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Let R be a commutative noetherian ring. Lindo and Pande have recently posed the question asking when every ideal of R is isomorphic to some trace ideal of R. This paper studies this question and gives several answers. In particular, a complete answer is given in the case where R is local: it is proved in this paper that every ideal of R is isomorphic to a trace ideal if and only if R is an artinian Gorenstein ring, or a 1-dimensional hypersurface with multiplicity at most 2, or a unique factorization domain.

In this paper, we study time-asymptotic propagation phenomena for a class of dispersive equations on the line by exploiting precise estimates of oscillatory integrals. We propose first an extension of the van der Corput Lemma to the case of phases which may have a stationary point of real order and amplitudes allowed to have an integrable singular point. The resulting estimates provide optimal decay rates which show explicitly the influence of these two particular points. Then we apply these abstract results to solution formulas of a class of dispersive equations on the line defined by Fourier multipliers. Under the hypothesis that the Fourier transform of the initial data has a compact support or an integrable singular point, we derive uniform estimates of the solutions in space-time cones, describing their motions when the time tends to infinity. The method permits also to show that symbols having a restricted growth at infinity may influence the dispersion of the solutions: we prove the existence of a cone, depending only on the symbol, in which the solution is time-asymptotically localized. This corresponds to an asymptotic version of the notion of causality for initial data without compact support., Comment: This paper is an improved and extended version of arXiv:1507.00883. Moreover this second version contains supplementary information on wave packets to motivate our results and comments on the applicability of our method to the study of certain hyperbolic equations

In this paper we consider the following question. When does there exist a square root of a probability measure supported on R+? This question is naturally related to subnormality of weighted shifts. The main result of this paper is that if μ is a finitely atomic probability measure having at most 4 atoms, then μ has a square root, i.e., there exists a measure ν such that μ=ν*ν (* means the convolution) if and only if the Aluthge transform of a subnormal weighted shift with Berger measure μ is subnormal. As an application of them, we give non-trivial, large classes of probability measures having a square root. We also prove that there are 6 and 7-atomic probability measures which don't have any square root. Our results have a connection to the following long-open problem in Operator Theory: characterize the subnormal operators having a square root.

In this paper we prove a sharp distortion property of the Cassinian metric under Mobius transformations of a punctured ball onto another punctured ball. The paper also deals with discussion on local convexity properties of the Cassinian metric balls in proper subdomains of Rn. Inclusion properties of the Cassinian metric balls with other hyperbolic-type metric balls are also investigated. In particular, several conjectures are also stated in response to sharpness of the inclusion relations.

In this paper we study direct and inverse problems for discrete and continuous skew-selfadjoint Dirac systems with rectangular (possibly non-square) pseudo-exponential potentials. For such a system the Weyl function is a strictly proper rational matrix function and any strictly proper rational matrix function appears in this way. In fact, extending earlier results, given a strictly proper rational matrix function we present an explicit procedure to recover the corresponding potential using techniques from mathematical system and control theory. We also introduce and study a nonlinear generalized discrete Heisenberg magnet model, extending earlier results for the isotropic case. A large part of the paper is devoted to the related discrete systems of which the pseudo-exponential potential depends on an additional continuous time parameter. Our technique allows us to obtain explicit solutions for the generalized discrete Heisenberg magnet model and evolution of the Weyl functions.

The paper is devoted to the existence and uniqueness of local solutions for the density-dependent non-Newtonian compressible fluids with vacuum in one-dimensional bounded intervals. The important points in this paper are that the initial density may vanish in an open subset and the viscosity coefficient is nonlinearly dependent of density and shear rate.

The paper introduces a class of functions where the resolving operator for a system of Kolmogorov–Feller-type equations with a small parameter is well posed in forward and backward times. The introduced class of functions is invariant under the resolving operator if the solution is understood in the weak sense with an exponential weight. The paper continues the study of [6].

