Diversifying the Use of Molasses Towards Improving the Infrastructure and Economy of Kenya

   Sugar factories in the sugar belt of Kenya produce a lot of molasses. Sony Sugar factory alone for example, produces about 140,000tonnes of molasses annually. All the sugar factories in Kenya in 2002 milled a total of 5.3million tonnes of sugar cane with molasses production being about 30% of this tonnage. The molasses produced is sold to farmers as animal feed or to distillers and food processing factories. This paper is an analysis of the production of molasses and sugar in four factories in Kenya with an examination of these components and how they contribute to the economy and or infrastructure of the country. The study was conducted through laboratory analysis of cane molasses to establish the components of the molasses that have an impact on quality of road construction soil materials. Data on production was collected from four sugar factories through a questionnaire. The data on sugar production was found necessary because molasses production depend on sugar production. This implies that the higher the sugar production the higher the molasses production. The data also showed a growing trend in annual sugar productions. Consequently this would translate to an increase in molasses production annually. Keywords: Sugar molasses, Laboratory, Expansive soil, Stabilizatio

Balanced matrices

In this paper we introduce a particular class of matrices. We study the concept of a matrix to be balanced. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix statistics in this setting. The crux will be to understanding the determinants and the eigen-values of balanced matrices. It turns out that there does exist a direct communication among the leading entry, the trace, determinants and, hence, the eigen-values of these matrices of order $2\times 2$. These matrices have an interesting property that enables us to predict their quadratic forms, even without knowing their entries but given their spectrum.Comment: 14 page

Factors Associated with Delays Affecting Health Care Servicein Commencement of Tuberculosis Treatment in Kwale County, Kenya

Introduction: Tuberculosis (TB) is a communicable disease, a major cause of ill health and one of the top 10 causes of death worldwide. In 2018, an estimated 10 million people fell ill from TB with 1.5 million mortalities globally. Those were 5.7 million men, 3.2 million women and 1.1 million children. The prevalence of TB in Kenya was 558 per 100,000 adults an increase from the 2015 prevalence of 233/100,000. The highest disease burden was reported among people aged 25–34 years, males and those who lived in urban areas. Delay in treatment not only increased the risk of transmitting the infection but also led to an increase of multi drug resistant (MTR) TB. Nearly half of all estimated TB cases in Kwale County in Kenya had not been diagnosed, notified nor treated. Among children with TB, nearly two-thirds had not been diagnosed and approximately 80% of people with drug-resistant TB were neglected [6,8] Objectives : This study sought to establish health care service-related factors associated with delay in commencement of ant-TB drugs provision to TB patients in Kwale County, Kenya. Methodology:  This was an exploratory qualitative study. Data was collected from health care workers at the Ministry of Health, Kwale County. Key informants were purposively sampled based on staffing listing and departments. This yielded a total of 14 key informants to be interviewed. Data was collected until saturation, transcribed and analyzed using framework and thematic analysis methods. Results:  There existed barriers in provision of quality health care services in Kwale. Delays in treatment of TB not only increased the risk of transmitting the infection to healthy people but also led to an increase of multi drug resistance TB. Delay that was constituted by; elapsed time between onset of TB symptoms and first self-presentation to a formal health care facility, between first presentation to formal care and anti-TB treatment initiation. confirmed total delays as time elapsed between onset of TB symptoms, diagnosis and anti-TB treatment initiation. Conclusion: Based on the three themes that emerged from the data analysis, health care service-related factors associated with delay in commencement of TB treatment in Kwale County were lack of diagnostic machines, poor TB surveillance systems, and poor road transport network. Recommendation:  We recommend The County Government of Kwale to invest in GeneXpert MTB/RIF diagnostic machines, strengthen TB surveillance system by involving Community Health Workers (CHWs) and improve the road network in every Sub- County. That would help reduce the burden of TB in the region, Kenya and the rest of the world. Key Words: Tuberculosis, TB treatment delay, Health Service-Related Factors, Kwale County   &nbsp

Difference equations and pseudo-differential operators on ℤⁿ

In this paper we develop the calculus of pseudo-differential operators on the lattice Z(n), which we can call pseudo-difference operators. An interesting feature of this calculus is that the global frequency space (T-n) is compact so the symbol classes are defined in terms of the behaviour with respect to the lattice variable. We establish formulae for composition, adjoint, transpose, and for parametrix for the elliptic operators. We also give conditions for the l(2), weighted l(2) and l(p) boundedness of operators and for their compactness on l(p). We describe a link to the toroidal quantization on the torus T-n, and apply it to give conditions for the membership in Schatten classes on l(2)(Z(n)). Furthermore, we discuss a version of Fourier integral operators on the lattice and give conditions for their l(2)-boundedness. The results are applied to give estimates for solutions to difference equations on the lattice Z(n). Moreover, we establish Carding and sharp Girding inequalities, with an application to the unique solvability of parabolic equations on the lattice Z(n)

Evaluation of the medicinal potentials of Bulbine Abyssinica A. rich in the management of diabetes mellitus in the Eastern Cape, South Africa

