Abstract:
We study the lower bound for the Bergman kernel in terms of volume of sublevel sets of the pluricomplex Green function. We show that it implies a bound in terms of volume of the Azukawa indicatrix which can be treated as a multidimensional version of the Suita conjecture. We also prove that the corresponding upper bound holds for convex domains and discuss it in bigger detail on some convex complex ellipsoids.

Abstract:
It has been recently shown that for a convex domain $\Omega$ in $\mathbb C^n$ and $w\in\Omega$ the function $F_\Omega(w):=\big(K_\Omega(w)\lambda(I_\Omega(w))\big)^{1/n}$, where $K_\Omega$ is the Bergman kernel on the diagonal and $I_\Omega(w)$ the Kobayashi indicatrix, satisfies $1\leq F_\Omega\leq 4$. While the lower bound is optimal, not much more is known about the upper bound. In general it is quite difficult to compute $F_\Omega$ even numerically and the highest value of it obtained so far is $1.010182\dots$ In this paper we present precise, although rather complicated formulas for the ellipsoids $\Omega=\{|z_1|^{2m}+|z_2|^2<1\}$ (with $m\geq 1/2$) and all $w$, as well as for $\Omega=\{|z_1|+|z_2|<1\}$ and $w$ on the diagonal. The Bergman kernel for those ellipsoids had been known, the main point is to compute the volume of the Kobayashi indicatrix. It turns out that in the second case the function $\lambda(I_\Omega(w))$ is not $C^{3,1}$.

Abstract:
Purpose: The paper discusses two new technologies for producing magnetic materials which have been successfully developed in recent years at the Institute of Physics of the Czestochowa University of Technology and discusses properties of the materials obtained with the use of these methods.Design/methodology/approach: In this research the arc-plasma deposition of Nd2Fe14B powders onto a substrate either cooled with water or heated up to a temperature in the range from 773 to1023 K was applied. In the second method the suction of an arc-melted alloy to a water-cooled copper mould (the suction-casting method) was introduced. Moreover, microstructure, magnetic properties and domain structure of the produced samples were determined.Findings: It has been found that thin Nd2Fe14B strips obtained by the plasma method possess magnetic properties. It has also been demonstrated that the suction-casting method makes it possible to obtain both amorphous magnetically soft materials (e.g. Fe-Co-W-Zr-B), as well as magnetically hard nanocomposites (e.g. (Fe-Co)-(Pr-Dy)-B-Zr).Research limitations/implications: The main problem in the suction-casting method is to reduce the critical cooling rate required for the production of amorphous alloys and to increase the geometrical dimensions of amorphous specimens.Practical implications: Thin-layered Nd-Fe-B magnets produced by means of arc-plasma deposition can be applied directly onto the surface of electromagnetic equipment parts. Magnets with isotropic magnetic properties were obtained by applying layers onto the water-cooled copper substrate. Whereas, anisotropic magnets were obtained as a result of the arc-plasma deposition of powders onto the copper substrate heated up to 873 K. The most advantageous properties were achieved for the microcrystalline structure of a grain size close to the single-domain particle size (approx. 0.3 μm). Moreover, it has been demonstrated that the suction-casting method makes it possible to obtain bulk amorphous alloys of considerable sizes, such as rods of magnetically soft Fe-Co-W-Zr-B alloys of a diameter up to 2 mm, as well as Fe-Co-Pr-Zr-B tubes of a diameter up to 3 mm. It is also possible to produce magnetically hard nanocomposite materials of the (Fe-Co)-(Pr,Dy)-B-Zr type by annealing of metallic glasses.Originality/value: Successfully introduced new methods of magnetic materials manufacturing.

Abstract:
The T2K experiment is a long baseline neutrino oscillation experiment aiming to observe the appearance of {\nu} e in a {\nu}{\mu} beam. The {\nu}{\mu} beam is produced at the Japan Proton Accelerator Research Complex (J-PARC), observed with the 295 km distant Super- Kamiokande Detector and monitored by a suite of near detectors at 280m from the proton target. The near detectors include a magnetized off-axis detector (ND280) which measures the un-oscillated neutrino flux and neutrino cross sections. The present paper describes the outermost component of ND280 which is a side muon range detector (SMRD) composed of scintillation counters with embedded wavelength shifting fibers and Multi-Pixel Photon Counter read-out. The components, performance and response of the SMRD are presented.

