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Articles 2161 - 2190 of 2383

Full-Text Articles in Physical Sciences and Mathematics

On Torsion-Free Crawley Groups, Brendan Goldsmith, A. L. S. Corner, R. Gobel Jan 2005

On Torsion-Free Crawley Groups, Brendan Goldsmith, A. L. S. Corner, R. Gobel

Articles

The notion of a Crawley p-group is well known in Abelian group theory. In this present work, a corresponding concept is introduced for torsion-free groups. The principal result, which uses the set-theoretic notions of the diamond and Martin’s axiom, establishes an independence result for N1-free Crawley groups.

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An Explicit Mapping Between The Frequency Domain And The Time Domain Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov Jan 2005

An Explicit Mapping Between The Frequency Domain And The Time Domain Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov

Articles

Explicit expressions are presented that describe the input-output behaviour of a nonlinear system in both the frequency and the time domain. The expressions are based on a set of coefficients that do not depend on the input to the system and are universal for a given system. The anharmonic oscillator is chosen as an example and is discussed for different choices of its physical parameters. It is shown that the typical approach for the determination of the Volterra Series representation is not valid for the important case when the nonlinear system exhibits oscillatory behaviour and the input has a pole …

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Manev Potential And General Relativity, Rossen Ivanov, Emil Prodanov Jan 2005

Manev Potential And General Relativity, Rossen Ivanov, Emil Prodanov

Articles

Manevis classical potential is known to successfully modify Newtonian celestial mechanics, in accordance with the general-relativistic description. The idea of replacing the exact solution of Einsteinis equations, describing orbiting bodies, with a classical potential is widely used today. These models are not restricted to planetary motion only, but also include numerous interesting astrophysical phenomena such as accretion of matter around black holes or massive stars.

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Zeros Of The Jost Function For A Class Of Exponentially Decaying Potentials, Daphne Gilbert, Alain Kerouanton Jan 2005

Zeros Of The Jost Function For A Class Of Exponentially Decaying Potentials, Daphne Gilbert, Alain Kerouanton

Articles

We investigate the properties of a series representing the Jost solution for the differential equation $-y''+q(x)y=lambda y$, $x geq 0$, $q in mathrm{L}({mathbb{R}}^{+})$. Sufficient conditions are determined on the real or complex-valued potential $q$ for the series to converge and bounds are obtained for the sets of eigenvalues, resonances and spectral singularities associated with a corresponding class of Sturm-Liouville operators. In this paper, we restrict our investigations to the class of potentials $q$ satisfying $|q(x)| leq ce^{-ax}$, $x geq 0$, for some $a>0$ and $c$ greator than 0.

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Interaction Of Single Walled Carbon Nanotubes With Starch-Based Systems, Alan Casey, Gerald Farrell, Mary Mcnamara, Hugh Byrne, Gordon Chambers Jan 2005

Interaction Of Single Walled Carbon Nanotubes With Starch-Based Systems, Alan Casey, Gerald Farrell, Mary Mcnamara, Hugh Byrne, Gordon Chambers

Conference papers

The interaction of carbon nanotubes with soft organic molecules such as cyclodextrins and other saccharides has recently been shown to produce water-soluble composites. Such systems offer considerable advantages over polymer based composites due to their biocompatibility and noncovalent coupling which can potentially preserve the unique properties of the tubes. The mechanism of interaction of such systems has been proposed to be dominated by hydrophobic and hydrophilic interactions along the surface of the tube. In this study a number of composite systems have been formed with HiPco carbon nanotubes using starch and starch based polymers. The first composite formed with starch …

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Temperature Dependent Spectroscopic Studies Of Hipco Swnt Composites, Sinead Keogh, Theresa Hedderman, Garrett Farrell, M Ruether, Elizabeth Gregan, Mary Mcnamara, Gordon Chambers, Hugh Byrne Jan 2005

Temperature Dependent Spectroscopic Studies Of Hipco Swnt Composites, Sinead Keogh, Theresa Hedderman, Garrett Farrell, M Ruether, Elizabeth Gregan, Mary Mcnamara, Gordon Chambers, Hugh Byrne

Articles

No abstract provided.

