„… contrast, the hypoplastic material model is more complex and follows a different approach [76, 77]. Here …” „… the normal of the yield surface fσ. Otherwise it is called non-associative. During plastic loading …” „… material used in the experiments presented later. A simple approach to describe differences in material …”

„… conducted. This approach is called direct identification [137]. On the other hand, a numerical optimization …” „… identification. Due to the approach of a direct parameter identification, followed by a numerical correction …” „… Figure 4.4: Sieve distribution for Poraver depending on the applied normal stress in the oedometer test …”

„… with other approaches to increase the collision safety, it has to be economically worthwhile. The costs …” „… choose a function [52, 125]. For the diameter, a normal distribution is assumed. This leads to a diameter …” „… combined with the diameter distribution. Second, a similar approach is used for the Young’s modulus …”

„… + w0 = 0 (78)with the normal vector w and the position w0 [8]. If w is of unit length, then w0 is …” „… operate withvectors - sometimes called free vectors - that define a direction and magnitude and are …” „… notconstrained to originate at a specific point [134]. In the context of this thesis, vectors areused, for …”

„… . Example curve progressions can be seen in Figure 2.The rehabilitation of a normal gait pattern that has …” „… calculate the jointmoments from the GRF vector, its center of pressure (COP), the geometry of the …” „… dynamics approach is to considerall body parts in a free body diagram. The sum of all acting forces …”

„… including the derived cetane number. The resulting virtual fuel screening approach is applied to the task …” „… Akaike’s information criterion corrected for small sample size IX Notation b product flow kmol/h b vector …” „… of product flows kmol/h c vector of weights (PLS) C pathway conversion Cant,1 − Cant,7 parameters for …”

„… applicability domain concept. The revised approach is outlined in this Chapter. Its basic principles have …” „… theoretical description of the QSPR modeling approach. Furthermore, the QSPR models are compared to …” „… ) regression (Höskuldsson, 1988), constitute the cornerstones of the approach. The modeling strategy presented …”

„… slightly modified form (Dahmen and Marquardt, 2016). CAMD approaches relying on similar ways of targeted …” „… , the CRPM approach has some similarities to the 43 3 Targeted generation of candidate structures …” „… identities used to connect carbon chains chains 1 nC number of carbon atoms p−OH position vector of alcohol …”

„… ; Ulonska et al., 2016b; Dahmen and Marquardt, 2016). A first attempt at bringing the two approaches …” „… . The approach followed by Zalfen (2014), however, has multiple shortcomings. First, Zalfen (2014) did …” „… is then applied to a case study in order to demonstrate the feasibility of the approach. The case …”

„… approximation of the normal distribution. Note that it was decided not to model the DCN directly. The rationale …” „… logarithmic ignition delay yti = ln τi are distinguished by means of the model candidate index t. The vector …” „… Gt holds the parameters related to the structural groups. Dt denotes the vector of parameters related …”

„… combustion chamber (Allard et al., 1997, 1996; Kalghatgi, 2014a). Advantages of this approach include …” „… . (2012) have developed a three-stage Arrhenius approach describing the ignition delay as a function of …” „… how close the performance of a practical process approaches the ideal case (Cherubini and Stromman …”

„… vector sTi (ui,Θ ∗) = [ ∂yi(ui,Θ ∗) ∂Θ∗1 , .., ∂yi(ui,Θ ∗) ∂Θ∗14 ] (C.2) for the model inputs uTi …” „… = [gi,di] T. Given the model structure yi (cf. Table 4.9) the entries of the vector sTi can be written as …” „… QSPR modeling in Chapter 5. Figure D.1 shows the bisection approach that is used to control the …”

„… unit normal vector. The stresses are connected to the strains with the generalized Hooke’s law ∼σ …” „… of the load vector in each cell. Numerical studies suggest that this approach leads to a very …” „… , f b denotes the vector of body force per unit volume, u and ̈u are respectively the displacement …”

„… FCM with regard to such problems and, accordingly, propose several approaches to obtain a reliable …” „… load vector are similar to Eq. (2.31), except for the facts that α is equal to one in this case and …” „… different approaches that are suitable to deal with this kind of problems. 4.2 Local refinement and …”

„… Multiscale Analysis Approach. Elsevier, 2013. [18] M. Ainsworth and H. Wajid. Dispersive and dissipative …” „… . Zander, S. Kollmannsberger, and E. Rank. Normal contact with high order finite elements and a fictitious …” „… vector sequences applied to multi-physics problems. Proceedings in Applied Mathematics and Mechanics …”

„… . in the eXtended/generalized finite element method or in the partition of unity based approaches [27 …” „… rules [14, 39, 107, 125, 166]. These approaches, which are referred to as the composed integration …” „… quadrature rule. This approach is actually the main idea of the composed integration, as to be explained in …”

„… , VariationalAutoencoders (VAEs) [67] force the latent vectors to follow a certaindistribution, usually a normal …” „… distribution. With that, as long as a codevector is sampled from that normal distribution, the decoder can be …” „… highdimensional input into low dimensional latent vector. This vector isdecoded back to the size of the original …”

„… originalauthors [80] propose to use a weighted approach:F(p,q) = w ·DKL(p,q) + (1−w) ·DKL(q,p). (4.8)Fig. 4.5 …” „… sections.These results show that training just one scale, i. e. just a normal fullyconvolutional GAN is possible …” „… embeddings, a new metric proposedalong with TOAD-GAN. An embedding is a learned vector that representsa (part …”