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2020, Volume 21, Issue 3  


From the editor
5
Boris Beniaminovich Lur'e
S. V. Vostokov
6
To the 75th anniversary of Sergei Vladimirovich Vostokov
I. B. Zhukov
10
To the 80th anniversary of Anatoly Vladimirovich Yakovlev
B. B. Lur'e
15
On the trigonometric sum modulo subdivision of the real axis
A. A. Artemov, V. N. Chubarikov
18
The hearts of weight structures are the weakly idempotent complete categories
M. V. Bondarko, S. V. Vostokov
29
Schnirelmann's integral and analogy of Cauchy integral theorem for two-dimensional local fields
S. V. Vostokov, T. Yu. Shashkov, S. S. Afanas'eva
39
Inaba extension of complete field of characteristic $0$
S. V. Vostokov, I. B. Zhukov, O. Yu. Ivanova
59
On Langlands program, global fields and shtukas
N. M. Glazunov
68
Representing matrices over fields as square-zero matrices and diagonal matrices
P. Danchev
84
The Braun–Kemer–Razmyslov theorem for affine $PI$-algebras
Alexei Kanel Belov, Louis Rowen
89
Mathematical model of a digital control system with background controllers of the Neuman type for complex multicirculated objects
E. V. Larkin, A. N. Privalov, T. A. Akimenko, I. N. Larioshkin
129
Lower estimates of polynomials and linear forms in the values of $F$-series
A. Kh. Munos Vaskes
142
Smooth manifold of one-dimensional lattices
E. N. Smirnova, O. A. Pikhtil'kova, N. N. Dobrovol'skii, I. Yu. Rebrova, N. M. Dobrovol'skii
165
On the asymptotic behavior of some sums involving the number of prime divisors function
M. E. Changa
186
On the mean value of functions related to the divisors function in the ring of polynomials over a finite field
V. V. Iudelevich
196

BRIEF MESSAGE
Approximation of quadratic algebraic lattices by integer lattices — II
A. N. Kormacheva
215
Quality function for the approximation of quadratic algebraic nets — II
A. V. Mikhlyaeva
223
Asymptotic estimation for trigonometric sums of algebraic grids
E. M. Rarova, N. N. Dobrovol'skii, I. Yu. Rebrova
232
Hyperbolic parameter of approximation of quadratic algebraic lattices
A. V. Rodionov
241
Best quadrature formulas calculation of curvilinear integrals for some classes of functions and currves
M. Sh. Shabozov, M. K. Abdukarimzoda
250

HISTORY OF MATH AND APPLICATIONS
Mathematical modeling of elasticity properties in the mechanics of composite materials
I. K. Arkhipov, V. I. Abramova, A. E. Gvozdev, O. V. Kuzovleva
262
Empirical mathematical models of plasticity, strength and wear resistance of materials on the example of P18 steel
A. D. Breki, A. E. Gvozdev, O. V. Kuzovleva, V. Yu. Kuzovlev
272
The development of a mathematical complex for modeling the progress of destruction of composite structures based on hight-speed deformation models
G. M. Zhuravlev, V. G. Telichko, N. S. Kurien, A. E. Gvozdev, O. V. Kuzovleva
292
Legendre spectral element for plastic localization problems at large scale strains
V. A. Levin, K. M. Zingerman, K. Yu. Krapivin, M. Ya. Yakovlev
306

MEMORABLE DATE
The 80th anniversary of professor Vladimir Nikolaevich Bezverkhnii
A. E. Ustyan, I. V. Dobrynina, Yu. E. Trubitsyn, A. S. Ugarov, N. M. Dobrovolsky, I. Yu. Rebrova
317

LETTER TO THE EDITOR
Letter to the Editor
D. V. Gorbachev, I. A. Martyanov
336–338
 
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