Global branch from the second eigenvalue for a semilinear Neumann problem in a ball

Let (n?3) be a ball, and let f∈C³. We are concerned with the Neumann problem

     

Simultaneous Diophantine approximation on manifolds and Hausdorff dimension

Let M be an m-dimensional, C^k manifold in , for any , and for any τ>0 let

     

Adams' inequalities for bi-Laplacian and extremal functions in dimension four

Let Ω⊂R⁴ be a smooth oriented bounded domain, be the Sobolev space, and be the first eigenvalue of the bi-Laplacian operator Δ². Then for any α: 0?α<λ(Ω), we have

     

Precise rates in the law of logarithm for the moment convergence of i.i.d. random variables

Let be a sequence of i.i.d. random variables with EX=0 and EX²=σ²<∞. Set , Mn=maxk?n|Sk|, n?1. Let r>1, then we obtain

     

Lipschitz constant for bi-Lipschitz automorphism on Moran-like sets

This paper proves that if F⊂R¹ is a complete set equipped with some suitable Moran-like structure, then there is a constant c₀>1 such that for any bi-Lipschitz bijection ,

     

Exceptional congruences for the coefficients of certain eta-product newforms

Let F(z)=∑_n=1^∞a(n)qⁿ denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that

     

On the stability of limit cycles for planar differential systems

We consider a planar differential system , , where P and Q are C¹ functions in some open set U⊆R², and . Let γ be a periodic orbit of the system in U. Let f(x,y):U⊆R²→R be a C¹ function such that

     

Norm estimates of almost Mathieu operators

We estimate the norm of the almost Mathieu operator , regarded as an element in the rotation C^*-algebra . In the process, we prove for every λ∈R and the inequality

     

On strong uniform distribution III

Let a = (a_ii=1^∞ be a strictly increasing sequence of natural numbers and let be a space of Lebesgue measurable functions defined on [0,1). Let <y> denote the fractional part of the real number y. We say that a is an ^∗ sequence if for each f ?

     

Derivatives of the L-cosine transform

The L^p-cosine transform of an even, continuous function is defined by

     

Estimates of majorizing sequences in the Newton-Kantorovich method: A further improvement

Let be an operator, with X and Y Banach spaces, and f^′ be Hölder continuous with exponent θ. The convergence of the sequence of Newton-Kantorovich approximations

     

A min-max theorem for complex symmetric matrices

We optimize the form Re x^tTx to obtain the singular values of a complex symmetric matrix T. We prove that for ,