub-process and then provide some new concepts for solving problems in MOO, which comes due to periodical objectives that do not stay for the entire duration of process lifetime, unlike permanent objectives which are optimized once for the entire process duration. A methodology based on partial optimization that optimizes each objective iteratively and weight convergence method that optimizes sub-group of objectives are given. Furthermore, another method is introduced which involve objective classification, ranking, estimation and prediction where objectives are classified based on their properties, and ranked using a given criteria and in addition estimated for an optimal weight point (pareto optimal point) if it certifies a coveted optimal weight point. Then finally predicted to find how far it deviates from the estimated optimal weight point. A Sample Mathematical Tri-Objectives and Real world Optimization was analyzed using partial method, ranking and classification method, the result showed that an objective can be added or removed without affecting previous or existing optimal solutions. Therefore suitable for handling time governed MOO. Although this paper presents concepts work only, it’s practical application are beyond the scope of this paper, however base on analysis and examples presented, the concept is worthy of igniting further research and application.

Preprint ARTICLE | doi:10.20944/preprints202202.0021.v1

Examination the abc conjecture using some functions.

Seiji Fujino

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Number theory; Diophantine equation; abc conjecture

Online: 1 February 2022 (21:29:47 CET)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v4

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Sieve of Eratosthenes; Goldbach’s conjecture; Polignac’s conjecture; Twin Prime conjecture

Online: 14 January 2022 (14:43:54 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v15

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function

Online: 13 January 2022 (13:21:18 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0429.v1

Sums and Partial Sums of Horadam Sequences: The Sum Formulas of $\sum_{k=0}^{n}x^{k}W_{k}$ and $ \sum_{k=n}^{n+m}x^{k}W_{k}$ via Generating Functions

Yüksel Soykan

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Horadam numbers; Horadam sequence; sum; partial sum; Fibonacci numbers; Lucas numbers

Online: 27 December 2021 (13:48:06 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0423.v1

Sums Over Primes II

Rusen Li

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: sums over primes; generalized alternating hyperharmonic numbers; asymptotic formula; numbers with $k$-prime factors

Online: 27 December 2021 (11:10:43 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0249.v4

Distribution of Composite Numbers and Determination of Prime Numbers

Ahmet Furkan Gocgen

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: composite number; composite numbers distribution; composite numbers generation; prime number

Online: 24 December 2021 (07:36:30 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v14

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function

Online: 21 December 2021 (12:30:36 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0249.v3

Distribution of Composite Numbers and Determination of Prime Numbers

Ahmet Furkan Gocgen

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: composite number; composite numbers distribution; composite numbers generation; prime number

Online: 20 December 2021 (11:53:57 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0272.v1

Solving the Quintic: A New Approach to Bring's Transformation

Jorge Franco

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Solution of the Quintic by Radicals; Solution of the Sextic by Radicals; Solution of the De Moivre Equation of any degree by Radicals; Eliminating Four Terms at once from the Septic.

Online: 16 December 2021 (12:26:29 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0249.v2

Distribution of Composite Numbers and Determination of Prime Numbers

Ahmet Furkan Gocgen

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: composite number; composite numbers distribution; composite numbers generation; prime number

Online: 16 December 2021 (10:52:02 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0249.v1

Distribution of Composite Numbers and Determination of Prime Numbers

Ahmet Furkan Gocgen

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: composite number; composite numbers distribution; composite numbers generation; prime number

Online: 15 December 2021 (08:35:38 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v13

A Proof of the Riemann Hypothesis Based on A New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function

Online: 9 December 2021 (10:23:43 CET)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v3

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Sieve of Eratosthenes; Goldbach’s conjecture; Polignac’s conjecture; Twin Prime conjecture

Online: 7 December 2021 (20:52:47 CET)

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Preprint ARTICLE | doi:10.20944/preprints202102.0260.v3

SimulaD: A Novel Feature Selection Heuristics for Discrete Data

Mohammad Reza Besharati, Mohammad Izadi

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Feature Selection; Discrete Data; Heuristics; Running average

Online: 7 December 2021 (11:28:35 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0079.v1

Is Complex Number Theory Free From Contradiction?

