On L. Fejes Tóth’s “sausage-conjecture”

Letk non-overlapping translates of the unitd-ballB ^d ⊂E ^d be given, letC _k be the convex hull of their centers, letS _k be a segment of length 2(k−1) and letV denote the volume. L. Fejes Tóth's sausage conjecture, says that ford≧5V(S _k +B ^d ) ≦V(C _k +B ^d In the paper partial results are given.     

Optimization of Transducer Location for Novel Non-Intrusive Methodologies of Diagnosis in Diesel Engines

The health monitoring has been studied to ensure integrity of design of engine structure by detection, quantification, and prediction of damages. Early detection of faults may allow the downtime of maintenance to be rescheduled, thus preventing sudden shutdown of machines. In cylinder pressure developed, vibrations and noise emissions data provide a rich source of information about condition of engines. Monitoring of vibrations and noise emissions are novel non-intrusive methodologies for which positioning of various transducers are important issue. The presented work shows applicability of these diagnosis methodologies adopted in case of diesel engines. The effects of changing various fuel injection parameters was analyzed. Scope of using non-intrusive technique has been analyzed by changing locations of microphone. Novelty of this worklies in exploring signal processing methods for various locations around the engine test set up. Various frequency ranges of contributing noise and vibration sources were identified. Time-Frequency analysis showed the onset of various cyclic. Based on the identification of various frequency bands, it is possible to device suitable filters in order to extract more information.     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.     

On the Π-operator in hyperholomorphic function theory

We consider a class of generalizations of the complex one-dimensional II-operator in spaces of quaternion-valued functions depending on four real variables and study some of its basic properties.     

Strongly nonlinear variational inequalities and generalized pseudocontractions

The solvability of a class of generalized strongly nonlinear variational inequality problems on nonempty closed convex sets in Hilbert spaces is presented.     

Vortex penetration depth of κ-(ET)2Cu[N(CN)2]Br

The magnetic field dependence of the in-plane penetration depth λ_|(H) for single crystal κ-(ET)₂Cu[N(CN)₂]Br has been measured at 3, 9.6, and 36 MHz. Over a limited range, λ_| scales with a characteristic field H^*(T) that coincides with a shoulder in the λ_| vs. H curves. Above that field, λ_| increases sharply toward a second inflection point at H^**(T) that coincides with is close to the irreversibility line measured by magnetization. For fields larger than H^** the penetration depth diverges, suggesting that the vortex lattice has melted. The field dependence at one frequency agrees qualitatively with a model of pinned vortices at low fields giving way to flux flow at higher fields. However, the observed frequency dependence deviates significantly from the predictions of this model, suggesting that collective effects play a major role. Our technique also yields a new measurement for the interplane penetration depth λ 300 μm, implying an anisotropy λ/λ_| > 200.     

Evidence for superconductivity in fluorinated La2CuO4 at 35 K: Microwave investigations

In the fluorinated La₂CuO_4−x prepared using a solid state reaction with NH₄HF₂ as a fluorinating agent at 550 K at ambient pressure, superconductivity was detected by microwave and EPR techniques with aT _c of 35 K.     

Influence of radiation-induced clusters on transport properties of silicon

Summary A calculation method for the scattering cross-section σ of charged carriers on radiation-induced cluster defects has been developed using a spherical cluster model with rectangular potential barrier shape, of radius and height of 15 nm and 0.6 eV, respectively. Values of the cluster cross-section around 2·10⁻¹¹ cm² have been obtained for charged carrier energies from 10⁻⁴ eV to over 600 eV. Applying the relaxation-time approximation of the Boltzmann equation, the influence of clusters on silicon transport properties has been observed to be close to the acoustic-phonon one. The dependence of the Hall factor on radiation-induced clusters has been determined numerically for temperatures ranging from 5 K to 400 K. The results indicate that the presence of clusters of such dimensions would not change significantly the Hall coefficientR _H.     

Compact tunable mid-infrared laser source by difference frequency generation of two diode-lasers

Two continuous-wave single mode diode-lasers (Hitachi HL 7851G and Toshiba TOLD 9150) are applied as signal and pump sources for difference frequency generation (DFG) in an AgGaS2 crystal with a length of 30 mm. For 90° type I phase matching tunable mid-infrared laser radiation around 5 µm is obtained with an output power of up toP _DFG = 0.2 µW while the diode lasers are operated with powers of 30 and 50 mW at the center wavelengths 682 and 791 nm, respectively. The performance of the diode-laser-DFG system is shown as the absorption spectrum of CO for the P(28) rotational line around 2023 cm^–1 is probed in a 10cm long cell and in the exhaust of an engine.This research was supported by the Technologiestiftung Schleswig-Holstein under contract 94-35i.     

Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type

In this paper we study hybrid iterative scheme for finding a common element of set of solutions of generalized mixed equilibrium problem, set of common fixed points of finite family of weak relatively nonexpansive mapping and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and generalize the results of several authors which are announced recently. Application of our theorem to solution of equations of Hammerstein-type is of independent interest.