In this paper we consider the system of the non-steady Navier–Stokes equations with mixed boundary conditions. We study the existence and uniqueness of a solution of this system. We define Banach spaces X and Y, respectively, to be the space of “possible” solutions of this problem and the space of its data. We define the operator and formulate our problem in terms of operator equations. Let and be the Frechet derivative of at . We prove that is one-to-one and onto Y. Consequently, suppose that the system is solvable with some given data (the initial velocity and the right hand side). Then there exists a unique solution of this system for data which are small perturbations of the previous ones. The next result proved in the Appendix of this paper is W2, 2-regularity of solutions of steady Stokes system with mixed boundary condition for sufficiently smooth data.

In this paper, we consider the following fractional Kirchhoff equation with critical nonlinearity a+b∫R3(−Δ)s2u2dx(−Δ)su+V(x)u=Q(x)f(u)+|u|2s∗−2u,x∈R3,where a,b>0, (−Δ)s is the fractional Laplace operator with s∈(34,1), V vanishes at infinity and 2s∗=63−2s. Under appropriate assumptions on f, we prove the existence of positive solution by using the variational method.

We study some classical uniqueness and existence results, such as Peano's or Osgood's uniqueness criteria, in the context of Stieltjes differential equations. This type of equation is based on derivatives with respect to monotone functions, and enables the investigation of discrete and continuous problems from a common standpoint. We compare our results with previous work on the topic and illustrate the advantages of the theorems presented in this paper with an example. Finally, we make some remarks regarding analogous uniqueness results which can be derived for measure differential equations.

The main focus of this paper is on study of s‐numbers for a higher order Sobolev embedding on an interval and also for the corresponding Hardy‐type operator. Upper and lower estimates for approximation and Bernstein numbers are described and their relations with results for lower order Sobolev embeddings are discussed.

In this paper we consider laminated beams modelled from the well established Timoshenko system, which is a structure given by two identical layers uniform on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. By using semi‐group approach, we prove the global well‐posedness of the system when a viscoelastic dissipation acts on the three equations. In addition, we prove that the dissipation through memory terms is strong enough to get exponential decay of the system without the condition of equal wave speeds.

In this paper, we define and study Gevrey spaces associated with a Hormander family of (globally defined) vector fields and its corresponding sub‐Laplacian. We show some natural relations between the various Gevrey spaces in this setting on general manifolds, and more particular properties on Lie groups with polynomial growth of the volume. In the case of the Heisenberg group and of SU(2), we show that all our descriptions coincide.

For a character χ of a finite group G, the number χc(1)=[G:kerχ]χ(1) is called the codegree of χ. Let N be a normal subgroup of G and set Irr(G|N)=Irr(G)−Irr(G/N).Let p be a prime. In this paper, we first show that if for two distinct prime divisors p and q of |N|, pq divides none of the codegrees of elements of Irr(G|N), then Fit(N)≠{1} and N is either p‐solvable or q‐solvable. Next, we classify the finite groups with exactly one irreducible character of the codegree divisible by p and, also finite groups whose codegrees of irreducible characters which are divisible by p are equal. Then, we prove that p‐length of a finite p‐solvable group is not greater than the number of the distinct codegrees of its irreducible characters which are divisible by p. Finally, we consider the case when the codegree of every element of Irr(G|N) is square‐free.

This paper is concerned with the following elliptic problem: P (−Δ)mu=u+m∗−1+λu−s1φ1,inB1,u∈D0m,2(B1),(P)where (−Δ)m is the polyharmonic operator, m∗=2NN−2m is the critical Sobolev embedding exponent. B1 is the unit ball in RN, s1 and λ>0 are parameters, φ1>0 is the eigenfunction of (−Δ)m,D0m,2(B1) corresponding to the first eigenvalue λ1 with maxy∈B1φ1(y)=1, u+=max(u,0). By using the Lyapunov–Schimit reduction method combining with the minimax argument, we construct the solutions to (P) with many peaks near the boundary but not on the boundary of the domain. Moreover, we prove that the number of solutions for the problem (P) is unbounded as the parameter tends to infinity, therefore proving the Lazer–McKenna conjecture for the higher order case with critical growth.