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The Determination Of Environmentally Important Metals In Marine Sediments, Linda Tyrrell Jan 2005

The Determination Of Environmentally Important Metals In Marine Sediments, Linda Tyrrell

Masters

Surface sediment samples were collected at sites within the Rockall Through at water depth ranges from 700 – 2774 metres. The study area was predefined by the availability of samples. Samples were collected by the British Geological Survey during their gravity core survey undertaken in 1998. Methods were optimised and validated for lead, cadmium, chromium, copper, nickel, zinc, lithium and aluminium using atomic absorption spectroscopy following total digestion, and for mercury, using cold vapour atomic fluorescence spectroscopy following partial digestion. The measured metal concentration were normalised to Li to compensate for the influence of natural variability in the concentration of …

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The Simultaneous Onset And Interaction Of Taylor And Dean Instabilities In A Couette Geometry, C. P. Hills, A. P. Bassom Jan 2005

The Simultaneous Onset And Interaction Of Taylor And Dean Instabilities In A Couette Geometry, C. P. Hills, A. P. Bassom

Articles

The fluid flow between a pair of coaxial circular cylinders generated by the uniform rotation of the inner cylinder and an azimuthal pressure gradient is susceptible to both Taylor and Dean type instabilities. The flow can be characterised by two parameters: a measure of the relative magnitude of the rotation and pressure effects and a non-dimensional Taylor number. Neutral curves associated with each instability can be constructed but it has been suggested that these curves do not cross but rather posses `kinks'. Our work is based in the small gap, large wavenumber limit and considers the simultaneous onset of Taylor …

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Future Reasoning Machines: Mind And Body, Brian Duffy, Gregory O'Hare, John Bradley, Bianca Schoen-Phelan Jan 2005

Future Reasoning Machines: Mind And Body, Brian Duffy, Gregory O'Hare, John Bradley, Bianca Schoen-Phelan

Articles

In investing energy in developing reasoning machines of the future, one must abstract away from the specific solutions to specific problems and ask what are the fundamental research questions that should be addressed. This paper aims to revisit some fundamental perspectives and promote new approaches to reasoning machines and their associated form and function. Core aspects are discussed, namely the one-mind-many-bodies metaphor as introduced in the Agent Chameleon work. Within this metaphor the agent’s embodiment form may take many guises with the artificial mind or agent potentially exhibiting a nomadic existence opportunistically migrating between a myriad of instantiated embodiments. We …

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An Assessment Of Case-Based Reasoning For Spam Filtering, Sarah Jane Delany, Padraig Cunningham, Lorcan Coyle Jan 2005

An Assessment Of Case-Based Reasoning For Spam Filtering, Sarah Jane Delany, Padraig Cunningham, Lorcan Coyle

Articles

Because of the changing nature of spam, a spam filtering system that uses machine learning will need to be dynamic. This suggests that a case-based (memory-based) approach may work well. Case-Based Reasoning (CBR) is a lazy approach to machine learning where induction is delayed to run time. This means that the case base can be updated continuously and new training data is immediately available to the induction process. In this paper we present a detailed description of such a system called ECUE and evaluate design decisions concerning the case representation. We compare its performance with an alternative system that uses …

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A Compact Electronic Speckle Pattern Interferometry System Using A Photopolymer Reflection Holographic Optical Element, Guntaka Tulasi Sridhar Reddy, Raghavendra Jallapuram, Vincent Toal, Izabela Naydenova, Suzanne Martin, Svetlana Mintova Jan 2005

A Compact Electronic Speckle Pattern Interferometry System Using A Photopolymer Reflection Holographic Optical Element, Guntaka Tulasi Sridhar Reddy, Raghavendra Jallapuram, Vincent Toal, Izabela Naydenova, Suzanne Martin, Svetlana Mintova

Conference Papers

A simple and compact electronic speckle pattern interferometry system using a reflection holographic optical element is presented. The reflection holographic optical element is recorded on an acrylamide based photopolymer formulated and prepared at the Centre for Industrial & Engineering Optics. Light intensity of 40mW/cm2 with an exposure time of 60 seconds was used in fabricating the holographic optical element. The vibration mode patterns of a 4 cm diameter thin circular sheet of brass metal attached to a 4 cm diameter paper cone loud speaker are presented.

