A note on a multivalued iterative equation.
Pulling back cohomology classes and dynamical degrees of monomial maps
We study the pullback maps on cohomology groups for equivariant rational maps (i.e., monomial maps) on toric varieties. Our method is based on the intersection theory on toric varieties. We use the method to determine the dynamical degrees of monomial maps and compute the degrees of the Cremona involution.
Permanence and global attractivity of discrete predator-prey system with Hassell-Varley type functional response.
Stabilization of monomial maps in higher codimension
A monomial self-map on a complex toric variety is said to be -stable if the action induced on the -cohomology is compatible with iteration. We show that under suitable conditions on the eigenvalues of the matrix of exponents of , we can find a toric model with at worst quotient singularities where is -stable. If is replaced by an iterate one can find a -stable model as soon as the dynamical degrees of satisfy . On the other hand, we give examples of monomial maps , where this condition...
An identity related to Jordan's inequality.
Digit sets of integral self-affine tiles with prime determinant
Let M ∈ Mₙ(ℤ) be expanding such that |det(M)| = p is a prime and pℤⁿ ⊈ M²(ℤⁿ). Let D ⊂ ℤⁿ be a finite set with |D| = |det(M)|. Suppose the attractor T(M,D) of the iterated function system has positive Lebesgue measure. We prove that (i) if D ⊈ M(ℤⁿ), then D is a complete set of coset representatives of ℤⁿ/M(ℤⁿ); (ii) if D ⊆ M(ℤⁿ), then there exists a positive integer γ such that , where D₀ is a complete set of coset representatives of ℤⁿ/M(ℤⁿ). This improves the corresponding results of Kenyon,...
Sufficient conditions for the spectrality of self-affine measures with prime determinant
Let be a self-affine measure associated with an expanding matrix M and a finite digit set D. We study the spectrality of when |det(M)| = |D| = p is a prime. We obtain several new sufficient conditions on M and D for to be a spectral measure with lattice spectrum. As an application, we present some properties of the digit sets of integral self-affine tiles, which are connected with a conjecture of Lagarias and Wang.
Nonlinear Markov processes in big networks
Big networks express multiple classes of large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to constructing a broad class of nonlinear continuous-time block-structured Markov processes, which can be used to deal with many practical stochastic systems. Firstly,...
On the strengthened Jordan's inequality.
Multiple solutions of quasilinear elliptic equations in .
Existence of three solutions to a double eigenvalue problem for the p-biharmonic equation
Using a three critical points theorem and variational methods, we study the existence of at least three weak solutions of the Navier problem ⎧ in Ω, ⎨ ⎩u = Δu = 0 on ∂Ω, where (N ≥ 1) is a non-empty bounded open set with a sufficiently smooth boundary ∂Ω, λ > 0, μ > 0 and f,g: Ω × ℝ → ℝ are two L¹-Carathéodory functions.
Properties of the Salagean operator.
Multiple positive solutions of semilinear elliptic problems in exterior domains.
Multiple positive solutions for singular elliptic equations with concave-convex nonlinearities and sign-changing weights.
Progress in developing Poisson-Boltzmann equation solvers
This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nanoobjects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided...
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