We prove a Bonnet theorem for isometric immersions of submanifolds into the products of an arbitrary number of simply connected real space forms. Then, we prove the existence of associated families of minimal surfaces in such products. Finally, in th...
We prove that finding an $ε$-approximate Nash equilibrium is PPAD-complete for constant $ε$ and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As corollaries, we also prove s...
5 days ago · 14 Proven Fixes to Make Windows 11 Lightning Fast Use these tips to speed up your Windows 11 PC—no matter its age or hardware—while keeping its look and full functionality intact.
We prove a conjecture of Adamaszek generalizing the seating couples problem to the case of $2n$ seats. Concretely, we prove that given a positive integer $n$ and $d_1,\ldots,d_n\in(\mathbb{Z}/2n)^*$ we can partition $\mathbb{Z}/2n$ into $n$ pairs wit...
We expand FLew with a unary connective whose algebraic counterpart is the operation that gives the greatest complemented element below a given argument. We prove that the expanded logic is conservative and has the Finite Model Property. We also prove...
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We prove the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in Winfree's abstract Tile Assembly Model, when restricted to use only n...
A classical theorem of Wielandt states that any two subnormal subgroups of a finite group $G$ generate a subnormal subgroup of $G$. We prove versions of this theorem for regular localities and for fusion systems. Along the way we prove also a purely...
We prove that the asymptotic Assouad-Nagata dimension of a connected Lie group $G$ equipped with a left-invariant Riemannian metric coincides with its topological dimension of $G/C$ where $C$ is a maximal compact subgroup. To prove it we will compute...
To prove means to establish the truth or validity of a statement, theory or concept through sufficient and compelling evidence, logic, factual information, experimental data or demonstration.
Jan 20, 2026 · prove (third-person singular simple present proves, present participle proving, simple past proved, past participle proved or proven) (transitive) To demonstrate that something is true or viable; …
Definition of prove verb in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
Two centuries ago, Sophie Germain began to work on her grand plan to prove the theorem of Fermat, the famous conjecture that $x^n + y^n = z^n$ is impossible for nonzero integral values of $x$, $y$, and $z$, when $n > 2$. At that time, this was an ope...
As the title says, I conducted a querying experiment to prove a point to myself. I figured some people here may be interested in what happened and maybe I can prove the same point to others. This'll...
This paper presents the CRISTAL-iSE project as a framework for the management of provenance information in industry. The project itself is a research collaboration between academia and industry. A key factor in the project is the use of a system know...