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This paper deals with a two-species chemotaxis-competition system in a setting that not only accounts for a class of nonlinear variants of the chemotactic cross-diffusion processes, but also involves an external source describing a superlinear growth effect under nonlocal resource consumption. Apart from that, the considered chemoattractant is assumed to be produced according to a fairly general power law. We first confirm the global existence and boundedness of classical solutions to an associated Neumann initial-boundary value problem under some appropriate parameter conditions. Moreover, it is shown that these global bounded solutions converge to the spatially homogeneous coexistence state as time tends to infinity.

We discuss families of hypersurfaces with isolated singularities in projective space with the property that the sum of the ranks of the rational homotopy and the homology groups is finite. They represent infinitely many distinct homotopy types with all hypersurfaces having a nef canonical or anti-canonical class. In the Appendix, we show that such an infinite family of smooth rationally elliptic 3-folds does not exist.

In this paper, we evaluate c-Entropy of perturbed L-systems introduced in Belyi and Tsekanovskii [Complex Anal. Oper. Theory 13 (2019), no. 3, 1227–1311]. Explicit formulas relating the c-Entropy of the L-systems and the perturbation parameter are established. We also show that c-Entropy attains its maximum value (finite or infinite) whenever the perturbation parameter vanishes so that the impedance function of such a L-system belongs to one of the generalized (or regular) Donoghue classes.

In this paper, we study a higher-order Laplacian operator in the framework of Orlicz–Sobolev spaces, the biharmonic g-Laplacian

A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is concerned and the uniform exponential decay of solutions is obtained by combining the energy estimates with suitable Lyapunov functionals and an integral inequality under suitable conditions.

We obtain an $��L^1�\to �L^p�$ estimate in weighted $�L^p$ norms for the $�\overline{\partial }$-equation in $�C^n$ under a coercivity condition of the associated weighted Kohn Laplacian.

We study continuity of the multiplier operator $�e^{�i�q�}$ acting on Gelfand–Shilov spaces, where $�q$ is a polynomial on $�R^d$ of degree at least two with real coefficients. In the parameter quadrant for the spaces, we identify a wedge that depends on the polynomial degree for which the operator is continuous. We also show that in a large part of the complement region the operator is not continuous in dimension one. The results give information on well-posedness for linear evolution equations that generalize the Schrödinger equation for the free particle.

In this paper, we introduce the notion of algebraic $�*$-Ricci solitons of three-dimensional almost contact Lorentzian Lie groups, which represents a fundamentally novel class of solitons. We give the classification of algebraic $�*$-Ricci solitons of three-dimensional Lorentzian contact unimodular and non-unimodular Lie groups. At last we give an example of expanding algebraic $�*$-Ricci soliton.

In this paper, we study geometric and analytical features of complete noncompact $�\rho$-Einstein solitons, which are self-similar solutions of the Ricci–Bourguignon flow. We study the spectrum of the drifted Laplacian operator for complete gradient shrinking $�\rho$-Einstein solitons. Moreover, similar to classical results due to Calabi–Yau and Bishop for complete Riemannian manifolds with nonnegative Ricci curvature, we prove new volume growth estimates for geodesic balls of complete noncompact $�\rho$-Einstein solitons. In particular, the rigidity case is discussed. In addition, we establish weighted volume growth estimates for geodesic balls of such manifolds.

In this paper, we study stronger forms of Goldbach's conjecture enriched with the linear representations of prime numbers given by the classical Dirichlet theorem and its extensions. We call such a representation a Goldbach–Dirichlet representation (GD-representation). Among other results, we show that Dirichlet's theorem on arithmetic progressions is, in general, not true in the ring of formal power series over the integers. Additionally, we use a polynomial version of the Schinzel hypothesis due to A. Bodin, P. Dèbes, and S. Najib to prove the existence of GD-representations for a wide collection of polynomial rings over special families of fields of characteristic zero, among others. Moreover, we study the (non)validity of Dirichlet's theorem over several families of commutative rings with unity like polynomial and formal series rings. Finally, we obtain a generalization for polyomial rings of the celebrated Green–Tao theorem.