We present a set of quantum-mechanical Hamiltonians which can be written as the

Supersymmetric (pseudoclassical) mechanics has recently been generalized to fractional supersymmetric mechanics. In such a construction, the action is invariant under fractional supersymmetry transformations, which are the F th roots at time translations ( with F = 1, 2,…). Associated with these symmetries, there are conserved charges with fractional canonical dimension 1+1/F. Using paragrassmann variables satisfying θF=0, we present a fractional-superspace formulation of this construction.

We present a fractional superspace formulation of the centerless parasuper-Virasoro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro algebra generated by the infinitesimal diffeomorphisms of the superline. We work on the fractional superline parametrized by t and θ, with t a real coordinate and θ a paragrassmann variable of order M and canonical dimension 1/F . We further describe a more general structure labelled by M and F with M ≥ F . The case F = 2 corresponds to the parasuper-Virasoro algebra of order M , while the case F = M leads to the fractional super-Virasoro algebra of order F . The ordinary super-Virasoro algebra is recovered at F = M = 2. The connection with q-oscillator algebras is discussed.

Today, several applications require using electrostatic microphones in environments and/or in frequency ranges, which are significantly different from those they were designed for. When low uncertainties on the behavior of acoustic fields, generated or measured by these transducers, are required, the displacement field of the diaphragm of the transducers (which can be highly nonuniform in the highest frequency range) must be characterized with an appropriate accuracy. An analytical approach, which leads to results depending on the location of the holes in the backing electrode (i.e., depending on the azimuthal coordinate) not available until now (regarding the displacement field of the membrane in the highest frequency range, up to 100 kHz), is presented here. The holes and the slit surrounding the electrode are considered as localized sources described by their volume velocity in the propagation equation governing the pressure field in the air gap (not by nonuniform boundary conditions on the surface of the backing electrode as usual). Experimental results, obtained from measurements of the displacement field of the membrane using a laser scanning vibrometer, are presented and compared to the theoretical results.

Demand for calibration at infrasonic frequencies has emerged in response to earth monitoring problems. The primary standard for sound pressure is defined through the reciprocity calibration method specified in the International Electrotechnical Commission (IEC) Standard 61094-2:2009. This method is based on the use of closed couplers and is routinely applied by the National Metrology Institutes for a large frequency range; however, infrasonic frequencies below 2 Hz have not been explored until recently. The acoustic transfer admittance of the coupler, including the heat conduction effects of the fluid, must be modelled precisely to obtain accurate microphone sensitivity. IEC 61094-2:2009 provides two standardised solutions for the correction of heat conduction. However, researchers have noted significant deviations between these corrections at low frequencies in plane wave couplers, indicating that one or both techniques incorrectly calculate the influence of heat conduction. In this paper, the limitations of the standardised formulations at infrasonic frequencies are identified and two alternative solutions are proposed. An experiment is also reported, which highlights the discussed limitations of the standardised formulations for acoustic transfer admittance, while also demonstrating the validity of the proposed alternative formulations at frequencies down to 0.04 Hz.

A class of Hamiltonians with parasupersymmetry of order p is presented and algebraically characterized. Conformal invariant cases are discussed.

Conformal parasupersymmetry of order 2 is exemplified using a one-dimensional quantum mechanical system. Symmetry generators are seen to realize trilinear structure relations. The relevant representations of this novel symmetry algebra are constructed and shown to allow for a complete determination of the energy spectrum and wave functions of the system.

Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the F th power of a conserved charge: H = Q F with F = 2, 3, ... . This construction, called fractional supersymmetric quantum mechanics, was realized in terms of a paragrassmann variable θ of order F , which satisfies θ F = 0. Here, we present an alternative realization of such an algebra in which the internal space of the Hamiltonians is described by a tensor product of two paragrassmann variables of orders F and F − 1 respectively. In particular, we find q-deformed relations (where q are roots of unity) between different conserved charges. *