Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n−2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues.The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces.     

A characterization of annularity for area-preserving toral homeomorphisms

We prove that if an area-preserving homeomorphism of the torus in the homotopy class of the identity has a rotation set which is a nondegenerate vertical segment containing the origin, then there exists an essential invariant annulus. In particular, some lift to the universal covering has uniformly bounded displacement in the horizontal direction.     

Location-allocation models for traffic police patrol vehicles on an interurban network

This research investigates the traffic police routine patrol vehicle (RPV) assignment problem on an interurban road network through a series of integer linear programs. The traffic police RPV’s main task, like other emergency services, is to handle calls-for-service. Emergency services allocation models are generally based on the shortest path algorithm however, the traffic police RPV also handles other roles, namely patrolling to create a presence that acts as a deterrence, and issuing tickets to offenders. The RPVs need to be located dynamically on both hazardous sections and on roads with heavy traffic in order to increase their presence and conspicuousness, in an attempt to prevent or reduce traffic offences, road accidents and traffic congestion. Due to the importance of the traffic patrol vehicle’s location with regard to their additional roles, allocation of the RPVs adheres to an exogenous, legal, time-to-arrival constraint. We develop location-allocation models and apply them to a case study of the road network in northern Israel. The results of the four models are compared to each other and in relation to the current chosen locations. The multiple formulations provide alternatives that jointly account for road safety and policing objectives which aid decision-makers in the selection of their preferred RPV assignments. The results of the models present a location-allocation configuration per RPV per shift with full call-for-service coverage whilst maximizing police presence and conspicuousness as a proxy for road safety.     

Increasing the detection speed of an all-electronic real-time biosensor

Biosensor response time, which depends sensitively on the transport of biomolecules to the sensor surface, is a critical concern for future biosensor applications. We have fabricated carbon nanotube field-effect transistor biosensors and quantified protein binding rates onto these nanoelectronic sensors. Using this experimental platform we test the effectiveness of a protein repellent coating designed to enhance protein flux to the all-electronic real-time biosensor. We observe a 2.5-fold increase in the initial protein flux to the sensor when upstream binding sites are blocked. Mass transport modelling is used to calculate the maximal flux enhancement that is possible with this strategy. Our results demonstrate a new methodology for characterizing nanoelectronic biosensor performance, and demonstrate a mass transport optimization strategy that is applicable to a wide range of microfluidic based biosensors.     

The locomotive fleet fueling problem

This paper considers the problem of how to determine an optimal fueling schedule and contracting policy with fuel suppliers so as to minimize the total cost of the fueling operation. The problem is formulated as a mixed integer program and the formulation is enhanced by valid inequalities and domination rules. The enhanced model allows us to obtain near optimal solutions for large scale instances.     

Prostatic Zn determination for prostate cancer diagnosis

We present our studies of prostatic Zn concentration measurements, carried out in the light of a novel prostate cancer (CAP) diagnosis method proposed by us. The method is based on in vivo prostatic Zn mapping by XRF trans-rectal probe.

We report on the extensive clinical studies, intended to assess the validity of the novel proposed diagnostic method. Zn content was measured in vitro in needle-biopsy samples from several hundreds of patients, and was correlated with histological findings and other patient parameters. For this purpose, a technique of absolute Zn content determination in 1 mm³ fresh tissue samples by XRF was developed. The experimental details and the main clinical-evaluation results are presented.

We further outline the suggested design of the XRF trans-rectal probe for an efficient in vivo detection and mapping of the Zn fluorescence radiation from the prostate through the rectal wall. Laboratory phantom studies, a preliminary design concept and its expected performance are also reported.     

Isotope abundance analysis methods and software for improved sample identification with supersonic gas chromatography/mass spectrometry

We present newly developed isotope abundance analysis (IAA) methods and software which are used to derive elemental formula information from experimental mass spectral data of molecular ion isotopomeric abundances. The software, using a novel method, can also be used to automatically confirm or reject NIST library search results, thereby significantly improving the confidence level in sample identifications. In the case of IAA confirmation of the NIST library results, sample identification is unambiguous, since the confirmation is achieved by two independent sets of data and analytical methods. In the case of a rejection, such as when the molecule is not included in the library's databases, the IAA software independently provides a list of elemental formulae with declining order of matching to the isotopomeric experimental data, in a similar way to accurate mass measurements with costly instruments. IAA is ideally applicable to gas chromatography/mass spectrometry (GC/MS) (and liquid chromatography/electron ionization mass spectrometry (LC/EI-MS)) with a supersonic molecular beam (SMB) since it requires a trustworthy and highly abundant true molecular ion that is unique to the SMB-MS systems, plus the absence of self chemical ionization and vacuum background noise, again unique features of GC/SMB-MS. The various features of the IAA methods and software are described, their performance is demonstrated with the analysis of experimental GC-SMB-MS data and the IAA concept is compared with accurate mass alternatives. The combination of IAA and GC/SMB-MS is believed to be superior to accurate mass GC/MS in view of the general availability of trustworthy molecular ions for an extended range of compounds.     

Experimental and Theoretical Investigation of M-Array Pulse Amplitude Modulation Transmission for Reach Extension

We present here the M-array modulation scheme that enables transmission of higher data rates at the same spectral bandwidth. The results indicate that the M-array technique can be implemented. This scheme leads to a significant narrowing of the optical spectrum which, in turn, enables a significant extension of dispersion-limited links.