The year 2006 has seen renewed interest in the mathematics of Aryabhata (473c.550), the great mathematician-astronomer of Classical India, for potential applications to cryptography. Rao and Yang [1] recently published an analysis of the Aryabhata algorithms for finding of multiplicative inverse of a group modulo a prime as well as the solution to multiple congruences. The RSA 2006 Conference h...

We prove that every separable and metrizable space admits a metrizable compactification with a remainder that is both path connected and locally path connected. This result answers a question of P. Simon. Connectedness and compactness are two fundamental topological properties. A natural question is whether a given space admits a connected (Hausdorff) compactification. This question has been st...

We investigate cut points of subcontinua of βR \ R. We find, under CH, the topologically smallest type of subset of R that can support such a cut point. On the other hand we answer Question 66 of Hart and van Mill’s Open problems on βω [Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North-Holland, Amsterdam, 1990, pp. 97–125] by showing that it is consistent that all cut points a...

The characterization of chemical compounds based on their molecular graphs is an important task for identifying properties such as toxicity or mutagenicity. We used different groups of topological descriptors using the AMES mutagenicity data. Instead of optimizing the classification performance, the aim of this study is to perform a structural analysis of the underlying set of molecular graphs ...

1.2 Definition (modular reduction). Suppose we divide a and b by m, obtaining integer quotients and remainders, where the remainders are between 0 and m − 1. That is, a = q1m + r1 and b = q2m+ r2, where 0 ≤ r1 ≤ m− 1 and 0 ≤ r2 ≤ m− 1. Then it is not difficult to see that a ≡ b (mod m) if and only if r1 = r2. We will use the notation a mod m (without parentheses) to denote the remainder when a ...

We present the two-loop QCD helicity amplitudes for quark-quark and quark-antiquark scattering. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the ‘t Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization and present the scheme dependence of the results. We ve...

In this paper‎, ‎we mainly investigate how the generalized metrizability properties of the remainders affect the metrizability of rectifiable spaces‎, ‎and how the character of the remainders affects the character‎ ‎and the size of a rectifiable space‎. ‎Some results in [A. V‎. ‎Arhangel'skii and J‎. ‎Van Mill‎, ‎On topological groups with a first-countable remainder‎, ‎Topology Proc. 42 (2013...