On rotational solutions for elliptically excited pendulum

The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact rotational solutions in the case of circular pivot trajectory and zero gravity. The conditions for existence and stability of such solutions are derived. Assuming that the amplitudes of excitations are not small while the pivot trajectory has small ellipticity the approximate solutions are found both for high and small linear damping. Comparison between approximate and numerical solutions is made for different values of the damping parameter.Comment: 16 pages, 5 figures, 1 tabl

On Nonlinear Dynamics of the Pendulum with Periodically Varying Length

Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the pendulum with periodically varying length which is also treated as a simple model of child's swing. Asymptotic expressions for boundaries of instability domains near resonance frequencies are derived. Domains for oscillation, rotation, and oscillation-rotation motions in parameter space are found analytically and compared with numerical study. Two types of transitions to chaos of the pendulum depending on problem parameters are investigated numerically.Comment: 8 pages, 8 figure

Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.A. Belyakov was supported by the Austrian Science Foundation (FWF) under grant No P 24125-N13. A.L. Dontchev was supported by NSF Grant DMS 1008341 through the University of Michigan. M. López was supported by MINECO of Spain, Grant MTM2011-29064-C03-02

Heterogeneous consumption in OLG model with horizontal innovations

The paper develops a general equilibrium endogenous growth model involving heterogeneous consumption by an age-structured population with uncertain but limited life span and balanced life-time budget without bequests. The heterogeneity is introduced via weights which the individuals attribute in their utility function to consumption of different goods depending on the vintage of the good. The goods are produced by monopolistically competitive firms and the variety of available goods/technologies is determined endogenously through R&D investments. A competitive bank sector provides financial resources for investments, secured by agents’ savings and future firms profits. The general equilibrium is characterized by a system of functional equations and is analytically or numerically determined for several particular weight functions. It is shown that the investments by agents alone may be insufficient to sustain growth, while additional investments provided by the bank sector may lead to growth. The resulting imbalance between agents’ assets and the total value of firms can grow unboundedly in the case of homogeneous consumption. The results exhibit the qualitative difference between the dynamics of the model with heterogeneous versus homogeneous consumption. In particular heterogeneous con- sumption (when old goods are discounted) reduces the additional investments by the financial sector so that the values of firms become balanced by the assets of agents in the long run.info:eu-repo/semantics/publishedVersio

Optimal Cyclic Exploitation of Renewable Resources

The paper contributes to the topic of optimal utilization of spatially distributed renewable resource. Namely, a problem of "sustainable" optimal cyclic exploitation of a renewable resource with logistic law of recovery is investigated. The resource is distributed on a circle and is collected by a single harvester moving along the circle. The recovering and harvesting rates are position dependent, and the latter depends also on the velocity of the harvester, which is considered as a control. The existnce of an optimal solution is proved, as well as necessary optimality conditions for the velocity of the harvester. On this base, a numerical approach is proposed, and some qualitative properties of the optimal solutions are established. The results are illustrated by numerical examples, which reveal some economically meaningful features of the optimal harvesting

DIFFERENTIAL IMMUNOGENICITY OF VACCINIA AND HIV-1 COMPONENTS OF A HUMAN RECOMBINANT VACCINE IN MUCOSAL AND BLOOD COMPARTMENTS

Mucosal immune responses induced by HIV-1 vaccines are likely critical for prevention. We report a Phase 1 safety and immunogenicity trial in 8 participants using the vaccinia -based TBC-3B vaccine given subcutaneously to determine the relationship between HIV-1 specific systemic and gastrointestinal mucosal responses. Across all subjects, detectable levels of blood vaccinia - and HIV-1-specific antibodies were elicited but none were seen mucosally. While the vaccinia component was immunogenic for CD8 + T lymphocyte (CTL) responses in both blood and mucosa, it was greater in blood. The HIV-1 component of the vaccine was poorly immunogenic in both blood and mucosa. Although only 8 volunteers were studied intensively, the discordance between mucosal and blood responses may highlight mechanisms contributing to recent vaccine failures