Related papers: A Note on a Recent Conjecture in Mathematics Magaz…
In this Note, we provide the comments on the paper [A note on the hit problem for the polynomial algebra in the case of odd primes and its application] which was published in the RACSAM [Rev. Real. Acad. Cienc. Exactas. Fis. Nat. Ser.…
We present a selection of known as well as new variants of the Sensitivity Conjecture and point out some weaker versions that are also open.
We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.
In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
This paper aims to expand and detail the notion of formal semantics of Conjectures by applying a theoretic-model approach. After a short introduction to the concepts and basics of Conjectures, we will start from the notion of Simple…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
We prove a conjecture due to Y. Last on Jacobi matrices.
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.
This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…
In this short note, we will give the key point of the section conjecture of Grothendieck, that is reformulated by monodromy actions. Here, we will also give the result of the section conjecture for algebraic schemes over a number field.
We establish a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of M\"{o}bius and divisor functions. Specifically, we prove that the ratios conjecture and an…
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
This note formally defines the concept of coinductive validity of judgements, and contrasts it with inductive validity. For both notions it shows how a judgement is valid iff it has a formal proof. Finally, it defines and illustrates the…
Analogy has received attention as a form of inductive reasoning in the empirical sciences. However, its role in pure mathematics has received less consideration. This paper provides an account of how an analogy with a more familiar…
It is noted that some results of the author's research papers cited in the comprehensive review paper "The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets" by G. H. Jones et al. (2018) have been factually misrepresented. The…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
Let $p$ be an odd prime. In the paper we collect the author's various conjectures on congruences modulo $p$ or $p^2$, which are concerned with sums of binomial coefficients, Lucas sequences, power residues and special binary quadratic…
A conjecture concerning some pairs of interfering estimates for some integrals is formulated in three equivalent versions. Its importance for the the Paley problem for plurisubharmonic functions and for certain classes of extremal problems…