Diabetes mellitus is a chronic physiological carbohydrate metabolic disorder with significant impact on the economy, quality of life and life expectancy in South Africa. Herbal medicine has become the alternative therapy in the management of this disease. However, their safety and effectiveness have not been investigated. To address this, one of the plants used in Eastern Cape Province, South Africa, Bulbine abyssinica A. Rich (Asphodelaceae), was evaluated. Bulbine abyssinica is one of the species used in the management of diabetes mellitus. This plant was mentioned during an ethnobotanical survey conducted in Nkonkobe municipality of the Eastern Cape Province. Though a decoction prepared from the whole plant is used in the treatment of diabetes mellitus, the mechanism of action and its safety has not been elucidated. Thus, this research work was designed to contribute to the understanding of the possible mechanism of action of B. abyssinica as an antidiabetic medicinal plant and its toxic potentials to the users. The aqueous extract exhibited remarkable inhibitory activity onα-amylase (estimated inhibitory concentration (IC)50 value of 3.28 μg/ml), while the acetone extract exhibited weak inhibitory activity. The acetone extract exhibited notable α-glucosidase inhibitory activity (IC50 value of 4.27 μg/ml) while aqueous extract had significantly weak activity. The Lineweaver-Burk double reciprocal plots revealed that the aqueous extract exerts noncompetitive inhibition on the α-amylase activity while the acetone extract exerts a near competitive inhibitory pattern on the α-glucosidase activity. The extracts from the plant possessed high free radical scavenging activities, with acetone extract exhibiting the highest activities in all assay models used except with ferric reducing power and nitric oxide (NO) scavenging ability. The aqueous extract exhibited the highest ferric reducing power and nitric oxide radical mopping strength while the essential oil exhibited the highest scavenging activities with 1,1-diphenyl-2-picrylhydrazyl (DPPH) and relatively high ferric reducing power and nitric oxide scavenging ability. The acetone extract and the essential oil of this species exhibited higher albumin denaturation inhibition than the aqueous extract while the latter showed the greatest membrane lysis protection. The essential oil, acetone and aqueous extracts from this plant significantly inhibited the growth of Shigelle flexneri, Pseudomonas aeruginosa, Staphylococcus aureus and Enterococcus faecalis. Klebsiella pneumonia, Proteus vulgaris and Streptococcus pyogens growth were inhibited by acetone and aqueous extracts. The essential oil also showed inhibitory activity against Proteus vulgaris. However, the extracts were active against the growth of only three fungi species. The essential oil showed significant inhibitory activity against Trichophyton rubrum. The aqueous extract inhibited the growth of Microsporum gypseum while the acetone extract was active against Microsporum canis, and Microsporum gypseum. The carbohydrate, crude fibre, moisture, ash, crude protein and crude fat of approximately 74.8 percent, 8.9 percent, 8.8 percent, 8 percent, 7.7 percent and 0.6 percent, respectively, were detected in this plant. The species is characterized by moderate levels of oxalates, phytic acids, Vitamin A, Vitamin C and Vitamin E. Potassium and calcium were present in highest levels, while magnesium, iron, sodium, aluminium and phosphorus were moderately present. Manganese, zinc and copper where in low amounts. These vitamins and mineral elements were within their recommended daily allowance (RDA) in humans. The investigation also revealed appreciable amounts of total phenols, flavonoids, flavanols, proanthocyanidins and alkaloids in both acetone and aqueous extracts while saponins and tannins were in trace amounts. The essential oil was characterized by large quantities of terpenes (91.9 percent) and small fraction of esters (8.01 percent)

MINERAL COMPOSITION AND NUTRITIVE ANALYSIS OF BULBINE ABYSSINICA A. RICH. USED IN THE TREATMENT OF INFECTIONS AND COMPLICATIONS ASSOCIATED WITH DIABETES MELLITUS IN THE EASTERN CAPE PROVINCE, SOUTH AFRICA

Background: B. abyssinica is a succulent member of the genus Bulbine (Asphodelaceae). It occurs from the Eastern Cape, through Swaziland and further north to Ethiopia. The species is used in traditional medicine to treat rheumatism, dysentery, bilharzia, cracked lips and diabetes. The tea leaf is used to treat cough, vaginal and bladder problems. Whereas B. abyssinica has ethno medicinal value, not much data concerning its phytonutrient, macro and micro element composition can be found in literature. Materials and Methods: Therefore, the present study was undertaken to determine the nutritional quantitative composition of the plant using standard procedures. Results: The proximate analysis revealed the carbohydrate, crude fibre, moisture, ash, crude protein and crude fat contents as 74.8%, 8.9%, 8.8%, 8%, 7.7% and 0.6%, respectively. The species showed high levels of oxalates and phytic acids, moderate levels of alkaloids, flavonoids, saponins and phenols, while tannins were in low levels. Vitamin A, C and E contents were 12, 12.3 and 22.1 mg/100g, respectively. Amongst the mineral elements investigated, potassium and calcium were in high levels. Magnesium, iron, sodium, aluminium and phosphorus were moderately present, while manganese, zinc and copper where in low amounts. These vitamins and mineral elements were within their recommended daily allowance in humans. Conclusion: The amount of these phytochemicals suggests the plant can serve as nutritional supplements which are vital in maintaining good health status. These findings also suggest the potential role of B. abyssinica in the treatment of infections and some chronic diseases, especially diabetes mellitus

Difference equations and pseudo-differential operators on Zn\mathbb{Z}^n

29 pages29 pagesIn this paper we develop the calculus of pseudo-differential operators on the lattice $\mathbb{Z}^n$, which we can call pseudo-difference operators. An interesting feature of this calculus is that the phase space is compact so the symbol classes are defined in terms of the behaviour with respect to the lattice variable. We establish formulae for composition, adjoint, transpose, and for parametrix for the elliptic operators. We also give conditions for the $\ell^2$, weighted $\ell^2$, and $\ell^p$ boundedness of operators and for their compactness on $\ell^p$. We describe a link to the toroidal quantization on the torus $\mathbb{T}^n$, and apply it to give conditions for the membership in Schatten classes on $\ell^2(\mathbb{Z}^n)$. Furthermore, we discuss a version of Fourier integral operators on the lattice and give conditions for their $\ell^2$-boundedness. The results are applied to give estimates for solutions to difference equations on the lattice $\mathbb{Z}^n$