We propose a definition of a “C-Eberlein” algebra, which is a weak form of a C-bialgebra with a sort of “unitary generator”. Our definition is motivated to ensure that commutative examples arise exactly from semigroups of contractions on a Hilbert space, as extensively studied recently by Spronk and Stokke. The terminology arises as the Eberlein algebra, the uniform closure of the Fourier-Stiel...

For certain negative rational numbers κ0, called singular values, and associated with the symmetric group SN on N objects, there exist homogeneous polynomials annihilated by each Dunkl operator when the parameter κ = κ0. It was shown by the author, de Jeu and Opdam (Trans. Amer. Math. Soc. 346 (1994), 237-256) that the singular values are exactly the values − n with 2 ≤ n ≤ N , m = 1, 2, . . . ...

Motivated by black hole physics in N = 2, D = 4 supergravity, we study the geometry of quaternionic-Kähler manifolds M obtained by the c-map construction from projective special Kähler manifolds Ms. Improving on earlier treatments, we compute the Kähler potentials on the twistor space Z and Swann space S in the complex coordinates adapted to the Heisenberg symmetries. The results bear a simple ...

BACKGROUND The heat shock response (HSR) is an ancient and highly conserved program of stress-induced gene expression, aimed at reestablishing protein homeostasis to preserve cellular fitness. Cells that fail to activate or maintain this protective response are hypersensitive to proteotoxic stress. The HSR is mediated by the heat shock transcription factor 1 (HSF1), which binds to conserved hea...

This paper deals with a new analytic type of vectorand Clifford algebra valued automorphic forms in one and two vector variables. For hypercomplex generalizations of the classical modular group and their arithmetic congruence subgroups Eisensteinand Poincaré type series that are annihilated by Dirac operators, and more generally, by iterated Dirac operators on the upper half-space of Rn are dis...

Turbulence control in the two-dimensional complex Ginzburg-Landau equation is investigated. An approach is proposed for the purpose of control. In the presence of a small spiral wave seed initiation, a fully developed turbulence can be completely annihilated by injecting a single periodic signal into a small fixed space area around the spiral wave tip. The control is achieved in a parameter reg...

We study classical solutions of vacuum version of Berkovits’ superstring field theory, focusing on the (super)ghost sector. We first argue that the supersliver state which is annihilated by η0, though it has the correct quantum numbers and solves the equation of motion, is actually non-perturbatively pure-gauge, and hence it fails to describe a D-brane. As a step toward the construction of non-...

We consider a class of stochastic models on a lattice in which particles are created and annihilated with given rates. The class include very distinct models such as the contact process and the stochastic Ising model. We show how to set up stochastic models with the dynamics that conserve the number of particles that are equivalent, in the thermodynamic limit, to the creation-annihilation model...

Physical limits place bounds on the divergent behaviour of dynamical systems. The paper explores this situation, providing an example where generator field-voltage limits capture behaviour, giving rise to a stable, though non-smooth, limit cycle. It is shown that shooting methods can be adapted to solve for such non-smooth switching-induced limit cycles. By continuing branches of switching-indu...