Inhomogeneous Cosmological Models with Flat Slices Generated from the EINSTEIN‐DE SITTER Universe
A family of cosmological models in considered which in a certain synchronized system of reference possess flat slices t = const. They are generated from the EINSTEIN-DE SITTER universe by a suitable transformation. Under physically reasonable presumptions these transformed models fulfil certain energy conditions. 
 
 
 
Es wird eine Familie kosmologischer Modelle betrachtet, die in einemi gewissen synchronisierten Bezugssystem flache Schichten t = const. besitzen. Sie werden mittels einer geeigneten Transformation aus dem EINSTEIN-DE SITTER-Universum erzeugt. Diese transformierten Modelle erfullen unter physikalisch sinnvollen Voraussetzungen gewisse Energie bedingungen.

title: The Newtonian limit of fourth-order gravity
abstract: The weak-field slow-motion limit of fourth-order gravity will be discussed. Let us consider the gravitational theory defined by the Lagrangian Lg = (8πG) −1 ( R/2 + (αRijR ij + βR)l ) . (1) G is Newton’s constant, l a coupling length and α and β numerical parameters. Rij and R are the Ricci tensor and its trace. Introducing the matter Lagrangian Lm and varying Lg + Lm one obtains the field equation Eij + αHij + βGij = 8πGTij . (2) For α = β = 0 this reduces to General Relativity Theory. The explicit expressions Hij and Gij can be found in STELLE (1978). In a well-defined sense, the weak-field slow-motion limit of Einstein’s theory is just Newton’s theory, cf. DAUTCOURT (1964). In the following we consider the analogous problem for fourth order gravity eqs. (1), (2). For the special cases α = 0 (PECHLANER, SEXL(1966), POLIJEVKTOVNIKOLADZE (1967)), α + 2β = 0 (HAVAS (1977), JANKIEWICZ (1981)) 1 and α+ 3β = 0 (BORZESZKOWSKI, TREDER, YOURGRAU (1978)) this has already been done in the past. Cf. also ANANDAN (1983), where torsion has been taken into account. The slow-motion limit can be equivalently described as the limit c→ ∞, where c is the velocity of light. In this sense we have to take the limit G→ 0 while G · c and l remain constants. Then the energy-momentum tensor Tij reduces to the rest mass density ρ: Tij = δ 0 i δ 0 j ρ , (3) x = t being the time coordinate. The metric can be written as ds = (1 − 2φ)dt − (1 + 2ψ)(dx + dy + dz) . (4) Now eqs. (3) and (4) will be inserted into eq. (2). In our approach, products and time derivatives of φ and ψ can be neglected, i.e., R = 4∆ψ − 2∆φ , where ∆f = f,xx + f,yy + f,zz . Further R00 = −∆φ, H00 = −2∆R00 − ∆R and G00 = −4∆R, where l = 1. Then it holds: The validity of the 00-component and of the trace of eq. (2), R00 −R/2 + αH00 + βG00 = 8πGρ (5) and − R− 4(α+ 3β)∆R = 8πGρ , (6) imply the validity of the full eq. (2). Now, let us discuss eqs. (5) and (6) in more details: Eq. (5) reads − ∆φ−R/2 + α(2∆∆φ− ∆R) − 4β∆R = 8πGρ . (7)

title: COMMENT: Fourth-order gravity and conformal transformations

title: On an algorithm solving two-level programming problems with nonunique lower level solutions
abstract: In the paper, an algorithm is presented for solving two-level programming problems. This algorithm combines a direction finding problem with a regularization of the lower level problem. The upper level objective function is included in the regularzation to yield uniqueness of the follower's solution set. This is possible if the problem functions are convex and the upper level objective function has a positive definite Hessian. The computation of a direction of descent and of the step size is discussed in more detail. Afterwards the convergence proof is given.Last but not least some remarks and examples describing the difficulty of the inclusion of upper-level constraints also depending on the variables of the lower level are added.