The author shows that the (partial) standard Langlands L-functions on quarternion groups have at most simple poles at certain positive integers.

In this paper, the authors consider inverse problems of determining a coefficient or a source term in an ultrahyperbolic equation by some lateral boundary data. The authors prove Hölder estimates which are global and local and the key tool is Carleman estimate.

Let M be a compact orientable 3-manifold with ∂M connected. If V ∪ _S W is a Heegaard splitting of M with distance at least 6, then the ∂-stabilization of V ∪ _S W along ∂M is unstabilized. Hence M has at least two unstabilized Heegaard splittings with different genera. The basic tool is a result on disk complex given by Masur and Schleimer.

Let u _k(2, r) be a little q-Schur algebra over k, where k is a field containing an l′-th primitive root ɛ of 1 with l′ ≥ 4 even, the author constructs a certain monomial base for little q-Schur algebra u _k(2, r).

In this paper, stochastic global exponential stability criteria for delayed impulsive Markovian jumping reaction-diffusion Cohen-Grossberg neural networks (CGNNs for short) are obtained by using a novel Lyapunov-Krasovskii functional approach, linear matrix inequalities (LMIs for short) technique, Itô formula, Poincaré inequality and Hardy-Poincaré inequality, where the CGNNs involve uncertain parameters, partially unknown Markovian transition rates, and even nonlinear p-Laplace diffusion (p > 1). It is worth mentioning that ellipsoid domains in ℝ ^m (m ≥ 3) can be considered in numerical simulations for the first time owing to the synthetic applications of Poincaré inequality and Hardy-Poincaré inequality. Moreover, the simulation numerical results show that even the corollaries of the obtained results are more feasible and effective than the main results of some recent related literatures in view of significant improvement in the allowable upper bounds of delays.

Let M ⁿ be a smooth closed n-manifold with a locally standard (ℤ₂) ⁿ-action. This paper deals with the relationship among the mod 2 Betti numbers of M ⁿ, the mod 2 Betti numbers and the h-vector of the orbit space of the action.

In this paper, the multivariate Bernstein polynomials defined on a simplex are viewed as sampling operators, and a generalization by allowing the sampling operators to take place at scattered sites is studied. Both stochastic and deterministic aspects are applied in the study. On the stochastic aspect, a Chebyshev type estimate for the sampling operators is established. On the deterministic aspect, combining the theory of uniform distribution and the discrepancy method, the rate of approximating continuous function and L ^p convergence for these operators are studied, respectively.

This paper deals with the existence of periodic solutions of a nonhomogeneous string with Dirichlet-Neumann condition. The authors consider the case that the period is irrational multiple of space length and prove that for some irrational number, zero is not the accumulation point of the spectrum of the associated linear operator. This result can be used to prove the existence of the periodic solution avoid using Nash-Moser iteration.

Let (Ω*(M), d) be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex (Ω*(M), d + H _∧) and its associated twisted de Rham cohomology H*(M,H). The authors show that there exists a spectral sequence {E _r ^p,q, d _r} derived from the filtration F_p (\Omega ^ * (M)) = \mathop \oplus \limits_{i \geqslant p} \Omega ^i (M) of Ω*M, which converges to the twisted de Rham cohomology H*(M,H). It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.

This paper is concerned with the global existence and pointwise estimates of solutions to the generalized Benjamin-Bona-Mahony equations in all space dimensions. By using the energy method, Fourier analysis and pseudo-differential operators, the global existence and pointwise convergence rates of the solution are obtained. The decay rate is the same as that of the heat equation and one can see that the solution propagates along the characteristic line.

The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the graphs for which the bounds are attained. Moreover, some known lower bounds on the spectral radius and the Laplacian spectral radius of unweighted graphs can be deduced from the bounds.