Related papers: Crux's Crux's crux
We introduce a family of reconfiguration puzzles arising from ideas in geometry and topology. We present their construction from square-tiled shapes, discuss some of the underlying mathematics and describe how they are naturally associated…
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.
It is shown that a kind of solutions of n-simplex equation can be obtained from representations of braid group. The symmetries in its solution space are also discussed.
An interpolation problem related to the elliptic Painlev\'e equation is formulated and solved. A simple form of the elliptic Painlev\'e equation and the Lax pair are obtained. Explicit determinant formulae of special solutions are also…
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
We investigate the complexity of a puzzle that turns out to be NL-complete.
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of…
We show a simple and easily implementable solution to the word problem for virtual braid groups.
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.
New formulas for the construction of Pythagorean triples and generalizations to equations of higher powers. Application of formulas to some problems, in particular Fermat's equation with n=4.
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.
We present in this paper a result about existence and convexity of solutions to a free boundary problem of Bernoulli type, with non constant gradient boundary constraint depending on the outer unit normal. In particular we prove that, in…
A recent problem [B. Gardas, J. Math. Phys. 52, 042104 (2011)] concerning an antilinear solution of the Riccati equation is solved. We also exemplify that a simplification of the Riccati equation, even under reasonable assumptions, can lead…
A construction is given for the recovery of a disjoint union of strictly convex smooth planar obstacles from travelling-time information. The obstacles are required to be such that no Euclidean line meets more than two of them.
The issue of the cosmological constant is discussed in details and a solution to the problem is suggested.
We make two tiny corrections to our previous paper with the same title, and also obtain, as a bonus, something new.
Taking a new approach towards analyzing the Collatz Problem, or, 3x+1 conjecture. Introducing some new functions, the Collatz-2 and Collatz-3 sequences, as well as deducing results related to Collatz-2 and Collatz-3 sequences.
We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices.
In math.GT/0002110 the author's Theorems 1.1 and 1.2, combined, implied that iterated torus knots are transversally simple. This result is in error and this erratum pin points the error. In "An addendum on iterated torus knots" a more…