Isolated resonances and nonlinear damping

We analyze isolated resonance curves (IRCs) in single-degree-of-freedom systems possessing nonlinear damping. Through the combination of singularity theory and the averaging method, the onset and merging of IRCs, which coincide to isola and simple bifurcation singularities, respectively, can be analytically predicted. Numerical simulations confirm the accuracy of the analytical developments. Another important finding of this paper is that we unveil a geometrical connection between the topology of the damping force and IRCs. Specifically, we demonstrate that extremas and zeros of the damping force correspond to the appearance and merging of IRCs. Considering a damping force possessing several minima and maxima confirms the general validity of the analytical result. It also evidences a very complex scenario for which different IRCs are created, co-exist and then merge together to form a super IRC which eventually merges with the main resonance peak.     

Synthesis and Crystal Structure of New Indium Iodate (K<Subscript>0.6</Subscript>Na<Subscript>0.4</Subscript>Ba)In[IO<Subscript>3</Subscript>]<Subscript>6</Subscript>

Crystals of new indium iodate (K_0.6Na_0.4Ba)In[IO₃]₆ were prepared by the hydrothermal synthesis. The unit-cell parameters are a = 11.3984(3) Å, с = 11.3817(3) Å, sp. gr. R3?. The chemical formula of the compound was derived from the structure determination and refinement with anisotropic displacement parameters to R = 0.0284. In the structure the InO₆ octahedra share vertices with six umbrella-like [IO₃]–groups typical of iodates and form isolated 3?-symmetric charged \(\rm{In[IO_{3}]_6^{3-}}\) clusters. Large Ba, K, and Na cations occupy a common site on a threefold axis due to the isomorphous substitution and compensate the charge of the clusters. The new structure extends the family of the recently discovered alkali-metal and barium iodates containing Ti and Zr atoms in octahedral sites. The iodate K₂Ge[IO₃]₆ containing Ge atoms in the centers of octahedra is the parent compound of this structural family.     

Finite groups with a given number of relative centralizers

We will study all finite groups and their subgroups with at most four relative centralizers.     

Corrigendum to: When is a sum of annihilator ideals an annihilator ideal?

In this corrigendum, we correct the statement and proof of Lemma 3.2, revise the proofs of Lemma 3.3 and Theorem 3.5, retract Proposition 3.10 and correct several typographical errors.     

Σ-Definability in Hereditarily Finite Superstructures and Computable Analysis

We construct a computable real function not Σ-definable in hereditarily finite superstructures over the extensions with decidable theory of the reals.     

Static Charge Susceptibility in the <Emphasis Type="Italic">t-J-V</Emphasis> Model

We describe the static charge susceptibility and correlation function of the charge density in the twodimensional t-J-V model based on the method of equations of motion for the relaxation functions of the Hubbard operators. We obtain the dependence of the susceptibility and correlation function on the hole concentration and temperature. Charge density waves can develop if the intersite Coulomb interaction is sufficiently strong.