Rigidity of joinings for some measure-preserving systems

We introduce two properties: strong R-property and $C(q)$ -property, describing a special way of divergence of nearby trajectories for an abstract measure-preserving system. We show that systems satisfying the strong R-property are disjoint (in the sense of Furstenberg) with systems satisfying the $C(q)$ -property. Moreover, we show that if $u_t$ is a unipotent flow on $G/\Gamma $ with $\Gamma $ irreducible, then $u_t$ satisfies the $C(q)$ -property provided that $u_t$ is not of the form $h_t\times \operatorname {id}$ , where $h_t$ is the classical horocycle flow. Finally, we show that the strong R-property holds for all (smooth) time changes of horocycle flows and non-trivial time changes of bounded-type Heisenberg nilflows.

Seasonal effects in the long-term correction of short-term wind measurements using reanalysis data

Measure-Correlate-Predict (MCP) approaches are often used to correct wind measurements to the long-term wind conditions on site. This paper investigates systematic errors in MCP-based long-term corrections which occur if the measurement on site covers only a few months (seasonal biases). In this context, two common linear MCP methods are tested and compared, namely Variance Ratio and Linear Regression with Residuals. Wind measurement data from 18 sites with different terrain complexity in Germany are used (measurement heights between 100 and 140 m). Six different reanalysis data sets serve as the reference (long-term) wind data in the MCP calculations. Besides experimental results, theoretical considerations are presented which provide the mathematical background for understanding the observations. General relationships are derived which trace the seasonal biases to the mechanics of the methods and the properties of the reanalysis data sets. This allows the transfer of the results of this study to different measurement durations, other reference data sets and other regions of the world. In this context, it is shown both theoretically and experimentally that the results do not only depend on the selected reference data set but also significantly change with the choice of the MCP method.

Quasi-Affine, Noetherian, Jacobi Hulls and Computational Geometry

Let us assume $| {O^{(\rho)}} | = 1$. Mike Hugo's classification of non-linear, left-simply standard, essentially Wiles categories was a milestone in abstract measure theory. We show that $\bar{K}$ is not comparable to $\kappa$. In this setting, the ability to classify graphs is essential. The work in \cite{cite:0} did not consider the ultra-minimal case.

Abstract measure algebras over homogeneous spaces of compact groups

This paper presents a systematic study for abstract Banach measure algebras over homogeneous spaces of compact groups. Let [Formula: see text] be a closed subgroup of a compact group [Formula: see text] and [Formula: see text] be the left coset space associated to the subgroup [Formula: see text] in [Formula: see text]. Also, let [Formula: see text] be the Banach measure space consists of all complex measures over [Formula: see text]. Then we introduce the abstract notions of convolution and involution over the Banach measure space [Formula: see text].

Integrating the Dynamic Modulus of Asphalt Mixes in the 1993 AASHTO Design Method

The AASHTO Guide for Design of Pavement Structures 1993 (1993 Design Guide) remains the most widely used pavement design manual by highway agencies and design consultants around the world. As defined in the 1993 Design Guide, the structural coefficient of a pavement layer ( ai) is an abstract measure of the relative ability of a unit thickness of a given material to function as a structural component of the pavement. Nevertheless, the assumed ai values of the asphalt layers and a proposed relationship between ai and the resilient modulus do not account for the mechanical and physical properties of asphalt materials, traffic volume and speed, layer thicknesses (thin versus thick pavements), climate, and unbound layer properties. The purpose of this research was to enhance the design methodology incorporated in the 1993 Design Guide by integrating asphalt mixture properties in the design process. The objective was to devise a relationship between the structural coefficient ( ai) of the asphalt layer and the effective dynamic modulus (|E*|eff.) of the corresponding asphalt mix to yield a more realistic estimate of the structural capacity of the asphalt layer. The paper illustrates the development of a multilinear relationship between ai, (|E*|eff.), and the resilient modulus of the aggregate base layer. Pavement structural designs for various asphalt mixes and design inputs using the developed ai–(|E*|eff.) relationship yielded asphalt layer thicknesses that were generally smaller than those obtained using the typical ai value of 0.44 for the asphalt layer and closer to thicknesses obtained with the AASHTO mechanistic–empirical design method using the Pavement ME software.