Related papers: Proofs of some Conjectures from the OEIS
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
In this exposition-type note we present detailed proofs of certain assertions concerning several algebraic properties of the cone and cylinder algebras. These include a determination of the maximal ideals, the solution of the B\'ezout…
We briefly review superstring theories, highlighting the important concepts, developments, and open problems of the subject.
Open-string theories may be related to suitable models of oriented closed strings. The resulting construction of ``open descendants'' is illustrated in a few simple cases that exhibit some of its key features.
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
Motivated by the convolutive behavior of the counting function for partitions with designated summands in which all parts are odd, we consider coefficient sequences $(a_n)_{n\ge 0}$ of primitive eta-products that satisfy the generic…
Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.
In a recent paper published in the Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87, 5309-5419 (2007), arXiv:0705.1045], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here we…
In this paper we propose a conjecture about integer solutions to any equations, based on Primal algebra specifically this conjecture is a corollary of the Acu\~na Theorem in that article. Also some problems are proposed which, if the…
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
We prove that Ma\~n\'e's conjecture, as stated in {\em Lagrangian flows: the dynamics of globally minimizing orbits}, Bol. Soc. Brasil. Mat. (N.S.) 28 (1997), no. 2, 141--153, contains another conjecture of Ma\~n\'e, stated in {\em Generic…
We prove several extensions of the Erdos-Fuchs theorem.
Explaining predictions from Bayesian networks, for example to physicians, is non-trivial. Various explanation methods for Bayesian network inference have appeared in literature, focusing on different aspects of the underlying reasoning.…
This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
This mostly expository paper records some basic facts about towers of homotopy fiber sequences. We give a proof that a pairing of towers induces a pairing of associated spectral sequences, for towers of spaces and towers of spectra.
We obtain new partial results supporting the spectral set conjecture in dimension 1.
Investigation on open questions about perturbation of Hermitian sequences and their spectral symbols. Results on normal sequences are also furnished.
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
This report argues that, even in the simplest cases, IE is an ontology-driven process. It is not a mere text filtering method based on simple pattern matching and keywords, because the extracted pieces of texts are interpreted with respect…