Starting with a given generalized boson algebra U〈q〉(h(1)) known as the bosonized version of the quantum super-Hopf Uq(osp(1|2)) algebra, we employ the Hopf duality arguments to provide the dually conjugate function algebra Fun〈q〉(H(1)). Both the Hopf algebras being finitely generated, we produce a closed form expression of the universal T matrix that caps the duality and generalizes the famili...

Intercellular communication is fundamental in many biological processes involved in cell growth, differentiation, development, and reproduction of living organisms and secretory proteins are among the most important messengers in this network of information. The vast majority of extracellular proteins are exported from cells by the endoplasmic reticulum/Golgi-dependent secretory pathway. Howeve...

We consider a system composed of a two-level system (i.e., a qubit) and a harmonic oscillator in the ultrastrongcoupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. Special emphasis is placed on the possibility of preparing nonclassical states in this system. These nonclassical states include squeezed states, Schrödinger-cat states, and entangled...

We study the exact solutions of the cascade three-level atom interacting with a single mode classical and quantized field with different initial conditions of the atom. For the semiclassical model, it is found that if the atom is initially in the middle level, the time dependent populations of the upper and lower levels are always equal. This dynamical symmetry exhibited by the classical field ...

Crystallization of calcite from differently concentrated calcium chloride solutions by the CO2 gas diffusion technique in the presence of polystyrene sulfonate yields crystal superstructures with unusual morphology. From the typical calcite rhombohedra as a starting situation, the morphology can be systematically varied via rounded edges and truncated triangles to finally concavely bended lens-...

The classical pitchfork of singularity theory is a twice-degenerate bifurcation that typically occurs in dynamical system models exhibiting Z2 symmetry. Nonclassical pitchfork singularities also occur in many non-symmetric systems, where the total bifurcation environment is usually more complex. In this paper threedimensional manifolds of critical points, or limit-point shells, are introduced b...

We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Boussinesq equation, which has the classical Boussinesq equation as an special case. We study the class of functions f(u) for which this equation admit either the classical or the nonclassical method. The reductions obtained are derived. Some new exact solutions can be der...

In the paper, we proposed a new approach to producing the qubits in electron transport in low-dimensional structures such as double quantum wells or double quantum wires (DQW). The qubit could arise as a result of quantum entanglement of two specific states of electrons in DQW structure. These two specific states are the symmetric and antisymmetric (with respect to inversion symmetry) states ar...