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# Advanced Nuclear Science and Technology Techniques Workshop

Africa/Johannesburg
Visitors Centre (NRF-iThemba LABS, Old Faure Road, Cape Town)

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Description

The 4th Advanced Nuclear Science and Technology Techniques (ANSTT4) workshop is scheduled to take place from 16 – 20 May 2022 at NRF-iThemba LABS, Cape Town.
The 5-day event will be offered as an in-person-event under strict COVID-19 protocol.

The focus will be on Metrology, Neutrons, Nuclear Structure, AMS, Environmental Measurements and Networking.  The ANSTT will make provision for the inclusion of  round table discussions aimed at providing updates on our inter-Africa and international collaborations from previous meetings. This follows on from the ANSTT series of meetings held in 2018, 2019 and 2021

Collaborations both UK-Africa and inter-Africa will again be at the forefront of the workshop, including Memoranda of Understanding.

The workshop offers a comprehensive programme of invited talks, accepted talks, poster presentations by students and round-table discussions

Participation (presentation and poster) is subject to abstracts being accepted by an advisory panel

For enquiries or further information, contact the Event Coordinator: Michelle van der Ventel-Bark on anstt2020@tlabs.ac.za

Registration
ANSTT4 Registration
Participants
• Abraham Avaa
• Alice McKnight
• Alison Bruce
• Andy Buffler
• Ayabulela Tsewu
• Ayoub Elhihy
• Chloe Sole
• Daniel BONGUE
• Emmanuel Ojo
• Erin Jarvie
• Ferdie van Niekerk
• Ferdie van Niekerk
• Innocent Lugendo
• Jacobus Diener
• Josiah De Klerk
• kwame appiah
• Lindsay Donaldson
• Luna Pellegri
• Matteo Saviozzi
• Mike van Heerden
• Milton van Rooy
• Mistura Bolaji Ajani
• Mojisola Rachael USIKALU
• Munirat Bashir
• Nalesi Segale
• Nhlakanipho Mdziniso
• Omphile Monnapula
• Pete Jones
• Remember Ayanda
• Robert Bark
• Robert van der Merwe
• Samuel Terungwa Temaugee
• SEBENZILE PRETTY ENGELINAH MAGAGULA
• Shanyn-Dee Hart
• Sizwe Mhlongo
• Skhanyiso Lwazi Shabane
• Skye Segal
• Stephan Woodborne
• Steve Peterson
• Tanya Hutton
• Zina Ndabeni
Support
• Monday, 16 May
• 09:00 09:30
Registration 30m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 09:30 10:00
Welcome Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Pete Jones (iThemba LABS)
• 09:30
Welcome 30m
Speaker: Rudzani Nemutudi (iThemba LABS)
• 10:00 11:00
Accelerator Mass Spectrometry Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Pete Jones (iThemba LABS)
• 10:00
Does Accelerator Mass Spectrometry have a place in an emerging economy? 45m

South Africa’s science infrastructure is required to respond to a mandate that specifies a number of outcomes, and one of the core tenets is that science must impact on wellbeing in the country. Extremely expensive science platforms, such as the recently commissioned Accelerator Mass Spectrometry (AMS) facility at iThemba LABS, must respond by facilitating research for users; by training the next generation of scientists; and by leading cutting edge research with a local benefit. The AMS facility is the only one of its kind on the African continent and will grow to serve not only the South African science community, but also the wider African community until it has a continental footprint. In meeting the mandate the AMS facility must operate in a partnership with the user base, both in the provision of know-how to run analyses on a science agenda set by the users, but also in leading in-house research that accommodates academic partners and facilitates post-graduate student participation. Many of the societal benefits of AMS are not to be found in the particle physics domain, but rather in the applied science that falls in to other disciplines. The basis of these applications is in the systematics of rare element production, decay and distribution among different reservoirs. Scientists at iThemba LABS are partnering with users who require traditional chronology-based applications of AMS, but they are also using the AMS facility across a wide range of novel applied domains. These include: testing climate change forecasts, dating groundwater recharge, assessing global phenomenon such as magnetic field fluctuations over the last 50 000 years. The essence of the program is to use particle physics for the benefit of the people of South Africa, and Africa.

Speaker: Stephan Woodborne
• 11:00 11:30
Coffee Break | Group Photo 30m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 11:30 13:00
Metrology and Applications Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 11:30
NMISA Keynote Speaker 45m
Speaker: Dr Wynand Louw (NMISA)
• 12:15
Update on NMISA radioactivity standards lab activities since 2020 20m

An update on the NMISA RS lab activities since the start of 2020 will be provided. This comprises international comparisons of activity measurements using primary methods, participation in proficiency tests using gamma-spec and liquid scintillation counting, and low-level comparisons. An update on our scope of accreditation will also be provided and various types of client work that has been completed. Future plans will also be discussed.

Speaker: Milton van Rooy (NMISA)
• 13:00 14:00
Lunch 1h Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 14:00 15:30
The MeASURe experience Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Thomas Leadbeater (University of Cape Town)
• 14:00
MeASURe: the art and science of nuclear measurement at the University of Cape Town 1h 30m

The Metrological and Applied Sciences University Research Unit (MeASURe) was established in the Department of Physics at the University of Cape Town in 2018 to consolidate and expand research programs in applied nuclear physics, nanophysics, and measurement education and training. Integral to MeASURe is a robust understanding of reference standards, uncertainties, traceability, and how this translates into the development of novel measurement techniques to address real-world problems. Central to these activities is access to particle beams and radioisotopes through niche fast neutron facilities, proton therapy research beamline, and position emission particle tracking laboratories at the University of Cape Town and iThemba LABS.

We present the current state-of-the-art of neutron- and gamma ray-based research within MeASURe, including the development of detectors and instrumentation, advanced computation and stochastic modelling, and the applications of such measurements and techniques. A subset of current postgraduate students will present their research into modern fast neutron detector systems, positron emission particle tracking and prompt gamma ray imaging. Future avenues of research at MeASURe are explored with respect to the SDGs and potential impact to the African continent and beyond.

Speakers: Andy Buffler (UCT) , Ms Chloe Sole (University of Cape Town) , Mr Josiah De Klerk (University of Cape Town) , Mr Mike Van Heerden (University of Cpe Town) , Mr Robert Van der Merwe (University of Cape Town) , Prof. Steve Peterson (University of Cape Town) , Dr Tanya Hutton (University of Cape Town) , Dr Tom Leadbeater (University of Cape Town) , Dr Zina Ndabeni (University of Cape Town)
• 15:30 16:00
Tea Break 30m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 16:00 17:00
Function: Tour of iThemba LABS
• 17:00 18:00
Posters
• 18:00 20:00
Function: Welcome Function Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• Tuesday, 17 May
• 10:00 11:05
Environmental Applications Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Innocent Jimmy Lugendo (University of Dar es Salaam)
• 10:00
Spectroscopic Systems: From research to applications 45m

H C Boston, on behalf of the Nuclear Physics Group, Department of Physics, University of Liverpool, UK

The University of Liverpool Nuclear Physics research group has been involved in studying the structure of the nucleus at the frontiers of nuclear stability since its inception. To compliment these studies, and to push the boundaries of our knowledge we have been forefront at designing and implementing arrays to be used by the Nuclear Physics community.

The evolution of radioactive ion-beam facilities has necessitated a step change in both the sensitivity of the nuclear instrumentation and in the data analysis techniques used in these challenging experiments and campaigns to study novel and exciting nuclear phenomena.

The detection of gamma radiation is at the heart of nuclear structure physics experiments and is key to the success of many industrial and medical applications involving gamma ray imaging. Projects such as the Advanced Gamma Tracking Array (AGATA) in Europe and the Gamma-ray Energy Tracking Array (GRETA) in the United States have pushed the technical boundaries needed to realise spectrometers capable of measuring nuclei far from stability.

This presentation will focus on how the technology designed for Nuclear Physics experiments has found application in areas outside of the core physics programme. Sensors developed for Medical, Security, Environmental and Nuclear imaging systems will be presented and discussed.

Speaker: Helen Boston (University of Liverpool)
• 10:45
Design and construction of a gamma-ray spectrometer with water shielding for low-level natural occurring radioactive material measurement 20m

Gamma-ray spectrometer with a single HPGe or NaI:Tl detector shielded with lead is often used to measure the activity concentration of radionuclides in soil samples. A passive water shield to reduce background radiation reaching the detectors was designed using GEANT4 Monte Carlo simulations and then constructed. IAEA-375 soil and beach sand each placed in Marinelli beaker were measured for 48 hours using two LaBr$_3$:Ce detectors placed inside the constructed water shield. The samples were also measured for 24 hours using a NaI:Tl detector inside the constructed water shield and HPGe shielded with lead and copper to compare and validate the results from measurements with the LaBr$_3$:Ce detectors. Both the simulated and measured results show that the water shield attenuates the 2614.5 keV gamma rays by over 90 % and energies lower than the 2614.5 keV by far above 90 %. The activity concentration of $^{40}$K radionuclide in IAEA-375 soil and beach sand measured using the LaBr$_3$:Ce detectors was below the minimum detectable activity (MDA) due to the internal activity of the detector. The measured activity concentrations of $^{238}$U and $^{232}$Th series and $^{40}$K radionuclides in IAEA-375 soil were comparable with certified values to within measurement uncertainties. The activity concentrations of $^{238}$U and $^{232}$Th series radionuclides in beach sand were determined using all the measurement geometries and consistent to within 1$\sigma$ to 2$\sigma$ level.

Speaker: Dr Munirat Bashir (Ibrahim Badamasi Babangida University, Lapai. Nigeria)
• 11:05 11:30
Coffee Break 25m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 11:30 12:00
Environmental Applications Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Innocent Jimmy Lugendo (University of Dar es Salaam)
• 12:00 13:00
Neutron physics and applications Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Milton van Rooy (US/iThemba LABS Student)
• 12:00
Magnetized dense neutron and neutron star matter 45m

A neutron star is one of the possible end states of a massive star. It is compressed by gravity and stabilized by the nuclear degeneracy pressure. Despite its name, the composition of these objects are not exactly known. However, from the inferred densities, neutrons will most likely compose a significant fraction of the star’s interior. While all neutron stars are expected to have a magnetic field, some neutron stars ("magnetars") are much more highly magnetized than others: the inferred magnetar surface magnetic field is between $10^{14}$ to $10^{15}$ gauss.

