A probability operator
- Authors: Sinclair, Allan M
- Date: 1965
- Subjects: Mathematics , Probabilities
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5423 , http://hdl.handle.net/10962/d1007702 , Mathematics , Probabilities
- Description: From Introduction: In probability theory it is often convenient to represent laws by characteristic functions, these being particularly suited to classical analysis. Trotter has suggest ted that probability laws can also be represented by probability operators. These operators are easily handled since they are continuous, and hence bounded, positive linear operators on a normed linear space. This representation arises because distribution functions and their complete convergence correspond to probability operators and their complete convergence. Hence the relations between distribution functions and probability operators will be discussed before the introduction of probability laws.
- Full Text:
- Date Issued: 1965
- Authors: Sinclair, Allan M
- Date: 1965
- Subjects: Mathematics , Probabilities
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5423 , http://hdl.handle.net/10962/d1007702 , Mathematics , Probabilities
- Description: From Introduction: In probability theory it is often convenient to represent laws by characteristic functions, these being particularly suited to classical analysis. Trotter has suggest ted that probability laws can also be represented by probability operators. These operators are easily handled since they are continuous, and hence bounded, positive linear operators on a normed linear space. This representation arises because distribution functions and their complete convergence correspond to probability operators and their complete convergence. Hence the relations between distribution functions and probability operators will be discussed before the introduction of probability laws.
- Full Text:
- Date Issued: 1965
The effect of different levels and intervals of application of ammonium sulphate on the growth, chemical composition and yield of cayenne and queen pineapple plants under field conditions
- Van Lelyveld, Louis Johannes
- Authors: Van Lelyveld, Louis Johannes
- Date: 1965
- Subjects: Pineapple -- Crop yields , Plants -- Nutrition -- South Africa , Growth (Plants) , Nitrogen fertilizers , Field Crops -- Nutrition , Ammonium sulfate
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4263 , http://hdl.handle.net/10962/d1013422
- Description: From the Introduction. The fertilisation of pineapples in the Eastern Cape Province is still a relatively new practice which started approximately twelve years ago. Even after this time many growers still insist that pineapples can be grown without fertilisation on virgin soils. As the available virgin soil decreased, however, so the interest in fertiliser application increased. Very little basic research on the fertiliser requirements of pineapples in the Eastern Cape was done to serve as a guide to growers. The available advisory literature by le Roux (1951), Malan (1954) and Lewcock (1956) were based on overseas experience. When pineapple research was started on a large scale, in 1955, it was realised that emphasis should be placed on the nutritional requirements on virgin as well as replanted soils. From initial experiments it was clear that the main response in plant growth and yield was obtained from nitrogenous fertilisers.
- Full Text:
- Date Issued: 1965
- Authors: Van Lelyveld, Louis Johannes
- Date: 1965
- Subjects: Pineapple -- Crop yields , Plants -- Nutrition -- South Africa , Growth (Plants) , Nitrogen fertilizers , Field Crops -- Nutrition , Ammonium sulfate
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4263 , http://hdl.handle.net/10962/d1013422
- Description: From the Introduction. The fertilisation of pineapples in the Eastern Cape Province is still a relatively new practice which started approximately twelve years ago. Even after this time many growers still insist that pineapples can be grown without fertilisation on virgin soils. As the available virgin soil decreased, however, so the interest in fertiliser application increased. Very little basic research on the fertiliser requirements of pineapples in the Eastern Cape was done to serve as a guide to growers. The available advisory literature by le Roux (1951), Malan (1954) and Lewcock (1956) were based on overseas experience. When pineapple research was started on a large scale, in 1955, it was realised that emphasis should be placed on the nutritional requirements on virgin as well as replanted soils. From initial experiments it was clear that the main response in plant growth and yield was obtained from nitrogenous fertilisers.
- Full Text:
- Date Issued: 1965
The effect of varying heavy metal balances in the nutrient medium, on the growth and development of Aspergillus Sp. and Penicillium Sp.
- Authors: Breen, C M
- Date: 1965
- Subjects: Heavy metals -- Absorption and adsorption , Aspergillus -- Growth , Penicillium -- Growth , Fungi -- Nutrition
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4268 , http://hdl.handle.net/10962/d1014597
- Description: The study was conducted to investigate the effects of: (i) varying the level of supply of the heavy metals iron, manganese, copper and zinc. (ii) varying the ratio between different pairs of metals in the medium. In particular the iron:manganese and zinc:copper ratios were studied. Initially the two fungi Aspergillus niger van Tieghem, (variety and strain) and Penicillium notatum Westling, were used. Penicillium notatum Westling was subsequently discarded, in favour of Penicillium glancum Link, because it did not sporulate freely in liquid culture. The fungi were grown in controlled nutrient solutions, and during the course of tho growth and development, the form and sporulation of the felts was noted. After a period of growth, the felts were removed, dried and weighed. The pH of the liquor was measured. the results were studied to determine the effect of varying levels of supply of the heavy metals, and of the varying heavy metal ratios in the culture solution. In the investigation of the effect of varying the level of supply of individual heavy metals, optimum concentrations were demonstrated for copper and manganese. Increaning the concentration of pairs of heavy metals cimultaneously was found to influence the appearance and degree of symptoms of toxicity. Cultures of Aspergillus and Penicillium were found to be able to tolerate concentrations of copper, in particular, considerably greater than the observed optima, when zinc was present in equal concentration. Citric acid, and subsequently ethylene- diaminetetra-acetic acid, were used as chelating agents, in order to prevent the precipitation of the metals in the culture solution during autoclaving. It was found that the use of chelating agents markedly reduced symptoms of toxicity. There was no conclusive evidence that the iron:manganese ratio in the culture medium was an important factor in the growth and development of cultures of Aspergillus and Penicillium. However there is considerable evidence that in cultures of Penicillium, the zinc:copper ratio in the medium is of some importance in the determination of the dry weight yield trends. This effect was not demonstrated in cultures of Aspergillus.