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Optimization Of An Acrylamides-Based Photopolymer For Reflection Holographic Recording, Raghavendra Jallapuram Jan 2005

Optimization Of An Acrylamides-Based Photopolymer For Reflection Holographic Recording, Raghavendra Jallapuram

Doctoral

Photopolymers have been the subject of special attention in the last two decades. The advantage of being self-developing makes them a practical alternative to silver halide photographic emulsions in holographic interferometry applications. This thesis is aimed at understanding diffusion properties and optimization of an acrylamide-based green sensitized photopolymer material for reflection holographic recording. The composition of the photopolymer includes a green sensitive dye (erythrosine B), acrylamide (monomer), electron donor (triethanolamine) a cross linking monomer (NN’methylenebisacrylamide) and a binder (polyvinyl alcohol). On illumination with light of the appropriate wavelength the dye absorbs a photon and enters into an excited state. The …

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Characterisation Of An Acrylamide-Based Photopolymer For Holographic Data Storage, Hosam Sherif Jan 2005

Characterisation Of An Acrylamide-Based Photopolymer For Holographic Data Storage, Hosam Sherif

Masters

An acrylamide-based photopolymer, formulated in the Centre for Industrial and Engineering Optics, was investigated as a recording material for holographic data storage applications. Holographic data storage (HDS) is an optical storage technique, which theoretically allows densities as high as tens of TB/cm2 with data transfer rates of many GB/s/. HDS has unique advantages, such as the ability to perform parallel data searches (associative recall) and implement novel encryption techniques. At present, many materials have been investigated to determine their suitability for use as HDS media. As yet, no one material possesses all the properties that are required to realise the …

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An Investigation Of The Effect Of Variation In Surface Electrode Type And Placement On Action Potentials Elicited By Peripheral Nerve Simulation, Jacinta Augustine Jan 2005

An Investigation Of The Effect Of Variation In Surface Electrode Type And Placement On Action Potentials Elicited By Peripheral Nerve Simulation, Jacinta Augustine

Masters

Several experiments were designed and carried out in order to compare the performances of five commercially available EMG surface electrodes. The aim was to identify the optimal surface recording electrode from the samples examined. The particular interest was to assess the comparative performance of the electrodes routinely used in our hospital Neurophysiology laboratory. It is envisaged that the conclusions from the study might be applied to improve the quality and reproducibility of nerve conduction techniques use din our department. A literature survey was carried out to identify some of the factors that influence the recording of evoked potentials from peripheral …

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On The Integrability Of A Class Of Nonlinear Dispersive Wave Equations, Rossen Ivanov Jan 2005

On The Integrability Of A Class Of Nonlinear Dispersive Wave Equations, Rossen Ivanov

Articles

We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations.

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Investigation Of The Effect Of Subcutaneous Fat On Image Quality Performance Of 2d Conventional Imaging And Tissue Harmonic Imaging, Jacinta Browne, Amanda Watson, Peter Hoskins, Alex Elliott Jan 2005

Investigation Of The Effect Of Subcutaneous Fat On Image Quality Performance Of 2d Conventional Imaging And Tissue Harmonic Imaging, Jacinta Browne, Amanda Watson, Peter Hoskins, Alex Elliott

Articles

Tissue harmonic imaging (THI) has been reported to improve contrast resolution, tissue differentiation and overall image quality in clinical examinations. However, a study carried out previously by the authors (Browne et al. 2004) found improvements only in spatial resolution and not in contrast resolution or anechoic target detection. This result may have been due to the homogeneity of the phantom. Biologic tissues are generally inhomogeneous and THI has been reported to improve image quality in the presence of large amounts of subcutaneous fat. The aims of the study were to simulate the distortion caused by subcutaneous fat to image quality …

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Structure-Property Relationships For Electron-Vibrational Coupling In Conjugated Organic Oligomeric Systems, Luke O'Neill, Hugh Byrne Jan 2005

Structure-Property Relationships For Electron-Vibrational Coupling In Conjugated Organic Oligomeric Systems, Luke O'Neill, Hugh Byrne