Neutron stars are the densest stable states of matter that can currently be directly observed. Some neutron stars ("pulsars") emit strongly in the radio part of the electromagnetic spectrum. Observation of this radiation is one of the major observational targets of what will the world's largest radio telescope, the Square Kilometre Array.

While neutron stars are macroscopic objects, due to the extreme value of the stars' energy, pressure, and magnetic field the physics of the microscopic scale can be imprinted on the star's large scale behaviour. Thus the study of these objects are a combination of various fields of physics ranging from Quantum Mechanics to General Relativity. One of the main inputs to any calculation of neutron star properties is the equation of state of the matter that comprises the interior of the star.

This talk will focus on describing the thermodynamics of magnetized dense neutron and neutron star matter, its equation of state, and how the equation of state is applied to study observational consequences in neutron stars.

Speaker: Dr Jacobus Diener (Botswana International University of Science and Technology)
• 13:00 14:00
Lunch 1h Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 14:00 14:50
Neutron physics and applications Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Dr Milton van Rooy (NMISA)
• 14:30
Evaluation of Nuclear Radiation Damage on Lutetium-Aluminium for Practical Applications Using Neutron Irradiation Technique 20m

Keywords: Radiation Damage, DPA, Monte Carlo Simulation, NAA.

Speaker: Mr Samuel Terungwa Temaugee (School of Physics, University of the Witwatersrand, Johannesburg, South Africa)
• 14:50 16:00
Discussion Session: Neutron Physics and Applications Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Conveners: Helen Boston (University of Liverpool) , Thomas Leadbeater (University of Cape Town)
• 16:00 16:30
Tea Break 30m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 16:30 17:00
Posters
• 16:30
Level structure and transition multipolarities in 54Mn 20m

Electromagnetic transition probabilities are of great interest to nuclear physicists as they provide detailed information about the nature of the wave functions of the initial and the final states. Odd-odd nuclei in the vicinity of Z = N = 20 and 28 shell closure present a unique opportunity for testing the underlying proton-neutron residual interaction. These nuclei exhibit a complex level structure due to many possible couplings of unpaired nucleons to the even-even core [1]. Hence, the investigation of their nuclear properties provides scope for understanding the single-particle energies and the residual neutron-neutron interactions in the shell model substructure [1,2]. The properties of the low and high spin states in odd-odd 54Mn (Z = 25, N = 29) have been studied [1-3] via different probes. Spectroscopic information such as -ray branching ratios, and multipole mixing ratios, were determined for transition energies, 54 keV up to 1509 keV (from J = 2+ up to 6+) [4,5]. The lifetimes of many states have been also measured [6]. In Kumar et al., [2], the excited states in 54Mn were populated using 51V(20Ne,xn,yp)54Mn reaction up to excitation energy of 5 MeV, = 15+. However, the information on the reduced transitions probabilities in 54Mn is still scarce despite numerous studies.

We shall report on the first conversion electron and electron-positron pair conversion study of 54Mn. Excited states up to 3 MeV have been populated in the 54Cr(p,n)54Mn reaction at 5.4 MeV bombarding energy, using DC beams from ANU Heavy Ion Accelerator Facility (HIAF). Internal Conversion Coefficients (ICC) for the low-lying states in 54Mn were determined in several transitions for the first time [6]. The deduced conversion coefficients allow for the assignment of multipolarities for transition energies > 1 MeV up to ~ 2.1 MeV ( = 1+ up to 4+). The results are compared with shell-model calculations as a test of agreement between theory and the experiment.

[1] S. Basu, et al., 64th DAE BRNS Symp. on Nucl. Phys. 64 66-67 (2019).
[2] G. K. Kumar, et al., Jour. Phys. G: Nucl. Part. Phys. 35 095104 (2008).
[3] A. R. Poletti, et al., Physical Review C 10 2329-2339 (1974).
[4] M. Ogawa and H. Taketani, Nucl. Phys. A 194 259-291 (1972).
[5] D.C.Radford, A.R.Poletti, J. Phys. G 5, 409 (1979).
[6] A.A. Avaa, et al., Physical Review C (in preparation)

Speaker: Abraham Avaa (iThemba/Wits)
• 17:00 19:00
Function: Braai Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• Wednesday, 18 May
• 10:00 11:05
Environmental Applications Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Daniel BONGUE (Centre for Atomic Molecular Physics and Quantum Optics (CEPAMOQ) - Faculty of Science - University of Douala - Cameroon)
• 10:00
Environmental Radioactivity Monitoring and Radiological Impact Assessment of Agbara Industrial Area, Ogun State, Nigeria 45m

Naturally occurring radionuclides of terrestrial origin exists in every component of the earth. Making humankind to be continuously exposed to ionizing radiation, which is dangerous to human health. Monitoring of environmental radioactivity is very crucial to minimizing exposure above the threshold limit. Consequently, the background radioactivity due to 232Th, 238U, and 40K for some locations in Agbara industrial area of Ogun State was determined using RS230 Gamma Spectrometer (a portable NaI [Tl] detector). The mean activity concentration of the primordial radionuclides ranges between below detectable limit (in Mentos area) and 472.14 Bqkg-1 (Access Bank area) with an overall average value of 177.87 Bqkg-1. The in-situ measured dose rate (DR) ranges between 12. 18 nGyh-1 (Access Bank area) and 97.95 nGyh-1 (Market area), with an average value of 47.22 nGyh-1. The measured and estimated absorbed dose rates were within the safe limit of 57 nGyh-1 provided by UNSCEAR. The mean values of all the estimated radiological parameters were within the recommended threshold values. It could be concluded that the risk of exposure higher level of ionizing radiation is low for all the area in Agbara industrial area of Ogun State, but there is possibility of cancer risk for someone that has stayed in the area for 70 years and above.

Speaker: Dr Mojisola Usikalu (Covenant University)
• 10:45
SURVEY OF RADIATION LEVELS AT ITHEMBA LABS USING A MOBILE RADIATION DETECTION UNIT EQUIPPED WITH A LaBr3:Ce DETECTOR 20m

Speaker: Ferdie van Niekerk (Tshwane University of Technology)
• 11:05 11:30
Coffee Break 25m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 11:30 13:05
Environmental Applications Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Gharib Mohamed (The State University of Zanzibar)
• 11:30
EVALUATION OF RADIOLOGICAL HAZARDS DUE TO NATURAL RADIOACTIVITY IN SOIL SAMPLES COLLECTED IN AND AROUND SOME GOLD MINING AREAS OF THE MAYO-KEBBI REGION IN CHAD WITH STATISTICAL ANALYSES. 45m

In this work, a HPGe detector in a low-background setup was used to determine the activity concentrations of 238U, 232Th and 40K in soil samples collected in and around some gold mining areas of the Mayo-Kebbi region in Chad. Subsequently, the radiological risks due to these natural radionuclides were also assessed. The range of activity concentrations of 238U, 232Th and 40K varied respectively from 1.42 to 430.88 Bq/kg, 1.19 to 56.61 Bq/kg and 27.38 to 840.51 Bq/kg with respective average values of 29.67 Bq/kg, 11.98 Bq/kg and 234.43 Bq/kg. The highest value of 238U, 232Th and 40K concentrations were found in soil sample collected at gold mining area of Zabili. Correlation studies between 238U versus 232Th, 40K versus 238U, and 40K versus 232Th were performed. The results showed a good correlation between the pairs (238U, 232Th) however a weak correlation was observed between the pairs (238U, 40K) and (232Th, 40K). In order to investigate the statistical variation of the data and its implications on environmental exposure, the hierarchical binary cluster tree was implemented. The mean annual effective dose of the soil samples collected in the studied area was found to be 0.18 mSv/y. The calculated mean values of the external hazard index (Hex) and the internal hazard index (Hin) of the study area were 0.26, 0.26, respectively. These values are lower than unity. Therefore, mining activities in Mayo-kebbi region do not present any radiological hazard to the general public.

Speakers: Daniel BONGUE (Centre for Atomic Molecular Physics and Quantum Optics (CEPAMOQ) - Faculty of Science - University of Douala - Cameroon) , Mr Samafou Penabei
• 12:15
Radioactivity assessment of radium and radon concentrations in water sources at and near selected former uranium mines in the West-Rand area of Johannesburg 20m

The present work aimed at establishing the extent and distribution of the activity concentration levels of 238U daughter-nuclides; 226Ra and 222Rn in the
West Rand-area of Johannesburg. The main motive was to ascertain whether
the exposure of the nearby residents to ionising radiation due to former mining
activities was within the maximum acceptable limit of 1.0 mSv/y for the public. Measurements include the use of Alpha Spectroscopy system (Canberra)
with Passivated Implanted Planar Silicon (PIPS) and Solid-state Alpha Detectors for Radon measurements (RAD-7) detectors to identify radionuclides,
quantify and analyze isotopes of interest.
A seasonal collection of a total 32 water samples from the mining areas
was carried out and analysed for 226Ra and 222Rn. The results of radium
(
226Ra) concentration in water samples obtained by using alpha spectrometry
ranged from (1.58±2.74 to 164.42±18.47) mBq/l, (11.23±3.89 to 136.01±15.4)
mBq/l, (-3.38±-2.39 to 156.15±18.14) mBq/l, and (4.25±1.23 to 108±8) for
June 2019, September 2019, December 2019 and March 2020 water samples,
respectively. The radium values were lower than the suggested maximum contamination levels by US-EPA 555 mBq/L.
The results shows that the range of radon (222Rn) concentration values
vary from (37.1±74.1 to 269±79.2) mBq/l, (57.2±73.9to 190±94.9) mBq/l,
(76.6±63.2 to 211±146) mBq/l, and (56.3±71.1 to 289±272) mBq/l for June
2019, September 2019, December 2019 and March 2020, respectively. The obtained 222Rn concentration results in drinking water samples in the current
study are low than the approved maximum contamination level (MCL) 11.1
Bq/l as approved by US-EPA.
The observed radon annual ingestion dose from the current study were
lower than the European Commission and the World Health Organization proiii
posed concentration of 222Rn in drinking water of 100 Bq/l [1]. The results of
this study indicates that the total annual effective doses from possible intake
of 226Ra and 222Rn radionuclides in sampled water in West-Rand area were
found below the World Health Organisation (WHO) recommended limit of 0.1
worldwide due to ingestion of natural radionuclides assessed by UNSCEAR 2002

