Symmetry problems in harmonic analysis are formulated and solved. One of these is equivalent to the refined Schiffer’s conjecture which was recently proved by author. Let $$k=const>0$$ be fixed, $$S^2$$ unit sphere $${\mathbb R}^3$$ , D a connected bounded domain with $$C^2-$$ smooth boundary S, $$j_0(r)$$ spherical Bessel function. The symmetry stated following theorems. Theorem A Assume ...

Background. Low Back Pain (LBP) is a prevalent phenomenon in athletes and asymmetrical loading on the limbs has been proposed as a risk factor related to this disease. Objectives. The purpose of the present study was to compare the asymmetry of loading applied on the legs between men with and without LBP during gait. Methods. A total of 40 participants, comprising 20 men with non-specific LBP...

We describe an extension to the SOFTSUSY program that provides for the calculation of the sparticle spectrum in the Next-to-Minimal Supersymmetric Standard Model (NMSSM), where a chiral superfield that is a singlet of the Standard Model gauge group is added to the Minimal Supersymmetric Standard Model (MSSM) fields. Often, a Z3 symmetry is imposed upon the model. SOFTSUSY can calculate the spec...

In this paper we elaborate on the idea of an emergent spacetime which arises due to the dynamical breaking of diffeomorphism invariance in the early universe. In preparation for an explicit symmetry breaking scenario, we consider nonlinear realizations of the group of analytical diffeomorphisms which provide a unified description of spacetime structures. We find that gravitational fields, such ...

Chiral symmetry breaking in a non-local Nambu-Jona-Lasinio like 4-fermi model, derived from the intersecting brane model of Sakai and Sugimoto in the weak coupling limit, was found to occur only above a critical value of the coupling. Numerical investigations showed, contrary to what had been suggested in the literature, that this feature persists even when the radius of the circle on which the...

We study the problem of joint estimation and control for a small example for which we can numerically compute the exact solution. We demonstrate, that optimal exploration is achieved through symmetry breaking in the Bellman equation; that optimal actions can be discontinuous in the beliefs; and that the optimal value function is typically non-differentiable. This could pose a challenge for the ...