Bialgebras with a left antipode but no right antipode were constructed in the early 1980s in [quantum-like Hopf algebras which remain noncommutative when q = 1, Lett. Math. Phys. 61 (2002) 41-50] we tried to construct such a onesided Hopf algebra within the framework of quantum groups, starting with roughly half the defining relations for quantum GL(2). Asking that the left antipode constructed be an algebra antimorphism led to some additional relations, but the result was a new (two-sided) Hopf algebra. Now we start with roughly half the relations for quantum SL(2) but ask that our left antipode constructed reverse order only on irreducible monomials in the generators. The result is a quantum group with a left antipode but no right antipode.

A complete classification is given of all inner actions on the Clifford algebra C(1,3) defined by representations of the quantum group GLq(2, C), qm # 1, which are not reduced to representations of two commuting "q-spinors". As a consequence of this classification it is shown that the space of invariants of every GL,(2, C)-action of this type, which is not an action of SLq(2, C), is generated by 1 and the value of the quantum determinant for the given representation.

were synthesized to act as potential skin drug carriers. A novel multiscale non-linear model, based on an oscillatory mechanism, which includes polymerization, de-polymerization, re-polymerization and cluster dynamics, is shown to fit the kinetics experimental data and it is used to estimate the amount of potentially histotoxic by-products (i.e. residual monomers or very low molecular weight oligomers).

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indicates a series of phase transitions in ice and gives evidence of the important role the kinetics plays in the process of dynamic phase transformations in ice. In order to model multiple phase changes in ice subjected to impulsive loading, thermodynamic equations of state of ices Ih, III, V, and VI and liquid water are used in the pressure range 0-2100 MPa and the temperature range 230-350 K. A kinetic model is presented that makes it possible to describe quantitatively a complex picture of the phase transitions in ice. The results of computer simulations of shock-wave loading of ice are consistent with the available experimental data.

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Starting from the photon self-energy tensor in a magnetized medium, the 3D complete antisymmetric form of the conductivity tensor is found in the static limit of a fermion system C non-invariant under fermion-antifermion exchange. The massless relativistic 2D fermion limit in QED is derived by using the compactification along the dimension parallel to the magnetic field. In the static limit and at zero temperature the main features of quantum Hall effect (QHE) are obtained: the half-integer QHE and the minimum value proportional to e 2 /h for the Hall conductivity . For typical values of graphene the plateaus of the Hall conductivity are also reproduced.2D massless QED Hall half-integer conductivity and graphene 2