Speaker: Ayabulela Tsewu (Student)
• 12:35
Implementation of the k0-based Neutron Activation Analysis (NAA) methodology and k0-IAEA program at the Centre for Energy Research and Training (CERT), Zaria, Nigeria 30m

Implementation of the k0-standardization method of Neutron Activation Analysis (NAA) technique and k0-IAEA program with the Nigeria Research Reactor-1 (NIRR-1) laboratories’ irradiation and counting facilities was carried out as part of a series of projects aimed at achieving one of the goals of the Strategic Utilization Plan for NIRR-1. Adoption of the k0-standardization method of NAA technique and the k0-IAEA gamma-ray spectrum analysis software was due to versatility in meeting the criteria of experimental simplicity, analytical accuracy, and flexibility (with respect to activation and counting conditions). The application of this methodology involved the installation of the k0-IAEA software, editing of its permanent database, calibration of HPGe detectors, and characterization of the irradiation facility prior to its use for routine analysis. IAEA (Soil-7) certified reference material was used to evaluate the validity of this method in NIRR-1 NAA laboratories by analyzing the elemental concentrations with respect to the certified values. In general, good agreement was obtained between the results of this work and values in the certificate of the reference material, thus validating the k0 standardization method of NAA using the k0-IAEA program and confirming its suitability for environmental studies in NIRR-1 laboratories.

Keywords: Neutron activation analysis, k0-standardization, k0-IAEA program, irradiation facility, HPGe detectors.

Speaker: Dr Michael Adeleye (Bingham University, Nigeria)
• 13:05 14:00
Lunch 55m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 14:00 14:30
Environmental Applications Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 14:00
Gamma-ray spectroscopy and its associated radiological risk of beach sand and soil samples from Zanzibar, United Republic of Tanzania 30m

Everyone on the planet is exposed to some background radiation. Human exposure to ionising radiation is one of the scientific subjects that attract public attention, since radiation of natural origin is responsible for most of the total radiation exposure of the human exposure.
This study presents the results of Gamma-ray spectroscopy and its associated radiological risk of beach sand and soil samples from Zanzibar, United Republic of Tanzania. The activity concentration of natural radionuclides (40K, and 232Th and 238U decay products) in beach sand and soil samples were measured using a combination of in-situ and ex-situ gamma-ray spectroscopy. The in-situ gamma-ray survey was conducted using the Multi Element Sediment Detector for Underwater Sediment Activity (MEDUSA) detector. The detector was mounted on the front of a 4×4 vehicle, 60 cm off the ground. Activity concentrations of the primordial radionuclides were extracted from the MEDUSA spectra using the Full Spectrum Analysis (FSA) procedure. The collected beach sands and soil samples from the beaches and the land mapped using the MEDUSA detector were analysed using a Hyper Purity Germanium (HPGe) detector.
The activity concentrations of 40K, 238U and 232Th in beach sand are much lower than in soil samples, with one major exception at Kukuu. Two beach sand samples from Kukuu beach were found to have enhanced radioactivity levels due to the presence of heavy minerals.
The spatial distributions maps for 40K, 238U and 232Th show large variation in soil samples for two relatively small islands. These strong variations are unexpected, that could have implications for agriculture.
The outdoor gamma dose rates obtained in beach sand and soil samples ranged from 3 to 2156 nGy h-1 and 50 to 294 nGy h-1, respectively. The highest absorbed dose rates in soil samples and beach sand are respectively 5 and 38 times higher than the average world level of 57 nGyh-1 for terrestrial doses. Apart from the Kukuu black sand samples that contain the high 238U and 232Th levels, the beach sands and soil in this study do not pose any radiological threat to the public using beaches for various activities.

Speaker: Gharib Mohamed (The State University of Zanzibar)
• 14:30 15:30
Discussion Session: Environmental Measurements Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Conveners: Daniel BONGUE (Centre for Atomic Molecular Physics and Quantum Optics (CEPAMOQ) - Faculty of Science - University of Douala - Cameroon) , Stephan Woodborne
• 15:30 16:00
Tea Break 30m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 16:00 17:00
Professional Development Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• Thursday, 19 May
• 10:00 11:05
Nuclear Structure Studies Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Lindsay Donaldson (iThemba Laboratory for Accelerator Based Sciences)
• 10:00
Lifetime measurements on A∼100 nuclei using LaBr3(Ce) arrays. 45m

The region of the nuclear chart around neutron-rich A~100 nuclei is one where prolate and oblate nuclear shapes are predicted to be in close competition. An indirect measurement of the shape of the nucleus can be obtained from measuring level lifetimes which relate, via transition rates, to beta_2 deformation. In order to make measurements of level lifetimes in the sub nanosecond range an array of 36 LaBr3(Ce) detectors has been constructed for use at the FAIR facility in Darmstadt, Germany. This presentation will give an overview of the array and examples of its use in commissioning experiments at the RIKEN Nishina Center in Japan and the Argonne National Laboratory in the USA.

Speaker: Prof. Alison Bruce (University of Brighton)
• 10:45
Overview on the African LaBr Array at iThemba LABS 20m

The African LaBr Array (ALBA) consists of 21 large volume LaBr3:Ce. The characteristics of these crystals, such as the good energy resolution and the high efficiency, make this array very useful for the detection of high-energy gamma rays. The ALBA project foresees the use of the gamma spectrometer in stand-alone mode and coupled to the K600 spectrometer or to silicon-detector arrays for the particle identification. A Digital acquisition system based on XIA PIXIE 16 cards (12 bit 500Mz digitization) will be used. The 21 detectors of ALBA arrived in 2021 and the S-line support frame is now being completed. An overview of the project will be given underling the physics program that is envisage for the upcoming future.

Speaker: Luna Pellegri (University of the Witwatersrand and iThemba LABS)
• 11:05 11:30
Coffee Break 25m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 11:30 13:00
Nuclear Structure Studies Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Dr Zina Ndabeni (University of Cape Town)
• 11:30
Strength of the scissors resonance in 151Sm 20m

The number of stable isotopes of samarium (Sm), makes this isotopic chain interesting to study at stable ion beam facilities. The scissors resonance (SR) of 151Sm was studied with the aim of understanding the evolution of the SR along the Sm isotopic chain. Change in deformation of a nucleus as it transitions from prolate through spherical to oblate, leads to changes in statistical properties particularly the nuclear level density (NLD) and γ-strength function (γSF). The evolution of resonances observed in the γSF, such as the SR which is sensitive to changes in deformation across the isotopic chain, was studied in this work. The experiment was performed at the Oslo Cyclotron laboratory where a 152Sm self-supporting target was bombarded with a 13.5 MeV deuteron beam. The reaction 152Sm (d,tγ)151Sm populated the nucleus of interest. An array of NaI(Tl) detectors, CACTUS [1], detected γ-rays and the silicon particle telescope array, SiRi [2], was used to detect charged particles in coincidence. The NLD and γSF were extracted from the particle-γ coincidences below the neutron separation energy, Sn, using the Oslo Method [3].
These results are used to place the SR in 151Sm and its magnetic dipole strength B(M1) value into the context of previously measured samarium isotopes[4, 5, 6]. I will present the results for 151Sm, which depicts a near complete picture of the evolution of the strength of the SR [B(M1)] for the stable Sm isotopic chain.

Speaker: Ms Sebenzile Magagula (SSC Laboratory, iThemba labs, Somerset west, 7129, South Africa)
• 11:50
Photon strength functions from (p, γ) reactions 20m

In the 1970s and 80s (p, γ) reactions were successfully utilized to measure the photon strength function (PSF) using the Average Resonance Capture Method [1] and this work seeks to explore these reactions to measure the PSF using the ratio and X2 method [2]. The 50Cr(p, γ)51Mn capture reaction has been used to study primary γ-ray transitions from the entry states between the proton and neutron separation energies to discrete states of known spins and parities. For a proof-of-principle experiment, the Tandetron accelerator at iThemba LABS was used to deliver proton beams of 2.5 to 3 MeV and 3.675 to 4.498 MeV in intervals of 20-25 keV with beam currents of up to 5 𝜇A. The primary γ-rays emitted from the reaction were detected using one segmented Clover detector placed at 90° to the beam direction. A total of 64 gamma-ray spectra were collected with 26 and 38 of these spectra collected for 2.5 to 3 MeV and 3.675 to 4.498 MeV beam energies respectively. The level scheme of the 51Mn compound nucleus was built with several new transitions and states being identified. The average intensities of the primary γ-rays decaying to discrete states of known spin and parity were extracted. The PSF of 51Mn will be extracted using the ratio and X2 method [2]. In this talk, I will present the analysis and preliminary results on the extraction of the PSF of 51Mn populated using 50Cr(p, γ) reaction.

Speaker: Mr Adivhaho Netshiya (iThemba LABS and WITS)
• 12:10
Ion source development for the LERIB test facility 20m

Ion-source development for the LERIB test facility

Skye Segal1, J. Abrahams1, H. Anderson1, S. Baard1, R. Bark1, H. Barnard1, J. Conradie1, B. Cornelius1, A. Crombie1, J. de Villiers1, W. Duckitt1, C. Ellis1, D. Fourie1 and P. Van Schalkwyk1

1iThemba LABS, South Africa

At the off-line test facility of the Low-Energy Radioactive-Ion Beam, or LERIB [1] project, at iThemba LABS, two ion-sources are being developed: a surface ion source, and a Forced Electron Beam Induced Arc Discharge, or FEBIAD, plasma ion-source [2].
The hot-cavity type surface ionization source has already undergone some development at the LERIB off-line test facility. The production of ions from group 1 was accomplished with the creation of stable beams of 39K+, 41K+ and 23Na+, and beam currents were measured in the µA range. This source is a good choice as a pilot beam for similar mass beams that could eventually be used for RIB experiments - stable and bright beams can be created, and they can be switched on or off quickly by limiting heating current through the tantalum oven.
The LERIB FEBIAD is in its initial stages of development. The FEBIAD will be essential for the production of RIBs, as a wide variety of elements can be ionized with it through the process of electron-impact ionization. The FEBIAD under consideration will include the use of magnetic fields for the confinement of the electron beam. Magnetic fields produced by solenoids have been shown to improve the ionization in plasma ion sources [3]. Electromagnetic solenoid fields as well as arrays of permanent magnets will be studied for use in the LERIB FEBIAD.

