In this paper, we give a detailed description of the local behavior of theLipschitz-1/2 modulus for cumulative hazard process and PL-process when the data are subject to lefttruncation and right censored observations....In this paper, we give a detailed description of the local behavior of theLipschitz-1/2 modulus for cumulative hazard process and PL-process when the data are subject to lefttruncation and right censored observations. We establish laws of the iterated logarithm of theLipschitz-1/2 modulus of PL-process and cumulative hazard process. These results for the PL-processare sharper than other results found in the literature, which can be used to establish theasymptotic properties of many statistics.展开更多
The main purpose of this article is to choose among advanced rheological models used in the French rational design, one that best represents the viscoelastic behavior of asphalt mixtures mixed with aggregates of Seneg...The main purpose of this article is to choose among advanced rheological models used in the French rational design, one that best represents the viscoelastic behavior of asphalt mixtures mixed with aggregates of Senegal. The model chosen will be the basis for the development of computational tools for stress and strain for Senegal. However, the calibration of these models needs complex modulus test results. In opposition to mechanical models the complex modulus can directly characterize the viscoelastic behavior of bituminous materials. Here determination is performed in the laboratory by using several types of tests divided into two groups: homogeneous tests and non-homogeneous tests. The choice of model will be carried out by statistical analysis through the least squares method. To this end, a study was carried out to “Laboratory of Pavement and Bituminous Materials” (LCMB) with asphalt concrete mixed with aggregate from Senegal named basalt of Diack and quartzite of Bakel. In this study, the test used to measure the complex modulus is the Canadian test method LC 26-700 (Determination of the complex modulus by tension-compression). There mainly exist two viewing complex modulus planes for laboratory test results: the Cole and Cole plane and the Black space. The uniqueness of the data points in these two areas means that studied asphalt concretes are thermorheologically simple and that the principle of time-temperature superposition can be applied. This means that the master curve may be drawn and that the same modulus value can be obtained for different pairs (frequency-temperature). These master curves are fitted during the calibration process by the advanced rheological models. One of the most used software in the French rational design for the visualization of complex modulus test results and calibration of rheological models developed tools is named Visco-analysis. In this study, its use in interpreting the complex modulus test results and calibration models shows that, the studied asphalt concretes are thermorheologically simple, because they present good uniqueness of their Black and Cole and Cole and Black diagrams. They allow a good application of the principle of time temperature superposition. The statistical analysis of calibration models by the least squares method has shown that the three studied models are suitable for modeling the linear viscoelastic behavior of asphalt mixtures formulated with the basalt of Diack and the quartzite of Bakel. Indeed their calibration has very similar precision values of “Sum of Squared Deviation” (SSD) about 0.185. However, the lower precision value (0.169) is obtained with the 2S2P1D model.展开更多
文摘In this paper, we give a detailed description of the local behavior of theLipschitz-1/2 modulus for cumulative hazard process and PL-process when the data are subject to lefttruncation and right censored observations. We establish laws of the iterated logarithm of theLipschitz-1/2 modulus of PL-process and cumulative hazard process. These results for the PL-processare sharper than other results found in the literature, which can be used to establish theasymptotic properties of many statistics.
文摘The main purpose of this article is to choose among advanced rheological models used in the French rational design, one that best represents the viscoelastic behavior of asphalt mixtures mixed with aggregates of Senegal. The model chosen will be the basis for the development of computational tools for stress and strain for Senegal. However, the calibration of these models needs complex modulus test results. In opposition to mechanical models the complex modulus can directly characterize the viscoelastic behavior of bituminous materials. Here determination is performed in the laboratory by using several types of tests divided into two groups: homogeneous tests and non-homogeneous tests. The choice of model will be carried out by statistical analysis through the least squares method. To this end, a study was carried out to “Laboratory of Pavement and Bituminous Materials” (LCMB) with asphalt concrete mixed with aggregate from Senegal named basalt of Diack and quartzite of Bakel. In this study, the test used to measure the complex modulus is the Canadian test method LC 26-700 (Determination of the complex modulus by tension-compression). There mainly exist two viewing complex modulus planes for laboratory test results: the Cole and Cole plane and the Black space. The uniqueness of the data points in these two areas means that studied asphalt concretes are thermorheologically simple and that the principle of time-temperature superposition can be applied. This means that the master curve may be drawn and that the same modulus value can be obtained for different pairs (frequency-temperature). These master curves are fitted during the calibration process by the advanced rheological models. One of the most used software in the French rational design for the visualization of complex modulus test results and calibration of rheological models developed tools is named Visco-analysis. In this study, its use in interpreting the complex modulus test results and calibration models shows that, the studied asphalt concretes are thermorheologically simple, because they present good uniqueness of their Black and Cole and Cole and Black diagrams. They allow a good application of the principle of time temperature superposition. The statistical analysis of calibration models by the least squares method has shown that the three studied models are suitable for modeling the linear viscoelastic behavior of asphalt mixtures formulated with the basalt of Diack and the quartzite of Bakel. Indeed their calibration has very similar precision values of “Sum of Squared Deviation” (SSD) about 0.185. However, the lower precision value (0.169) is obtained with the 2S2P1D model.