Articles

A series of ð-conjugated oligomers containing one to six monomer units were studied by absorption and photoluminescence spectroscopy. As is common for these systems, a linear relationship between the positioning of the lowest-energy absorption and the highest-energy photoluminescence maxima plotted versus inverse conjugation length is observed, in good agreement with a simple nearly free electron model, one of the earliest descriptions of the properties of one-dimensional organic molecules. It was observed that the Stokes shift and therefore Huang-Rhys factor also exhibit a well-defined relationship with increasing conjugation length, implying a correlation between the electron-vibrational coupling and chain length. This correlation …

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Characterisation Of An Acrylamide-Based Photopolymer For Data Storage Utilizing Holographic Angular Multiplexing, Hosam Sherif, Izabela Naydenova, Suzanne Martin, Colm Mcginn, Vincent Toal Jan 2005

Characterisation Of An Acrylamide-Based Photopolymer For Data Storage Utilizing Holographic Angular Multiplexing, Hosam Sherif, Izabela Naydenova, Suzanne Martin, Colm Mcginn, Vincent Toal

Articles

An acrylamide-based photopolymer formulated in the Centre for Industrial and Engineering Optics has been investigated with a view to further optimisation for holographic optical storage. Series of 18 to 30 gratings were angularly multiplexed in a volume of photopolymer layer at a spatial frequency of 1500 lines/mm. Since the photopolymer is a saturable material, an exposure scheduling method was used to exploit the entire dynamic range of the material and allow equal strength holographic gratings to be recorded. This investigation yielded the photopolymer M/# for moderately thin layers. Photopolymer temporal stability was also studied by measuring variations of material shrinkage, …

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Modernization Of The Hilger And Watts Guage-Block Interferometer, Michael O'Hora, Brian Bowe, Vincent Toal, Sean Peyton Jan 2005

Modernization Of The Hilger And Watts Guage-Block Interferometer, Michael O'Hora, Brian Bowe, Vincent Toal, Sean Peyton

Articles

The Hilger & Watts gauge-block interferometer was designed and manufactured commercially in the 1950s. The instrument uses isotope lamps as wavelength standards to perform absolute length calibration of gauge blocks (slip gauges) up to 100 mm in length, to an accuracy of approximately 1 ppm. It is entirely manually operated. In order to make the instrument more suitable for the modern laboratory, new hardware has been added, and a customized software package developed to automate the measurement process. This paper shows how interferograms may be imaged successfully at each of the eight available wavelengths, and the critical fringe fraction measurement …

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Efficacy Of Innovative Anti-Microbial Decontamination Of Minimally Processed Vegetables, Christina Busquets I Tortosa Jan 2005

Efficacy Of Innovative Anti-Microbial Decontamination Of Minimally Processed Vegetables, Christina Busquets I Tortosa

Masters

Chlorine has widespread use commercially as a disinfectant wash for raw vegetables. However, it is an extremely corrosive gas and it may have severe health and environmental implications. The aim of this thesis was to find safe, alternative decontamination treatments for ready-to-eat Iceberg lettuce. The efficacy of 1% acetic acid, 2% citric acid; calcium lactate concentrations of 0.5%, 1.5%, 2.5% and 3% at wash temperature of 4,25 and 50°C, ozone alone (1 mg 1-1) and in combination with calcium lactate (2.5%) were compared with chlorine as decontaminating treatments. Microbiological analyses were performed following decontamination treatments using the pour plate method …

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Study Of An Acrylamide-Based Photopolymer For Use As A Holographic Data Storage Medium, Hosam Sherif, Izabela Naydenova, Suzanne Martin, Colm Mcginn, G Berger, C Denz, Vincent Toal Jan 2005

Study Of An Acrylamide-Based Photopolymer For Use As A Holographic Data Storage Medium, Hosam Sherif, Izabela Naydenova, Suzanne Martin, Colm Mcginn, G Berger, C Denz, Vincent Toal

Conference Papers

An acrylamide-based photopolymer formulated in the Centre for Industrial and Engineering Optics has been investigated with a view to further optimisation for holographic optical storage. Series of 15 to 30 gratings were angularly multiplexed in a volume of the photopolymer layers with different thickness at a spatial frequency of 1500 lines/mm. Since the photopolymer is a saturable material, an exposure scheduling method was used to exploit the entire dynamic range of the material and allow equal strength gratings to be recorded. From this investigation the photopolymer layer’s M/# was determined with regard to the recording geometry used. The temporal stability …

