Conjecture Research Articles

The chronotype conjecture in the association between dietary carbohydrate intake and high-sensitivity C-reactive protein (hs-CRP): a cross-sectional study from NHANES 2015 data.

Substantial evidence suggests that the timing of macronutrient intake affects cardiovascular health. The present study aims to assess the association between the dietary carbohydrate intake (DCI) and the high-sensitivity C-reactive protein (hs-CRP) combined with the implication of the chronotype. Thus, we explored the most recently released National Health and Nutrition Examination Survey (NHANES) data. We analysed data from 5,616 participants of the NHANES in 2015. We selected participants with available data for the DCI, sleep and wake-up time, and the hs-CRP. Chronotypes were categorized according to the sleep times. Binary logistic regression analysis was performed to predict participants with low or high levels of hs-CRP based on the DCI and chronotypes. Moderation analysis was used to investigate the effect of the chronotypes on the DCI-hs-CRP’s association. A higher DCI was significantly associated with the higher hs-CRP levels (odds ratio (OR) = 1.36, 95% confidence interval (CI) = [0.9-1.8]). Moderate evening (ME) chronotypes had higher risk for high hs-CRP level (OR = 1.15, 95% CI = [1.22-1.23]) compared to the intermediate and the morning chronotypes. The chronotype significantly moderated the hs-CRP given the DCI (moderation coefficient, α2=0.05, 95% CI = [0.01-0.08]). The chronotype diminished the hs-CRP predicted by the DCI. The findings of the study underscore the significance of assessing the protective effect of individuals’ chronotype concerning cardiovascular health.

Negative Answer of Hilbert’s Sixth Mathematical Conjecture<br/>—Mathematical Reasoning of Philosophical Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Philosophy (I)

Hilbert (David Hilbert, 1862-1943 a.d) is a well-known German mathematician. He introduced 23 of the most important problem for twentieth century mathematicians to study, this is the famous “Hilbert 23 problems”. Hilbert’s sixth mathematical conjecture has attracted the attention of many mathematicians over the past century. Traditional Chinese Philosophy (TCP) differs from Western philosophy mainly in that TCP contains biological energy called qi or Chi or energy of the system. This biological energy is everywhere. Logically, therefore, no single axiom system is recognized. It is considered that the world is composed of several incompatible axiom systems with the killing relationship and the loving relationship, which form five kinds of states of qi or Chi or energy of the system. Therefore, human understanding of the world cannot proceed from observation and hypothesis, but from the five kinds of the whole, using non-generative logic, using obtaining image from classification or classification taking image technology, through the global to local to consider the killing relationship and the loving relationship, reproducibility results can be obtained. This philosophical thought is the opposite of the philosophical implications of Hilbert’s sixth mathematical conjecture. Therefore, on the basis of explaining eastern philosophy, this paper gives a negative answer to Hilbert’s sixth mathematical conjecture from the perspective of philosophy and mathematics. The main frame in a more direct way of TCP includes the non-authigenic logic as the no Axiom system, the loving analysis as the preconception principle, the killing analysis as the integration coordination combination principle, the killing reproducibility as the logic layering principle and the loving reproducibility as the automation principle.

Between Knowledge and Conjecture: An Emerging Discussion about the Baltic Mounds

Rec.: Manvydas Vitkūnas, Gintautas Zabiela. Baltų piliakalniai: nežinomas paveldas. Vilnius: Lietuvos archeologijos draugija, 2017, 88 p.

Constructing-Evaluating-Refining Mathematical Conjectures and Proofs

This study focused on investigating the ability of 58 pre-service mathematics teachers' (PSMTs) to construct-evaluate-refine mathematical conjectures and proofs. The PSMTs enrolled in a three-credit mathematics course that offered various opportunities for them to engage with mathematical activities including constructing-evaluating-refining proofs in various topics. The PSMTs' proof constructions were coded in three categories as: Type P1, Type P2 and Type P3 in decreasing levels of sophistication (from a mathematical stand point) and the constructions of conjectures were coded in two categories as: Type C1: correct conjectures and Type C2: incorrect conjectures. In addition to classifying the PSMTs' proof and conjecture constructions, how they reacted when they needed to refine conjectures and proofs were also classified. Samples of classroom episodes were provided to exemplify these different proof-conjecture constructions-evaluations-refining processes. The results of the study demonstrated that the combined construction-evaluation-refining activities of conjectures and proofs were not only helpful to better illuminate the PSMTs' understanding of mathematical proofs, but they were also an essential instructional tool to help PSMTs comprehend mathematical ideas and relations.

