A reduction theorem for tau -rigid modules

We prove a theorem which gives a bijection between the support τ -tilting modules over a given finite-dimensional algebra A and the support τ -tilting modules over A / I, where I is the ideal generated by the intersection of the center of A and the radical of A. This bijection is both explicit and well-behaved. We give various corollaries of this, with a particular focus on blocks of group rings of finite groups. In particular we show that there are τ -tilting-finite wild blocks with more than one simple module. We then go on to classify all support τ -tilting modules for all algebras of dihedral, semidihedral and quaternion type, as defined by Erdmann, which include all tame blocks of group rings. Note that since these algebras are symmetric, this is the same as classifying all basic two-term tilting complexes, and it turns out that a tame block has at most 32 different basic two-term tilting complexes. We do this by using the aforementioned reduction theorem, which reduces the problem to ten different algebras only depending on the ground field k, all of which happen to be string algebras. To deal with these ten algebras we give a combinatorial classification of all τ -rigid modules over (not necessarily symmetric) string algebras

Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations

In this paper we perform the parameter-dependent center manifold reduction near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf bifurcations in delay differential equations (DDEs). This allows us to initialize the continuation of codimension one equilibria and cycle bifurcations emanating from these codimension two bifurcation points. The normal form coefficients are derived in the functional analytic perturbation framework for dual semigroups (sun-star calculus) using a normalization technique based on the Fredholm alternative. The obtained expressions give explicit formulas which have been implemented in the freely available numerical software package DDE-BifTool. While our theoretical results are proven to apply more generally, the software implementation and examples focus on DDEs with finitely many discrete delays. Together with the continuation capabilities of DDE-BifTool, this provides a powerful tool to study the dynamics near equilibria of such DDEs. The effectiveness is demonstrated on various models

The real time mass evaluation system as a tool for detection of undeclared cascade operation at GCEPs

Given the flexibility of current cascade designs a real time mass monitoring system is preferred for safeguarding Gas Centrifuge Enrichment Plants. However, if such a system is to be installed in a GCEP it must not impinge on plant operation or be intrusive. Since load cells are already part of the operational process and located outside the cascade hall their exploitation for safeguards purposes is an obvious development. The paper describes, through dynamic simulations, how transients would be observed in real-time mass balances when undeclared cascade operation takes place in a declared facility

Behavior of self-propelled acetone droplets in a Leidenfrost state on liquid substrates

It is demonstrated that non-coalescent droplets of acetone can be formed on liquid substrates. The fluid flows around and in an acetone droplet hovering on water are recorded to shed light on the mechanisms which might lead to non-coalescence. For sufficiently low impact velocities, droplets undergo a damped oscillation on the surface of the liquid substrate but at higher velocities clean bounce-off occurs. Comparisons of experimentally observed static configurations of floating droplets to predictions from a theoretical model for a small non-wetting rigid sphere resting on a liquid substrate are made and a tentative strategy for determining the thickness of the vapor layer under a small droplet on a liquid is proposed. This strategy is based on the notion of effective surface tension. The droplets show self-propulsion in straight line trajectories in a manner which can be ascribed to a Marangoni effect. Surprisingly, self-propelled droplets can become immersed beneath the undisturbed water surface. This phenomenon is reasoned to be drag-inducing and might provide a basis for refining observations in previous work

On Local Bifurcations in Neural Field Models with Transmission Delays

Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay equations, among which DDE. In particular, it may be used advantageously for the investigation of stability and bifurcation of steady states. After introducing the neural field model in its basic functional analytic setting and discussing its spectral properties, we elaborate extensively an example and derive a characteristic equation. Under certain conditions the associated equilibrium may destabilise in a Hopf bifurcation. Furthermore, two Hopf curves may intersect in a double Hopf point in a two-dimensional parameter space. We provide general formulas for the corresponding critical normal form coefficients, evaluate these numerically and interpret the results

Tolerance and safety evaluation of N, N-dimethylglycine, a naturally occurring organic compound, as a feed additive in broiler diets

N, N-dimethylglycine (DMG) is a tertiary amino acid that naturally occurs as an intermediate metabolite in choline-to-glycine metabolism. The objective of the present trial was to evaluate tolerance, safety and bioaccumulation of dietary DMG in broilers when supplemented at 1 g and 10 g Na-DMG/kg. A feeding trial was conducted using 480 1-d-old broiler chicks that were randomly allocated to twenty-four pens and fed one of three test diets added with 0, 1 or 10 g Na-DMG/kg during a 39 d growth period. Production performance was recorded to assess tolerance and efficacy of the supplement. At the end of the trial, toxicity was evaluated by means of haematology, plasma biochemistry and histopathology of liver, kidney and heart (n 12), whereas bioaccumulation was assessed on breast meat, liver, blood, kidney and adipose tissue (n 8). Carcass traits were similar between the control and 1 g Na-DMG/kg feed groups (P>0·05), but the feed:gain ratio was significantly improved at 1 g Na-DMG/kg feed compared with the control or the 10-fold dose (P = 0·008). Histological examinations showed no pathological effects and results of haematology and plasma biochemistry revealed similar values between the test groups (P>0·05). Bioaccumulation occurred at the 10-fold dose, but the resulting DMG content in breast meat was comparable with, for instance, wheat bran and much lower than uncooked spinach. In conclusion, DMG at 1 g Na-DMG/kg improved the feed:gain ratio in broilers without DMG being accumulated in consumer parts. Furthermore, dietary supplementation with DMG up to 10 g Na-DMG/kg did not induce toxicity or impaired performance in broilers