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Solution of the Dirac equation with pseudospin symmetry for a new harmonic oscillatory ring-shaped noncentral potential J. Math. Phys. 53, 082104 (2012) Effect of tensor interaction in the Dirac-attractive radial problem under pseudospin symmetry limit J. Math. Phys. 53, 082101 (2012) Asymptotic stability of small gap solitons in nonlinear Dirac equations J. Math. Phys. 53, 073705 (2012) On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization J. Math. Phys. 53, 063503 (2012) Quasi-exact treatment of the relativistic generalized isotonic oscillator The high-energy-limit of the scattering operator for multidimensional relativistic dynamics, including a Dirac particle in an electromagnetic field, is investigated by using time-dependent, geometrical methods. This yields a reconstruction formula, by which the field can be obtained uniquely from scattering data. © 1997 American Institute of Physics. ͓S0022-2488͑97͒02701-1͔

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For complex quadratic polynomials, the topology of the Julia set and the dynamics are understood from another perspective by considering the Hausdorff dimension of biaccessing angles and the core entropy: the topological entropy on the Hubbard tree. These quantities are related according to Thurston. Tiozzo [60] has shown continuity on principal veins of the Mandelbrot set M . This result is extended to all veins here, and it is shown that continuity with respect to the external angle θ will imply continuity in the parameter c. Level sets of the biaccessibility dimension are described, which are related to renormalization. Hölder asymptotics at rational angles are found, confirming the Hölder exponent given by Bruin-Schleicher [11]. Partial results towards local maxima at dyadic angles are obtained as well, and a possible self-similarity of the dimension as a function of the external angle is suggested. Proposition 3.8 (β -type Misiurewicz points)Suppose c is a β -type Misiurewicz point of preperiod k ≥ 1. 1. The Markov matrix A is irreducible and primitive. 2. The largest eigenvalue satisfies λ k ≥ 2, so h(c) ≥ log 2 k , with strict inequality for k ≥ 2. 3. For the Thurston matrix F according to Proposition 3.5, the arc [c, β c ] is generating an irreducible primitive block B of F, which corresponds to the largest eigenvalue λ .Proof: Consider the claim that the union), 1 ≤ j ≤ k, provides arcs from α c to all endpoints except β c . When an arc from α c is crossing z = 0, then either its endpoint is behind −α c and the part before −α c is chopped away before the next iteration. Or this arc is branching off between 0 and −α c , and further iterates will be branching from arcs at α c constructed earlier. This proves the claim. 2. Now the arc [0, β c ] is containing preimages of itself, so f k c ([0, β c ]) is the Hubbard tree T c . Since f k c (z) is even, every arc of the Hubbard tree has at least two preimages underEvery edge e of T c covers z = 0 in finitely many iterations. Then it is iterated to an arc at β c , so the edge e contains an arc iterated to [0, β c ]. Now f n c (e) = T c for n ≥ n e , and A n is strictly positive for n ≥ max{n e | e ⊂ T c }, thus A is irreducible and primitive. (Alternatively, this follows from Lemma 3.9.4, since f c is not renormalizable.) Finally, if k ≥ 2 and we had λ k = 2, the characteristic polynomial of A would contain the irreducible factor x k − 2 and A would be imprimitive. 3. Denote the postcritical points by c j = f j−1 c (c) again. The iteration of any arc is giving two image arcs frequently, but at least one of these has an endpoint with index j growing steadily, so reaching β c = c k+1 . Further iterations produce the arc [c, β c ] after the other endpoint was in part A of K c \ {0}, which happens when it becomes −β c or earlier. So the forward-invariant subspace generated by [c, β c ] corresponds to an irreducible block B of F. It is primitive by the same arguments as above, since [c, β c ] → [c, β c ] + [c, c 2 ].Consider the lift F c : X c → X c from the proof o...

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On subsets of the Mandelbrot set, E M ⊂ M, homeomorphisms are constructed by quasi-conformal surgery. When the dynamics of quadratic polynomials is changed piecewise by a combinatorial construction, a general theorem yields the corresponding homeomorphism h : E M → E M in the parameter plane. Each h has two fixed points in E M , and a countable family of mutually homeomorphic fundamental domains. Possible generalizations to other families of polynomials or rational mappings are discussed. The homeomorphisms on subsets E M ⊂ M constructed by surgery are extended to homeomorphisms of M, and employed to study groups of nontrivial homeomorphisms h : M → M. It is shown that these groups have the cardinality of R, and they are not compact.

In den letzten Jahren wurden viele Modelle zur analytischen Bestimmung des Verbundes zwischen Faser und Matrix aus Pull-Out-Versuchen entwickelt. Diese beruhen jedoch auf einer begrenzten Anzahl zu variierender materialspezifischer Parameter und erlauben somit keine freie mathematische Beschreibung des Verbundgesetzes. Im vorliegenden Beitrag wird ein analytisches Modell vorgestellt, das die direkte inverse Berechnung eines Verbundgesetzes, bestehend aus N linearen Teilstücken auf Basis von Last-Verformungs-Kurven eines Pull-Out-Tests ermöglicht, bei dem die Anzahl N nicht begrenzt ist. Das Verbundgesetz kann somit ohne mathematische Einschränkungen beschrieben werden. Die Anwendbarkeit des vorgestellten Modells wird anhand einer Auswertung von Stahlfaser-Pull-Out-Versuchsergebnissen demonstriert. Evaluation of a bond versus slip relation on basis of single fiber pull-out tests. An analytical simulation procedure for a pull-out test is proposed in the present study, which is based on an inverse boundary problem and allows the straightforward calculation of a N-piecewise linear bond law τ(s) with no limitation of N on basis of an experimentally determined load displacement distribution P(ω). The presented model is applied and validated using experimental results of pull-out tests, carried out on smooth and straight steel fiber/fine grained concrete systems. It is found that the determined bond stress versus slip relation τ(s) is a material parametersince it is not dependent on geometric factors of fiber and matrix, e. g. fiber diameter and embedded length. However, experimental tests not published in this study showed so called stochastic size effects, i. e. if the fiber diameter is small in regard to the maximum grain size used in the cement based matrix, the pull-out behavior is influenced more significantly in the post failure region due to e. g. abrasion effects. Nevertheless, with the presented model bond characteristics of different fiber/matrix systems can be compared much more in detail, because the complete bond stress versus slip relation is known. Furthermore, only if τ(s) is known, a tailoring of the interface properties in regard to an optimized mechanical performance of the composite material with enhanced characteristics is possible. Future work on this model includes e. g. the implementation of effects due to lateral pressure on the fiber, constant loading, and repeated load cycles.