We consider the linearized and nonlinear stationary incompressible flow around rotating and translating body in the exterior domain R 3 ∖ D ¯ , where D ⊂ R 3 is open and bounded, with Lipschitz boundary. We derive the pointwise estimates for the pressure in both cases. Moreover, we consider the linearized problem in a truncation domain D R : = B R ∖ D ¯ of the exterior domain R 3 ∖ D ¯ under certain

The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field ( K , ν ) and an extension ω of ν to a finite extension L of K. Then we study when the valuation ring of ω is essentially finitely generated over the valuation ring of ν. We present a necessary condition in terms of classic invariants of the

Let S be a split family of del Pezzo surfaces over a discrete valuation ring such that the general fiber is smooth and the special fiber has ADE ‐singularities. Let G be the reductive group given by the root system of these singularities. We construct a G‐torsor over S whose restriction to the generic fiber is the extension of structure group of the universal torsor. This extends a construction of

It is shown that the calculation of the sum of the spaces of the K‐Peetre interpolation method can be reduced to the calculation of the sum of the cones of the concave functions included by the parameter in the definition of the spaces of the K‐Peetre interpolation method. As an example, a new extrapolation theorem for operators in Lipschitz spaces is obtained.

We study the well‐posedness of the fractional degenerate integro‐differential equations ( P α ) : D α ( M u ) ( t ) = A u ( t ) + ∫ − ∞ t a ( t − s ) A u ( s ) d s + ∫ − ∞ t b ( t − s ) B u ( s ) d s + f ( t ) , ( t ∈ T : = [ 0 , 2 π ] ) , in Lebesgue–Bochner spaces L p ( T ; X ) and Besov spaces B p , q s ( T ; X ) , where A, B and M are closed linear operators on a Banach space X satisfying D ( A

The aim of this paper is to study the existence of solution to an equation involving the Bessel operator in R N ( I − Δ ) α u + λ V ( x ) u = γ f ( x , u ) , where λ , γ are real positive parameters, V : R N → R + is a continuous function, 0 < α < 1 with 2 α < N , f is a continuous function on R N × R which does not satisfy the Ambrosetti–Rabinowitz condition. By using the Fountain theorem and Morse

In this manuscript we study geometric regularity estimates for problems driven by fully nonlinear elliptic operators (which can be either degenerate or singular when “the gradient is small”) under strong absorption conditions of the general form: G ( x , D u , D 2 u ) = f ( u ) χ { u > 0 } in Ω , where the mapping u ↦ f ( u ) fails to decrease fast enough at the origin, so allowing that nonnegative

We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0, p). As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic (0, p) of integral canonical

Let G be a regular Lie group which is a directed union of regular Lie groups G i (all modelled on possibly infinite‐dimensional, locally convex spaces). We show that G = lim ⟶ G i as a regular Lie group if G admits a so‐called direct limit chart. Notably, this allows the regular Lie group Diff c ( M ) of compactly supported diffeomorphisms to be interpreted as a direct limit of the regular Lie groups

The goal of this article is to investigate nontrivial m‐quasi‐Einstein manifolds globally conformal to an n‐dimensional Euclidean space. By considering such manifolds, whose conformal factors and potential functions are invariant under the action of an ( n − 1 ) ‐dimensional translation group, we provide a complete classification when λ = 0 and m ≥ 1 or m = 2 − n .

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.

Let M be a Hopf hypersurface in a nonflat complex space form M 2 ( c ) , c ≠ 0 , of complex dimension two. In this paper, we prove that M has η‐recurrent Ricci operator if and only if it is locally congruent to a homogeneous real hypersurface of type (A) or (B) or a non‐homogeneous real hypersurface with vanishing Hopf principal curvature. This is an extension of main results in [17, 21] for real hypersurfaces

In this paper, we consider the scattering theory of the radial solution to focusing energy‐subcritical Hartree equation with inverse‐square potential in the energy space H 1 ( R d ) using the method from [4]. The main difficulties are the equation is not space‐translation invariant and the nonlinearity is non‐local. Using the radial Sobolev embedding and a virial‐Morawetz type estimate we can exclude

In this article, we study the critical points of the total scalar curvature functional restricted to the space of metrics with constant scalar curvature of unitary volume, for simplicity, CPE metrics. Here, we prove that a CPE metric admitting a non‐trivial closed conformal vector field must be isometric to a round sphere metric, which provides a partial answer to the CPE conjecture.

Homothetic and translating solitons for the inverse mean curvature flow (IMCF) in R n + 1 are self‐similar solutions deformed by only homothety and translation under IMCF, respectively. In this paper, we address some geometric properties of these solitons. To be specific, the incompleteness for the homothetic soliton of velocity C with 0 < C < 1 n and for any translating soliton are proved. In addition

In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the non‐attainability of the constants in the inequalities are also proved.