Abstract:
Purpose: The paper presents influence of high-energy mechanical milling process, isothermal annealing and toa combination of these two technologies of cobalt base metallic glasses Co77Si11.5B11.5 on magnetic propertiesand their structure.Design/methodology/approach: The powder test piece obtained from the input amorphous ribbon in highenergyball milling. The diffraction examinations and examinations of thin foils were made on the JEOL JEM200CX transmission electron microscope. Observations of the structure of powders were made on the OptonDSM-940 scanning electron microscope. The X-ray tests were realized with the use of the XRD 7 SEIFERTFPMdiffractometer.Findings: analysis of the magnetic properties test results of the of the Co77Si11.5B11.5 powders obtained inthe high-energy ball of milling process proved that the process causes significant decrease in the magneticproperties. The structure and magnetic properties of this material may be improved by means of a proper choiceof parameters of this process as well as the final thermal treatment.Research limitations/implications: For the powders, further magnetical, structure and composition examinationsare planed.Practical implications: The amorphous and nanocrystalline metal powders obtained by high-energy ballmilling of metallic glasses feature an alternative to solid alloys and make it possible to obtain the ferromagneticnanocomposites, whose shape and dimensions can be freely formed.Originality/value: The paper presents influence of parameters of the high-energy ball milling process onstructure and magnetic properties of soft magnetic powder materials obtained in this technique. Results and adiscussion of the influence of high energy mechanical milling process on particle size and their distribution aswell as structure and magnetic properties of investigated samples is presented.

Abstract:
Description of a nuclear system in its ground state and at low excitations based on the equation of state (EoS) around normal density is presented. In the expansion of the EoS around the saturation point additional spin polarization terms are taken into account. A correction for the surface effects is introduced for atomic nuclei. The ground state configurations for the N=Z even-even nuclei, obtained with the proposed EoS, exhibit a clear cluster structure. At the nuclear surface these clusters can be identified as alpha particles. Taking into account an additional interaction between clusters the binding energies and sizes of the considered nuclei are very accurately described. The limits of the EoS parameters are established from the properties of the $\alpha$, $^{3}He$ and $t$ particles.

Abstract:
Microstructure and phase constitution of the LaFe11.0Co0.8Si1.2 bulk and ribbon samples in as-cast state and after annealing, were studied. For both samples in as-cast state the dominant dendritic α-Fe phase was formed. Annealing of the samples resulted in homogenization of the microstructure and change of the phase constitution. The heat treatment resulted in development of almost single-phase of the NaZn13-type structure identified as LaFe11.0Co0.8Si1.2 with minor fraction of the α-Fe. The evolution of microstructure and phase constitution was verified by EDX analysis and M ssbauer spectroscopy.

Abstract:
Purpose: The paper presents the results of the microstructural and magnetic examinations of Nd-Fe-B type magnets produced by the mechanical powder milling method and doped with tungsten.Design/methodology/approach: The effect of the grain size and addition of tungsten on the microstructure and magnetic properties of nanocrystalline alloys of the basic composition of Nd10Fe84B6, as produced by the method of mechanical alloying in the process of prolonged milling, was investigated in the study. Powders were subjected to milling for a duration ranging from 10 to 120 hours in an Ar protective atmosphere. Moreover tungsten was added to the base alloy that exhibited the best magnetic parameters. The tungsten content of alloys varied in a broad range from 0 to 33 at%.Findings: The examinations have shown that the grinding duration, for which the best magnetic properties are obtained, is 90 hours. Prolonged grinding has a significant effect on the grain size and microstructure refinement. The alloy addition in the form of tungsten, similarly as in the case of prolonged grinding, leads to a structure refinement. In the case of W addition, an increase in the coercive field, with a simultaneous decrease in the value of remanence and magnetic energy density (BH)max, is observed.Practical implications: Development of relatively cheap Nd10Fe56W28B6 magnets of good service properties.Originality/value: Determination of the effect of grain size and tungsten content on the magnetic properties and microstructure of the Nd-Fe-B magnets.

Abstract:
We present an elementary proof that the Schur polynomial corresponding to an increasing sequence of exponents (c_0,..., c_{n-1}) with c_0 = 0 is irreducible over every field of characteristic p whenever the numbers d_i = c_{i+1} - c_i are all greater than 1, not divisible by p, and satisfy gcd(d_i, d_{i+1}) = 1 for every i.

Abstract:
We obtain a description of the dynamics of ultracold Bose gases that includes both classical and quantum fluctuations and is applicable at temperatures too high for a Bogoliubov description, e.g. quasicondensates. Such calculations have been elusive in the past because existing methods for higher temperature gases such as the Stochastic Gross-Pitaevskii (SGPE) method omit quantum field effects like pairing and quantum depletion. To overcome this, we developed a hybrid description that combines the thermal fluctuations of the SGPE with the quantum effects of the positive-P representation. As a demonstration, we track the appearance and stabilization of quantum fluctuation effects after turning on the hybrid description in trapped quasicondensates with pre-existing thermal excitations. We observe counter-propagating atom pairs, additional loss of the coherence like in a quantum quench, antibunching, as well as density correlation waves.