In this paper, we look at a probabilistic approach to a non-local quadratic form that has lately attracted some interest. This form is related to a recently introduced non-local normal derivative. The goal is to construct two Markov process: one corresponding to that form and the other which is related to a probabilistic interpretation of the Neuman problem. We also study the Dirichlet-to-Neumann operator for non-local operators., Comment: 21 pages

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 $(K,\nu)$ and an extension $\omega$ of $\nu$ to a finite extension $L$ of $K$. Then we study when the valuation ring of $\omega$ is essentially finitely generated over the valuation ring of $\nu$. We present a necessary condition in terms of classic invariants of the extension by Hagen Knaf and show that in some particular cases, this condition is also sufficient. We also study when the corresponding extension of graded algebras is finitely generated. For this problem we present an equivalent condition (which is weaker than the one for the finite generation of the valuation rings).

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 $H^{1}(\mathbb{R}^d)$ using the method from \cite{Dodson2016}. The main difficulties are the equation is \emph{not} space-translation invariant and the nonlinearity is non-local. Using the radial Sobolev embedding and a virial-Morawetz type estimate we can exclude the concentration of mass near the origin. Besides, we can overcome the weak dispersive estimate when $a

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., 31 pages. We add "Note added to Proof" in Introduction and several references

In this paper, the weak Harris theorem developed in \cite{HMS11} 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 $\mathcal{P}$ is a decomposition $\mathcal{P}=\mathcal{P}_1+\cdots+\mathcal{P}_r$ such that each $\mathcal{P}_i$ 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 nef-partitions. In the present paper, by means of Gr\"{o}bner basis techniques, we give a large family of nef-partitions arising from unimodular configurations., Comment: 12 pages, typos are corrected, the writing is improved

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 the analysis.

In this paper, we obtain a boundary Schwarz lemma for C1 (pluriharmonic, holomorphic) mappings from the unit polydisc Un in Cn to irreducible bounded symmetric domains realized as the unit ball BX of an N‐dimensional simple JB*‐triple X. In particular, we obtain a version of the boundary Schwarz lemma for C1 (pluriharmonic, holomorphic) mappings from Un into the Euclidean unit ball BN in CN. These results are generalizations of recent results regarding boundary Schwarz lemma in higher dimensions.

In this paper, we are concerned with the Hardy–Henon equations −Δu=|x|aupandΔ2u=|x|aupwith a∈R and p∈(0,1]. Inspired by Serrin and Zou [25], we prove Liouville theorems for nonnegative solutions to the above Hardy–Henon equations (Theorem 1.1 and Theorem 1.3), that is, the unique nonnegative solution is u≡0.

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with (p,q)‐growth. We obtain an optimal global Calderon–Zygmund type estimate for the obstacle problem with double phase in the borderline case.

In this paper we deal with the following class of quasilinear elliptic problems −Δpu=λ|u|p−2u+u+p∗−1+g(x,u+)+f(x)inΩ,u=0on∂Ω,where 1≤p

In this paper, we determine the type numbers of the pseudo‐hyperbolic Gauss maps of all oriented Lorentzian surfaces of constant mean and Gaussian curvatures and non‐diagonalizable shape operator in the 3‐dimensional anti‐de Sitter space. Also, we investigate the behavior of type numbers of the pseudo‐hyperbolic Gauss map along the parallel family of such oriented Lorentzian surfaces in the 3‐dimensional anti‐de Sitter space. Furthermore, we investigate the type number of the pseudo‐hyperbolic Gauss map of one of Lorentzian hypersurfaces of B‐scroll type in a general dimensional anti‐de Sitter space.