[1] J. Conradie, et al., Progress with a New Radioisotope Production Facility and Construction of Radioactive Beam Facility at iThemba LABS, (2016).
[2] T. Stora, Radioactive Ion Sources, CERN Yellow Report CERN-2013-007 pp.331-349 (2014).
[3] J. Ballof, et al., A cold electron-impact ion source driven by a photo-cathode, (2022).

Speaker: Dr Skye Segal (iThemba LABS)
• 13:00 14:00
Lunch 1h Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 14:00 15:00
Discussion Session: Nuclear Structure Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Conveners: Jacobus Diener (Botswana International University of Science and Technology) , Luna Pellegri (University of the Witwatersrand and iThemba LABS)
• 15:00 15:30
Tea Break 30m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• Friday, 20 May
• 10:00 10:45
Collaborations and Networking Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Convener: Alison Bruce (University of Brighton)
• 10:00
The Role of Inter-Africa UK Collaboration in Improving Nuclear Instrumentation for Research and Development in Africa 45m

In the current world of science and technology, the contribution of nuclear science, technology and techniques cannot be overestimated. Humankind have benefited from many aspects of nuclear science and technology especially in areas such as power production, health services, agricultural developments and security. Moreover, nuclear techniques have continued to be beneficial for analysing food as well as environmental samples hence promoting good quality of life for everyone. Such benefits are the outcomes of continuous research efforts and knowledge expansion in nuclear science. That is to say, continuous research and development (R&D) activities is the key to the future success. Yet, the R&D activities require reliable expertise and instrumentation, which are vital aspects for safe and effective use of several nuclear techniques and technology. Nevertheless, most developing countries are far behind the developed countries in terms the aforementioned aspects. This causes not only difficulties in conducting cutting edge nuclear researches in the developing countries but also failure to take full advantage of the available nuclear technology, which could hugely boost the economies of these countries. In order to ease the situation, research collaborations between the less developed, developing and developed countries have always been suggested to take advantage of the available nuclear instruments. Thus, nuclear instrumentation and expertise make an important point of focus for collaborations between African countries and the United Kingdom (UK). This talk will highlight the importance of the inter-Africa and United Kingdom (UK) collaborations in the development of nuclear instrumentation and nuclear technology in Africa taking Tanzania as a case study.

Speaker: Innocent Jimmy Lugendo (University of Dar es Salaam)
• 10:45 11:15
Function: Tour: SAIF Facility Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 11:15 11:45
Coffee Break 30m Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 11:45 12:30
Collaborations and Networking Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
Conveners: Alison Bruce (University of Brighton) , Pete Jones (iThemba LABS)
• 12:30 13:00
Closing and Final Remarks Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E
• 13:00 14:00
Lunch 1h Visitors Centre

### Visitors Centre

#### NRF-iThemba LABS, Old Faure Road, Cape Town

NRF-iThemba LABS Old Faure Road Cape Town GPS Co-ordinates 34.025°S 18.716°E


text:
# The 3 cute roots

Algebra Level 4

Given that $$a,b$$ and $$c$$ are the roots of the equation $iz^ 3+6z^2 - 11iz - 6=0.$

Find the value of $$a^2+b^2+c^2$$.

×

format: plain


text:
Get A+ with YaClass!
Register now to understand any school subject with ease and get great results on your exams!

### Theory:

You can use LibreOffice without needing a pointing device, such as a mouse or trackball, by using its in-built keyboard shortcuts. Tasks as diverse and complex as docking and un-docking toolbars and windows or adjusting the size or location of objects can all be performed with only a keyboard. Although LibreOffice has its own large set of keyboard shortcuts, each component provides others that are specific to its work.

Impress Function Keys:

A function key is a key on a keyboard that can be programmed to cause an operating system (OS) command interpreter or application program to perform specific actions, a form of a soft key.

 Shortcut Keys Effect $$F1$$ Open LibreOffice Impress Help. $$F2$$ Select the text tool and edit the text. $$Ctrl+F2$$ Starts a slide show. $$F3$$ Enter group and edit group. $$Shift+F3$$ Duplicate object. $$Ctrl+F3$$ Exit group. $$F4$$ Open Position and Size dialogue. $$F5$$ Starts a slide show. $$Shift+F5$$ Restart a slide show at the current slide where the slide show waspreviously stopped at. $$Alt+Shift+F5$$ Go to the first slide in a presentation when in Normal view. $$Ctrl+Shift+F5$$ Open Navigator. $$F6$$ Forward navigation within the on-screen elements without usingmouse. $$Shift+F6$$ Backward navigation within the on-screen elements without usingmouse. $$F7$$ Start spelling checker. $$Ctrl+F7$$ Open thesaurus. $$F8$$ Edit points. $$Ctrl+Shift+F8$$ Fit text to frame. $$Shift+F10$$ Open context menu of a selected object. $$F11$$ Open Styles and Formatting dialog.

Reference:
https://commons.wikimedia.org/wiki/File:ISO_keyboard_(105)_QWERTY_UK.svg


text:
# Tag Archives: Pythagorean theorem

## Math2111: Chapter 1: Fourier series. Section 2: Inner product and norm

In this blog entry you can find lecture notes for Math2111, several variable calculus. See also the table of contents for this course. This blog entry printed to pdf is available here.

We repeat two fundamental concepts which you should have seen in linear algebra already.
Inner product and norm in $\small \mathbb{R}^n$
Let $\boldsymbol{u}, \boldsymbol{v} \in \mathbb{R}^n$ be vectors with

$\displaystyle \boldsymbol{u} = (u_1, \ldots, u_n)^\top, \quad \boldsymbol{v} = (v_1,\ldots, v_n)^\top$

where $(u_1,\ldots, u_n)^\top$ stands for the transpose of the vector $(u_1,\ldots, u_n)$.

Then the dot product of these vectors is defined by Continue reading


text:
## manoj12 Group Title A man in a train traveling at 30 km/hr notices that a train going in the opposite direction passes him in 9 seconds. If the length of this train is 200m, find its speed? 3 years ago 3 years ago

1. satellite73 Group Title

solve $200=(30+r)9$ for r

2. GoBlue Group Title

distance=rate x time The train's relative speed is 200/9 m/s=80 km/hr Speed=80-30=50 km/hr

3. siddharth Group Title

Let the other train's speed be v km/hr. Now, if we consider the man to be stationary (his frame of reference), the other train will be travelling at 30+v km/hr in the opposite direction. So, other train travels 200m in 9 seconds. Distance = speed * time 200/1000 km = (30+v) km/hr * 9/3600 hrs 20 = (30+v)/4 v = 50 km /hr

4. manoj12 Group Title

Hello, siddharth, but 200/1000 is 0.2

5. siddharth Group Title

I did some simplification: $\frac{200}{1000} = \frac{9(30+v)}{3600}$ multiply both sides by 1000: $200 = \frac{9(30+v)}{3600} \times 1000$ $200 = \frac{9(30+v)}{36} \times 10$ divide both sides by 10 $20 = \frac{9(30+v)}{36}$


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# 30.3 Bohr’s theory of the hydrogen atom  (Page 6/14)

 Page 6 / 14

But there are limits to Bohr’s theory. It cannot be applied to multielectron atoms, even one as simple as a two-electron helium atom. Bohr’s model is what we call semiclassical . The orbits are quantized (nonclassical) but are assumed to be simple circular paths (classical). As quantum mechanics was developed, it became clear that there are no well-defined orbits; rather, there are clouds of probability. Bohr’s theory also did not explain that some spectral lines are doublets (split into two) when examined closely. We shall examine many of these aspects of quantum mechanics in more detail, but it should be kept in mind that Bohr did not fail. Rather, he made very important steps along the path to greater knowledge and laid the foundation for all of atomic physics that has since evolved.

## Phet explorations: models of the hydrogen atom

How did scientists figure out the structure of atoms without looking at them? Try out different models by shooting light at the atom. Check how the prediction of the model matches the experimental results.

## Test prep for ap courses

A hypothetical one-electron atom in its highest excited state can only emit photons of energy 2 E , 3 E , and 5 E before reaching the ground state. Which of the following represents the complete set of energy levels for this atom?

1. 0, 3 E , 5 E
2. 0, 2 E , 3 E
3. 0, 2 E , 3 E , 5 E
4. 0, 5 E , 8 E , 10 E

(a)

The Lyman series of photons each have an energy capable of exciting the electron of a hydrogen atom from the ground state (energy level 1) to energy levels 2, 3, 4, etc. The wavelengths of the first five photons in this series are 121.6 nm, 102.6 nm, 97.3 nm, 95.0 nm, and 93.8 nm. The ground state energy of hydrogen is −13.6 eV. Based on the wavelengths of the Lyman series, calculate the energies of the first five excited states above ground level for a hydrogen atom to the nearest 0.1 eV.

The ground state of a certain type of atom has energy – E 0 . What is the wavelength of a photon with enough energy to ionize an atom in the ground state and give the ejected electron a kinetic energy of 2 E 0 ?

1. $\frac{hc}{3{E}_{0}}$
2. $\frac{hc}{2{E}_{0}}$
3. $\frac{hc}{{E}_{0}}$
4. $\frac{2hc}{{E}_{0}}$

(a)

An electron in a hydrogen atom is initially in energy level 2 ( E 2 = -3.4 eV). (a) What frequency of photon must be absorbed by the atom in order for the electron to transition to energy level 3 ( E 3 = -1.5 eV)? (b) What frequency of photon must be emitted by the atom in order for the electron to transition to energy level 1 ( E 1 = -13.6 eV)?