Han Geurdes

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Basic complex number theory; Euler’s identity; contradiction

Online: 6 December 2021 (15:02:06 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0074.v1

Deriving Von Koch's inequality without using the Riemann Hypothesis.

Seiji Fujino

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Number theory; Von Koch's inequality; Riemann Hypothesis

Online: 6 December 2021 (12:57:54 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0522.v1

Some Examples of Nonassociative Coalgebras and Supercoalgebras

Daniyar Kozybaev, Ualbai Umirbaev, Viktor Zhelyabin

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: coalgebra; coderivation; differential algebra; Novikov algebra; Lie algebra; Jordan superalgebra; right-alternative algebra

Online: 29 November 2021 (11:35:43 CET)

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Preprint ARTICLE | doi:10.20944/preprints202104.0207.v4

Exponentials and Logarithms Properties in an Extended Complex Number Field

Daniel Tischhauser

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Complex number field; Complex exponentiation; Complex logarithm; Exponential and logarithm identities

Online: 29 November 2021 (11:11:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v12

A Proof of the Riemann Hypothesis Based on A New Expression of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function

Online: 26 November 2021 (10:15:27 CET)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v2

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Sieve of Eratosthenes; Goldbach’s conjecture; Polignac’s conjecture; Twin Prime conjecture

Online: 25 November 2021 (20:28:09 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0487.v1

Solving the Quintic: A New Approach to Bring's Transformation

Jorge Franco

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Solution of the Quintic by Radicals; Solution of the Sextic by Radicals; Solution of the De Moivre Equation of any degree by Radicals; Eliminating Four Terms at once from the Septic.

Online: 25 November 2021 (16:11:44 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0404.v1

Solution of the Quintic and Sextic by Radicals

Jorge A. Franco

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Solution of the Quintic by Radicals; Solution of the Sextic by Radicals; Solution of the De Moivre Equation of any degree by Radicals; Eliminating Four Terms at once from the Septic.

Online: 22 November 2021 (14:19:24 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v11

A Proof of the Riemann Hypothesis Based on MacLaurin Expansion and Hadamard Product of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function

Online: 12 November 2021 (14:54:48 CET)

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Preprint REVIEW | doi:10.20944/preprints202107.0028.v2

Depression Diagnosis by Deep Learning Using EEG Signals: A Systematic Review

Atefeh Safayari, Hamidreza Bolhasani

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Deep Learning; Depression; Electroencephalogram; EEG; Depressive Disorders; Systematic Literature Review

Online: 10 November 2021 (15:29:25 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0135.v1

Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves

Manuel Baptista Branco, Isabel Colaço, Ignacio Ojeda

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Binomial ideal; semigroup ideal; minimal systems of generators; determinantal ideal; Gröbner basis; Indispensability

Online: 8 November 2021 (12:37:42 CET)

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Preprint ARTICLE | doi:10.20944/preprints202105.0499.v2

3x + 1 Problem: Iterative Operations Neither Cause Loops nor Diverge to Infinity

Li Jiang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: 3x + 1 problem; Collatz conjecture; Syracuse problem; iteration

Online: 3 November 2021 (19:57:42 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v10

A Proof of the Riemann Hypothesis Based on MacLaurin Expansion and Hadamard Product of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function $\xi(s)$

Online: 25 October 2021 (13:31:43 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0480.v4

When the Riemann Hypothesis Might Be False

Frank Vega

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann hypothesis; Robin inequality; sum-of-divisors function; prime numbers

Online: 15 October 2021 (11:14:58 CEST)

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Preprint SHORT NOTE | doi:10.20944/preprints202002.0379.v9

Another Criterion For The Riemann Hypothesis

Frank Vega

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann hypothesis; Nicolas theorem; prime numbers; Chebyshev function

Online: 14 October 2021 (14:15:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v9