In this paper we prove sufficient conditions for the Fredholm property of a non-smooth pseudodifferential operator $P$ which symbol is in a Holder space with respect to the spatial variable. As a main ingredient for the proof we use a suitable symbol-smoothing.

"This is the peer reviewed version of the following article: Abad C, Bravo A, Villamayor U. OV. Finite morphisms and simultaneous reduction of the multiplicity. Mathematische Nachrichten. 2020;293:8–38, which has been published in final form at https://doi.org/10.1002/mana.201800470. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited", Let X be a singular algebraic variety defined over a perfect field k, with quotient field K ( X ) . Let s ≥ 2 be the highest multiplicity of X and let F s ( X ) be the set of points of multiplicity s. If Y ⊂ F s ( X ) is a regular center and X ← X 1 is the blow up at Y, then the highest multiplicity of X1 is less than or equal to s. A sequence of blow ups at regular centers Y i ⊂ F s ( X i ) , say X ← X 1 ← ⋯ ← X n , is said to be a simplification of the multiplicity if the maximum multiplicity of X n is strictly lower than that of X, that is, if F s ( X n ) is empty. In characteristic zero there is an algorithm which assigns to each X a unique simplification of the multiplicity. However, the problem remains open when the characteristic is positive. In this paper we will study finite dominant morphisms between singular varieties β : X ′ → X of generic rank r ≥ 1 (i.e., [ K ( X ′ ) : K ( X ) ] = r ). We will see that, when imposing suitable conditions on β, there is a strong link between the strata of maximum multiplicity of X and X ′ , say F s ( X ) and F r s ( X ′ ) respectively. In such case, we will say that the morphism is strongly transversal. When β : X ′ → X is strongly transversal one can obtain information about the simplification of the multiplicity of X from that of X ′ and vice versa. Finally, we will see that given a singular variety X and a finite field extension L of K ( X ) of rank r ≥ 1 , one can construct (at least locally, in étale topology) a strongly transversal morphism β : X ′ → X , where X ′ has quotient field L., The authors were partially supported by the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa” Programme for Centres of Excellence in R&D (SEV2015-0554), and through MTM2015-68524-P (MINECO/FEDER)

In this paper, we consider a non‐smooth atomic decomposition by using a smooth atomic decomposition. Applying the non‐smooth atomic decomposition, a local means characterization and a quarkonical decomposition, we obtain a pointwise multiplier and a trace operator for generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on the whole space. We also develop the theory of those spaces on domains. We consider an extension operator and a trace operator on the upper half space and on compact oriented Riemannian manifolds.

Suppose that T1 is a Calderon–Zygmund operator with isotropic homogeneity and T2 is a Calderon–Zygmund operator with non‐isotropic homogeneity. In this note, the boundedness of the composition operator T1∘T2 on the Hardy space is presented. The results in this paper extend earlier related results on convolution operators to non‐convolution setting.

In this paper, we generalize all the results obtained on para‐Kahler Lie algebras in [3] to para‐Kahler Lie algebroids. In particular, we study exact para‐Kahler Lie algebroids as a generalization of exact para‐Kahler Lie algebras. This study leads to a natural generalization of pseudo‐Hessian manifolds, we call them contravariant pseudo‐Hessian manifolds. Contravariant pseudo‐Hessian manifolds have many similarities with Poisson manifolds. We explore these similarities which, among others, leads to a powerful machinery to build examples of non trivial pseudo‐Hessian structures. Namely, we will show that given a finite dimensional commutative and associative algebra (A,.), the orbits of the action Φ of (A,+) on A∗ given by Φ(a,μ)=exp(La∗)(μ) are pseudo‐Hessian manifolds, where La(b)=a.b. We illustrate this result by considering many examples of associative commutative algebras and show that the resulting pseudo‐Hessian manifolds are very interesting.