## Section summary

• The planetary model of the atom pictures electrons orbiting the nucleus in the way that planets orbit the sun. Bohr used the planetary model to develop the first reasonable theory of hydrogen, the simplest atom. Atomic and molecular spectra are quantized, with hydrogen spectrum wavelengths given by the formula
$\frac{1}{\lambda }=R\left(\frac{1}{{n}_{\text{f}}^{2}}-\frac{1}{{n}_{\text{i}}^{2}}\right),$
where $\lambda$ is the wavelength of the emitted EM radiation and $R$ is the Rydberg constant, which has the value
$R=\text{1.097}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{-1}\text{.}$
• The constants ${n}_{i}$ and ${n}_{f}$ are positive integers, and ${n}_{i}$ must be greater than ${n}_{f}$ .
• Bohr correctly proposed that the energy and radii of the orbits of electrons in atoms are quantized, with energy for transitions between orbits given by
$\Delta E=\text{hf}={E}_{\text{i}}-{E}_{\text{f}},$
where $\Delta E$ is the change in energy between the initial and final orbits and $\text{hf}$ is the energy of an absorbed or emitted photon. It is useful to plot orbital energies on a vertical graph called an energy-level diagram.
• Bohr proposed that the allowed orbits are circular and must have quantized orbital angular momentum given by
$L={m}_{e}{\text{vr}}_{n}=n\frac{h}{2\pi }\left(n=1, 2, 3 \dots \right),$
where $L$ is the angular momentum, ${r}_{n}$ is the radius of the $n\text{th}$ orbit, and $h$ is Planck’s constant. For all one-electron (hydrogen-like) atoms, the radius of an orbit is given by
${r}_{n}=\frac{{n}^{2}}{Z}{a}_{\text{B}}\text{(allowed orbits}\phantom{\rule{0.25em}{0ex}}n=1, 2, 3, ...\right),$
$Z$ is the atomic number of an element (the number of electrons is has when neutral) and ${a}_{\text{B}}$ is defined to be the Bohr radius, which is
${a}_{\text{B}}=\frac{{h}^{2}}{{4\pi }^{2}{m}_{e}{\text{kq}}_{e}^{2}}=\text{0.529}×{\text{10}}^{-\text{10}}\phantom{\rule{0.25em}{0ex}}\text{m}\text{.}$
• Furthermore, the energies of hydrogen-like atoms are given by
${E}_{n}=-\frac{{Z}^{2}}{{n}^{2}}{E}_{0}\left(n=1, 2, 3 ...\right)\text{,}$
where ${E}_{0}$ is the ground-state energy and is given by
${E}_{0}=\frac{{2\pi }^{2}{q}_{e}^{4}{m}_{e}{k}^{2}}{{h}^{2}}=\text{13.6 eV.}$
Thus, for hydrogen,
${E}_{n}=-\frac{\text{13.6 eV}}{{n}^{2}}\left(n,=,1, 2, 3 ...\right)\text{.}$
• The Bohr Theory gives accurate values for the energy levels in hydrogen-like atoms, but it has been improved upon in several respects.

#### Questions & Answers

Suppose a speck of dust in an electrostatic precipitator has 1.0000×1012 protons in it and has a net charge of –5.00 nC (a very large charge for a small speck). How many electrons does it have?
Alexia Reply
how would I work this problem
Alexia
how can you have not an integer number of protons? If, on the other hand it supposed to be 1e12, then 1.6e-19C/proton • 1e12 protons=1.6e-7 C is the charge of the protons in the speck, so the difference between this and 5e-9C is made up by electrons
Igor
what is angular velocity
Obaapa Reply
Why does earth exert only a tiny downward pull?
Mya Reply
hello
Islam
Why is light bright?
Abraham Reply
what is radioactive element
Attah Reply
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
Aisha Reply
thanks so much. i undersooth well
Valdes Reply
what is physics
Nwafor Reply
is the study of matter in relation to energy
Kintu
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
Obrian Reply
what is power?
aron Reply
power P = Work done per second W/ t. It means the more power, the stronger machine
Sphere
e.g. heart Uses 2 W per beat.
Rohit
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
Alona Reply
did you solve?
Shii
1.75cm
Ridwan
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
Abu
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
Sphere
what do we call velocity
Kings
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
Kavita Reply
hi
Godfred
what about the wind vane
Godfred
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
Anurag Reply
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
Jaydie Reply
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
Princewill Reply

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# How come Cartan did not notice the close relationship between symmetric spaces and isoparametric hypersurfaces?

Elie Cartan made fundamental contributions to the theory of Lie groups and their geometrical applications. Among those, we can list the introduction of the remarkable family of Riemannian symmetric spaces, and his four papers that revolutionized the theory of isoparametric hypersurfaces.

How come Cartan did not notice the close relationship between symmetric spaces and isoparametric hypersurfaces?

Starting in 1926, Cartan developed his theory of symmetric spaces and published papers between 1927 and 1935. He first introduced them as Riemannian manifolds with parallel curvature tensor, under the name "espaces $\mathcal E$". Then he noticed that an equivalent, more geometric definition is to require that the geodesic symmetric around any point is an isometry and, around 1929, changed their name to "espaces symetriques'". The second definition implies that a symmetric space is a homogeneous space $G/K$ and there is a decompositon $\mathfrak g=\mathfrak k+\mathfrak p$ into the eigenspaces of an involution induced by conjugation by the geodesic symmetry at the basepoint. The adjoint action of $K$ on $\mathfrak p$ is equivalent to the linear isotropy representation of the symmetric space. The rank of $G/K$ is the dimension of a maximal flat, and coincides with the codimension of the principal orbits of this representation.

Isoparametric hypersurfaces in space forms are hypersurfaces with the simplest local invariants, namely, they have constant principal curvatures. They existed before Cartan, but between 1937 and 1940 he published four papers that completely revolutionized the field. Among other things, he showed that isoparametric hypersurfaces in spheres is a much more interesting subject than in Euclidean or hyperbolic spaces. Denote by $g$ the (constant) number of principal curvatures. The initial cases are not very interesting; in a sphere $S^{n+1}$, an isoparametric hypersurface with $g=1$ is an umbilic sphere, and with $g=2$ is the standard product of two spheres. Cartan showed that in case $g=3$ there are exactly four examples, of dimension $n=3d$ where $d=1$, $2$, $4$ or $8$ is the uniform multiplicity of the principal curvatures, each related to an embedding of a projective plane over one the normed division algebras $\mathbb R$, $\mathbb C$, $\mathbb H$, $\mathbb O$. He notes that those examples are all homogeneous and determines their isometry groups; in particular, he is pleased with the appearance of the exceptional group $F_4$ the case $n=24$, "(...) the first appearance of the simple $52$-dimensional group in a geometric problem (...)"; this group had already appeared in his classification of symmetric spaces. Later Cartan discusses the case $g=4$ and shows there are only two examples where the multiplicities of principal curvatures are all equal, namely, one in $S^5$ and one in $S^9$.

Cartan ends his third paper on the subject (Sur quelques familles remarquables d'hypersurfaces, C. R. Congres Math. Liege (1939), 30-41. Also in: Oeuvres Completes, Partie I11, Vol. 2, 1481-1492.) with three questions, one of which asking whether there exist isoparametric hypersurfaces in spheres with $g>3$ such that multiplicities of principal curvatures are unequal. In 1971, Hsiang and Lawson published a paper (Minimal submanifolds of low cohomogeneity, J. Differential Geom. 5 (1971), 1-38.) including a classification of (maximal) subgroups of $SO(n+2)$ whose principal orbits have cohomogeneity $1$ in $S^{n+1}$, and remarked that they precisely coincide with the linear isotropy representations of symmetric spaces of rank two. In 1972, Takagi and Takahashi (On the principle curvatures of homogeneous hypersurfaces in a sphere, Differential Geometry, in Honor of K. Yano, Kinokuniya, Tokyo (1972), 469--481.) remarked that Hsiang-Lawson's result yields a classification of homogeneous isoparametric hypersurfaces in spheres and computed their invariants; in particular, they found examples with $g=4$ and unequal multiplicities.

The relation is that the principal orbits of the linear isotropy representations of symmetric spaces rank two (resp. arbitrary rank) yield beautiful examples of isoparametric hypersurfaces (resp. submanifolds) in spheres.

This relation is relatively easy to explain today. Cartan was the master of both subjects in the late 1930's. Is there anything interesting that can be said about the situation of differential geometry and Lie group theory at that time that prevented him to grasp this connection?

