The number of boundedly generated semigroups is super-exponential in the cardinality

We show that the asymptotic number of 2-generated semigroups is super-exponential in the cardinality. This answers a question raised by Bailey et al. (Isr J Math 215(1):459–501, 2016).     

On suborbital graphs and related continued fractions

In this paper, we study suborbital graphs for congruence subgroup Γ₀(n) of the modular group Γ to have hyperbolic paths of minimal lengths. It turns out that these graphs give rise to a special continued fraction which is a special case of very famous fraction coming out from Pringsheim’s theorem.     

Conductivity and interfacial behaviour of bis-1,4-dioxapentyl sulfate (IV) and 1,4,7-trioxaoctyl sulfate (IV) based electrolyte for lithium batteries

The electrolytic conductivity and viscosity of lithium perchlorate in bis-1,4-dioxapentyl sulfate (IV) [OS22] and 1,4,7-trioxaoctyl sulfate (IV) [OS32] were determined as a function of salt concentration (0.00005–2 M) and temperature (286–318 K). At 298 K, the highest conductivity (=2.77×10^{–3 –1} cm^–1) was achieved for OS22 based solutions containing 1–2 M LiClO₄. Formation of electrically neutral ion pairs appeared to be the main reason for a continuous decline in the molar conductivity () observed in dilute solutions with increasing salt concentration. Additionally, an increase in the dynamic viscosity () accounted for a decrease in the mobility of charge carriers with increasing length of the oxaalkyl chain in the podand molecules. The temperature dependence of the conductivity and viscosity was found to be of the Arrhenius type for both systems investigated, while the activation energies, E ^# and E ^#, varied in parallel with the degree of interionic aggregation. CVs obtained on a polycrystalline Pt electrode indicated the electrochemical stability of OS22 in the potential range between –0.8 V and 4.7 V versus Li⁺/Li. A linear current density–potential dependence, with the same slope for the anodic and cathodic branches proved the reversibility of lithium electrodeposition and re-dissolution at the Pt/1 M LiClO₄+OS22 interface.     

Properties of long superconducting variable thickness bridges

We have studied the properties of long (lengthL20m) superconducting threads (Pb of Sn) formed by pulse electrical breakdown in monocrystalline silicon. These variable thickness bridges have well defined dc and ac Josephson effects in wide temperature range. Some interesting results on the quasiparticle subharmonic gap structures are also reported.The authors would like to express their thanks to J.Móza and A.Neasová for technical assistance.     

Conductivity studies of aqueous solutions of stereoisomers of tartaric acids and tartrates. Part II: D-, L-, andmeso-tartaric acids

Conductivity measurements on aqueous solutions of D-tartaric acid, L-tartaric acid, andmeso-tartaric acid were performed in the temperature range 278.15–308.15 K. The equivalent limiting conductivity of the bitartrate anion, λ°(HTar^-), is evaluated with regard to the primary and secondary steps of dissociation of the acids in aqueous solutions by use of the Quint and Viallard equation for unsymmetrical electrolytes.     

Jets of nuclear matter in He-A T inelastic collisions at 4.5 A GeV/c

The problem of the nuclear matter jets in nucleus-nucleus collisions at 4.5 A GeV/c is discussed. The global analysis of experimental data, namely the sphericity tensor, is used to evidence such jets. The experimental results are compared with those obtained in the same collisions for hydrodynamic flow and thrust. The experiments have been performed in the frame of the SKM 200 Collaboration from JINR Dubna. Received: 20 March 1997 / Revised version: 20 July 1997     

<Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">K</Emphasis></Subscript> from the lattice with Wilson quarks

We report our results for the bag parameter B _K obtained from the quenched simulations on the lattice with Wilson fermions for three values of the lattice spacing. We implemented the method by which no subtraction of the mixing with other four-fermion operators is needed. Our final result, in terms of the renormalization group invariant bag parameter, is .Received: 9 July 2004, Revised: 27 July 2004, Published online: 21 September 2004     

Cross sections and rate coefficients of transitions in He and He-like ions induced by collisions with heavy particles

An approach to calculating the exitation cross sections and rate coefficients for a wide class of transitions in atoms and ions induced by collisions with heavy charged particles in considered. Calculations were carried out in terms of the Born approximation in the impact parameter representation with the normalization and Coulomb repulsion (in the case of an ionic target). Transitions between levels in He and He-like ions without changes of the principal quantum number are considered for n=2–4. Fitting formulas are suggested for transition rate coefficients. Tables of cross sections and parameters of fitting formulas are given for He and C⁴⁺.