In this paper, we study the following quasilinear Schrodinger equations of the form −Δu+V(x)u−Δ(|u|2α)|u|2α−2u=g(x,u),x∈RN,where α>34, V∈C(RN,R), g∈C(RN×R,R). Some existence results for positive solutions, negative solutions and sequence of high energy solutions are obtained via a perturbation method.

In this paper, we propose a method to decompose an integral self-affine ${\mathbb Z}^n$-tiling set $K$ into measure disjoint pieces $K_j$ satisfying $K=\displaystyle\bigcup K_j$ in such a way that the collection of sets $K_j$ forms an integral self-affine collection associated with the matrix $B$ and this with a minimum number of pieces $K_j$. When used on a given measurable $\mathbb{Z}^n$-tiling set $K\subset\mathbb{R}^n$, this decomposition terminates after finitely many steps if and only if the set $K$ is an integral self-affine multi-tile. Furthermore, we show that the minimal decomposition we provide is unique.

The purpose of the paper is to obtain estimates for differences of functions of two pairs of commuting contractions on Hilbert space. In particular, Lipschitz type estimates, H\"older type estimates, Schatten--von Neumann estimates are obtained. The results generalize earlier known results for functions of self-adjoint operators, normal operators, contractions and dissipative operators.

The aim of this paper is to extend Sawyer's duality principle from the cone of decreasing functions of the Lebesgue space to the cone of decreasing functions of the grand Lebesgue space and to prove the boundedness of classical Hardy operators in the grand Lebesgue spaces.

Let $A$ be an expanding $d\times d$ matrix with integer entries and ${\mathcal D}\subset {\mathbb Z}^d$ be a finite digit set. Then the pair $(A, {\mathcal D})$ defines a unique integral self-affine set $K=A^{-1}(K+{\mathcal D})$. In this paper, by replacing the Euclidean norm with a pseudo-norm $w$ in terms of $A$, we construct a hyperbolic graph on $(A, {\mathcal D})$ and show that $K$ can be identified with the hyperbolic boundary. Moreover, if $(A, {\mathcal D})$ safisfies the open set condition, we also prove that two totally disconnected integral self-affine sets are Lipschitz equivalent if an only if they have the same $w$-Hausdorff dimension, that is, their digit sets have equal cardinality. We extends some well-known results in the self-similar sets to the self-affine sets.

In this paper, we are concerned with Lindelof type theorems for monotone (in the sense of Lebesgue) Sobolev functions u on a uniform domain D⊂Rn satisfying ∫D|∇u(z)|n−1φ(|∇u(z)|)ωδD(z)dz

In this paper we study the spectral heat content for various L\'evy processes. We establish the asymptotic behavior of the spectral heat content for L\'{e}vy processes of bounded variation in $\mathbb{R}^{d}$, $d\geq 1$. We also study the spectral heat content for arbitrary open sets of finite Lebesgue measure in $\mathbb{R}$ with respect to L\'{e}vy processes of unbounded variation under certain conditions on their characteristic exponents. Finally we establish that the asymptotic behavior of the spectral heat content is stable under integrable perturbations to the L\'{e}vy measure., Comment: 19 pages

Geodesic balls in a simply connected space forms Sn, Rn or Hn are distinguished manifolds for comparison in bounded Riemannian geometry. In this paper we show that they have the maximum possible boundary volume among Miao–Tam critical metrics with connected boundary provided that the boundary of the manifold has a lower bound for the Ricci curvature. In the same spirit we also extend a rigidity theorem due to Boucher et al. and Shen to n‐dimensional static metrics with positive constant scalar curvature, which gives us a partial answer to the Cosmic no‐hair conjecture.

