Related papers: A generalization of Pappus chain theorem

We generalize and prove a result which was first shown by Zippin, and was explicitly formulated by Benyamini.

We generalize a well-known theorem binding the elementary equivalence relation on the level of PAC fields and the isomorphism class of their absolute Galois groups. Our results concern two cases: saturated PAC structures and non-saturated…

Assuming the Generalized Riemann Hypothesis we obtain uniform, effective number-field analogues of Mertens' theorems.

We present a relative form of the Toponogov comparison theorem.

By combining Tur\'an's proof of Fabry's gap theorem with a gap theorem of P. Sz\"usz we obtain a gap theorem which is more general then both these theorems.

The Theorems of Pappus and Desargues are generalized by two special formulas that hold in the three-dimensional vector space over a field.

We generalize Rado's extension theorem to complex spaces.

We analyze a system of linear algebraic equations whose solutions lead to a proof of a generalization of Boole's formula. In particular, our approach provides an elementary and short alternative to Katsuura's proof of this generalization.

We prove a series of Stephan's conjectures concerning Pascal triangle modulo 2 and give a polynomial generalization.

We establish a q-analogue of Wolstenholme's harmonic series congruence.

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

We introduce the discrete hierarchy which naturally generalizes well known discrete KP hierarchy.

We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of an auxiliary Markov chain.

The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.

We propose a simple model which possesses the chain fountain effect.

We prove a generalization of Tur\'{a}n's theorem proposed by Balogh and Lidick\'{y}.

In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.

We introduce a Zariskian analogue of the theory of Huber's adic spaces.

We give an elementary proof to Hasse theorem.

We develop the theory of group graded division ring parallel to the one by P. Cohn for (ungraded) division rings.