4. Lagrange Formalism
Similar **to** **entropy**, the Lagrange formalism also plays **a** significant role in many areas of physics. In addition **to** the derivation of the Boltzmann factor depicted above, the Lagrange formalism is **a** major foundation for quantum mechanics and, in particular, has been used **to** derive relations between symmetries and conservation laws. The Noether theorems, which were derived using the Lagrange formalism, showed that invariance of physical laws subject **to** **a** translation implies the conservation of momentum and invariance subject **to** translation in time implies the conservation of energy. **A** further striking observation is that major physical laws all contain **a** Laplacian operator (that is, are **a** Poisson-type equation) somehow suggesting **a** common ground of all these models, which comprise all different length scales like gravitation, electrostatics, thermal conductivity, diffusion, flow, **phase**-**field**, Schrödinger equations, density functional equations and many others. Some operators present in the Lagrange scheme have the property of generating Laplacian operators. The basic concept of the Lagrange formalism is based on **a** functional being **a** scalar function F of **a** variable Φ i which, itself, is **a** function of space and time Φ i = Φ i ( r, t ) , and being an integral of **a** density function f.

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The calculation of the SH coefficients can only be solved by means of global data coverage. This could only be achieved after the first geodetic satellite missions (like the LAGEOS, GRACE, GOCE and CHAMP missions). The satellite missions are utilizing different types of measurement principles. The LAGEOS satellites apply the principle of Satellite Laser Ranging (SLR), while the CHAMP mission uses the principle of Satellite-**to**-Satellite tracking in high- low mode, where the residual **gravity** accelerations are additionally measured by means of an accelerometer. The GRACE Satellite mission uses the principle of Satellite-**to**-Satellite tracking in low-low mode, where the **gravity** differences between two satellites separated by hundreds of kilometers are observed. The most modern GOCE mission uses the principle of **gravity** gradiometry using **a** group of accelerometers fixed on the three axes of the satellite. The combination of satellite observations with terrestrial measurements led **to** the **combined** **gravity** models (e.g. EGM98A, EGM96, EIGEN06c and EGM2008). The SH can be calculated by two methods: the first is the integration method that keeps the orthogonality conditions of the SH, and second is the least squares estimation (Fan, 2004).

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system as **a** toy model and studied its **phase** transition. At the quantum crit- ical point, the first Bogoliubov mode becomes light, increasing the density of states. The number of nearly degenerate states is not excessive, however, be- cause the minimal mass gap scales like N −1/3 , **a** far cry from the exponential degeneracy of black holes. It is still one of the important unsolved questions of the graviton condensate picture **to** plausibly explain the black hole **entropy**. Simply replacing the Lieb-Liniger coupling α with **a** momentum dependent term proportional **to** k 2 looks somewhat plausible with the graviton interac- tion in mind and would hint at many more Bogoliubov modes becoming light in (2.24). Whether the resulting model is viable, however, is **a** completely separate question. **A** momentum dependent coupling was already introduced in [BM+13] and analyzed more closely with the black hole **entropy** in mind in [DF+15]. More investigations regarding the **entropy** are, however, clearly mandated, especially as BMS transformations at the horizon [HPS16] have also been considered **to** provide the required states in the graviton condensate model [AD+16].

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After discussing non perturbative physics in the context of nonabelian gauge theories we will now discuss aspects of **gravity**. The most puzzling object in **gravity** is certainly **a** black hole with two of the big open questions being the origin of black hole **entropy** and the so called information paradox. Accord- ing **to** an argument by Bekenstein black holes should have an **entropy** [3–5], which is proportional **to** the horizon area of the black hole measured in planck units. **A** clear microscopic interpretation of this **entropy** has not been found so far. There have been microscopic computations of the degeneracy of ex- tremal black holes in the context of string theory, which provides an ultra- violet completion **to** general relativity. This **approach** has been pioneered in **a** seminal paper by Strominger and Vafa [6], where they compute the degeneracy of BPS black holes using an intricate series of very indirect ar- guments. However due **to** their indirect nature, these computations do not give **a** clear interpretation of the degeneracy, however they provide **a** clear check as **to** the correctness of associating an **entropy** **to** black holes. It is not clear whether these arguments can be extended **to** Schwarzschild black holes. The information paradox [7] arises when quantizing **a** **field** theory on **a** black hole background. Hawking has shown [8], that due **to** quantum fluctuations **a** black hole will emit particles with **a** thermal spectrum with **a** temperature proportional **to** the inverse Schwarzschild radius T H ∼ R −1 . The information

