Yet another topological type of a Lagrangian submanifold in the Grassmannian $$\operatorname{Gr}(1, n)$$ is presented, which supplements the list of examples of various homogeneity degrees constructed by using a generalization of A. E. Mironov’s construction.

We prove that a nondecreasing sequence of positive numbers $$\omega_n$$ is a Weyl multiplier for the almost everywhere unconditional convergence of series in Ciesielski systems if and only if the inequality $$\sum_{n=1}^{\infty}(n\omega_n)^{-1}<\infty$$ holds.

Maxwell’s equations with temporal dispersion and localized initial data are considered. Using the Maslov canonical operator, we construct a uniform asymptotic solution expressed in terms of the derivative of the Airy function of composite argument in a neighborhood of regular points of the leading wave front.

We present an algorithm determining the existence of an isomorphic embedding of one finitely generated partially commutative nilpotent group of class $$2$$ in another. It is shown how such embeddings can be constructed. We also describe an algorithm determining the existence of an embedding of a finitely generated partially commutative nilpotent group of arbitrary class $$l$$ with respect to a graph of nonzero radius in a free nilpotent group of class $$l$$ .

On the real line, we study the generalized Dunkl harmonic analysis depending on a parameter $$r\in\mathbb{N}$$ . The case of $$r=0$$ corresponds to the usual Dunkl harmonic analysis. All constructions depend on the parameter $$r\ge 1$$ . The differences and moduli of smoothness are defined using a generalized translation operator. The Sobolev space and the $$K$$ -functional are defined using a differential-difference operator. An approximate Jackson-type inequality is proved. The equivalence of the $$K$$ -functional and the modulus of smoothness is established.

Z. S. Aygin and P. C. Toh have developed a technique using the theory of modular forms to determine all the eta quotients whose derivative is also an eta quotient up to level 36. The aim of the present paper is to develop a theory for level 18 eta quotient identities and derive all the identities of Aygin and Toh of level 18 by using this theory.

The paper considers $$n \times n$$ systems of ordinary differential equations of the form $$y'-By-C(\cdot, \lambda)y=\lambda Ay, \qquad y=y(x), \quad x \in [0, 1],$$ where $$A=\operatorname{diag}\{a_1(x), \dots, a_n(x)\}$$ , $$B=\{b_{jk}(x)\}_{j, k=1}^n$$ , and $$C= \{c_{jk}(x, \lambda)\}_{j, k=1}^n$$ . All functions in these matrices are complex-valued and integrable over $$x \in [0, 1]$$ , and $$\|c_{jk}(\cdot, \lambda)\|_{L_1} \to 0$$ as $$\lambda \to \infty$$ . The theorems proved in the paper generalize the results of the classical Birkhoff–Tamarkin–Langer theory concerning asymptotic representations of fundamental solutions in sectors and half-strips of the complex plane as $$\lambda \to \infty$$ . The focus is on the minimality of the smoothness requirements on the coefficients.

In this paper, we investigate the structure of finite groups and obtain the classification of nonabelian chief factors by considering $$\mathcal{M}$$ -permutable maximal subgroups of Sylow $$p$$ -subgroups. We also consider the application of such formations in the theory of finite groups.

We study a boundary value problem for a mathematical model describing the nonisothermal steady-state flow of a viscous fluid in a 3D (or 2D) bounded domain with locally Lipschitz boundary. The heat and mass transfer model considered here has the feature that a regularized Rayleigh dissipation function is used in the energy balance equation. This permits taking into account the energy dissipation due to the viscous friction effect. A theorem on the existence of a weak solution is proved under natural assumptions on the model data. Moreover, we establish extra conditions guaranteeing that the weak solution is unique and/or strong.