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2. On the age-distribution of replaceable ranked elements
- Author
-
J Gani
- Subjects
Discrete mathematics ,Partial differential equation ,Rank (linear algebra) ,Applied Mathematics ,Erlang distribution ,Poisson distribution ,Erlang (unit) ,Combinatorics ,symbols.namesake ,Pi ,symbols ,Age distribution ,Constant (mathematics) ,Analysis ,Mathematics - Abstract
In this paper we consider the age-distributions of n ranked elements whose ages at time t = 0 are 0 < x1 < x2 < … < xn; any single element may be replaced at random, the probability of replacement of the element of rank i at time t being pi(t) > 0, where ∑ni = 1 pi(t) = 1.It is assumed in the first instance that the replacement times form a Poisson process with parameter λ(t). If we denote by [fi(x, t ¦xi, 0)] the age distribution functions of the elements of rank i, these are shown to satisfy certain partial differential equations; explicit solutions to these are obtained. When λ(t) = λ and pi(t) = pi are constant, they simplify to an elementary form.The methods used for the Poisson replacement process apply with some modifications to the case where replacement times are distributed according to an Erlang distribution. Solutions are obtained for the age distribution functions of ranked elements in each of the k different stages of the Erlang process when λ(t) = λ and pi(t) = pi are constant.
- Published
- 1965
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3. Splenoportographic evaluation of portal hypertension in children
- Author
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Ghassan K. Rizk and Rafic E. Melhem
- Subjects
Liver Cirrhosis ,Male ,medicine.medical_specialty ,Gastrointestinal bleeding ,Adolescent ,Manometry ,Collateral Circulation ,Contrast Media ,Hypertension, Portal ,Methods ,medicine ,Humans ,Child ,Portal obstruction ,Portography ,business.industry ,General surgery ,General Medicine ,medicine.disease ,Child, Preschool ,Pediatrics, Perinatology and Child Health ,Portal hypertension ,Female ,Surgery ,Age distribution ,business ,Venous Pressure - Abstract
Since 1956, 105 patients were examined by splenoportography in the Department of Radiology of the American University of Beirut. Of those, 17 were children. The purpose of this paper is to report the splenoportographic findings in this group of children with reference to the frequency and age distribution of intrahepatic versus extrahepatic portal obstruction. In our experience, intrahepatic obstruction was found more commonly in children having portal hypertension with or without gastrointestinal bleeding, than extrahepatic obstruction. This is contrary to reports from other parts of the world where extrahepatic obstruction is cited to be the commonest cause of portal hypertension. 1–6
- Published
- 1970
4. A Study of the Maximal Ventilatory Flow Rates in Health and Disease
- Author
-
Harold A. Lyons and Harold W. March
- Subjects
Spirometry ,medicine.medical_specialty ,medicine.diagnostic_test ,business.industry ,Liter ,General Medicine ,Normal values ,Pulmonary function testing ,Surgery ,Inspiratory flow ,Internal medicine ,medicine ,Cardiology ,Humans ,Age distribution ,business ,Normal range ,Maximal Expiratory Flow Rate - Abstract
1 The maximal expiratory and inspiratory flow rates, abbreviated as the MEFR and MIFR is a rapid, practical test and compared to the maximal breathing capacity less demanding on patients who more willingly offer full participation and the required maximal effort. It is only rarely that the test cannot be done because of the patient's clinical condition. 2 The initial 1000-1500 cc. of expired volume is often represented as a steep rectilinear line of maximal flow, and the MEFR 780 and MEFR 1280 are derived from this segment. 3 The MEFR decreases with age, and within the same age group women have lower flow values than men. The same is true of the MIFR which in young normals and elderly men is approximately 55 per cent of the MEFR, but older women have a proportionately higher MIFR/MEFR ratio due to a greater fall in MEFR. 4 The correlation of maximal expiratory flow rate and maximal breathing capacity in all groups is reported, but for reasons outlined in the paper it is not as good as in other studies whose primary purpose was to correlate the two tests. The MEFR should be performed as an independent pulmonary function test and not as an indirect estimate of MBC. 5 The normal range of the MEFR 280-1280 was 477 liter per minute ± 143 liters per minute for men between 20-35 years, and 304 liters per minute ± 123 liters per minute for men older than 45. For women 309 liters per minute ± 88 liters per minute and 180 liters per minute ± 59 liters per minute for the respective age distribution. For abnormals it has shown considerable reduction, but marked restrictive disease measurement at MEFR 280-780 will give normal values. The explanations for this are described.
- Published
- 1960
5. Simulation and projection of metropolitan housing conditions
- Author
-
E. Philip Howrey
- Subjects
Economics and Econometrics ,education.field_of_study ,Time path ,Strategy and Management ,Geography, Planning and Development ,Population ,Management Science and Operations Research ,Metropolitan area ,Physical capital ,Econometrics ,Environmental science ,Population growth ,Age distribution ,Operations management ,Statistics, Probability and Uncertainty ,education ,Stock (geology) - Abstract
The historical evolution of the population of a metropolitan area clearly has an important influence on the current condition of the physical capital of the area. In this paper, a vintagetype model of residential construction which is based on an acceleration principle in which population changes determine the amount of construction that is undertaken at any point in time is developed. The model is used to simulate the age distribution of New York City given the historical time path of population. The simulation results provide a test of the validity of the model as well as some insight into the magnitude of the problem associated with the deterioration of the housing stock. Several types of population growth trends are estimated and used in conjunction with the simulation model to generate projections of future housing conditions.
- Published
- 1969
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