A Proof of the Riemann Hypothesis Based on MacLaurin Expansion and Hadamard Product of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function $\xi(s)$

Online: 14 October 2021 (14:14:19 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0480.v3

Disproof of the Riemann Hypothesis

Frank Vega

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann hypothesis; Nicolas inequality; Chebyshev function; prime numbers

Online: 12 October 2021 (14:31:46 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0480.v2

Disproof of the Riemann Hypothesis

Frank Vega

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann hypothesis; Robin inequality; sum-of-divisors function; prime numbers

Online: 11 October 2021 (15:38:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0101.v1

On Generalized Padovan Numbers

Yüksel Soykan

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Padavon numbers; Perrin numbers; Padovan-Perrin numbers

Online: 6 October 2021 (10:35:34 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0087.v1

On the Additive and Subtractive Representation of Even Numbers from Primes

Ali Shehu, Jetmira Uka

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Sieve of Eratosthenes; Goldbach’s conjecture; Polignac’s conjecture; Twin Prime conjecture

Online: 5 October 2021 (14:48:18 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v8

A Proof of the Riemann Hypothesis Based on MacLaurin Expansion of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function $\xi(s)$

Online: 5 October 2021 (12:40:07 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0486.v1

On Weakly S-Primary Ideals of Commutative Rings

Ece Yetkin Celikeli, Hani Khashan

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: S--prime ideal; S-primary ideal; weakly S-prime ideal; S-n-ideal; weakly S-n-ideal; weakly S-primary ideal

Online: 29 September 2021 (10:31:20 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0480.v1

The Complete Proof of the Riemann Hypothesis

Frank Vega

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann hypothesis; Robin inequality; sum-of-divisors function; prime numbers

Online: 29 September 2021 (08:30:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v7

A Proof of the Riemann Hypothesis Based on MacLaurin Expansion of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function $\xi(s)$

Online: 27 September 2021 (12:22:55 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v6

A Proof of the Riemann Hypothesis Based on MacLaurin Expansion of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function $\xi(s)$

Online: 22 September 2021 (10:16:56 CEST)

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Working Paper ARTICLE

Higher Regularity, Inverse and Polyadic Semigroups

Steven Duplij

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: regular semigroup; inverse semigroup; polyadic semigroup; idempotent; neutral element

Online: 22 September 2021 (10:06:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202104.0207.v3

Exponentials and Logarithms Properties in an Extended Complex Number Field

Daniel Tischhauser

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Complex number field; Complex exponentiation; Complex logarithm; Exponential and logarithm identities

Online: 20 September 2021 (12:09:28 CEST)

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WATS-SMS: A T5-based French Wikipedia Abstractive Text Summarizer for SMS

Jean Louis Ebongue Kedieng Fendji, Désiré Manuel Taira, Marcellin Atemkeng, Adam Musa Ali

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Text summarization; Fine-tuning; Transformers; SMS; Gateway; French Wikipedia.

Online: 14 September 2021 (10:48:55 CEST)

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Working Paper ARTICLE

Higher Regularity, Inverse and Polyadic Semigroups

Steven Duplij

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: regular semigroup; inverse semigroup; polyadic semigroup; idempotent; neutral element

Online: 9 September 2021 (10:49:30 CEST)

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DASTEX: a New Readability Formula based on Semantic Complexity of Text

Mohammad Reza Besharati, Mohammad Izadi

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Semantic Complexity; Semantics; Text Complexity; Readability Formulae

Online: 6 September 2021 (13:33:34 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0097.v1

Bounds on the Number of Primes in Ramanujan Interval

Jan Feliksiak

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Prime counting function Supremum/Infimum; prime numbers distribution; Ramanujan Interval; Ramanujan primes

Online: 6 September 2021 (13:21:06 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0572.v1

Powers of Elliptic Scator Numbers

Manuel Fernandez-Guasti

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Functions of hypercomplex variables; Algebraic geometry; Scator algebra.

