We present a uniform framework for establishing Nullstellensätze for power series rings using quantifier elimination results for valued fields. As an application, we obtain Nullstellensätze for -adic power series (both formal and convergent) analogous to Rückert's complex and Risler's real Nullstellensatz, as well as a -adic analytic version of Hilbert's 17th Problem. Analogous statements for restricted power series, both real and -adic, are also considered.
Garonzi and Lucchini explored finite groups possessing a normal 2-covering, where no proper quotient of exhibits such a covering. Their investigation offered a comprehensive overview of these groups, delineating that such groups fall into distinct categories: almost simple, affine, product action, or diagonal.
In this paper, we focus on the family falling under the diagonal type. Specifically, we present a thorough classification of finite diagonal groups possessing a normal 2-covering, with the attribute that no proper quotient of has such a covering.
With deep appreciation to Martino Garonzi and Andrea Lucchini, for keeping us entertained.
We present a general approach to the parametrix construction. We apply it to prove the uniqueness and existence of a weak fundamental solution for the equation with nonsymmetric nonlocal operators
We compute a lower bound for the scalar curvature of a gradient Einstein soliton under a certain assumption on its potential function. We establish an asymptotic behavior of the potential function on a noncompact gradient shrinking Einstein soliton. As a result, we obtain the finiteness of its fundamental group and its weighted volume. We also prove some geometric and analytic results for constructing gradient Einstein solitons that are realized as warped metrics, and we give a few explicit examples.
The purpose of this paper is twofold. The first aim is to study the comparison of generalized squeezing functions and Fridaman invariants of some special domains. Then, the second aim is to give estimates for these two invariants and discuss their boundary behavior near inessential boundary points.
The goal of this paper is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these nonexistence results generalize to a broader context certain estimates and rigidity obtained when studying warped product Einstein manifolds. When the soliton is shrinking, it is presented as a nonexistence theorem with no counterpart in the Einstein case, which is proved using properties of the first eigenvalue of a weighted Laplacian.
In this paper, we discuss the boundedness of mixed Journé's class operators on weighted multi-parameter mixed Hardy spaces via atoms decomposition. Moreover, we give a specific singular integral operator in mixed Journé's class which has better properties.
In this paper, we consider a class of upper critical Kirchhoff-type fractional Laplacian system with Choquard nonlinearities and magnetic fields. With the help of the limit index theory and the concentration–compactness principles for fractional Sobolev spaces, we establish the existence of infinitely many nontrivial radial solutions for the above system. A distinguished feature of this paper is that the above Kirchhoff-type system is degenerate, that is, the Kirchhoff term is zero at zero.
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