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卷 216, 编号 6 (2025)
- 年: 2025
- 文章: 7
- URL: https://bakhtiniada.ru/0368-8666/issue/view/20349
Half-duplex communication complexity with adversary can be less than the classical communication complexity
摘要
3-45
On the $L^r$-differentiability of two Lusin classes and a full descriptive characterization of the $HK_r$-integral
摘要
It is proved that any function in a Lusin-type class, the class of $ACG_r$-functions, is differentiable almost everywhere in the sense of a derivative defined in the space $L^r$, $1\leqslant r < \infty$. This leads to a full descriptive characterization of a Henstock–Kurzweil-type integral, the $HK_r$-integral, which serves to recover functions from their $L^r$-derivatives. The class $ACG_r$ is compared with the classical Lusin class $ACG$, and it is shown that continuous $ACG$-functions can fail to be $L^r$-differentiable almost everywhere.
46-58
Belyi's theorem for smooth complete intersections of general type in generalized Grassmannians and weighted projective spaces
摘要
We show that Javanpeykar's proof of Belyi's theorem for smooth complete intersections of general type in ordinary projective spaces can be generalised to smooth complete intersections of general type in generalised Grassmannians and weighted projective spaces. We propose an approach to the generalisation of this result to smooth complete intersections of general type in more general Mori dream spaces.
59-76
Weak semiregular solutions to the Dirichlet problem for quasilinear elliptic equations in divergence form with discontinuous weak nonlinearities
摘要
In a bounded domain of an $N$-dimensional space we study the homogeneous Dirichlet problem for a quasilinear elliptic equation in divergence form with a discontinuous weak nonlinearity of power growth at infinity. Using a variational method based on the concept of quasipotential operator we obtain a theorem on the existence of a weak semiregular solution to the problem under study. The semiregularity of a solution means that, almost everywhere in the domain in which the boundary value problem is considered, its values are continuity points of the weak nonlinearity with respect to the phase variable. Next, a positive parameter is introduced into the equation as a multiplier of the weak nonlinearity, and the question of the existence of nontrivial weak semiregular solutions to the resulting boundary value problem is studied. In this case the existence of a trivial solution for all values of the parameter is assumed. A theorem on the existence of a nontrivial weak semiregular solution for sufficiently large values of the parameter is established.
77-93
Topological properties of caustics in five-dimensional spaces
摘要
We present a list of universal linear relations between the Euler characteristics of manifolds consisting of multisingularities of a generic Lagrangian map into a five-dimensional space. From these relations it follows, in particular, that the numbers $D_5A_2$, $A_4A_3$, $A_4A^2_2$ of isolated self-intersection points of the corresponding types on any generic compact four-dimensional caustic are even. The numbers $D^+_4 A_3 + D^-_4 A3 + E_6 $ and $D^+_4 A^2_2 + D^-_4 A^2_2 + \frac12 A_4A_3$ are also even.
94-106
A coupled system consisting of an evolution inclusion with maximal monotone operators and a prox-regular sweeping process
摘要
107-137
On the density of the additive semigroup generated by a subset of a Hilbert–Schmidt ellipsoid
摘要
138-150