CUPPING AND JUMP CLASSES IN THE COMPUTABLY ENUMERABLE DEGREES

AbstractWe show that there is a cuppable c.e. degree, all of whose cupping partners are high. In particular, not all cuppable degrees are${\operatorname {\mathrm {low}}}_3$-cuppable, or indeed${\operatorname {\mathrm {low}}}_n$cuppable for anyn, refuting a conjecture by Li. On the other hand, we show that one cannot improve highness to superhighness. We also show that the${\operatorname {\mathrm {low}}}_2$-cuppable degrees coincide with the array computable-cuppable degrees, giving a full understanding of the latter class.

On the Brauer Group of an Arithmetic Model of Strictly Complete Intersection in a HyperkÄhler Variety Over a Number Field

We prove the Artin conjecture asserting the finiteness of the Brauer group of an arithmetic model of a smooth projective variety V over a number field k under the assumptions that V admits a k-embedding V ↪ W to a smooth projective hyperkahler ksubvariety $$ W\to {\mathbb{P}}_k^N $$ such that V = H1 ∩ … ∩ Hr ∩ W in the sense of the theory of schemes for some k-hypersurfaces H1, . . .,Hr in the space $$ {\mathbb{P}}_k^N $$ ; moreover, for any i ≤ r the variety H1 ∩ . . . ∩ Hi ∩ W is smooth, has codimension i in the variety W, and dimkV ≥ 3.

Proof of a q-supercongruence conjectured by Guo and Schlosser

In this paper, we confirm the following conjecture of Guo and Schlosser: for any odd integer $$n>1$$ and $$M=(n+1)/2$$ or $$n-1$$ , $$\begin{aligned} \sum _{k=0}^{M}[4k-1]_{q^2}[4k-1]^2\frac{(q^{-2};q^4)_k^4}{(q^4;q^4)_k^4}q^{4k}\equiv (2q+2q^{-1}-1)[n]_{q^2}^4\pmod {[n]_{q^2}^4\Phi _n(q^2)}, \end{aligned}$$ where $$[n]=[n]_q=(1-q^n)/(1-q),(a;q)_0=1,(a;q)_k=(1-a)(1-aq)\cdots (1-aq^{k-1})$$ for $$k\ge 1$$ and $$\Phi _n(q)$$ denotes the n-th cyclotomic polynomial.

Justin Clarke-Doane* Morality and Mathematics.

This excellent book compares and contrasts morality and mathematics. Their similarities and differences are not what one might naïvely suppose, as the author demonstrates. The book is highly recommended to philosophers interested in both subjects, and to anyone who seeks a global understanding of how morality and mathematics fit into our belief system. In Chapter 1 the reader is introduced to the author’s understanding of two key terms: realism and objectivity. One overarching opinion presented in this book is that these notions are in tension, and here the motivation for this view is put forward. First, a general recipe for a ‘realist’ view of some subject matter F is devised, with candidate ingredients being examined one by one before being either included or rejected. In the end, the author advocates an understanding of ‘F-realism’ as the view that F-sentences should be interpreted at face-value, that they are commonly used to express beliefs and typically have truth values, that some atomic F-sentences (not merely tautologous compounds) are true, and finally that the F-truths hold independently of mind and language. Surprisingly, among the ingredients rejected by Clarke-Doane is objectivity. Though he denies that the term is being used here in a revisionary or technical sense, he also wishes to deny that ‘objectivity’ should be taken to mean the same as either intersubjectivity or mind-independence. Rather, objectivity here just means a kind of anti-pluralism: we can call the answer to a question an objective one just in case that answer is uniquely correct. Now the idea of treating a matter as objective just in cases where there is only ‘one right answer’ seems, at first blush, to accord with common usage. It is only when the author begins to push on this line that it shows itself to be rather more radical. To use his own example: it is not an objective matter whether the parallel postulate holds (as a pure mathematical conjecture), even if robust platonism is true, since it is true in Euclidean space but not in hyperbolic space (or rather, true of Euclidean lines, but not of hyperbolic lines). There is thus not a unique right answer to the question ‘Is the parallel postulate true?’ To go in for an illustrative moral example, error theorists about morality could plausibly be called moral objectivists (though importantly, not realists) in Clarke-Doane’s sense, given that they give one and only one answer — namely, ‘no’ — to any question at all of whether something is right, wrong, good, bad, etc. The idea of separating the notions of realism and objectivity, if cogent, is clearly one with a great deal of potential, ripe for application to more diverse areas of philosophical dispute. In one light, the present monograph might be seen as a proof-of-concept for a more general metaphilosophical project, the broader horizons of which are sketched in the Conclusion.

