Stationary Nonlinear Schr\"odinger Equation on Simplest Graphs: Boundary conditions and exact solutions

We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs consisting of three bonds. It is shown that the method can be extended for the case of arbitrary number of bonds of star graphs and for other simplest topologies such as tree and loop graphs. The case of repulsive and attractive nonlinearities are treated separately

A multidisciplinary approach to study precipitation kinetics and hardening in an Al-4Cu (wt. %) alloy

A multidisciplinary approach is presented to analyse the precipitation process in a model Al-Cu alloy. Although this topic has been extensively studied in the past, most of the investigations are focussed either on transmission electron microscopy or on thermal analysis of the processes. The information obtained from these techniques cannot, however, provide a coherent picture of all the complex transformations that take place during decomposition of supersaturated solid solution. Thermal analysis, high resolution dilatometry, (high resolution) transmission electron microscopy and density functional calculations are combined to study precipitation kinetics, interfacial energies, and the effect of second phase precipitates on the mechanical strength of the alloy. Data on both the coherent and semi-coherent orientations of the {\theta}"/Al interface are reported for the first time. The combination of the different characterization and modelling techniques provides a detailed picture of the precipitation phenomena that take place during aging and of the different contributions to the strength of the alloy. This strategy can be used to analyse and design more complex alloys

Structure-property relations of metallic materials with multiscale microstructures

Nanostructured metals have higher strength than those of the coarse grained metals but suffer from the extremely limited ductility. Development of the multiscale microstructures can improve the ductility of these high strength materials due to the introduction of a specific range of grain sizes in micro level. The present work relates the multiscale microstructures in metals to their overall structure properties using a fractal theory and the modified mean-field method, where three microstructural parameters are introduced and thus mechanical properties such as strength and ductility are presented as a function of these microstructural parameters. Meanwhile, with the applications of the finite element method, the multiscale unit cell approach is also critically developed and applied with a focus on predicting the related stress-strain relations of the metals with multiscale microstructures. For verification of these proposed theoretical and numerical algorithms, the mechanical properties of the pure copper with three-grain microstructures are investigated and the results from FEA and theoretical solutions have a reasonable agreement

Measurement of air fluorescence light yield induced by an electromagnetic shower

For most of the Ultra High Energy Cosmic Ray (UHECR) experiments and projects (HiRes, AUGER, TA, JEM-EUSO, TUS,...), the detection technique of Extensive Air Showers (EAS) is based, at least, on the measurement of the air fluorescence induced signal. The knowledge of the Fluorescence Light Yield (FLY) is of paramount importance for the UHECR energy reconstruction. The MACFLY experiment was designed to perform such FLY measurements. In this paper we will present the results of dry air FLY induced by 50 GeV electromagnetic showers as a function of shower age and as a function of the pressure. The experiment was performed at CERN using an SPS electron test beam line. It is shown that the FLY is proportional to deposited energy in air (E_d) and that the ratio FLY/E_d and its pressure dependence remain constant independently of shower age and more generally independently of the excitation source used (single electron track or air shower).For most of the Ultra High Energy Cosmic Ray (UHECR) experiments and projects (HiRes, AUGER, TA, JEM-EUSO, TUS,...), the detection technique of Extensive Air Showers (EAS) is based, at least, on the measurement of the air fluorescence induced signal. The knowledge of the Fluorescence Light Yield (FLY) is of paramount importance for the UHECR energy reconstruction. The MACFLY experiment was designed to perform such FLY measurements. In this paper we will present the results of dry air FLY induced by 50 GeV electromagnetic showers as a function of shower age and as a function of the pressure. The experiment was performed at CERN using an SPS electron test beam line. It is shown that the FLY is proportional to deposited energy in air (E_d) and that the ratio FLY/E_d and its pressure dependence remain constant independently of shower age and more generally independently of the excitation source used (single electron track or air shower)

Measurement of air and nitrogen fluorescence light yields induced by electron beam for UHECR experiments