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In order **to** make our ideas transparent, we applied these constructions **to** concrete physical systems. In the case of the auxiliary current description, we were mostly inter- ested in black hole physics. Understanding the black hole quantum state in terms of **a** multi-graviton state on flat space-time, we were able **to** compute observables connected **to** the black hole interior such as the density of gravitons in momentum space or their energy density at the parton level and in the large mass limit. Consistency of our results then implied that the total mass of the black hole must scale as the number of fields composing the auxiliary current. We found that the distribution of gravitons in the black hole is dominated by quanta of large wavelength which resonates with the ideas put forward in the Black Hole Quantum N Portrait. Based on these results, we explained that the distri- bution function of gravitons is directly accessible in S-matrix processes. As **a** consequence, an outside observer can in principle reconstruct the internal structure of the black hole. Thus, no loss of information as well as the existence of quantum hair are expected in our **approach**. Finally, we showed how the Schwarzschild metric emerges from our **approach**. The basic insight was **to** replace **a** classical black hole source characterized by the mass by the corresponding microscopic quantum source. This quantum source was identified with the energy density of gravitons inside the black hole. On the one hand, the mass arises as **a** collective effect of N gravitons. On the other hand, for any finite N , we argued that there are corrections **to** the classical notion of mass which can be absorbed in **a** wave function renormalization. Using this result **combined** with the finding of [67] it was straightforward **to** show that in our description, classical geometry indeed emerges in the limit N → ∞.

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As discussed above, the recently developed TRIP-assisted DP- HEAs show comparable strengthening mechanisms and hence mechanical properties found also in many advanced steels, e.g., DP and TRIP steels ( Hadfield, 1888; Curtze et al., 2009; Raabe et al., 2013 ). Many of these steels show positive and strong strain rate sensitivity upon deformation ( Curtze et al., 2009 ). This feature has been attributed **to** the rationale that at higher strain rates the time for **a** dislocation **to** be rendered immobile in front of an obstacle (e.g., grain boundaries, twin boundaries and **phase** interfaces) before it can propagate upon gaining additional thermal energy is shorter than that at lower strain rates ( Meyers, 1994; Curtze et al., 2009 ). For instance, high manganese containing TRIP/TWIP steels usually undergo deformation driven transformations involving formation of ε and α martensite as well as mechanical twins ( Grässel et al., 2000; Gutierrez-Urrutia and Raabe, 2011; Wong et al., 2016 ). The transformation paths could be affected by strain rate as the adiabatic heating modifies the **phase** transformation rate, leading **to** change in mechanical properties such as ultimate strength, uniform and total elongations ( Sato et al., 1989; Grässel et al., 2000 ). Also, DP steels with **a** ferritic-martensitic microstructure ( Fu et al., 2012; Tasan et al., 2015 ) are generally more sensitive **to** strain rate changes compared **to** TRIP steels consisting of bainite, martensite, retained austenite and ferrite matrix ( Grässel et al., 2000; Huh et al., 2008 ).

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I awoke the next day **to** **a** sound like sizzling bacon, the noise made by ice melting in **a** pan on **a** primus. In the months after Antarctica, I often heard it in the boneless moments between sleep and consciousness; then memories ached like an old wound. Sunshine was pouring through the window. Steve brought tea **to** our bunks. Some of the ice must have been brackish, as it was salty. I made up **a** jug of milk for our breakfast cereal, and that was salty too. I wasn’t having much luck with breakfasts. But it didn’t matter. Nothing mattered. We basked on our veranda, and **a** flock of Antarctic terns flew by, their high-pitched chirp exotically foreign after the coarse squawk of the skuas. Later, we took the boats out and followed **a** minke whale around the bergs, sailing through Daliesque arches and poking into cold blue grottoes. The sun was low, and the honeyed air was so still that the growlers and bergy bits were barely moving. It was **a** golden evening. **A** day like that made everything worthwhile.

