The purpose of this article is to study representations of δ-BiHom-Jordan-Lie superalgebras. In particular, adjoint representations, trivial representations, deformations of δ-Bihom-Jordan-Lie superalgebras are studied in detail. Derivations of δ-BiHom-Jordan-Lie algebras are also discussed as an application.
We obtain new reverse Bonnesen-type inequalities for a surface of constant curvature by estimating the containment measure in integral geometry. These inequalities are generalizations and improvements of known Bottema inequality and new reverse Bonnesen-type inequalities in the Euclidean plane.
Let A be a factor von Neumann algebra. We prove that each nonlinear mixed ξ-Jordan triple derivable map φ:A → A is an additive *-derivation and φ(ξA)=ξφ(A) for all A ∈ A with ξ≠ 0, -1
In this paper, we generalize Vogt theorem in G-n-normed spaces:A mapping between two G-n-normed spaces which preserves ρ-gauge distance is affine.
This paper is concerned with the Cauchy problem of the non-resistive magnetohydrodynamics equations in Rd for d=2, 3. The local well-posedness in Sobolev space Hs-1×Hs for s > d/2 is obtained by establishing a commutator estimate.
Denote by pn(A1, …, An) the (n-1)-commutator of A1, …, An. Assume that M is a von Neumann algebra, n ≥ 2 is any positive integer and L:M → M is a mapping. It is shown that, if M has no central summands of type I1 and L satisfies L(pn(A1, …, An))=∑k=1n pn(A1, …, Ak-1, L(Ak), Ak+1, …, An) for all A1, A2, …, An ∈ M with A1A2=0, then L(A)=φ(A) + f(A) for all A ∈ M, where φ:M → M and f:M → Z (M) (the center of M) are two mappings such that the restriction to PiMPj of φ is an additive derivation and f(pn(A1, A2, …, An))=0 for all A1, A2, …, An ∈ PiMPj with A1A2=0 (1 ≤ i, j ≤ 2), P1 ∈ M is a core-free projection and P2=I -P1; if M is a factor and n ≥ 3, then L satisfies L(pn(A1, A2, …, An))=∑k=1n pn(A1, …, Ak-1, L(Ak), Ak+1, …, An) for all A1, A2, …, An ∈ M with A1A2A1=0 if and only if L(A)=φ(A) + h(A)I for all A ∈ M, where φ is an additive derivation on M and h is a functional of M such that h(pn(A1, A2, …, An))=0 for all A1, A2, …, An ∈ M with A1A2A1=0.
We dedicate to study the compactness of commutators for fractional integral operators, Marcinkiewicz integrals and pseudo-differential operators with smooth symbols on the generalized Morrey spaces Mp,ω(Rn). Notice the differences of dealing method respectively.
Let T be the singular integral operator with variable kernel and Dγ (0 ≤ γ ≤ 1) be the fractional differentiation operator. Denote T* and T# be the adjoint of T and the pseudo-adjoint of T respectively. In this paper, via the expansion of the spherical harmonical polynomials, the boundedness on ?q,λω (Rn) is shown to hold for TDγ-DγT and (T*-T#)Dγ. Meanwhile, the authors also establish various weighted norm inequalities for the product T1T2 and the pseudo-product T1°T2.
In this paper, we discuss the computational problem of a hybrid power mean involving character sums of polynomials and two-term cubic exponential sums, by using analytic methods and the properties of two-term exponential sums and Dirichlet characters. Meanwhile, we obtain a sharp asymptotic formula.
The Lie algebra W (2, 2) is one kind of infinite-dimensional Lie algebras, which plays a key role in classification of vertex operator algebras generated by weight 2 vectors. Hom-Lie algebras are algebras with an algebra structure and a Lie algebra structure, both of which satisfy the Leibniz rule. This paper mainly determine all Hom-Lie structures on the Lie algebra W (2, 2). It is the main result that all Hom-Lie algebra structures are trivial on the Lie algebra W (2, 2), which will be helpful to the further researches on the Lie algebra W (2, 2).
In 2006, Schuster introduced the concept of radial Blaschke-Minkowski homomorphisms. Afterwards, Wang et al. extended this notion to Lp radial Blaschke-Minkowski homomorphisms. In this paper, we establish some inequalities of Lp dual geominimal surface areas for Lp radial Blaschke-Minkowski homomorphisms, including the Brunn-Minkowski type and monotonic inequalities. And we give an affirmative form and a negative form of Busemann-Petty problem for Lp radial Blaschke-Minkowski homomorphisms.
