Moscow University Mathematics Bulletin
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An estimate for the number of consecutive quadratic residues
Moscow University Mathematics Bulletin - Tập 64 - Trang 24-28 - 2009
The problem of estimation of the maximal number H of consecutive integer numbers such that they all are either quadratic residues or quadratic nonresidues modulo a prime number p is considered.
Liouville classification of integrable geodesic flows on a torus of revolution in a potential field
Moscow University Mathematics Bulletin - Tập 72 - Trang 121-128 - 2017
A Liouville classification of integrable Hamiltonian systems being geodesic flows on a twodimensional torus of revolution in an invariant potential field is obtained in the case of linear integral. This classification is obtained using the Fomenko–Zieschang invariant (so called marked molecules) of the systems under consideration. All types of bifurcation curves are described. A classification of ......
The Hamilton nil-glamour of an affine algebraic plane
Moscow University Mathematics Bulletin - Tập 65 - Trang 51-54 - 2010
Properties of finite nil-indexed polynomial vector fields on an affine plane are studied.
Summation of the euler function values over numbers of the form p − 1
Moscow University Mathematics Bulletin - Tập 64 - Trang 41-43 - 2009
An asymptotic formula is proved for the sum of values of the Euler function on numbers of the form p − 1 not exceeding x. The order of the remainder of the asymptotics corresponds to the modern bound for zeros of the zeta function.
Homogenization of variational inequalities for a biharmonic operator with constraints on subsets ε-periodically placed along a manifold of large dimension
Moscow University Mathematics Bulletin - Tập 62 - Trang 192-203 - 2007
Behavior of solutions of variational inequalities for a biharmonic operator is studied. These inequalities correspond to one-sided constraints on subsets of a domain Ω placed ε-periodically. All possible behavior types of solutions u
ε
of variational inequalities are considered for ε → 0 depending on relations between small parameters, which are the structure pe......
Square exponent of irrationality of ln2
Moscow University Mathematics Bulletin - Tập 67 - Trang 23-28 - 2012
A new proof of the theorem on the non-quadraticity measure ln 2 is given in the paper.
The Method of Searching for Zeros of Functionals on a Conic Metric Space and its Stability Issues
Moscow University Mathematics Bulletin - Tập 75 - Trang 58-64 - 2020
A method of searching for zeros of cone functionals is proposed and issues of its stability are considered.
Linear mappings preserving coincidence of factorized and boundary ranks of matrices over semirings
Moscow University Mathematics Bulletin - Tập 63 - Trang 270-272 - 2009
A problem of characterization of linear bijective mappings preserving coincidence of factorized and boundary ranks over a semiring is considered. A complete classification of those mappings over antinegative commutative rings with a unit and without divisors of zero is obtained.
Absolute L-Realizability and Intuitionistic Logic
Moscow University Mathematics Bulletin - Tập 74 - Trang 79-82 - 2019
An absolute L-realizability of predicate formulas is introduced for all countable extensions L of the language of arithmetic. It is proved that the intuitionistic logic is not sound with this semantics.
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