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457 of the European Union and zero otherwise. The estimated coefficient EU membership is positive and has **a** very high estimated value. The coefficient is also statistically significant at the 5% level. The impacts of EU membership are all positively significant. The intra-EU trade volumes were positively affected by the enlargement of the European Community with the accession of new member states .In estimating the bilateral trade within the EU seven models were set up according **to** the panel analysis between 2000 and 2010 (OLS, Random effects (RE) fixed effects (FE)).Dependent variable is log bilateral exports. Country pair fixed effects, exporter- year and importer-year dummies included. According **to** the panel fixed effect estimation the exporter GDP and importer GDP are positive as expected and significant at 5% (any unit increase of **a** country’s GDP raises its exports **to** other EU countries by 1.535% more). When one country of the country pair is the member of EU and the other is not then the export raises with exp (0. 23) =25.6%. When both the countries are members of the EU, the estimated coefficient EU membership is positive and has **a** very high estimated value of exp (0.38) =1.462.The EU dummy is 0.545.

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The fish short-term reproduction assay (FSTRA) is **a** common in vivo screening assay for assessing endocrine effects of chemicals on reproduction in fish. However, the current reliance on measures such as egg number, plasma vitellogenin concentration and morphological changes **to** determine endocrine effects can lead **to** false labelling of chemicals with non-endocrine modes- of-action. Here, we integrated quantitative liver and gonad shotgun proteomics into the FSTRA in order **to** investigate the causal link between an endocrine mode-of-action and adverse effects assigned **to** the endocrine axis. Therefore, we analyzed the molecular effects of fadrozole-induced aromatase inhibition in zebrafish (Danio rerio). We observed **a** concentration-dependent decrease in fecundity, **a** reduction in plasma vitellogenin concentrations and **a** mild oocyte atresia with oocyte membrane folding in females. Consistent with these apical measures, proteomics revealed **a** significant dysregulation of proteins involved in steroid hormone secretion and estrogen stimulus in the female liver. In the ovary, the deregulation of estrogen synthesis and binding of sperm **to** zona pellucida were among the most significantly perturbed pathways. **A** significant deregulation of proteins targeting the transcriptional activity of estrogen receptor (esr1) was observed in male liver and testis. Our results support that organ- and sex-specific quantitative proteomics represent **a** promising tool for identifying early gene expression changes preceding chemical-induced adverse outcomes. these data can help **to** establish consistency in chemical classification and labelling.

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These shortcomings ultimately led **to** the advent of quantum **field** theory (although previous attempts date back **to** the early days of quantum me- chanics, cf. [2] and [3]). Starting from classical **field** theory – which does not account for quantum aspects, e. g., like the particle nature of the photon – one promotes the infinity of classical oscillators representing the modes of the classical fields **to** quantum harmonic oscillators and therefore quantizing the theory. In this so-called canonical quantization **approach**, the fields be- come operator valued distributions labeled by **a** space-time coordinate and particles emerge as excited states of these fields, the so called **field** quanta. Thus, **a** (relativistic) quantum **field** theory unifies the concepts of classical **field** theory, quantum mechanics and special relativity. The first major the- ory of that kind and the prototype of **a** successful quantum **field** theory was quantum electrodynamics (QED) which proved **to** be extraordinarily success- ful in describing electromagnetic interactions. In the early days QED was plagued by the so called problem of infinities, i. e., basic physical properties like the electron self-energy diverged. The techniques of renormalization and regularization overcame this problem and QED was brought into its final form most notably by Richard Feynman, Julian Schwinger and Shin’ichir¯o Tomonaga. QED is an example of an abelian gauge theory. In simple terms, **a** gauge theory is **a** theory which is invariant under some local, continuous symme- try transformations in an internal space which form **a** Lie group (the gauge group), in the case of QED it is the commutative circle group U(1). Thus, one of the four fundamental forces of nature, namely the electromagnetic force, could be described in **a** satisfactory way within the framework of gauge theories, where the photon is the carrier of this force and in this context is termed gauge boson. Since the corresponding symmetries constrain and dictate the form of

