We prove that the homogeneously polyanalytic functions of total order m, defined by system equations $$\overline{D}^{(k_1,\ldots ,k_n)} f=0$$ with $$k_1+\cdots +k_n=m$$ , can be written as polynomials degree $$<m$$ in variables $$\overline{z_1},\ldots ,\overline{z_n}$$ some analytic coefficients. establish a weighted mean value property for such functions, using reproducing Jacobi polynomials. ...

We use recent extensions of the Borsuk–Ulam theorem for Stiefel manifolds to generalize ham sandwich mass assignments. A k-dimensional assignment continuously imposes a measure on each affine subspace $${\mathbb {R}}^d$$ . Given finite collection assignments different dimensions, one may ask if there is some sequence subspaces $$S_{k-1} \subset S_k \ldots S_{d-1} {\mathbb such that $$S_i$$ bise...

Abstract An evasion differential game of one evader and many pursuers is studied. The dynamics state variables $$x_1,\ldots , x_m$$ x 1 , … m are described by linear equations. control functions p...

An edge-ordered graph is a with total ordering of its edges. A path $$P=v_1v_2\ldots v_k$$ in an called increasing if $$(v_iv_{i+1}) < (v_{i+1}v_{i+2})$$ for all $$i = 1,\ldots,k-2$$ ; and it decreasing > . We say that P monotone or decreasing. rooted tree T either every from the root to leaf Let G be graph. In straight-line drawing D G, vertices are drawn as different points plane edges straig...

For a graph G, and two distinct vertices u v of let $$ n_{{G(u,v)}} n G ( , ) be the number that are closer in to than v. Miklavi? Šparl arXiv:2011.01635v1 define distance-unbalancedness $${{\mathrm{uB}}}(G)$$ uB as sum $$|n_G(u,v)-n_G(v,u)|$$ | - over all unordered pairs G. positive integers up 15, they determine trees T fixed order with smallest largest values $${\mathrm{uB}}(T)$$ respectivel...

For every non-integral $\alpha \gt 1$, the sequence of integer parts $n^{\alpha }$ $(n=1,2,\ldots )$ is called Piatetski-Shapiro with exponent $ and let $\mathrm {PS}(\alpha denote set all terms this sequence.

Let $$S=\left\langle s_1,\ldots ,s_n\right\rangle $$ be a numerical semigroup generated by the relatively prime positive integers $$s_1,\ldots ,s_n$$ . $$k\geqslant 2$$ an integer. In this paper, we consider following k-power variant of Frobenius number S defined as $$\begin{aligned} {}^{k\!}r\!\left( S\right) := \text { largest } k {-power integer not belonging to S. \end{aligned}$$ investigat...

We consider, for $$n\geqslant 3$$ , K-quasiregular $$\mathrm {vol}_N^\times $$ -curves $$M\rightarrow N$$ of small distortion $$K\geqslant 1$$ from oriented Riemannian n-manifolds into product manifolds $$N=N_1\times \cdots \times N_k$$ where each $$N_i$$ is an n-manifold, and the calibration \in \Omega ^n(N)$$ sum volume forms {vol}_{N_i}$$ factors N. show that, in this setting, curves are car...

Abstract The article is concerned with systems of fractional discrete equations Δ α x ( n + 1 ) = F , <m:m...

The vibrational predissociation of van der Waals complexes has been the object study using a wide range theoretical and experimental methods, producing large number results. We focus here on ArBr $$_2$$ ( $$v=16,\ldots ,25$$ ) system. For its study, we employ two important methods: trajectory surface hopping (TSH) quasiclassical method (QCTM). In first case, dynamics system are reproduced poten...