Supersymmetry, Ricci flat manifolds and the String Landscape

A longstanding question in superstring/M theory is does it predict supersymmetry below the string scale? We formulate and discuss a necessary condition for this to be true; this is the mathematical conjecture that all stable, compact Ricci flat manifolds have special holonomy in dimensions below eleven. Almost equivalent is the proposal that the landscape of all geometric, stable, string/M theory compactifications to Minkowski spacetime (at leading order) are supersymmetric. For simply connected manifolds, we collect together a number of physically relevant mathematical results, emphasising some key outstanding problems and perhaps less well known results. For non-simply connected, non-supersymmetric Ricci flat manifolds we demonstrate that many cases suffer from generalised Witten bubble of nothing instabilities.

Nurturing the Generation and Exploration of Mathematical Conjectures with Preservice Teachers: An Example with a Perimeters Task.

Generating mathematical conjectures is an important mathematical habit of mind for preservice teachers to develop so that they can, in turn, help their students to develop this skill. In this paper we present a classroom episode in which preservice mathematics teachers experience conjecturing in the context of a rich, open-ended task. They also reflect, throughout the task, on how they might nurture the generation and exploration of mathematical conjectures with their own students.

On a conjecture of Gowers and Long

We show that rounding to a delta-net in SO(3) is not close to a group operation, thus confirming a conjecture of Gowers and Long.

Global universality of Macdonald plane partitions

Nous étudions les limites d’échelle de partitions planes tordues (skew) pondérées périodiquement, avec des interactions semi-locales et des conditions au bord générales. Ces interactions correspondent aux fonctions symétriques de Macdonald, qui sont des $(q,t)$-déformations des fonctions de Schur symétriques. Nous montrons que les fonctions de hauteur convergent vers une forme limite déterministe et que les fluctuations globales sont données par le champ libre gaussien $2$-dimensionnel, lorsque $q,t\to 1$ et que la maille du réseau tend vers $0$. En se restreignant au cas sans interactions, ceci confirme la conjecture de Kenyon–Okounkov pour le cas de la mesure $r^{\mathrm{volume}}$ pour des conditions au bord générales. Notre approche utilise des opérateurs aux différences agissant sur les processus de Macdonald.

Conjecturing Ability Dalam Pembelajaran Daring Masa Pandemi Covid-19

Dalam masa pandemi Covid-19 pembelajaran dilakukan secara daring sehingga menghambat dalam mengembangkan kemampuan-kemapuan kognitif matematis, padahal kemampuan ini merupakan penunjang kecakapan siswa dalam mempelajari matematika. Salah satu kemampuan kognitif yang dikembangkan adalah conjecturing ability atau kemampuan memformulasikan konjektur matematis siswa sekolah menengah pertama (SMP). Konjektur adalah alasan kenapa seseorang memiliki suatu keyakinan, sebuah penjelasan mengenai kenapa sebuah keyakinan adalah benar, atau bagaimana seseorang tahu apa yang diketahuinya. Sehingga perlu dilakukan kajian mendalam serta analisis yang terhadap conjecturing ability atau kemampuan konjektur matematis siswa. Dalam penelitian ini melibatkan subjek sebanyak 26 siswa di salah satu sekolah menengah pertama di Kota Serang, pendekatan yang digunakan dalam penelitian ini adalah pendekatan kualitatif. Hasil dari penelitian ini conjecturing ability atau kemampuan konjektur masih tergolong kurang baik pada kategori kemampuan siswa dalam membuat bukti terhadap solusi. Sehingga diberikan perbaikan dari masih kurangnnya conjecturing ability atau kemampuan konjektur matematis siswa.