The present paper is concerned with stability of the stationary solution of the Burgers equation in exterior domains in R n . In the previous papers [5, 6, 7] the asymptotic behavior of radially symmetric solutions for the multi‐dimensional Burgers equation in exterior domains in R n , n ≥ 3 , has been considered. The results [5, 6, 7] are restricted to stability of radially solutions within the class

We obtain pointwise upper bounds on the derivatives of the heat kernel on Damek–Ricci spaces and we study the L p ‐boundedness of Littlewood–Paley–Stein operators.

Following Mumford and Chiodo, we compute the Chern character of the derived pushforward ch ( R • π * O ( D ) ) , for D an arbitrary element of the Picard group of the universal curve over the moduli stack of stable marked curves. This allows us to express the pullback of universal Brill–Noether classes via Abel–Jacobi sections to the compactified universal Jacobians, for all compactifications such

We consider weak solutions ( u , π ) : Ω → R n × R to stationary p‐Stokes systems of the type − div a ( x , E u ) + ∇ π + [ D u ] u = f , div u = 0 in Ω ⊂ R n , where the function a ( x , ξ ) satisfies p‐growth conditions in ξ and depends Hölder continuously on x. By E u we denote the symmetric part of the gradient D u and we write [ D u ] u for the convective term. In this setting, we establish results

This paper is concerned with well‐posedness of the Cahn–Hilliard equation subject to a class of new dynamic boundary conditions. The system was recently derived in Liu–Wu (Arch. Ration. Mech. Anal. 233 (2019), 167–247) via an energetic variational approach and it naturally fulfils three physical constraints such as mass conservation, energy dissipation and force balance. The target problem examined

In terms of weak solutions of the fractional p‐Laplace equation with measure data, this paper offers a dual characterization for the fractional Sobolev capacity on bounded domain. In addition, two further results are given: one is an equivalent estimate for the fractional Sobolev capacity; the other is the removability of sets of zero capacity and its relation to solutions of the fractional p‐Laplace

We prove an extension theorem for ultraholomorphic classes defined by so‐called Braun–Meise–Taylor weight functions ω and transfer the proofs from the single weight sequence case from V. Thilliez to the weight function setting. We are following a different approach than the results obtained in a recent paper by the authors, more precisely we are working with real methods by applying the ultradifferentiable

A generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational characterization of abelian varieties. In particular we prove that, under the conjectures of the Minimal Model Program, a smooth projective variety is birational to

We prove a general result about the behaviour of minimizing sequences for nonlocal shape functionals satisfying suitable structural assumptions. Typical examples include functions of the eigenvalues of the fractional Laplacian under homogeneous Dirichlet boundary conditions. Exploiting a nonlocal version of Lions' concentration‐compactness principle, we prove that either an optimal shape exists or

Let Δ and L = Δ − ∥ x ∥ 2 be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space H 1 associated with the Dunkl harmonic oscillator by means of the nontangential maximal function with respect to the semigroup e t L . We prove that the space H 1 admits characterizations by relevant Riesz transforms and atomic decompositions. The atoms which occur in the atomic

We describe the Aluthge transform of an unbounded weighted composition operator acting in an L2‐space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize p‐hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation

In this paper we prove mixed inequalities for the maximal operator M Φ , for general Young functions Φ with certain additional properties, improving and generalizing some previous estimates for the Hardy–Littlewood maximal operator proved by E. Sawyer. We show that given r ≥ 1 , if u , v r are weights belonging to the A1‐Muckenhoupt class and Φ is a Young function as above, then the inequality u v

This paper introduces both notions of topological entropy and invariance entropy for semigroup actions on general topological spaces. We use the concept of admissible family of open coverings to extending and studying the notions of Adler–Konheim–McAndrew topological entropy, Bowen topological entropy, and invariance entropy to the general theory of topological dynamics.

In this note we study an abstract class of weakly dissipative second‐order systems with finite memory. We establish the polynomial decay of Rivera, Naso and Vegni for the solution of the system under a very weak condition on the relaxation function.

We prove a generalization of the Littlewood–Paley characterisation of the BMO space where the shifts of a Schwartz function are replaced by a family of functions with suitable conditions imposed on them. We also prove that a certain family of Triebel–Lizorkin spaces can be characterized in a similar way.