- Full Text:
- Date Issued: 1965
- Authors: Breen, C M
- Date: 1965
- Subjects: Heavy metals -- Absorption and adsorption , Aspergillus -- Growth , Penicillium -- Growth , Fungi -- Nutrition
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4268 , http://hdl.handle.net/10962/d1014597
- Description: The study was conducted to investigate the effects of: (i) varying the level of supply of the heavy metals iron, manganese, copper and zinc. (ii) varying the ratio between different pairs of metals in the medium. In particular the iron:manganese and zinc:copper ratios were studied. Initially the two fungi Aspergillus niger van Tieghem, (variety and strain) and Penicillium notatum Westling, were used. Penicillium notatum Westling was subsequently discarded, in favour of Penicillium glancum Link, because it did not sporulate freely in liquid culture. The fungi were grown in controlled nutrient solutions, and during the course of tho growth and development, the form and sporulation of the felts was noted. After a period of growth, the felts were removed, dried and weighed. The pH of the liquor was measured. the results were studied to determine the effect of varying levels of supply of the heavy metals, and of the varying heavy metal ratios in the culture solution. In the investigation of the effect of varying the level of supply of individual heavy metals, optimum concentrations were demonstrated for copper and manganese. Increaning the concentration of pairs of heavy metals cimultaneously was found to influence the appearance and degree of symptoms of toxicity. Cultures of Aspergillus and Penicillium were found to be able to tolerate concentrations of copper, in particular, considerably greater than the observed optima, when zinc was present in equal concentration. Citric acid, and subsequently ethylene- diaminetetra-acetic acid, were used as chelating agents, in order to prevent the precipitation of the metals in the culture solution during autoclaving. It was found that the use of chelating agents markedly reduced symptoms of toxicity. There was no conclusive evidence that the iron:manganese ratio in the culture medium was an important factor in the growth and development of cultures of Aspergillus and Penicillium. However there is considerable evidence that in cultures of Penicillium, the zinc:copper ratio in the medium is of some importance in the determination of the dry weight yield trends. This effect was not demonstrated in cultures of Aspergillus.
- Full Text:
- Date Issued: 1965
The geology of a portion of south-western Albany
- Meyer, W
- Authors: Meyer, W
- Date: 1965
- Subjects: Geology -- South Africa -- Eastern Cape , Silcrete , Geology, Stratigraphic
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5065 , http://hdl.handle.net/10962/d1013371
- Description: During 1963 an area was mapped around Sidbury, 23 miles south- west of Grahamstown. The object of the survey was to examine stratigraphic problems, which included the nature of a large occurrence of shale south of Alicedale in a region previously mapped as Witteberg, and the relationship between Silcrete and Calcrete. During the invest igation evidence of the existence of two, possibly three , major thrust-faults and of extensive overfolding to the south was discovered. There is reason to believe, that movement on the Zuurberg Fault was initiated in pre-Cretaceous times, and renewed in the early Cretaceous. The Silcrete is shown to be related to the pattern of presentday drainage. Stone implements found embedded in the Calcrete suggest that it is of Recent age.
- Full Text:
- Date Issued: 1965
- Authors: Meyer, W
- Date: 1965
- Subjects: Geology -- South Africa -- Eastern Cape , Silcrete , Geology, Stratigraphic
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5065 , http://hdl.handle.net/10962/d1013371
- Description: During 1963 an area was mapped around Sidbury, 23 miles south- west of Grahamstown. The object of the survey was to examine stratigraphic problems, which included the nature of a large occurrence of shale south of Alicedale in a region previously mapped as Witteberg, and the relationship between Silcrete and Calcrete. During the invest igation evidence of the existence of two, possibly three , major thrust-faults and of extensive overfolding to the south was discovered. There is reason to believe, that movement on the Zuurberg Fault was initiated in pre-Cretaceous times, and renewed in the early Cretaceous. The Silcrete is shown to be related to the pattern of presentday drainage. Stone implements found embedded in the Calcrete suggest that it is of Recent age.
- Full Text:
- Date Issued: 1965
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