Smooth Signals and Syntactic Change

A large body of recent work argues that considerations of information density predict various phenomena in linguistic planning and production. However, the usefulness of an information theoretic account for explaining diachronic phenomena has remained under-explored. Here, we test the idea that speakers prefer informationally uniform utterances on diachronic data from historical English and Icelandic. Our results show that: (i) the information density approach allows us to predict that Subject and Object type will affect the frequencies of OV and VO in specific ways, creating a complex Constant Rate Effect, (ii) the bias towards information uniformity explains this CRE and may help to explain others, and (iii) communities of speakers are constant in their average target level of information uniformity over long periods of historical time. This finding is consistent with an understanding of this bias which places it deep in the human language faculty and the human faculty for communication.

Linear Surjective Maps Preserving at Least One Element from the Local Spectrum

Let X be a complex Banach space and denote by ${\cal L}(X)$ the Banach algebra of all bounded linear operators on X. We prove that if φ: ${\cal L}(X) \to {\cal L}(X)$ is a linear surjective map such that for each $T \in {\cal L}(X)$ and x ∈ X the local spectrum of φ(T) at x and the local spectrum of T at x are either both empty or have at least one common value, then φ(T) = T for all $T \in {\cal L}(X)$. If we suppose that φ always preserves the modulus of at least one element from the local spectrum, then there exists a unimodular complex constant c such that φ(T) = cT for all $T \in {\cal L}(X)$.

Vibration and Damping Analysis of a Multilayered Composite Plate with a Viscoelastic Midlayer

Based on the theory of Donnell and Kirchhoff hypothesis and by using the complex constant model of viscoelastic materials, the vibration equations of five-layered constrained damping plate are established. The transfer matrix method (TMM) is improved and used to solve equations. The improved TMM is more effective to solve complex structural vibration. The influence of layer numbers, thickness of each layer, and arrangement of materials on vibration behavior are discussed. It is proved that multilayered plates can more effectively reduce natural frequency and obtain higher structural loss factor. The loss factor increases with the number of whole layers. Symmetrical structure can obtain higher structural loss factor than one-direction structure. Uniform arrangement of viscoelastic materials and constrained materials can obtain higher structural loss factor than nonuniform arrangement. There is different optimum frequency with different material thickness, and the optimum frequency is not dependent from layer numbers.

Results on the deficiencies of some differential-difference polynomials of meromorphic functions

In this paper, we study the relation between the deficiencies concerning a meromorphic function f(z), its derivative f′(z) and differential-difference monomials f(z)mf(z+c)f′(z), f(z+c)nf′(z), f(z)mf(z+c). The main results of this paper are listed as follows: Let f(z) be a meromorphic function of finite order satisfying $$\mathop {\lim \,{\rm sup}}\limits_{r \to + \infty } {{T(r,\,f)} \over {T(r,\,f')}}{\rm{ < }} + \infty ,$$ and c be a non-zero complex constant, then δ(∞, f(z)m f(z+c)f′(z))≥δ(∞, f′) and δ(∞,f(z+c)nf′(z))≥ δ(∞, f′). We also investigate the value distribution of some differential-difference polynomials taking small function a(z) with respect to f(z).

Bessel Equation in the Semiunbounded Intervalx∈[x0,∞]: Solving in the Neighbourhood of an Irregular Singular Point

This study expresses the solution of the Bessel equation in the neighbourhood ofx=∞as the product of a known-form singular divisor and a specific nonsingular function, which satisfies the corresponding derived equation. Considering the failure of the traditional irregular solution constructed with the power series, we adopt the corrected Fourier series with only limited smooth degree to approximate the nonsingular function in the interval[x0,∞]. In order to guarantee the series’ uniform convergence and uniform approximation to the derived equation, we introduce constraint and compatibility conditions and hence completely determine all undetermined coefficients of the corrected Fourier series. Thus, what we found is not an asymptotic solution atx→∞(not to mention a so-called formal solution), but a solution in the interval[x0,∞]with certain regularities of distribution. During the solution procedure, there is no limitation on the coefficient property of the equation; that is, the coefficients of the equation can be any complex constant, so that the solution method presented here is universal.