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Holographic Recording Of Patterns In Thin Film Acrylamide-Based Photopolymer, Izabela Naydenova, Kotakonda Pavani, Emilia Mihaylova, Katia Loudmer, Suzanne Martin, Vincent Toal Jan 2005

Holographic Recording Of Patterns In Thin Film Acrylamide-Based Photopolymer, Izabela Naydenova, Kotakonda Pavani, Emilia Mihaylova, Katia Loudmer, Suzanne Martin, Vincent Toal

Conference Papers

A study of the light induced surface relief modulation in thin photopolymer layers is reported. Due to the nature of the photopolymer used no additional post-processing is required after holographic recording. An investigation of the dependence of the amplitude of the photoinduced relief modulation on different parameters of recording such as spatial frequency, intensity of the beams and times of exposure has been carried out. The surface relief modulation is characterized by white light interferometry. Photopolymer layer thickness ranges from 1-5m. A model of the mechanism of surface relief formation is proposed on the basis of the measured dependencies. A …

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Investigation Of Polymerization Rate In An Acrylamide-Based Photopolymer Using Raman Spectroscopy, Raghavendra Jallapuram, Izabela Naydenova, Hugh Byrne, Suzanne Martin, Robert Howard, Vincent Toal Jan 2005

Investigation Of Polymerization Rate In An Acrylamide-Based Photopolymer Using Raman Spectroscopy, Raghavendra Jallapuram, Izabela Naydenova, Hugh Byrne, Suzanne Martin, Robert Howard, Vincent Toal

Conference Papers

Diffusion models predict that polymerization and diffusion rates are the key factors that control the dynamics and the final properties of a holographic grating recorded in a photopolymerizable material. Diffusion rates during the initial phase of holographic recording have already been studied and reported. We now report the investigation of the polymerization rate in an acrylamide-based photopolymer using Raman spectroscopy. The polymerization rate constant was estimated by monitoring the intensity of the characteristic Raman peaks at 1284 cm-1 corresponding to the bending mode of CH vinyl bond in acrylamide and 1609 cm-1 corresponding to the carbon-carbon double bond (C=C) in …

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Structure Property Relationships In Organic Conjugated Systems, Luke O'Neill, Patrick Lynch, Mary Mcnamara Jan 2005

Structure Property Relationships In Organic Conjugated Systems, Luke O'Neill, Patrick Lynch, Mary Mcnamara

Articles

A series of π conjugated oligomers were studied by absorption and photoluminescence spectroscopy. A linear relationship between the positioning of the absorption and photoluminescence maxima plotted against inverse conjugation length is observed. The relationships are in good agreement with the simple particle in a box method, one of the earliest descriptions of the properties of one-dimensional organic molecules. In addition to the electronic transition energies, it was observed that the Stokes shift also exhibited a well-defined relationship with increasing conjugation length, implying a correlation between the electron-vibrational coupling and chain length. This correlation is further examined using Raman spectroscopy, whereby …

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Structural Property Relationships In Conjugated Polymers, Patrick Lynch, Luke O'Neill, J. Whelan, Mary Mcnamara, Hugh Byrne Jan 2005

Structural Property Relationships In Conjugated Polymers, Patrick Lynch, Luke O'Neill, J. Whelan, Mary Mcnamara, Hugh Byrne

Articles

The synthesis of a series of PPV derivative polymers by the Wittig-Horner reaction is described. The structure of each polymer is varied and the effects of these variations on the optical properties is explored. The effects of alkyloxy side chains is observed between the PPV derivatives Poly(-p-phenylvinylene-co-2,5-bis-octyloxy phenylvinylene.) PPV-OPV and Poly (para-2,5-bis-(n-octyloxy)-phenylvinylene) POPV. The phenyl units of the soluble PPV derivative POPV are replaced by alternate naphthyl units in the polymer Poly(2,5-bis(n-octyloxy)-1,4-phenylene vinylene-1,5-bis(n-octyloxy)-2,6-naphthylene vinylene) POPN-ONV and then fully by naphthyl units in Poly(2,6-bis-(n-octyloxy)-1,5-NaphthyleneVinylene) PONV. The addition of alkyloxy sidechains served to red shift the fluorescence emission as expected. The systematic …