Most of the Ultra High Energy Cosmic Ray (UHECR) experiments and projects (HiRes, AUGER, TA, EUSO, TUS,...) use air fluorescence to detect and measure extensive air showers (EAS). The precise knowledge of the Fluorescence Light Yield (FLY) is of paramount importance for the reconstruction of UHECR. The MACFLY - Measurement of Air Cherenkov and Fluorescence Light Yield - experiment has been designed to perform such FLY measurements. In this paper we will present the results of FLY in the 290-440 nm wavelength range for dry air and pure nitrogen, both excited by electrons with energy of 1.5 MeV, 20 GeV and 50 GeV. The experiment uses a 90Sr radioactive source for low energy measurement and a CERN SPS electron beam for high energy. We find that the FLY is proportional to the deposited energy (E_d) in the gas and we show that the air fluorescence properties remain constant independently of the electron energy. At the reference point: atmospheric dry air at 1013 hPa and 23C, the ratio FLY/E_d=17.6 photon/MeV with a systematic error of 13.2%.Comment: 19 pages, 8 figures. Accepted for publication in Astroparticle Physic

Decomposition process in a FeAuPd alloy nanostructured by severe plastic deformation

The decomposition process mechanisms have been investigated in a Fe50Au25Pd25 (at.%) alloy processed by severe plastic deformation. Phases were characterized by X-ray diffraction and microstructures were observed using transmission electron microscopy. In the coarse grain alloy homogenized and aged at $450 ^{circ}\mathrm{C}$, the bcc \alpha-Fe and fcc AuPd phases nucleate in the fcc supersaturated solid solution and grow by a discontinuous precipitation process resulting in a typical lamellar structure. The grain size of the homogenized FeAuPd alloy was reduced in a range of 50 to 100nm by high pressure torsion. Aging at $450 ^{circ}\mathrm{C}$ this nanostructure leads to the decomposition of the solid solution into an equi-axed microstructure. The grain growth is very limited during aging and the grain size remains under 100nm. The combination of two phases with different crystallographic structures (bcc \alpha-Fe and fcc AuPd) and of the nanoscaled grain size gives rise to a significant hardening of the allo

FREQUENCY AND DEVELOPMENT CAUSES OF GINGIVAL RECESSION IN DIFFERENT AGE GROUPS ON THE EXAMPLE OF YUNUSABAD DISTRICT, TASHKENT

Research objective: to study the frequency and causes of the development of gingival recession in different age groups on the example of Yunusabad district in Tashkent city. Material and methods. The research covered a clinical examination of 645 patients with gingival recession who underwent treatment in the 2nd Pediatric Dental Clinic and in 7th City Hospital located in the Yunusabad district in the period from 2015 to 2019. Patients composed 4 age groups according to WHO recommendations: 15-25 years old, 26-40 years old, 40-64 years old, and over 64 years. Results and conslusion. Prevalence of gingival recession increased at age 15 from 11.8 % to 100% at the age of 64 and over. Morris Stahl’s index varied from 6.7% to 73.8%, the recession intensity made from 1.09 mm to 3.38 mm, the recession index (IR) - from 0.59 to 3.95 points. The most effective methods in diagnostics of gingival recession during dental investigation were Morris Stahl’s index (with the proposed interpretation) and the recession index developed by us. Those allowed to evaluate rapidly both incidence of pathology and its severity, without using special training or special devices. It was established, that at the young age, the incidence of gingival recession is mainly affected by long-term injury in the presence of predisposing physiological characteristics, in older age groups, gingival recession is the result of pathological changes in periodontal tissues and its aging

Direct Search for Charged Higgs Bosons in Decays of Top Quarks

We present a search for charged Higgs bosons in decays of pair-produced top quarks in pbar p collisions at sqrt(s) = 1.8 TeV using 62.2 pb^-1 of data recorded by the D0 detector at the Fermilab Tevatron collider. No evidence is found for signal, and we exclude at 95% confidence most regions of the (M higgs, tan beta) parameter space where the decay t->H b has a branching fraction greater than 0.36 and B(H -> tau nu) is large.Comment: 11 pages, 4 figures, submitted to Phys. Rev. Let