In this paper we consider the second order discontinuous equation in the real line, (ϕ(a(t)u′(t)))′=f(t,u(t),u′(t)),a.e.t∈R,u(−∞)=A,u(+∞)=B,with ϕ an increasing homeomorphism such that ϕ(0)=0 and ϕ(R)=R, a∈C(R) with a(t)>0, for t∈R, f:R3→R a L1‐Caratheodory function and A,B∈R verifying an adequate relation. We remark that the existence of heteroclinic solutions is obtained without asymptotic or growth assumptions on the nonlinearities ϕ and f. Moreover, as far as we know, our main result is even new when ϕ(y)=y, that is, for the equation (a(t)u′(t))′=f(t,u(t),u′(t)),a.e.t∈R.

The main objective of this paper is to study the warped product pointwise semi‐slant submanifolds which are isometrically immersed into Sasakian manifolds. First, we prove some characterizations results in terms of the shape operator, under which influence a pointwise semi‐slant submanifold of a Sasakian manifold can be reduced to a warped product submanifold. Then, we determine a geometric inequality for the second fundamental form regarding to intrinsic invariant and extrinsic invariant using the Gauss equation instead of the Codazzi equation. Evenmore, we give some applications of this inequality into Sasakian space forms, and we will investigate the status of equalities in the inequality. As a particular case, we provide numerous applications of the Green lemma, the Laplacian of warped functions and some partial differential equations. Some triviality results for connected, compact warped product pointwise semi‐slant submanifolds of Sasakian space form by means of Hamiltonian and the kinetic energy of warped function involving boundary conditions are established.

In this paper we study the blow‐up of solution of a mixed problem associated to a nonlinear wave equation with dissipative and source term in a bounded domain of Rn. On a boundary portion of the domain we consider a non‐porous viscoelastic acoustic boundary conditions to a non‐locally reacting boundary.

We present an existence result for L\'evy-type processes which requires only weak regularity assumptions on the symbol $q(x,\xi)$ with respect to the space variable $x$. Applications range from existence and uniqueness results for L\'evy-driven SDEs with H\"older continuous coefficients to existence results for stable-like processes and L\'evy-type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of L\'evy and L\'evy-type processes. The paper includes an extensive list of L\'evy(-type) processes satisfying the assumptions of our results.

In this paper, we study the boundedness of the Schrodinger propagator eiΔ on Wiener amalgam spaces. In particular, we determine the necessary and sufficient conditions for the propagator eiΔ to be bounded from Wp,qs to Wp,q0.

In this paper, we prove the results on existence and uniqueness of the maximal solutions for measure differential equations, considering more general conditions on functions f and g by using the correspondence between the solutions of these equations and the solutions of generalized ODEs. Moreover, we prove these results for the dynamic equations on time scales, using the correspondence between the solutions of these last equations and the solutions of the measure differential equations.

Existence and regularity of positive solutions of a degenerate elliptic Dirichlet problem of the form −div(a(x)∇u)=b(x)up in Ω, u=0 on ∂Ω, where Ω is a bounded smooth domain in RN, N≥1, are obtained via new embeddings of some weighted Sobolev spaces with singular weights a(x) and b(x). It is seen that a(x) and b(x) admit many singular points in Ω. The main embedding results in this paper provide some generalizations of the well‐known Caffarelli–Kohn–Nirenberg inequality.

In this paper we consider regularity coefficients of a discrete linear time‐varying systems. The main result presents a complete description of the relations between Lyapunov, Perron and Grobman regularity coefficients of mutually adjoint systems.

In this paper, helicoidal flat surfaces in the $3$-dimensional sphere $\mathbb{S}^3$ are considered. A complete classification of such surfaces is given in terms of their first and second fundamental forms and by linear solutions of the corresponding angle function. The classification is obtained by using the Bianchi-Spivak construction for flat surfaces and a representation for constant angle surfaces in $\mathbb{S}^3$., Comment: 14 pages, 3 figures

In this paper we mainly investigate the Cauchy problem of a generalized Camassa–Holm equation. We first derive two global existence results and two blow‐up results from the relationship between the Degasperis–Procesi equation and the generalized Camassa–Holm equation. We then prove the existence and uniqueness of global weak solutions under some certain sign conditions on the initial data.