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samples were subjected **to** ultrasonic cleaning with ethanol before proceeding **to** next step.
Microstructural characterization was carried out using electron backscattered diffraction (EBSD) and electron channeling contrast imaging (ECCI). EBSD measurements were performed in **a** dual-beam Zeiss-crossbeam XB1560 scanning electron microscope (SEM) equipped with the TSL OIM data collection software. ECCI analysis was conducted using **a** Zeiss-Merlin instrument ( Gutierrez-Urrutia et al., 2009 ). For the tensile tested samples, the deformation microstructures were analyzed via EBSD and ECCI at sample regions which had experienced different local strain levels. For the un-deformed samples, the compositional homogeneity was also analyzed by energy dispersive X-ray spectroscopy (EDS) using the Zeiss-Merlin instrument.

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Adopting rigorous and independent processing approaches, each AC will deliver consistent **gravity** **field** solutions. For the first time, **a** meaningful combination by the Analysis Center Coordinator (ACC) will be possible. This task will be coordinated by AIUB, it includes

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Iron is an example for an allotropic material. In this paper two allotrops are of interest. At room temperature and ambient pressure α-iron is the stable **phase**. It has **a** body centered cubic (bcc) crystal structure. If the temperature is increased, it transforms into the γ-iron, also called austenite. The austenitic crystal lattice consists of face cen- tered cubic (fcc) elementary cells. The change from austenite **to** α-iron depends on the cooling rate. If the probe is cooled slowly, the transformation is diffuse. For **a** sufficiently high cooling rate, **a** diffusionless transformation from the fcc **to** the bcc **phase** takes place, which is known as martensitic transformation in iron (Sandoval et al. (2009a)). The change of structure can be described by the Bain model (Bain (1924)) which defines **a** preexisting bcc unit cell within two fcc cells (Figure 2). **To** attain the martensitic bcc cell, **a** distortion of the preexisting bcc cell is necessary. The Bain model demonstrates that due **to** the crystallographic misfit an eigenstrain in the martensitic **phase** exits, which is considered in the proposed model for martensitic transformations.

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2. Theoretical Framework
**A** large literature regarding international trade and FDI shows that the relationship of inward FDI and the exports of host countries mainly concentrate on complementarity and substitution, usually with exports regressed on some measure of FDI and some other control variables. FDI can also affect the breakdown of exports by industry and geographical area. The main analysis on the effects of FDI on exports is based on the Heckscher (1919)-Ohlin (1933) model and it’s extensions (Mundell (1968); Kojima (1975, 1977, 1982); Krugman (1983); Helpman (1984); Horstmann and Markusen (1984); Helpman and Krugman (1985); Blomström (1990); Markusen (1992); Brian, Hanson, and Harrison (1997); Lipsey (1998, 2000, 2002); Helpman, Melitz, and Yeaple (2003); Barrios, Görg and Strobl (2005)).

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2 1. Introduction
**A** traditional **gravity** model describing trade in its simple form (Linnemann 1966; Tinbergen 1962) asserts that the volume of trade between **a** country pair is proportional **to** the product of their gross domestic products and inversely related **to** **a** measure of distance separating them, where distance is broadly defined as **a** function of several variables that can be viewed as trade resistance factors. The log-linear specification of the **gravity** model along with ordinary least squares (OLS) estimation has been widely used in the empirical literature (Egger 2002; Frankel and Rose 2002; Rose 2000), mostly because of its good empirical performance and, in later years, for the strong theoretical foundations provided in papers such as Anderson (1979) and Anderson and van Wincoop (2003). However, most recent contributions stress that null trade flows are **to** be specifically taken into account. Helpman et al. (2008) prove that disregarding countries that do not trade with each other generates biased estimates. Moreover, Santos Silva and Tenreyro (2006) show that log-linearization of the **gravity** model leads **to** inconsistent estimates in the presence of heteroscedasticity in trade levels. They propose **a** Poisson-type specification of the **gravity** model along with the Poisson pseudo-maximum likelihood (PPML) estimator, somehow similarly **to** the Poisson **approach** initially proposed by Flowerdew and Aitkin (1982). Santos Silva and Tenreyro (2006; 2011) also provide simulation evidence that the PPML estimator is well behaved, even when the conditional variance is far from being proportional **to** the conditional mean. Several empirical studies of trade have applied the PPML estimator (see Burger et al. 2009; Linders et al. 2008; Martin and Pham 2015; Martínez-Zarzoso 2013). Alternatively, in order **to** correct for overdispersion, **a** negative binomial (NB) regression model, which belongs **to** the family of Poisson models, and allows for the dispersion parameter **to** differ from 1, is employed. **A** wider discussion regarding the choice between Poisson and NB estimators (for the pseudo-ML case in particular), can be found, for example, in Bosquet and Boulhol (2014) and Head and Mayer (2015).

