In the problem of (simultaneous) Diophantine approximation in ℝ3 (in the spirit of Hurwitz’s theorem), lower bounds for the critical determinant of the special three-dimensional body K2 : (y2 + z2)(x2 + y2 + z2) ≤ 1 play an important role; see , . This article deals with estimates from below for the critical determinant ∆ (Kc) of more general star bodies Kc : (y2 + z2)c/2(x2 + y2 + z2) ≤ 1 ; where c is any positive constant. These are obtained by inscribing into Kc either a double cone, or an ellipsoid, or a double paraboloid, depending on the size of c.
 W.G. Nowak: The critical determinant of the double paraboloid and Diophantine approximation in R3 and R4. Math. Pannonica 10 (1999) 111-122.
 W.G. Nowak: Diophantine approximation in Rs: On a method of Mordell and Armitage. In: Algebraic number theory and Diophantine analysis. Proceedings of the conference held in Graz, Austria, August 30 to September 5, 1998, W. de Gruyter, Berlin. (2000) 339-349.
 W.G. Nowak: Simultaneous Diophantine approximation: Searching for analogues of Hurwitz's theorem. In: T.M. Rassias and P.M. Pardalos (eds.), Essays in mathematics and its applications. Springer, Switzerland (2016) 181-197.
 W.G. Nowak: On the critical determinants of certain star bodies. Comm. Math. 25 (1) (2017) 5-11.
 K. Ollerenshaw: The critical lattices of a sphere. J. London Math. Soc. 23 (1949) 297-299.
 J.V. Whitworth: The critical lattices of the double cone. Proc. London Math. Soc. 2 (1) (1951) 422-443.
SCImago Journal Rank (SJR) 2017: 0.128 Source Normalized Impact per Paper (SNIP) 2017: 0.476
Mathematical Citation Quotient (MCQ) 2017: 0.43
researchers in the fields of: algebraic structures, calculus of variations, combinatorics, control and optimization, cryptography, differential equations, differential geometry, fuzzy logic and fuzzy set theory, global analysis, mathematical physics and number theory