On some conjectures of Heywood

On some conjectures of Heywood

Automated Conjecturing II: Chomp and Reasoned Game Play

We demonstrate the use of a program that generates conjectures about positions of the combinatorial game Chomp—explanations of why certain moves are bad. These could be used in the design of a Chomp-playing program that gives reasons for its moves. We prove one of these Chomp conjectures—demonstrating that our conjecturing program can produce genuine Chomp knowledge.
 The conjectures are generated by a general purpose conjecturing program that was previously and successfully used to generate mathematical conjectures. Our program is initialized with Chomp invariants and example game boards—the conjectures take the form of invariant-relation statements interpreted to be true for all board positions of a certain kind. The conjectures describe a theory of Chomp positions.
 The program uses limited, natural input and suggests how theories generated on-the-fly might be used in a variety of situations where decisions—based on reasons—are required.

Mathematical Reasoning in Mathematics Learning on Pyramid Volume Concepts

The purpose of this study was to describe the standard process of mathematical reasoning in learning on pyramid volume concepts. The study was a study with descriptive qualitative approach, carried out by peer teaching in the classroom. The subjects of this research were Class B Postgraduate 2018 (S2) students, State University of Malang. The standard process of this activity was to recognize reasoning and verification as a basic aspect in mathematics, to make and investigate mathematical conjecture, to find out how to develop and evaluate mathematical arguments and verification, to find out how to choose and use various types of reasoning and proof methods.

Proof of a conjecture on the nullity of a graph

AbstractLet be a finite undirected graph without loops and multiple edges. The nullity of , written as , is defined to be the multiplicity of 0 as an eigenvalue of its adjacency matrix. The left problem of establishing an upper bound for an arbitrary graph in terms of order and maximum degree was recently solved by Zhou et al. Zhou et al proved that for an arbitrary graph without isolated vertices and with order , with maximum degree , the equality holds if and only if is the disjoint union of some copies of , and they posed a conjecture: If is assumed to be connected, the upper bound of can be improved to , and the upper bound is attained if and only if is a cycle with divisible by 4 or a complete bipartite graph with equal size of chromatic sets. The goal of the present paper is to give a proof confirming the conjecture.

A Mathematical Conjecture from P versus NP

A Mathematical Conjecture from P versus NP

Flows on flow-admissible signed graphs

In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits a nowhere-zero 6-flow. Bouchet himself proved that such signed graphs admit nowhere-zero 216-flows and Zýka further proved that such signed graphs admit nowhere-zero 30-flows. In this paper we show that every flow-admissible signed graph admits a nowhere-zero 11-flow.

Robustness and parameter geography in post-translational modification systems.

Biological systems are acknowledged to be robust to perturbations but a rigorous understanding of this has been elusive. In a mathematical model, perturbations often exert their effect through parameters, so sizes and shapes of parametric regions offer an integrated global estimate of robustness. Here, we explore this "parameter geography" for bistability in post-translational modification (PTM) systems. We use the previously developed "linear framework" for timescale separation to describe the steady-states of a two-site PTM system as the solutions of two polynomial equations in two variables, with eight non-dimensional parameters. Importantly, this approach allows us to accommodate enzyme mechanisms of arbitrary complexity beyond the conventional Michaelis-Menten scheme, which unrealistically forbids product rebinding. We further use the numerical algebraic geometry tools Bertini, Paramotopy, and alphaCertified to statistically assess the solutions to these equations at ∼109 parameter points in total. Subject to sampling limitations, we find no bistability when substrate amount is below a threshold relative to enzyme amounts. As substrate increases, the bistable region acquires 8-dimensional volume which increases in an apparently monotonic and sigmoidal manner towards saturation. The region remains connected but not convex, albeit with a high visibility ratio. Surprisingly, the saturating bistable region occupies a much smaller proportion of the sampling domain under mechanistic assumptions more realistic than the Michaelis-Menten scheme. We find that bistability is compromised by product rebinding and that unrealistic assumptions on enzyme mechanisms have obscured its parametric rarity. The apparent monotonic increase in volume of the bistable region remains perplexing because the region itself does not grow monotonically: parameter points can move back and forth between monostability and bistability. We suggest mathematical conjectures and questions arising from these findings. Advances in theory and software now permit insights into parameter geography to be uncovered by high-dimensional, data-centric analysis.