Spectral asymptotics and basis properties of fourth order differential operators with regular boundary conditions

In this paper, we consider the problem where λ is a spectral parameter; q(x) ∈ L₁(0,1) is complex‐valued function; α_s, s = 1,2,3, are arbitrary complex constants that satisfy α₂ = α₁ + α₃ and σ = 0,1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established. It is proved that all the eigenvalues, except for finite number, are simple and the system of root functions of this spectral problem forms a basis in the space L_p(0,1), 1 < p < ∞ , when ; moreover, this basis is unconditional for p = 2. We note that the considered problem was previously investigated in the condition of α₂ ≠ α₁ + α₃. Copyright © 2013 John Wiley & Sons, Ltd.     

特殊Cartan型李超代数的Borel子代数

本文研究了特征零的代数闭域上秩为4的有限维特殊Cartan型李超代数S的结构.利用正则元的划分,确定出S关于典范环面的所有正根系,从而得到了S的所有Borel子代数;对于每一个正根系,通过给出其单根系,得到了任何两个Borel子代数的连接关系;最后确定了每一个Borel子代数的极大可解性.本文所得结果可用于进一步研究Cartan型单李超代数的结构与表示.     

On the completeness of root vectors generated by systems of coupled hyperbolic equations

The paper is the second in a set of two papers, which are devoted to a unified approach to the problem of completeness of the generalized eigenvectors (the root vectors) for a specific class of linear non‐selfadjoint unbounded matrix differential operators. The list of the problems for which such operators are the dynamics generators includes the following: (a) initial boundary‐value problem (IBVP) for a non‐homogeneous string with both distributed and boundary damping; (b) IBVP for small vibrations of an ideal filament with a one‐parameter family of dissipative boundary conditions at one end and with a heavy load at the other end; this filament problem is treated for two cases of the boundary parameter: non‐singular and singular; (c) IBVP for a three‐dimensional damped wave equation with spherically symmetric coefficients and both distributed and boundary damping; (d) IBVP for a system of two coupled hyperbolic equations constituting a Timoshenko beam model with variable coefficients and boundary damping; (e) IBVP for a coupled Euler‐Bernoulli and Timoshenko beam model with boundary energy dissipation (the model known in engineering literature as bending‐torsion vibration model); (f) IBVP for two coupled Timoshenko beams model, which is currently accepted as an appropriate model describing vibrational behavior of a longer double‐walled carbon nanotube. Problems have been discussed in the first paper of the aforementioned set. Problems are discussed in the present paper.     

IS THERE UNIT ROOT IN THE NITROGEN OXIDES EMISSIONS: A MONTE CARLO INVESTIGATION?

Abstract Use of the time‐series econometric techniques to investigate issues about environmental regulation requires knowing whether air pollution emissions are trend stationary or difference stationary. It has been shown that results regarding trend stationarity of the pollution data are sensitive to the methods used. I conduct a Monte Carlo experiment to study the size and power of two unit root tests that allow for a structural change in the trend at a known time using the data‐generating process calibrated to the actual pollution series. I find that finite sample properties of the Perron test are better than the Park and Sung Phillips‐Perron (PP) type test. Severe size distortions in the Park and Sung PP type test can explain the rejection of a unit root in air pollution emissions reported in some environmental regulation analyses.     

Root filtration spaces from Lie algebras and abstract root groups

Both Timmesfeld's abstract root subgroups and simple Lie algebras generated by extremal elements lead to root filtration spaces: synthetically defined geometries on points and lines which can be characterized as root shadow spaces of buildings. Here we show how to obtain the root filtration space axioms from root subgroups and classical Lie algebras.     

KCl effect on the solubility of five different amino acids in water

Using the analytical gravimetric method the solubility of glycine and dl-alanine in aqueous systems of KCl at 323.15 K, and of l-isoleucine, l-threonine and l-serine in the same system, at 298.15 and 323.15 K, were measured for salt concentrations ranging up to 2.0 molal.     

Exact stability regions for quartic polynomials

Given an arbitrary real quartic polynomial, we find the exact region containing the coefficients of the polynomial such that all roots have absolute values less than 1.     

TEMPORAL AGGREGATION AND TESTING FOR TIMBER PRICE BEHAVIOR

ABSTRACT. Different harvest timing models make different assumptions about timber price behavior. Those seeking to optimize harvest timing are thus first faced with a decision regarding which assumption of price behavior is appropriate for their market, particularly regarding the presence of a unit root in the timber price time series. Unfortunately for landowners and investors, the literature provides conflicting guidance on this subject. One source for the ambiguous results of unit root tests of timber prices may involve data problems. We used Monte Carlo simulations to show that aggregating observations below their observed rate resulted in similar power reductions and empirical size distortions across three classes of unit root tests. Moving‐average error structures can also affect power and sizes of tests on period‐averaged data. Such error structures can also be created by the kind of temporal averaging common in reported timber prices. If we take timber prices at their face value and therefore ignore these sampling error and temporal aggregation complications, we find that unit root tests on southern timber prices support a unit root in 158 out of 208 product‐deflation combinations tested, random walks in 38 of the series found to be nonsta‐tionary, and stationarity in none. However, if we recognize temporal aggregation errors, unit root tests more commonly favor stationarity, especially for pulpwood stumpage. Because price trends for sawtimber and pulpwood products may behave differently even in the same region, stochastic harvest timing models must be developed that allow their multiple products to follow different price paths.     

Bounds for the Perron root, singularity/nonsingularity conditions, and eigenvalue inclusion sets

Using a unified approach based on the monotonicity property of the Perron root and its circuit extension, a series of exact two-sided bounds for the Perron root of a nonnegative matrix in terms of paths in the associated directed graph is obtained. A method for deriving the so-called mixed upper bounds is suggested. Based on the upper bounds for the Perron root, new diagonal dominance type conditions for matrices are introduced. The singularity/nonsingularity problem for matrices satisfying such conditions is analyzed, and the associated eigenvalue inclusion sets are presented. In particular, a bridge connecting Gerschgorin disks with Brualdi eigenvalue inclusion sets is found. Extensions to matrices partitioned into blocks are proposed.