On the Fay identity for KdV tau functions and the identity for the Wronskian of squared solutions of Sturm-Liouville equation

We show that the well known identity for the Wronskian of squared solutions of a Sturm-Liouville equation follows from the Fay identity. We also study some odd-order (($2^n -1$)-order, $n = 2, 3, ...$) identities which are specific for tau functions, related to the KdV hierarchy.Comment: Amstex, 13 page

Hadron Generator and Atmospheric Seasonal Variation Influence on Cosmic Ray Ionization computed with CORSIKA Code

Recently an essential progress in development of physical models for cosmic ray induced ionization in the atmosphere is achieved. Basically, the models are full target, i.e. based on Monte Carlo simulation of an electromagnetic-muon-nucleon cascade in the atmosphere. In general, the contribution of proton nuclei in those models is highlighted, i.e. primary cosmic ray $\alpha$-particles and heavy nuclei are neglected or scaled to protons. The development of cosmic ray induced atmospheric cascade is sensitive to the energy and mass of the primary cosmic ray particle. The largest uncertainties in Monte Carlo simulations of a cascade in the Earth atmosphere are due to assumed hadron interaction models, the so-called hadron generators. In the work presented here we compare the ionization yield functions $Y$ for primary cosmic ray nuclei, such as protons, $\alpha$-particles, Oxygen and Iron nuclei, assuming different hadron interaction models. The computations are fulfilled with the CORSIKA 6.9 code using GHEISHA 2002, FLUKA 2011, UrQMD hadron generators for energy below 80 GeV/nucleon and QGSJET II for energy above 80 GeV/nucleon. The observed difference between hadron generators is widely discussed. The influence of different atmospheric parametrizations, namely US standard atmosphere, US standard atmosphere winter and summer profiles on ion production rate is studied. Assuming realistic primary cosmic ray mass composition, the ion production rate is obtained at several rigidity cut-offs - from 1 GV (high latitudes) to 15 GV (equatorial latitudes) using various hadron generators. The computations are compared with experimental data. A conclusion concerning the consistency of the hadron generators is stated.Comment: 24 pages, 11 figures, extended version of paper accpted for publication in JAST

On the Zeros of the Solutions to Nonlinear Hyperbolic Equations with Delays

2002 Mathematics Subject Classification: Primary 35В05; Secondary 35L15We consider the nonlinear hyperbolic equation with delays uxy + λuxy(x - σ, у - τ) + c(x, у, u, ux, uy) = f(x, у) . We obtain sufficient conditions for oscillation of the solutions of problems of Goursat in the case, where λ>0.This work was partly supported by Grant MM-437 and Grant MM-516

ON ТНЕ DIAGNOSIS AND TREATMENT OF АСUТЕ PANCREATIТIS

In urgеnt abdominal surgery the acute inflammation of thе pancreas always creates difficulties in the differential diagnosis of the disorder. Treatment аnd prophylaxis which to а lаrgе extent dереnd оn correct аnd рrоmрt diagnosis recently also represent problems of interest. Тhе superior results from the conservative treatment impose to the surgeon higher precision in making the diagnosis of this ailment.During the past two years (1962-1963) in the Suгgical Clinic we had а number of cases of acute pancreatitis. For this period two of  the 15 patients with this diagnosis were admitted with the diagnosis of choelithiatic attack, two - with acute cholecystitis, two - with nephrolitiasis and ninе - with acute pancreatitis.In аll patients the diagnosis is elucidated within the first 24 houгs, and in 6 - even in the out-patient service. Diagnostic errors, in the sense of hyperdiagnosis, аге admitted in two patients (one sufferiпg from acute gastritis and the other with hernia inguinalis incarcerata).

Darboux Transformation and A-operator

Firstly, the fundamental equality of Darboux transformation of the differential operator H(u)=-∂^2+u is proved based on the Kupershmidt-Wilson factorization of the associated ∧-operator ∧(u)=∂^・(2^u'+u∂-4^∂^3). Secondly, elementary algebraic properties of the Darboux transformation are studied with the aid of ∧-operator. Finally, as an application of the fundamental equality of Darboux transformation, solutions of the higher order KdV equation are constructed

The first ground-level enhancement of solar cycle 25 on 28 October 2021

Aims. The first relativistic solar proton event of solar cycle 25 was detected on 28 October 2021 by neutron monitors (NMs) on the ground and particle detectors on board spacecraft in near-Earth space. This is the first ground-level enhancement (GLE) of the current cycle. A detailed reconstruction of the NM response together with the identification of the solar eruption that generated these particles is investigated based on in situ and remote-sensing measurements. Methods. In situ proton observations from a few MeV to similar to 500 MeV were combined with the detection of a solar flare in soft X-rays, a coronal mass ejection, radio bursts, and extreme ultraviolet (EUV) observations to identify the solar origin of the GLE. Timing analysis was performed, and a relation to the solar sources was outlined. Results. GLE73 reached a maximum particle rigidity of similar to 2.4 GV and is associated with type III, type II, and type IV radio bursts and an EUV wave. A diversity of time profiles recorded by NMs was observed. This points to the event having an anisotropic nature. The peak flux at E & x2004;>& x2004;10 MeV was only similar to 30 pfu and remained at this level for several days. The release time of >= 1 GV particles was found to be similar to 15:40 UT. GLE73 had a moderately hard rigidity spectrum at very high energies (gamma & x2004;similar to & x2004;5.5). Comparison of GLE73 to previous GLEs with similar solar drivers is performed.</p