Let H be a separable Hilbert space with the unit operator I, let A be a bounded linear operator in H with a Schatten–von Neumann Hermitian component ( A − A ∗ ) / 2 i ( A ∗ means the operator adjoint to A) and let f ( z ) be a function analytic on the spectra of A and A ∗ . For f ( A ) we obtain the representation in the form of the sum of a normal operator and a quasi‐nilpotent Schatten–von Neumann

We give an original representation integral formula for the resolvent families associated to the fractional Cauchy equation with memory effects C D t α u ( t ) − A u ( t ) + ∫ 0 t β ( t − s ) A u ( s ) d s = f ( t , u ( t ) ) , t ∈ [ 0 , T ] , T > 0 , where u ( 0 ) = u 0 ∈ X and A is a sectorial operator on a Banach space X. Moreover, we get spatial bounds for the resolvent families in order to study

The study of symmetries is a well known research topic in differential geometry with relevant physical interpretations. Given a Riemannian manifold ( M , g ) , we consider pseudo‐Riemannian g‐natural metrics G on its tangent bundle T M and characterize conformal, homothetic and Killing vector fields of ( T M , G ) obtained from natural lifts of vector fields of M.

Assume that G is a finite group. For every a , b ∈ N , we define a graph Γ a , b ( G ) whose vertices correspond to the elements of G a ∪ G b and in which two tuples ( x 1 , ⋯ , x a ) and ( y 1 , ⋯ , y b ) are adjacent if and only if ⟨ x 1 , ⋯ , x a , y 1 , ⋯ , y b ⟩ = G . We study several properties of these graphs (isolated vertices, loops, connectivity, diameter of the connected components) and

The global existence and asymptotic behavior for anisotropic parabolic equation in R n are considered. By using the classical Galerkin approximation and suitable conditions on the weighted function, it is obtained the global estimate and the uniformly estimates for the global weak solution. Besides, the L 2 ( R n ) ∩ L r ( R n ) global attractor for anisotropic parabolic p‐Laplacian equation is also

Let G be a simple graph on the vertex set [n] and let J G be the corresponding binomial edge ideal. Let G = v ∗ H be the cone of v on H. In this article, we compute all the Betti numbers of J G in terms of the Betti numbers of J H and as a consequence, we get the Betti diagram of wheel graph. Also, we study Cohen–Macaulay defect of S / J G in terms of Cohen–Macaulay defect of S H / J H and using this

For the spaces D L p , L p and M 1 , we consider the topology of uniform convergence on absolutely convex compact subsets of their (pre‐)dual space. Following the notation of J. Horváth's book we call these topologies κ‐topologies. They are given by a neighbourhood basis consisting of polars of absolutely convex and compact subsets of their (pre‐)dual spaces. In many cases it is more convenient to

For perturbed Stark operators H u = − u ′ ′ − x u + q u , the author has proved that lim sup x → ∞ x 1 2 | q ( x ) | must be larger than 1 2 N 1 2 in order to create N linearly independent eigensolutions in L 2 ( R + ) [29]. In this paper, we apply generalized Wigner–von Neumann type functions to construct embedded eigenvalues for a class of Schrödinger operators, including a proof that the bound 1

In this paper, we consider the following Klein–Gordon–Maxwell equations − Δ u + V ( x ) u − ( 2 ω + ϕ ) ϕ u = f ( x , u ) + h ( x ) in R 3 , − Δ ϕ + ϕ u 2 = − ω u 2 in R 3 , where ω > 0 is a constant, u, ϕ : R 3 → R , V : R 3 → R is a potential function. By assuming the coercive condition on V and some new superlinear conditions on f, we obtain two nontrivial solutions when h is nonzero and infinitely

Given B , C and W operators in the algebra L ( H ) of bounded linear operators on the Krein space H , the minimization problem min ( B X − C ) # W ( B X − C ) , for X ∈ L ( H ) , is studied when the weight W is selfadjoint. The analogous maximization and min‐max problems are also considered. Complete answers to these problems and to those naturally associated to trace clase operators on Krein spaces

We derive a formula for the discriminant of the ring class polynomial of conductor N associated to the j‐invariant and an imaginary quadratic field of odd discriminant − d using the theory of Borcherds lifts. When d is a prime and N = 1 , the formula recovers the Gross–Zagier discriminant formula.

In this paper, the weak Harris theorem developed in [18] is illustrated by using a straightforward Wasserstein coupling, which implies the exponential ergodicity of the functional solutions to a range of neutral type SDEs with infinite length of memory. A concrete example is presented to illustrate the main result.

Reflexive polytopes have been studied from viewpoints of combinatorics, commutative algebra and algebraic geometry. A nef‐partition of a reflexive polytope P is a decomposition P = P 1 + ⋯ + P r such that each P i is a lattice polytope containing the origin. Batyrev and van Straten gave a combinatorial method for explicit constructions of mirror pairs of Calabi–Yau complete intersections obtained from

There exists a mistake in the proof of Theorem 4.2. We present a new proof of this theorem, which shows that the main results of the paper are still true.

