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In the paper [1], the authors obtain a KAM theorem for nearly integrable hamiltonian systems under the Russmann’s non-degeneracy condition, which is known to be sharpest one for small divisor conditions. However, the Remark 1.3 is wrong because we have ignored the null set − ∗, which may contain zeros of ω of high order such that (1.4) does not hold for all p ∈ . The Remark 1.3 might mislead the readers that the condition (1.5) of Theorem B is equivalent to the Russmann’s non-degeneracy condition. Actually, the Russmann’s non-degeneracy condition is equivalent to the condition (1.4) of Theorem A as proved in [1]. Under the Russmann’s non-degeneracy condition (1.4), as proved in the Remark 3.1 the condition (1.5) holds if we replace n − 1 by a sufficiently large number N depending on h, and then the conclusion of Theorem B remains valid if in the measure estimate n − 1 is replaced by N .

Here we give a result on the postulation (i.e. the 2-normality) of nonlinearly normal embeddings of Abelian varieties. This result improves some of the results proved in a recent paper by Ch. Birkenhake.

Around 1900 some noted mathematicians published works developing geometry from its very beginning. They wanted to supplant approaches, based on Euclid's, which handled some basic concepts awkwardly...

In this note we point out that a simple proof of the lower bound of the sets (b, c), and so also of Ξ(b, c), defined in the previous paper [1] can be obtained as a simple application of a general method. By Example 4.6 from [2], if [0, 1] = E0⊃E1⊃ … are sets each of which is a finite union of disjoint closed intervals such that each interval of Ek−1, contains at least mk intervals of Ek which are separated by gaps of lengths at least ek, and if mk≥2 and ek≥ek+1>0, then the dimension of the intersection of Ek is at least

We note that Theorem 5.4 of the paper ``Characteristic cycles of perverse sheaves and Milnor fibers" (by P. Nang and K. Takeuchi, published online in Math. Zeitschrift, October 15, 2004) holds for "any" non-zero complex number $a$., Comment: 1page

The deadly coronavirus disease 2019 (COVID-19) has recently affected each corner of the world. Many governments of different countries have imposed strict measures in order to reduce the severity of the infection. In this present paper, we will study a mathematical model describing COVID-19 dynamics taking into account the government action and the individuals reaction. To this end, we will suggest a system of seven fractional deferential equations (FDEs) that describe the interaction between the classical susceptible, exposed, infectious, and removed (SEIR) individuals along with the government action and individual reaction involvement. Both human-to-human and zoonotic transmissions are considered in the model. The well-posedness of the FDEs model is established in terms of existence, positivity, and boundedness. The basic reproduction number (BRN) is found via the new generation matrix method. Different numerical simulations were carried out by taking into account real reported data from Wuhan, China. It was shown that the governmental action and the individuals' risk awareness reduce effectively the infection spread. Moreover, it was established that with the fractional derivative, the infection converges more quickly to its steady state.

E. Poletsky [5], [6], [7], has shown that certain disc functionals on domains in C have plurisubharmonic envelopes. Later, for three classes of disc functionals plurisubharmonicity of envelopes on a class of complex manifolds were shown by F. Larusson and R. Sigurdsson [4]. The paper is motivated by results from [4]. Let us consider the following two functionals. Let φ : X → R ∪ {−∞} be an upper semi-continuous function. Define the functional H1 = H 1 by the formula H1(f ) = 1 2π ∫ 2π

In the previous issue of Russian Mathematical Surveys (60:4) the name of one of the authors of the first article, "Lyudmila Vsevolodovna Keldysh", was misspelt: on page 588, line +9, "Charnavskii" "Chernavskii"

In our paper [1], in the proof of Proposition 1, we implicitly assume that the polynomial P is monic, although later we apply this proposition to polynomials which are not monic. The following corrections should be made in the proof of Proposition 1.

n the present note we give an interpolating inequality for Pachpatte's inequality from [1]. A discrete analogouos is also given.