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Correlation Of Spectroscopic And Biochemical Assays Postionising Radiation Exposure In Human Skin Cell Analogues, Aidan Meade, Hugh Byrne, Fiona Lyng Jan 2005

Correlation Of Spectroscopic And Biochemical Assays Postionising Radiation Exposure In Human Skin Cell Analogues, Aidan Meade, Hugh Byrne, Fiona Lyng

Conference papers

Raman spectroscopy, as an evaluation of the products of ionising radiation exposure in biological systems, has been utilised mainly in the evaluation of the impact of exposure in tissue, cellular constituents and live animals. It has also been recently demonstrated that Raman spectroscopy can demonstrate key spectroscopic changes in the live cell associated with significant apoptotic and necrotic chemical damage. The present preliminary work utilises Raman spectroscopy at 514.5 nm to evaluate the results of exposure to -rays in HaCaT cells from a Co-60 therapy source, in tandem with other biological assays. The results demonstrate that a number of spectral …

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Electroabsorption Studies Of Structurally Modified Fullerene Thin Films, Gerald Farrell, Gordon Chambers, Hugh Byrne Jan 2005

Electroabsorption Studies Of Structurally Modified Fullerene Thin Films, Gerald Farrell, Gordon Chambers, Hugh Byrne

Conference papers

Ultraviolet (UV/Vis) and Electroabsorption (EA) spectroscopy is used to examine and differentiate between intermolecular and intra molecular excited state species in fullerene films. Charge Transfer (CT) states are identified at 2.4 eV and 2.7 eV and dipole moments are calculated. Thermal annealing of C60 films is monitored in situ using absorption spectroscopy and electroabsorption spectroscopy. Recorded spectra display both some temperature dependent and partially irreversible effects, indicating the occurrence of an annealing process. EA shows that the CT states associated with the transferring an electron from the HOMO of one molecule located at the (0,0,0) position to the LUMO of …

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Use Of Raman Spectroscopy In The Investigation Of Debundling Of Single Walled Carbon Nanotubes, Elizabeth Gregan, Sinead Keogh, Theresa Hedderman, Gordon Chambers, Hugh Byrne Jan 2005

Use Of Raman Spectroscopy In The Investigation Of Debundling Of Single Walled Carbon Nanotubes, Elizabeth Gregan, Sinead Keogh, Theresa Hedderman, Gordon Chambers, Hugh Byrne

Conference papers

Samples of raw nanotubes are compared to those deposited from solutions to examine separation of nanotube bundles. Single wall nanotubes bundles produced by the arc-discharge and HiPco methods were solubilised in toluene, DMF and 1,2 dichloroethane. Resonant Raman spectroscopy was used to determine if debundling of the tubes sample occurred. The results showed some degree of debundling, best for the 1,2 dichloroethane solvent, which also shows long term solubility.

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A Context-Dependent Model Of Proximity In Physically Situated Environments, John D. Kelleher, Geert-Jan M. Kruijff Jan 2005

A Context-Dependent Model Of Proximity In Physically Situated Environments, John D. Kelleher, Geert-Jan M. Kruijff

Conference papers

The paper presents a computational model for a context-dependent analysis of a physical environment in terms of spatial proximity. The model provides a basis for grounding linguistic analyses of spatial expressions in visual perception. The model uses potential fields to model spatial proximity. It has been implemented, and when combined with a handcrafted grammar, is used to enable a conversational robot to carry out a situated dialogue with a human. The key concept in our approach is defining the region that is proximal to a landmark based on the spatial configuration of other objects in the scene. The model extends …

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Maintaining The Identity Of Dynamically Embodied Agents, Alan Martin, Gregory O'Hare, Brian Duffy, Bianca Schoen-Phelan, John Bradley Jan 2005

Maintaining The Identity Of Dynamically Embodied Agents, Alan Martin, Gregory O'Hare, Brian Duffy, Bianca Schoen-Phelan, John Bradley

Conference papers

Virtual agents are traditionally constrained in their embod- iment, as they are restricted to one form of body. We propose allowing them to change their embodiment in order to expand their capabili- ties. This presents users with a number of di±culties in maintaining the identity of the agents, but these can be overcome by using identity cues, certain features that remain constant across embodiment forms. This pa- per outlines an experiment that examines these identity cues, and shows that they can be used to help address this identity problem.

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