• This question reminds me of the many times I've seen something done by someone else and thought "Why didn't I think of that?" (because it seemed so obvious once it was pointed out); usually, I couldn't come up with any better answer than that I was thinking along different lines or about different examples. I imagine that even Cartan had this experience from time to time, and maybe he didn't have a better answer either. You can't think of everything, and some things are only 'obvious' in hindsight. – Robert Bryant Feb 9 '14 at 23:13


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# Special Relativity/Problems

## Problems

1. Sketch your personal world line on a spacetime diagram for the last 24 hours, labeling by time and location special events such as meals, physics classes, etc. Relate the slope of the world line at various times to how fast you were walking, riding in a car, etc.
2. Spacetime conversions:
1. What is the distance from New York to Los Angeles in seconds? From here to the moon? From here to the sun?
2. What is one nanosecond in meters? One second? One day? One year?
3. Three events have the following spacetime coordinates: A is at $(x,ct) = (2 \mbox{ m} , 1 \mbox{ m} )$; B is at $(x,ct) = ( -2 \mbox{ m} , 0 \mbox{ m} )$; C is at $(x,ct) = ( 0 \mbox{ m} , 3 \mbox{ m} )$.
1. A world line for an object passes through events B and C. How fast and in which direction is the object moving?
2. A line of simultaneity for a coordinate system passes through events A and B. How fast and in which direction is the coordinate system moving?
3. What is the invariant interval between events A and B? B and C? A and C?
4. Can a signal from event B reach event A? Can it reach event C? Explain.
Hint: Draw a spacetime diagram with all the events plotted before trying to answer the above questions.
4. In the following problem be sure to indicate the slope of on pertinent lines drawn.
1. In a spacetime diagram, sketch a line of simultaneity for a reference frame moving to the left at $V = c/2$, where $c$ is the speed of light.
2. Sketch the world line of an object which is initially stationary, but which accelerates to a velocity of $v = c/3$.
5. Suppose that an interstellar spaceship goes a distance $X = 100 \mbox{ light years}$ relative to the rest frame in $T' = 10 \mbox{ years}$ of its own time.
1. Draw a spacetime diagram in the rest frame showing $X$, $T'$, and the time $T$ needed for this journey relative to the rest frame.
2. Cmpute $T$, using your spacetime diagram as an aid.
3. Compute the speed of the spaceship.
6. If an airline pilot flies $80 \mbox{ hr}$ per month (in the rest frame) at $300 \mbox{ m} \mbox{ s}^{-1}$ for $30 \mbox{ years}$, how much younger will she be than her twin brother (who handles baggage) when she retires? Hint: Use $(1 - \epsilon )^x \approx 1 - x \epsilon$ for small $\epsilon$.
7. A mu particle normally lives about $2 \times 10^{-6} \mbox{ sec}$ before it decays. However, muons created by cosmic rays $20 \mbox{ km}$ up in the atmosphere reach the Earth's surface. How fast must they be going?
8. The Stanford Linear Accelerator accelerates electrons to a speed such that the $3 \mbox{ km}$ long accelerator appears to be $8 \mbox{ cm}$ long to the electron, due to the Lorentz contraction. How much less than the speed of light is the electron traveling? Hint: It is best to first develop an approximation for the relationship between $\gamma = (1 - v^2 /c^2 )^{-1/2}$ and the difference between $c$ and $v$ for a particle moving close to the speed of light.
9. How fast do you have to go to reach the center of our galaxy in your expected lifetime? At this speed, what does this distance appear to be? (We are about $30000 \mbox{ ly}$ from the galactic center.)
10. Two identical spaceships pass each other going in the opposite direction at the same speed.
1. Sketch a spacetime diagram showing the world lines of the front and rear of each spaceship.
2. Indicate an interval on the diagram corresponding to the rightward-moving spaceship's length in its own reference frame.
3. Indicate an interval corresponding to the leftward-moving spaceship's length in the reference frame of the rightward-moving spaceship.
4. Indicate an interval equal to the length of either spaceship in the rest frame.
11. George and Sally are identical twins initially separated by a distance $d$ and at rest. In the rest frame they are initially the same age. At time $t = 0$ both George and Sally get in their spaceships and head to the right at velocity $U$. Both move a distance $d$ to the right and decelerate to a halt. (See figure 4.10.)
1. When both are moving, how far away is Sally according to George?
2. How much older or younger is Sally relative to George while both are moving?
3. How much older or younger is Sally relative to George after both stop?

Hint: Draw the triangle ABC in a reference frame moving with George and Sally.

Figure 4.10: Sketch for moving identical twins. Line AC is the line of simultaneity for a reference frame moving with Sally and George.


text:
# Regularity and Positional Games

@article{Hales1963RegularityAP,
title={Regularity and Positional Games},
author={Alfred W. Hales and Robert I. Jewett},
journal={Transactions of the American Mathematical Society},
year={1963},
volume={106},
pages={222-229}
}
• Published 1 February 1963
• Mathematics
• Transactions of the American Mathematical Society
1.Introduction. Suppose X is a set, 𝒞 a collection of sets (usually subsets of X), and N is cardinal number. Following the terminology of Rado [1], we say 𝒞 is N-regular in X if,for any partition of X into N parts, some part has as a subset a member of 𝒞. if 𝒞 is n-regular in X for each integer n, we say 𝒞 is regular in X.
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### A Ramsey-Type Theorem in the Plane

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We show that, for any finite set P of points in the plane and for any integer k ≥ 2, there is a finite set R = R(P, k) with the following property: for any k-colouring of R there is a monochromatic

### Dense Subsets of Products of Finite Trees

• Mathematics
• 2013
We prove a “uniform” version of the finite density Halpern–Lauchli theorem. Specifically, we say that a tree T is homogeneous if it is uniquely rooted and there is an integer , called the branching

### Ramsey’s theorem for $n$-parameter sets

• Mathematics
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Classes of objects called «-parameter sets are defined. A Ramsey theorem is proved to the effect that any partitioning into r classes of the »c-parameter subsets of any sufficiently large «-parameter

### A study on some combinatorial sets in partial semigroups

• Arpita Ghosh
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Asian-European Journal of Mathematics
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In this article, we investigate the image and preimage of the important combinatorial sets such as central sets, $C$-sets, and $J_\delta$-sets which play an important role in the study of

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### On Representatives of Subsets

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text:
Mobile QR Code

1. (Department of Information Systems, Le Quy Don Technical University, Hanoi, Vietnam giangnv@mta.edu.vn)

X-ray imaging, Digital radiography, Deblurring, Denoising, Detector blur, Deconvolution

## 1. Introduction

Digital radiography (DR) is an X-ray radiographic imaging technology acquiring digital projection images using photo-stimulable storage phosphor (computed radiography, or CR), amorphous selenium, amorphous silicon, charge coupled devices (CCDs), or a metal-oxide semiconductor field effect transistor. Among many medical imaging modalities in digital radiography, the two most popular ones are computed radiography and flat-panel digital radiography [1].

In CR, a photo-stimulable phosphor is coated on the plate, referred to as an imaging plate (IP), which is housed in a cassette to protect it. The IP is then considered the digital detector in CR. However, this technology has some limitations. The spatial resolution is less than that from DR, and the total acquisition time and image reading time are much higher than DR. The durability of the IP is less than with a DR image.

Flat-panel digital radiography systems have been developed to overcome the shortcomings of CR systems. In DR, the digital detector is designed with a flat panel. Currently, there are two categories of flat-panel digital radiography imaging systems (based on the type of detector used [2]), and they have been popularly referred to as (i) indirect conversion digital radiography systems, and (ii) direct conversion digital radiography systems. The latter use detectors that convert X-rays directly to electronic signals, but in the former, X-rays are first converted into light using a phosphor. The emitted light from the phosphor falls upon a matrix array of electronic elements to create and store electrical charges in direct proportion to the X-ray exposure. The charges produce electrical signals that are subsequently digitized and processed by a computer to produce an image. These two types of modalities have high sensitivity but are expensive due to the involvement of a thin film transistor (TFT) array in the detector. In a second type of indirect conversion detector, charge coupled devices (CCDs) are coupled to a phosphor cesium iodide scintillator. X-rays hit the phosphor to produce light, which then hits the CCD array that converts the light into electrical signals, which are digitized and processed by a computer to produce an image.

While the above detector technologies result in superior DR image quality, the high price prevents use in rural areas and when imaging a large object. To reduce the price of the DR detector and increase its lifetime, attempts have been made to use a lens-coupled X-ray detector [3,4]. That approach photographs a screen (usually an X-ray scintillator) exposed to X-rays. This collection of X-ray photons can be done by coupling a scintillating screen and a camera, which captures the scintillating screen to create an X-ray image. However, since the optical sensors used in digital cameras are much smaller than the objects to be imaged, the camera must be moved far away from the illuminating scintillator so that the entire X-ray image fits on the sensor.

Inspired by that idea, in this paper, we built and investigated an imaging system that is likely to be cheaper than existing methods of X-ray imaging. Compared to the conventional indirect flat-panel system, the proposed imaging system uses a mirror to reflect the light from the scintillating screen to the camera. This mirror is used to prevent the incoming X-rays from hitting the camera sensor. This camera design is similar to the one used in high-resolution micro-CT [5], but not in digital radiography, as in this work.

On the one side, since the proposed imaging system shares some similarities with existing systems, the captured image has to go through an extensive image processing pipeline (described in Section 2) to produce the display image as closely as possible to currently used DR imaging techniques. One the other side, since the acquiring process is different from ordinary DR with existing flat-panel detectors, the acquired images are degraded by two factors: unwanted impulsive noise and blurring. The noise here is not only Poisson noise, but also $\textit{impulsive-style noise}$ that occurs during DSLR acquisition under dark conditions where the inner space containing the camera (including the mirror and the one side of the scintillator) has to be kept in total darkness to increase the sensitivity of the acquisition. The impulsive-style noise is caused by failures in sensors, readout circuits, A/D converters, or communication channels. This impulsive-style noise is not only found in our imaging system with a lens-coupled X-ray detector where the consumer camera takes the picture of the scintillating screen to create an X-ray image, but is also found in standard digital radiography, as reported in [6]. This impulsive-style noise, even at a low rate, leads to a poor visualization result (after the raw image goes through contrast enhancement). Furthermore, the acquired image in DR is also blurred due to source blur, detector blur, and motion blur. These two issues, especially the $\textit{impulsive-style noise}$, were not addressed in previous work [3-5].

To address the noise issue, we use a statistical-based impulsive noise removal method and make it work in separate channels of the color image captured by the DSLR camera. This is to ensure that only impulsive-style noise is removed, while the detail is kept perfectly in the acquired image. To deblur the image, rather than using the blind deblurring method, which might result in an artificial image (with unwanted nonrealistic patterns), we use non-blind deblurring with a systematically derived blur kernel. Our deblurring framework consists of two steps: (i) estimating the X-ray source and detector point spread functions (PSFs) via the radiographs of a pre-designed metal plate, and (ii) using the estimated PSFs (the blur kernel) to perform deblurring via a non-blind deconvolution method. Our deblurring process takes into account the distance to the detector plane from the object to be imaged.

In Section 2, we describe the imaging system used to acquire the DR image, as well as the image processing pipeline to produce the final ready-to-display DR image. The section also describes a method to remove impulsive-style noise, and a method to deblur DR images. Section 3 presents results from using experimental data with our prototype DR imaging system. Section 4 concludes the paper.