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Developing numerical models capable of simulat- ing the hydrodynamics of open-channel flows over rough and permeable beds is crucial for pre- dicting the morphodynamic evolution of alluvial channels and the complex physical-chemical processes occurring within the subsurface (hypor- heic zone) of river beds. However, most current numerical models assume that alluvial streams have an impermeable channel bed (Raudkivi, 1998). This represents **a** significant issue as ex- perimental observations have shown that such as- sumptions are erroneous as turbulence within gravel-beds can be significant (Bencala and Wal- ters, 1983). Thus, Darcian theory, suitable for low-conductivity porous media, should not be ap- plied within cohesionless gravel-bed rivers. The Navier Stokes (NS) equations can be used **to** model flow through **a** porous media if the internal morphology is known. However, this is rarely the case and the complexity of the internal morphol- ogy of the bed has meant that the normal **approach** **to** this problem is **to** volume-average the NS equa- tions and close them with the Hazen-Dupui-Darcy (HDD) model (Lage et al., 2002). However, if the internal morphology of the bed is known, **a** mass flux scaling algorithm that has been developed **to** include complex bed topography into **a** stable dis-

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These defects describe critical impurities of low dimensional quantum systems. For two dimensional CFTs defects can be thought of as lines separating two (possibly different) CFTs on each side of the defect. Thereby the defect, or also called interface, acts as **a** map from one CFT **to** the other and vice versa. Folding the CFTs along the defect line result in **a** tensor theory of the two CFTs with the defect representing **a** boundary condition [39]. In this way the notion of defects can be related **to** the area of determining boundary states in **a** CFT. As it turned out the defects generalize in **a** natural way the notion of boundary conditions by setting local gluing conditions along the defect line. Interfaces and their properties such as their transmissivity and reflectivity [49] or their implementation of symmetries [54] have been studied in various contexts and many of their properties have been discovered [50–54]. For example it has be shown that special defects can implement symmetries or dualities [45, 46] between the various CFTs.

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My sociological study gave me **a** different perspective on banlieues. In this context, I entered the suburbs through meeting families and spending time with them. I didn’t have **to** worry about pointing out problems or trying **to** sup- port people, but only about trying **to** understand their living situations. I par- ticipated in their daily activities or special family events such as weddings or engagement celebrations. I had meals with them and felt like **a** family friend, sometimes even as **a** family member. I also participated in activities organized for women such as sewing lessons or French and Arab classes. The families I met told me about their life stories and their daily life. They were just like any other family I had met in other contexts. I met their neighbors and saw the ways in which they were close **to** each other. This solidarity had also been visi- ble when I was in the social work **field**, but in **a** different way, more from the outside. Being inside the families gave me an entirely new perspective on the banlieues. Of course, I also saw social problems there. The families I visited for example were always worried my bike would get stolen while I was at their home. They took it **to** their basement and locked it there. They insisted on the fact however that even if it did get stolen, they would find it within **a** short pe- riod of time through the friends of their sons. Delinquency and social problems were present, but not in the overwhelming and sometimes threatening way I had experienced them in the context of social work. What was dominant was the normal daily life of the inhabitants with their difficulties, for example, higher unemployment rates than in other parts of the city and their strengths, for example, an intense solidarity through the family and neighborhood. I real- ized how different one and the same **field** can be according **to** one’s entry into it.

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