We classify totally geodesic and parallel hypersurfaces of four‐dimensional non‐reductive homogeneous pseudo‐Riemannian manifolds.

We present quantitative versions of Bohr's theorem on general Dirichlet series D = ∑ a n e − λ n s assuming different assumptions on the frequency λ = ( λ n ) , including the conditions introduced by Bohr and Landau. Therefore, using the summation method by typical (first) means invented by M. Riesz, without any condition on λ, we give upper bounds for the norm of the partial sum operator S N ( D )

Let M 2 → S 3 be an umbilic‐free surface. Four basic invariants of M2 under the Möbius transformation group of S 3 are the Möbius metric g, the Blaschke tensor A, the Möbius second fundamental form B and the Möbius form Φ. A symmetric (0,2) tensor D = A + μ B called Para‐Blaschke tensor, where μ is constant, is also Möbius invariant. In this paper, we classify the surfaces with isotropic Para‐Blaschke

We analyze the effect of nonlinear boundary conditions on an advection‐diffusion equation on the half‐line. Our model is inspired by models for crystal growth where diffusion models diffusive relaxation of a displacement field, advection is induced by apical growth, and boundary conditions incorporate non‐adiabatic effects on displacement at the boundary. The equation, in particular the boundary fluxes

In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse homotopy groups. The main result is that the coarse homotopy groups of a cone over a compact simplicial complex coincide with the usual homotopy groups of the underlying

Siegel proved that every totally positive element of a number field K is the sum of four squares, so in particular the Pythagoras number is uniformly bounded across number fields. The p‐adic Kochen operator provides a p‐adic analogue of squaring, and a certain localisation of the ring generated by this operator consists of precisely the totally p‐integral elements of K. We use this to formulate and

We introduce a class of null hypersurfaces of a semi‐Riemannian manifold, namely, screen quasi‐conformal hypersurfaces, whose geometry may be studied through the geometry of its screen distribution. In particular, this notion allows us to extend some results of previous works to the case in which the sectional curvature of the ambient space is different from zero. As applications, we study umbilical

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half‐planes { s ∈ C | Re s > ε } for each ε > 0 . The properties of the formal inverse of the differentiation are also investigated.

In this note, we continue to investigate common properties of the products in the setting of rings, bounded linear operators, or Banach algebras. We prove: (i) If a , b , c are elements in a unital associative ring R satisfying a b a = a c a , then von Neumann regularity (resp. generalized Fredholmness relative to an ideal I of R ) of 1 − a c is converted into that of 1 − b a . (ii) If A , B , C are

We establish the higher fractional differentiability of the solutions of a problem in divergence form of the type div A ( x , D u ) = div | F | p ( x ) − 2 2 F in Ω , u = 0 on ∂ Ω . The main features consist in assuming that the partial map ξ → A ( x , ξ ) has p ( x ) ‐growth, the datum F is Besov regular and both the partial map x → A ( x , ξ ) and the function x → p ( x ) are Orlicz–Besov regular

We obtain a new bound on the average value of the error term in the asymptotic formula for the number of k‐free numbers in arithmetic progressions. In particular, we improve the results of J. Gibson (2014) and C. Hooley (1975).

Let X be a complex algebraic variety. We say that X is Borel hyperbolic if, for every finite type reduced scheme S over the complex numbers, every holomorphic map from S to X is algebraic. We use a transcendental specialization technique to prove that X is Borel hyperbolic if and only if, for every smooth affine complex algebraic curve C, every holomorphic map from C to X is algebraic. We use the latter

In this article we classify isometric immersions f : M n ( c ) → S n + p × R of Riemannian manifolds of dimension n and constant sectional curvature c ≤ 1 into the product space S n + p × R , p ≤ n − 3 , where S m denotes the m‐dimensional unit sphere.

We obtain upper and lower Gaussian density estimates for the laws of each component of the solution to a one‐dimensional fully coupled forward‐backward SDE. Our approach relies on the link between FBSDEs and quasilinear parabolic PDEs, and is fully based on the use of classical results on PDEs rather than on manipulation of FBSDEs, compared to other papers on this topic. This essentially simplifies

In this paper we study 4‐dimensional affine hypersurfaces with a Lorentzian second fundamental form additionally equipped with an almost symplectic structure ω. We prove that the rank of the shape operator is at most one if R k · ω = 0 or ∇ k ω = 0 for some positive integer k. This result is the final step in a classification of Lorentzian affine hypersurfaces with higher order parallel almost symplectic forms