This autobiography presents the scientific living of Abraham Ungar and his role in Gyrogroups and Gyrovector spaces.‎

Gyrogroup theory [A.A. Ungar, Thomas precession: its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics, Found. Phys. 27 (1997), pp. 881-951] enables the study of the algebra of Einstein’s addition to be guided by analogies shared with the algebra of vector addition. The capability of gyrogroup theory to capture analogies is demonstrated in this article by...

We report on the very early time search for an optical afterglow from GRB 971227 with the Livermore Optical Transient Imaging System (LOTIS). LOTIS began imaging the ‘Original’ BATSE error box of GRB 971227 ∼ 14 s after the onset of gamma-ray emission. Continuous monitoring of the position throughout the evening yielded a total of 499 images (10 s integration). Analysis of these images revealed...

We report on the very early time search for an optical afterglow from GRB 971227 with the Livermore Optical Transient Imaging System (LOTIS). LOTIS began imaging the ‘Original’ BATSE error box of GRB 971227 approximately 14 s after the onset of gamma-ray emission. Continuous monitoring of the position throughout the evening yielded a total of 499 images (10 s integration). Analysis of these ima...

Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations Utx = f(U,Ut, Ux) for an N -component vector U(t, x) are considered. In each class we find all scalinghomogeneous equations admitting a higher symmetry of least possible scaling weight. Sigma model interpretations of these equations are presented.

In this paper we consider the conformal group of the unit sphere S, the proper Lorentz group Spin(1, n), for the study of spherical continuous wavelet transforms. The parameter space is determined by the factorization of the gyrogroup of the unit ball by an appropriate gyro-subgroup. We study two families of sections that give rise to anisotropic conformal dilation operators for the unit sphere...

we consider the fundamental relation  on a semihypergroup  to interpret the lower and upper approximations as subsets of the fundamental semigroup  and we give some results in this connection. also, we introduce the notion of a bi-hyperideal to study the relationship between approximations and bi-hyperideals.

Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations Utx = f(U,Ut, Ux) for an N -component vector U(t, x) are considered. In each class we find all scalinghomogeneous equations admitting a higher symmetry of least possible scaling weight. Sigma model interpretations of these equations are presented.

We report on the very early time search for an optical afterglow from GRB 971227 with the Livermore Optical Transient Imaging System (LOTIS). LOTIS began imaging the ‘Original’ BATSE error box of GRB 971227 ∼ 14 s after the onset of gamma-ray emission. Continuous monitoring of the position throughout the evening yielded a total of 499 images (10 s integration). Analysis of these images revealed...