## 2. Methods

### 2.1 Imaging Systems and Image Processing Pipelines

The working principle of the proposed imaging system is summarized in Fig. 1. It consists of an X-ray tube, a scintillating screen, a mirror, and a camera. When the X-rays are emitted, they come through the object being imaged. Some are attenuated by the object, and the remaining hit the scintillation screen. Depending on the number of X-rays that hit it, the scintillation screen will light up. At that moment, the camera opens its lens to capture an image of the scintillating screen. Note that, to protect the lens from being hit by X-rays passing through the scintillator, the camera takes an image of the mirrored scintillating screen. The captured image will be processed to generate a ready-to-display image.

Fig. 1. Diagram of the proposed imaging system.

To realize the idea, we built the prototype imaging system in Fig. 2. The system consists of the following main parts: (i) the X-ray source is a Toshiba Rotanode E7239X; (ii) the scintillator is a Hamamatsu GPXS J10666-100; and (iii) the consumer camera is a Canon EOS 750D. The X-ray source is synchronized with the camera so the camera will open its lens to acquire the light from the scintillating screen when it reaches its brightest state. The settings of the DSLR camera are as follows: shutter speed = 1/3 sec, ISO=800, and AV=10. The lens is locked in focus by taking an image of a resolution test chart placed behind the scintillating screen.

Fig. 2. Our prototype DR with an indirect DSLR-based detector.

In digital radiography, regardless of the imaging system (the DR scanner), radiologists always want to view the image in the display device (for example, on an LCD monitor), and images (from different scanners) of the same patient should be the same. Therefore, we need to adopt an image processing pipeline to generate standardized, ready-to-display images. Regarding our proposed imaging system (with a DSLR-based detector), we use an image processing pipeline that consists of the following steps.

(ii) Use flat-field correction to correct the varying flat field in the image [7].

(iii) Image scaling determines the actual object region in the DR image.

(iv) Image deblurring (or edge restoration) handles blurring due to the detector and the X-ray source.

(v) Apply dynamic range reduction and latitude reduction [8].

(vi) Use multiscale contrast enhancement [9,10]

The aim of image processing here is to eliminate all factors contributing to unwanted degradation in the acquired image, and to generate the final ready-to-display image (described in Section 3). Note that in our imaging system, steps (i) to (iv) are performed with a color image, while in steps (v) and (vi), the processing image is grayscale to match the standard in digital radiography.

Most factors that degrade the standard DR image quality (with an actual flat-panel detector) have been addressed in previous work [7-10]. However, regarding our DR imaging system with DSLR-based detector, there are two new degrading factors that have not been addressed in previous DR imaging systems. Those are impulsive-style noise, and blur in the image when capturing an object that is a little far from the scintillating screen.

### 2.2 Impulsive Noise Removal

In our imaging system, the acquired images are usually corrupted by impulsive noise, as shown in Figs. 3(a), 4(a) and 5(a). By analyzing the raw image (in our case, it is the CR2 file), which is a color sample output from an image sensor with a color filter array (CFA), we found that the noise shows up in the raw data (before demosaicing) and appears differently in different color filters and in nearby pixels. (See Figs. 3(b) to 3(e)). That eventually results in complex impulsive noise patches in the acquired RGB image in Fig. 3(a). We also found that the location of the impulsive noise here is random for each acquisition.

Fig. 3. Impulsive noise in the acquired RGB image and its raw images: (b)-(e) are the raw images for red, green, green, and blue before demosaicing to generate full-color image (a). Note that for a CR2 raw file, the output from the color filter array has the pattern RGGB.

When analyzing the acquired image in Fig. 4(a) in the $\textit{HSV}$ color space shown in Figs. 4(b)-(d), we realized that different noisy pixels in a color image have different contributions from the corresponding pixels in the image from each $\textit{H}$, $\textit{S}$, and $\textit{V}$ channel. Note that modeling in $\textit{HSV}$ in our case is from the fact that the acquisition process takes an image from a scintillating screen. For the full information, we configured the camera to take a color image. The $\textit{HSV}$ color space is selected since an $\textit{HSV}$ representation models how colors appear under light, and the $\textit{HSV}$ model has a better color description for human interpretation.

Furthermore, the region contaminated by impulsive noise varies in each channel, as seen in Figs. 4(b)-(d). The size of the region also changes in each channel (the noise patch gets larger in the $\textit{H}$ channel, and smaller in $\textit{S}$ and $\textit{V}$ channels). This fact is found not only in the illustrated samples in Fig. 4, but also in all images acquired using our proposed imaging system (such as the one of a chest region in Fig. 5).

Based on this observation, we performed denoising on each channel ($\textit{H}$, $\textit{S}$, and $\textit{V}$) separately. Since each channel was closed to noise that occurs in standard digital radiography, we employed a statistical-based impulsive noise filter [6] that was designed for standard digital radiography. (Note that in the image from our imaging system, the noise is not salt-and-pepper noise, since the region of degradation might occupy multiple pixels, and therefore, the standard salt-and-pepper noise filter cannot be used.)

Fig. 4. Illustration of denoising an electronic circuit board image: (a) the noisy image; (b)-(d) $\textit{H}$, $\textit{S}$, $\textit{V}$ channels, respectively, of the noisy image; (e)-(g) $\textit{H}$, $\textit{S}$, $\textit{V}$ channels, respectively, of the denoised image; (h) the denoised image.

Fig. 5. Illustration of denoising a chest region: (a) the noisy image; (b)-(d) $\textit{H}$, $\textit{S}$, $\textit{V}$ channels, respectively, of the noisy image; (e)-(g) $\textit{H}$, $\textit{S}$, $\textit{V}$ channels, respectively, of the denoised image; (h) the denoised image.

The statistical-based impulsive noise filter [6] is based on a switching scheme where all pulses are first detected by a pulse detector. The detector assumes that the major contribution to image noise is made by the photon-counting process, with some pixels corrupted by impulsive noise. This assumption is generally true when acquiring an image in a controlled environment, as in our imaging system. Having the estimated pulses, the noisy image is filtered with a standard median filter.

In the images acquired by our proposed system, the area of pulses in the image of the $\textit{H}$ channel is usually larger than in the $\textit{S}$ and $\textit{V}$ channels. Therefore, depending on the conditions of X-ray acquisition, we need to apply the statistical-based impulsive noise filter more than one time to the image of the $\textit{H}$ channel, rather than just one time in the images of the $\textit{S}$ and $\textit{V}$ channels.

It is important to note that the median filter (and its median root prior in a Bayesian framework [11]) is very popular in radiographic imaging, since it does not alter the valuable information in the image. This is different from data-driven, state-of-the-art Gaussian or Poisson denoising methods, which tend to remove noise and promote non-realistic details in radiographic imaging.

Finally, note that in practice, since the radiologist has no difficulties detecting a signal in the presence of Poisson noise, we did not try to eliminate Poisson noise. Here, we aim to get rid of the unwanted impulsive noise that leads to a poor visualization result.

### 2.3 Model-based Image Deblurring

Unlike consumer imaging where there are many uncertainties during image acquisition, especially camera motion and object motion, the acquisition in digital radiography is performed in a controlled environment. Therefore, to quantify radiographic blur, researchers in the field usually use a parametric mathematical model to describe the blurring process. The general blurring processes are usually modeled as

##### (1)
$y$=$x\ast k+n$

where $y$ is the observed blurry image, $x$ is the latent sharp image, $k$ is the approximated blur kernel, and $n$ models noise.

In our particular X-ray imaging system, we denote$p_{i}^{\left(s\right)}$ as the PSF of the X-ray source blur on the detector plane at a source-to-object distance (SOD) of $SOD_{i}$ and an object-to-detector distance (ODD) of $ODD_{i}$, where $p^{\left(d\right)}$ is the PSF of the detector. Different from source blur, detector blur does not vary with SOD and ODD. We simplified the model by ignoring motion blur on the assumption the patient does not move during data acquisition. Then, the blurring process is modeled as follows:

##### (2)
$y^{i}$=$x^{i}\ast k^{i}+n$

where

Fig. 6. (a) Image of the metal plate used to estimate the blur kernel; (b) extracted samples from an image when the distance from the object to the detector = 5 cm; (c) extracted samples from an image when the distance from the object to the detector = 40 cm.

##### (3)
$k^{i}$=$p_{i}^{\left(s\right)}$$\ast$$p^{\left(d\right)}$

is the blur kernel on the imaging plane, $y^{i}$ is the observed blurry image, and $x^{i}$ is the latent sharp image at $SOD_{i}$ and $ODD_{i}$.

The PSFs ($p_{i}^{\left(s\right)}$ and $p^{\left(d\right)}$) are usually derived using data-driven approaches where it estimates PSF directly from radiographs of known objects [12,13]. And in this work, we used a recently proposed systems approach to blur estimation and reduction (SABER) [12] for modeling and reducing the blur in our proposed X-ray DR imaging system. SABER consists of two steps: (i) estimation of the blur kernel; and (ii) deblurring using the estimated blur kernel.

To estimate the blur kernel, we illuminated a metal plate so it was perpendicular to the direction of the X-rays, and its edge was nearly horizontal and vertical. We acquire data when the object is placed in two different positions. In our experiment, one position was 5~cm from the detector (the scintillation screen) and the other was 40 cm (see Fig. 6). Having the two datasets, each with two projection images, the estimation involves the use of the L-BFGS-B algorithm (Details on blur kernel estimation can be found in [12]). Having the blur kernel, we can use either a Wiener filter [14] or a regularized least squares deconvolution (RLSD) algorithm to find sharp image $x^{i}$ in (2). However, since the DR image has a huge size (with a resolution of about $4000\times 6000$), we use a fast high-quality nonblind deconvolution based on adaptive-prior regularization [15], since it can find a state-of-the-art and stable deconvolution result in a relatively short time.

## 3. Results

To validate the performance of the proposed imaging system, as well as the denoising and deblurring methods, we acquired images from two objects: a human hand and an electronic circuit board. These samples were acquired by setting the following parameters in the scanner: accelerating voltage was 60 kV, the tube current was 160~mA, the distance from source to detector was 120 cm, and the distance from the scanning object to the detector was 2 cm.

