In this paper we show that harmonic compact operator-valued functions are characterized by having harmonic diagonal matrix coefficients in any choice of basis. We also give an example which shows that an operator-valued function with values outside the compact operators can have harmonic diagonal matrix coefficients in any choice of basis without being a harmonic operator-valued function. We us...

Harmonic Maass forms have recently been related to many different topics in number theory: Ramanujan’s mock theta functions, Dyson’s rank generating functions, Borcherds products, and central values and derivatives of quadratic twists of modular L-functions. Motivated by these connections, we obtain exact formulas for the coefficients of harmonic Maass forms of non-positive weight, and we obtai...

Two static-electric-field-induced effects on harmonic generation are demonstrated analytically and numerically: elliptic dichroism (in which the harmonic yield is different for right and left elliptically polarized laser fields) and elliptical polarization of harmonics produced by linearly polarized driving laser fields. Both effects stem from interference of real and imaginary parts of the non...

We analyze the conical second-harmonic generation via Cerenkov-type phase matching in two-dimensional decagonal nonlinear photonic quasi-crystals for linear, circular, and elliptical polarized fundamental beams. Depending on the polarization state, we observe either centrosymmetric or noncentrosymmetric intensity modulation of the second-harmonic rings. We explain this effect by employing the c...

Primarily for aerospace applications, harmonic drives (HD’s) are high-ratio, compact torque transmission systems. This mechanical transmission employs a continuous deflection wave along a non-rigid gear, the socalled ‘flexspline’, to allow gradual engagement of gear teeth. A harmonic drive also contains a wave-generator (a ball-bearing assembly with a rigid elliptical inner-race) and a circular...

This paper presents a significant modification of our previously proposed speech recognizer’s front-end based on perceptual harmonic cepstral coefficients. The spectrum is split into two frequency bands, which correspond to the harmonic and non-harmonic components. A weighting function, which depends both on the voiced/unvoiced/ transitional classification and on the prominence of harmonic stru...

A new dynamic friction model for modeling of elliptical vibration assisted turning (EVAT) was developed in this research. The periodic change of the friction force direction is known to be one of the most important causes of this phenomenon. In modeling of machining processes (including the EVAT process), static Coulomb friction model was employed by most of the researchers. Because of the peri...

Normal spiral galaxies have exponential disks and logarithmic arms (spirals). They must be interrelated and the relation is suggested to be iso-ratio. Assume you come off the disk center by such route that the ratio of the star density on your left side to the one on your right side is constant. The route (iso-ratio curve) turns out to be logarithmic spiral! Such distribution of iso-ratio densi...

A new dynamic friction model for modeling of elliptical vibration assisted turning (EVAT) was developed in this research. The periodic change of the friction force direction is known to be one of the most important causes of this phenomenon. In modeling of machining processes (including the EVAT process), static Coulomb friction model was employed by most of the researchers. Because of the peri...