Constant mean curvature hypersurfaces with constant δ-invariant

We completely classify constant mean curvature hypersurfaces (CMC) with constant δ-invariant in the unit 4-sphere S4 and in the Euclidean 4-space E4.

Comments on hydrographic and topographic LIDAR acquisition and merging with multibeam sounding data acquired in the Olympic Coast National Marine Sanctuary

In April 2005, a SHOALS 1000T LIDAR system was used as an efficient alternative for safely acquiring data to describe the existing conditions of nearshore bathymetry and the intertidal zone over an approximately 40.7 km2 (11.8 nm2) portion of hazardous coastline within the Olympic Coast National Marine Sanctuary (OCNMS). Data were logged from 1,593 km (860 nm) of track lines in just over 21 hours of flight time. Several islands and offshore rocks were also surveyed, and over 24,000 geo-referenced digital still photos were captured to assist with data cleaning and QA/QC. The 1 kHz bathymetry laser obtained a maximum water depth of 22.2 meters. Floating kelp beds, breaking surf lines and turbid water were all challenges to the survey. Although sea state was favorable for this time of the year, recent heavy rainfall and a persistent low-lying layer of fog reduced acquisition productivity. The existence of a completed VDatum model covering this same geographic region permitted the LIDAR data to be vertically transformed and merged with existing shallow water multibeam data and referenced to the mean lower low water (MLLW) tidal datum. Analysis of a multibeam bathymetry-LIDAR difference surface containing over 44,000 samples indicated surface deviations from –24.3 to 8.48 meters, with a mean difference of –0.967 meters, and standard deviation of 1.762 meters. Errors in data cleaning and false detections due to interference from surf, kelp, and turbidity likely account for the larger surface separations, while the remaining general surface difference trend could partially be attributed to a more dense data set, and shoal-biased cleaning, binning and gridding associated with the multibeam data for maintaining conservative least depths important for charting dangers to navigation. (PDF contains 27 pages.)

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

Asymptotic Hyperstability of a Class of Linear Systems under Impulsive Controls Subject to an Integral Popovian Constraint

This paper is focused on the study of the important property of the asymptotic hyperstability of a class of continuous-time dynamic systems. The presence of a parallel connection of a strictly stable subsystem to an asymptotically hyperstable one in the feed-forward loop is allowed while it has also admitted the generation of a finite or infinite number of impulsive control actions which can be combined with a general form of nonimpulsive controls. The asymptotic hyperstability property is guaranteed under a set of sufficiency-type conditions for the impulsive controls.

An observer-based vaccination control law for an SEIR epidemic model based on feedback linearization techniques for nonlinear systems

This paper presents a vaccination strategy for fighting against the propagation of epidemic diseases. The disease propagation is described by an SEIR (susceptible plus infected plus infectious plus removed populations) epidemic model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes the contacts among susceptible and infected more difficult. The vaccination strategy is based on a continuous-time nonlinear control law synthesised via an exact feedback input-output linearization approach. An observer is incorporated into the control scheme to provide online estimates for the susceptible and infected populations in the case when their values are not available from online measurement but they are necessary to implement the control law. The vaccination control is generated based on the information provided by the observer. The control objective is to asymptotically eradicate the infection from the population so that the removed-by-immunity population asymptotically tracks the whole one without precise knowledge of the partial populations. The model positivity, the eradication of the infection under feedback vaccination laws and the stability properties as well as the asymptotic convergence of the estimation errors to zero as time tends to infinity are investigated.

The effects of disorder in dimerized quantum magnets in mean field approximations

15 p.