Under the internal dissipative condition, the Cauchy problem for inhomogeneous quasilinear hyperbolic systems with small initial data admits a unique global C ¹ solution, which exponentially decays to zero as t → +∞, while if the coefficient matrix Θ of boundary conditions satisfies the boundary dissipative condition, the mixed initial-boundary value problem with small initial data for quasilinear hyperbolic systems with nonlinear terms of at least second order admits a unique global C ¹ solution, which also exponentially decays to zero as t → +∞. In this paper, under more general conditions, the authors investigate the combined effect of the internal dissipative condition and the boundary dissipative condition, and prove the global existence and exponential decay of the C ¹ solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small initial data. This stability result is applied to a kind of models, and an example is given to show the possible exponential instability if the corresponding conditions are not satisfied.

The main purpose of this paper is to study the deformed Riemannian extension ^∇ g+ ^V G ^•• in the cotangent bundle, where G is a twin Norden metric on the base manifold.

A Nash group is said to be almost linear if it has a Nash representation with a finite kernel. Structures and basic properties of these groups are studied.

Since the spherical Gaussian radial function is strictly positive definite, the authors use the linear combinations of translations of the Gaussian kernel to interpolate the scattered data on spheres in this article. Seeing that target functions are usually outside the native spaces, and that one has to solve a large scaled system of linear equations to obtain combinatorial coefficients of interpolant functions, the authors first probe into some problems about interpolation with Gaussian radial functions. Then they construct quasi-interpolation operators by Gaussian radial function, and get the degrees of approximation. Moreover, they show the error relations between quasi-interpolation and interpolation when they have the same basis functions. Finally, the authors discuss the construction and approximation of the quasi-interpolant with a local support function.

Let p ⩾ 7 be an odd prime. Based on the Toda bracket 〈α ₁ β ₁ ^p−1, α ₁ β ₁, p,γ _s〉, the authors show that the relation α ₁ β ₁ ^p−1 h _2,0 γ _s = β _p/p−1 γ _s holds. As a result, they can obtain α ₁ β ₁ ^p h _2,0 γ _s = 0 ∈ π _*(S ⁰) for 2 ⩽ s ⩽ p − 2, even though α ₁ h _2,0 γ _s and β ₁ α ₁ h _2,0 γ _s are not trivial. They also prove that β ₁ ^p−1 α ₁ h _2,0 γ ₃ is nontrivial in π _*(S ⁰) and conjecture that β ₁ ^p−1 α ₁ h _2,0 γ _s is nontrivial in π _*(S ⁰) for 3 ⩽ s ⩽ p − 2. Moreover, it is known that \beta _{p/p - 1} \gamma _3 = 0 \in Ext_{BP_* BP}^{5,*} (BP_* ,BP_* ), but β _p/p−1 γ ₃ is nontrivial in π _*(S ⁰) and represents the element β ₁ ^p−1 α ₁ h _2,0 γ ₃.

Based on the loop-algebraic presentation of 2-toroidal Lie superalgebras, a free field representation of toroidal Lie superalgebras of type A(m, n) is constructed using both vertex operators and bosonic fields.

The first cohomology group of generalized loop Virasoro algebras with coefficients in the tensor product of its adjoint module is shown to be trivial. The result is used to prove that Lie bialgebra structures on generalized loop Virasoro algebras are coboundary triangular. The authors generalize the results to generalized map Virasoro algebras.

The authors consider a family of finite-dimensional Lie superalgebras of O-type over an algebraically closed field of characteristic p > 3. It is proved that the Lie superalgebras of O-type are simple and the spanning sets are determined. Then the spanning sets are employed to characterize the superderivation algebras of these Lie superalgebras. Finally, the associative forms are discussed and a comparison is made between these Lie superalgebras and other simple Lie superalgebras of Cartan type.

In this paper, the authors first give the properties of the convolutions of Orlicz-Lorentz spaces Λ_{φ1, w} and Λ_{φ2, w} on the locally compact abelian group. Secondly, the authors obtain the concrete representation as function spaces for the tensor products of Orlicz-Lorentz spaces Λ_{φ1, w} and Λ_{φ2, w} and get the space of multipliers from the space Λ_{φ1, w} to the space M _{φ2*, w} Finally, the authors discuss the homogeneous properties for the Orlicz-Lorentz space Λ_{φ, w} ^{p, q}.