Online: 31 August 2021 (11:51:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v5

A Proof of the Riemann Hypothesis Based on MacLaurin Expansion of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function $\xi(s)$

Online: 30 August 2021 (10:33:44 CEST)

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Working Paper ARTICLE

WATS-SMS: A T5-based French Wikipedia Abstractive Text Summarizer for SMS

Jean Louis Ebongue Kedieng Fendji, Désiré Manuel Taira, Marcellin Atemkeng, Adam Musa Ali

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Text summarization; Fine-tuning; Transformers; SMS; Gateway; French Wikipedia.

Online: 27 August 2021 (12:56:05 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0479.v1

On Graded Weakly S-Prime Ideals

Hicham Saber, Tariq Alraqad, Rashid Abu-Dawwas, Hanan Shtayat, Manar Hamdan

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Graded weakly prime ideals; graded S-prime ideals; graded weakly S-prime ideals.

Online: 25 August 2021 (08:39:01 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v4

A Proof of the Riemann Hypothesis based on MacLaurin Expansion of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function $\xi(s)$

Online: 24 August 2021 (11:48:54 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v3

A Proof of the Riemann Hypothesis based on MacLaurin Expansion of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function $\xi(s)$

Online: 20 August 2021 (11:52:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202107.0428.v2

Euler's Totient Function, the Mangoldt Function, and a Sequence of Mertens Function Values

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Mobius function; Mangoldt function; summatory totient function

Online: 17 August 2021 (08:22:04 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0111.v2

A Bayesian Analysis of the Inversion of the SARS-COV-2 Case Rate in the Countries of the 2020 European Football Championship

Luca Casini, Marco Roccetti

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: SARS-COV-2; Bayesian regression; Changepoint detection; European football championship

Online: 16 August 2021 (10:57:52 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0311.v1

WATS-SMS: A T5-based French Wikipedia Abstractive Text Summarizer for SMS

Jean Louis Ebongue Kedieng Fendji, Désiré Manuel Taira, Marcellin Atemkeng, Adam Musa Ali

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Text summarization; Fine-tuning; Transformers; SMS; Gateway; French Wikipedia.

Online: 16 August 2021 (08:21:23 CEST)

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Working Paper ARTICLE

On Ultra Algebras

Bruno Ferreira

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Ultra algebra; Alternative ultra algebra; Jordan ultra algebra; Lie ultra algebra

Online: 11 August 2021 (08:31:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v2

A Proof of Riemann Hypothesis Based on MacLaurin Expansion of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function $\xi(s)$

Online: 9 August 2021 (12:41:53 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0176.v1

The Properties of the Arithmetic Function as the Consecutive Sum of Digits in Natural Numbers

Ramazanali Maleki Chorei

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: consecutive sum of the digits; algebraic equations; diophantine equations; arithmetic functions

Online: 9 August 2021 (07:52:49 CEST)

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Working Paper ARTICLE

Estimation of Gaussian Noise in Spectra by the Selective Polynomial Fit

Serguei Charonov

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Gaussian noise; variance estimation.

Online: 5 August 2021 (15:24:18 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0146.v1

A Proof of Riemann Hypothesis Based on MacLaurin Expansion of the Completed Zeta Function

Weicun Zhang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Riemann Hypothesis (RH); Proof; Completed zeta function $\xi(s)$

Online: 5 August 2021 (12:21:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202107.0253.v2

Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle

Ruofeng Rao

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Minimax principle; linear approximation theory; ecosystem; steady state solution

Online: 5 August 2021 (11:33:07 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0140.v1

A Comparison of K-Means and Mean Shift Algorithms

Mehak Nigar Shumaila

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: K-Mean, Mean-Shift, Performance, Accuracy

Online: 5 August 2021 (11:00:32 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0111.v1

A Bayesian Analysis of the Inversion of the SARS-COV-2 Case Rate in the Countries of the 2020 European Football Championship

Luca Casini, Marco Roccetti

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: SARS-COV-2; Bayesian regression; Changepoint detection; European football championship