Fig. 7 shows the acquired images with severe impulsive noise and the denoising results (using the standard median filter and the statistical-based impulsive noise filter). Using the statistical-based impulsive noise filter, almost all impulses were found, and the associated noise eliminated. Since the other image pixels remain untouched, the denoised image does not have any degradation (in comparison with the acquired noisy image). Meanwhile, the ordinary median filter could not reduce noise and preserve the radiographic features within the same time; the detail degraded while the noise remained, as indicated by the arrows at the top of Fig. 7(c). We conducted an independent image quality assessment with a radiologist, and the result confirmed the effectiveness of the proposed method in removing noise while retaining the radiographic information in the human hand. Note that the degree of noise in the acquired image is inversely proportional to the X-ray dose level passing through the patient—the lower the dose, the higher the noise. Therefore, our method to reduce noise is more important when reducing the X-ray dose.

Fig. 8 shows the results for the image of the electronic circuit board. Fig. 8(b) shows that in the denoised image, there was no loss of detail. Meanwhile, the standard median filter suffered loss of detail in the denoised images, as indicated by the arrows at the top of Fig. 8(c).

Fig. 7. Denoising result for a human hand: (a) the noisy image; (b) the image denoised by our method; (c) the image denoised by a median filter. Images on top of parts (a) to (c) are zoomed-in regions.

Fig. 8. Denoising results for an electronic circuit board: (a) the noisy image; (b) the image denoised by our method; (c) the image denoised by a median filter. Images on top of parts (a) to (c) are zoomed-in regions.

To check the effectiveness of the proposed method in eliminating noise while retaining radiographic detail, we show the results from chest-region imaging where the proposed method effectively removed impulsive noise while keeping most of the detail. See Fig. 9(b). The median filter removed the noise at the cost of degraded detail, as seen in Figs. 9(c) and (d). By using our method, the chest detail is preserved, as seen in Fig. 9(b), while it was degraded in Figs. 9(c) and (d). Note also that, by increasing the window size in the median filter, the noise might be controlled in Fig. 9(d), but the detail is smoothed out.

To quantitatively evaluate the performance of the denoising approach, we selected regions of interest (ROIs) containing detail but no impulsive noise, as indicated in Fig. 9(a), and we then computed the percentage error (PE) between the denoised image and the noisy image. (The ROI without impulsive noise in the noisy image is considered ground truth, since it contains most of the information required by a radiologist.) The PE is given by:

PE = x x ^ x × 100 % ,

Fig. 9. Image denoising results for the chest region: (a) the noisy image; (b) the image denoised by our method; (c) images denoised by a median filter with a window size of 5${\times}$5; (d) images denoised by a median filter with a window size of 7${\times}$7. The highlighted red boxes in Fig. 9(a) indicate the ROI in order to calculate the error between the denoised images and the original noisy image.

Table 1. Percentage error measured on the denoised images.

 ROI Proposed method Median filter with window size 5×5 Median filter with window size 7×7 1 0.44 2.52 3.03 2 0.45 2.56 3.02 3 0.26 2.26 2.68 4 0.27 2.34 2.83 5 0.35 2.42 2.86

where $\textit{x}$ is the noisy image, $\hat{x}$ is the denoised image, and $\left\| .\right\|$ denotes the $L_{2}$norm.

Fig. 10. Estimated blur kernel at a distance of 2~cm from the scintillating screen.

Fig. 11. Deblurring results for (a) the acquired image; (b) the deblurred image. Images in the top row are zoomed-in regions of the images in the bottom row. The global contrast factor for the acquired image is 1.52, while the value for the deblurred image is 1.73.

Table 1 lists the percentage error, showing that the proposed method achieved the smallest error with all designated ROIs.

The problem in our case is significantly different from standard image denoising, where the image might be altered to eliminate noise. Therefore, we compared only the standard median filter against our method. (The other well-known impulsive image denoising methods tend to smooth out the detail and the shadow detail in the radiographic image.)

Regarding deblurring, the estimated blur kernel was found, and the one for the image plane at the distance of 2 cm from the detector is shown in Fig. 10. (Note that the final blur kernel was computed from two PSFs: source and detector.) That blur kernel was then used to deblur the acquired image, and the deblurred result is shown in Fig. 11. To evaluate the quality of the deblurring method, we measured the global contrast factor (GCF) [16] for the original and deblurred images. GCF is considered a global focus measure, and is strongly correlated to human assessment in terms of the degree of focus of the image, where the higher the value, the better the degree of focus. The measured GCF value for the original image was 1.52, and the one for the deblurred image was 1.73. (The results for the zoomed-in region were 2.47 for the original image and 2.71 for the deblurred image).

As shown in Fig. 11(b), the deblurred image has sharper edges and is richer in detail. More importantly, it does not generate an artificial pattern in the deblurred image (as with the standard image-sharpening algorithm) since the PSF was systematically acquired. Since the deconvolution algorithm is a regularization method, we can control the degree of smoothness in the deblurred image with a special hyperparameter. The image in Fig. 11 was restored with a manually, specifically selected value of that hyperparameter.

Finally, to show the overall performance of the proposed imaging system in radiography, Fig. 12 is a final image that went through the image processing pipeline. Compared to the acquired image, the radiological features were preserved and are clearly displayed. In this particular case, the bone contrast was adjusted to satisfy the requirements of the radiologist.

Fig. 12. (a) The acquired image (in grayscale); (b) the post-processed image.

## 4. Conclusion

In this paper, we proposed and tested an imaging system to acquire digital radiography images using a consumer camera. To improve the image quality, we used a statistical-based impulsive noise removal method to get rid of impulsive noise where the rate is low but it significantly degrades the visualization results. We also used parametric modeled non-blind deconvolution to deblur the image.

Experiments show that the denoising method is capable of efficiently eliminating impulsive noise while preserving detail in the digital radiography images. Meanwhile, for deblurring, by combining a systems approach to blur estimation with fast non-blind deconvolution, we can accurately and quickly recover a sharp image from a blurred image.

The proposed imaging system, and denoising and deblurring methods, when plugged into an image processing pipeline, can quickly provide DR images with fine detail, and can be useful for radiography.

Though we tested our imaging system with only one particular type of camera, our denoising and deblurring methods are expected to work well with other cameras. An investigation on the use of other cameras in our imaging system is beyond the scope of this paper. However, we expect using our imaging system with different cameras will work well, since similar studies have been conducted in the field [4,17].

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## Author

##### Van-Giang Nguyen

Van-Giang Nguyen received the B.S. degree in computer science from Le Quy Don Technical University, Hanoi, Vietnam, in 2005, and the M.S. and Ph.D. degrees in electronic engineering from Paichai University, Daejeon, Korea, in 2009 and 2012, respectively. Since 2013, he has been with the Department of Information Systems, Le Quy Don Technical University, Hanoi, Vietnam. His current research interests include image processing, computer vision, and their applications to medical imaging and medical physics.


text:
College Algebra 7th Edition

$\frac{-v_0\pm\sqrt{v_0^{2}+2gh}}{g}$
$h = \displaystyle \frac{1}{2}gt^{2}+v_0t$ $\frac{1}{2}gt^{2}+v_0t-h = 0$ We use the quadratic formula: $t=\displaystyle \frac{-(v_0)\pm\sqrt{(v_0)^{2}-4(\frac{1}{2}g)(-h)}}{2(\frac{1}{2}g)}=\frac{-v_0\pm\sqrt{v_0^{2}+2gh}}{g}$


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# Areas Under Curve

In this section , there is only one curve above x-axis . We need to find the area of that curve in given interval . Let f(x) be the curve above x-axis .

The area of f(x) between x=a to x= b is $$\int_{a}^{b} f(x) dx$$ is the formula .

If f(x) is below x-axis then we get Area of f(x) =$$\int_{a}^{b} -f(x) dx$$.

Let us observe some of the questions on this .

Q1) Find the area of the function f(x)=x+1 between x=0 to 3.

Sol) Area = $$\int_{0}^{3} f(x) dx$$

=$$\int_{0}^{3} (x+1)dx$$

=$$[\frac{x^{2}}{2} + x ]_{0}^{3}$$

= $$\frac{3^2}{2} + 3 - 0$$

= $$\frac{9}{2} + 3$$

=$$\frac{15}{2}$$.

Therefore the area of the function f(x) is 15/2 =7.5 sq. units.

Q2) Find the area of the curve f(x)=4-x^2 between x=-2 to x=2 .

Sol) Area = $$\int_{-2}^{2} f(x) dx$$

= $$\int_{-2}^{2} (4-x^{2}) dx$$

= $$[4x - \frac{x^{3}}{3}]_{-2}^{2}$$

=$$4(2)-\frac{(2)^{3}}{3} - 4(-2) + \frac{(-2)^{3}}{3}$$

= $$8 - \frac{8}{3} + 8 - \frac{8}{3}$$

=$$16 - \frac{16}{3}$$

=$$\frac{32}{3}$$ sq.units.

Q3) Find the area of the curve f(x)=4-x between x=-1 to  x=2.

Sol) Area = $$\int_{-1}^{2}f(x) dx$$

= $$\int_{-1}^{2} 4-x dx$$

= $$[ 4x - \frac{x^{2}}{2}]_{-1}^{2}$$

= $$4(2) - \frac{2^{2}}{2} - 4(-1) + \frac{(-1)^{2}}{2}$$

= $$8 - 2 + 4 + \frac{1}{2}$$

= $$\frac{21}{2}$$ sq. units.

Q4) Find the area of the curve f(x) = Cos x   between x=$$\frac{-\prod}{2}$$ to x= $$\frac{\prod}{2}$$.

Solution:

Area = $$\int_{\frac{-\prod}{2}}^{\frac{\prod}{2}} cos x dx$$

= $$[Sin x ]_{\frac{-\prod}{2}}^{\frac{\prod}{2}}$$

= $$Sin( \frac{\prod}{2}) - Sin ( \frac{-\prod}{2} )$$

= 1 - ( -1)

= 2

Areas Under Curve

Sample Problems Related To Areas

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