Online: 4 August 2021 (12:58:33 CEST)

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Preprint TECHNICAL NOTE | doi:10.20944/preprints202108.0105.v1

Fundamentals of Physics-Informed Neural Networks Applied to Solve the Reynolds Boundary Value Problem

Andreas Almqvist

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: PINN; Reynolds equation; Machine Learning

Online: 4 August 2021 (09:45:41 CEST)

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Working Paper ARTICLE

Estimation of Gaussian Noise in Spectra by the Selective Polynomial Fit

Charonov Serguei

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Gaussian noise; variance estimation.

Online: 3 August 2021 (16:00:16 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0094.v1

Closing the Performance Gap between Siamese Networks for Dissimilarity Image Classification and Convolutional Neural Networks

Loris Nanni, Giovanni Minchio, Sheryl Brahnam, Davide Sarraggiotto, Alessandra Lumini

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Siamese networks; Ensemble of classifiers; Loss function; Discrete cosine transform

Online: 3 August 2021 (15:49:22 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202108.0093.v1

A New Mathematical Approach to Calculate the Area of a Trapezoid

Sunandan Dey

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Trapezoid; Area; Height; New formula

Online: 3 August 2021 (15:47:45 CEST)

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Gap Reconstruction in Optical Motion Capture Sequences Using Neural Networks

Przemysław Skurowski, Magdalena Pawlyta

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: motion capture; neural networks; reconstruction; gap filling; FFNN; LSTM; BILSTM; GRU

Online: 3 August 2021 (11:52:46 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0072.v1

Qualitative Parameter Analysis for Botrytis cinerea Forecast Modelling Using IoT Sensor Networks

Nenad Gligoric, Tomo Popovic, Dejan Drajic, Spasenija Gajinov, Srdjan Krco

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: IoT; Fungal disease forecast; Botrytis cinerea; Precise agriculture; Decision support

Online: 3 August 2021 (11:20:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0055.v1

On the Operator Method for Solving Linear Integro-Differential Equations with Fractional Conformable Derivatives

Batirkhan kh. Turmetov, Kairat I. Usmanov, Kulzina Zh. Nazarova

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: integro-differential equation; fractional derivatives; fractional conformable derivatives; normalized systems method.

Online: 2 August 2021 (15:46:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0029.v1

θ∗-Weak Contractions and Discontinuity at the Fixed Point With Applications to Matrix and Integral Equations

Atiya Perveen, Waleed Alfaqih, Salvatore Sessa, Mohammad Imdad

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: θ∗-weak contraction; fixed point; discontinuity at the fixed point; property P; matrix equation; integral equations

Online: 2 August 2021 (12:21:49 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0026.v1

Computational Analysis of Haemodynamic Indices in Synthetic Atherosclerotic Coronary Netwroks

Sergey Simakov, Timur Gamilov, Philipp Kopylov, Fuyou Liang

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: 1D haemodynamics, stenosis, systole variations, coronary circulation, tachycardia, boundary conditions, FFR, CFR, iFR.

Online: 2 August 2021 (12:08:24 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0021.v1

A Note on Stokes Approximations to Leray Solutions of the Incompressible Navier-Stokes Equations in Rn

Joyce Cristina Rigelo, Janaina Pires Zingano, Paulo Ricardo Zingano

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Navier-Stokes equations, Stokes flows, Leray solutions, large time behavior

Online: 2 August 2021 (11:47:33 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0011.v1

Transformer-Based Methods for Neural Decoding

Haonan He

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Transformer; spike; neural decoding; CNN; RNN; LSTM; deep learning; information; neuroscience

Online: 2 August 2021 (09:51:43 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202107.0711.v1

Mathematical Modelling from the Instrumentation of Improper Integrals

Enrique Mateus-Nieves, Hernández Montañez Wilfaver

Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Improper integral; Mathematical modelling; Mathematical instrumentation.

Online: 31 July 2021 (14:39:43 CEST)

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