An investor is often faced with the investment situation in which he/she has to decide how to allocate his/her limited funds optimally among different assets to maximize his/her expected utility over the holding period. To this end, this study sets up a dynamic model driven by three assets to characterize the stochastic nature of the securities market and uses stochastic control to derive an explicit formula for the optimal fraction invested in each of the three assets for an investor with a power utility and a holding period of 10 years. Using estimated parameter values as inputs and implicit finite difference method, we determine numerically the optimal percentages invested in the three assets at each time over the holding period for both less risk-averse and more risk-averse investors.

Abstract:
The identification of putative liver stem cells has brought closer the previously separate fields of liver development, regeneration, and carcinogenesis. Significant overlaps in the regulation of these processes are now being described. For example, studies in embryonic liver development have already provided the basis for directed differentiation of human embryonic stem cells and induced pluripotent stem cells into hepatocyte-like cells. As a result, the understanding of the cell biology of proliferation and differentiation in the liver has been improved. This knowledge can be used to improve the function of hepatocyte-like cells for drug testing, bioartificial livers, and transplantation. In parallel, the mechanisms regulating cancer cell biology are now clearer, providing fertile soil for novel therapeutic approaches. Recognition of the relationships between development, regeneration, and carcinogenesis, and the increasing evidence for the role of stem cells in all of these areas, has sparked fresh enthusiasm in understanding the underlying molecular mechanisms and has led to new targeted therapies for liver cirrhosis and primary liver cancers.

Abstract:
Farm forestry has proved to be an important enterprise for small- and large-scale farmers worldwide. It has the potential of improving forest/tree cover across the globe. In Kenya, the forest cover is less than 2%. The country envisions achieving 10% forest cover over the next decade through promotion of farm forestry. However, the decision to plant trees on farmers’ land could be difficult. The study aimed to analyze the determinants of tree retention on farm for improvement of forest cover. Stratified and simple random sampling techniques were used in selecting 209 farmers. The results showed that sites, land size, age, education level, monthly income, tree management, extension services, availability of markets, harvesting regulation, and aesthetic and environmental motivation were significant determinants of tree retention. In particular, the chances of farmers who had gained technical skills in tree management were about 2.2 times higher to retain trees as compared to those who had not acquired such skills. Similarly, chances of farmers motivated to plant trees for environmental conservation were about 3.5 times higher to retain trees as compared to the group of farmers planting trees as a source of livelihood. These determinants would be instrumental in strengthening the current policies and reforms in forestry and agricultural sectors to enable Kenya to achieve 10% of forest cover. 1. Introduction Farm forestry in the context of evergreen agriculture is emerging as an affordable and accessible science-based solution to caring better for the land and increasing small-scale food production [1]. It combines trees and food crops with principles of conservation farming. It has proved to be an important enterprise for small and large-scale farmers in low, medium and high potential areas worldwide [2]. In particular, it offers multiple benefits to farmers. This includes sources of green fertilizer, livestock fodder, timber, and fuel wood. Farm forestry has also other environmental benefits such as greater resilience to climate change and carbon storage, shelter, erosion control, watershed protection, and increased biodiversity [1]. The success of farm forestry may be assessed in terms of effects of various determinants such as advanced use of farm labour, positive environmental changes, increased financial returns among others [3]. When attempting to judge whether farm forestry is successful, it is important to note that the people involved may change their objectives over the years. For instance, markets may alter and force changes to the products

Abstract:
In this paper, we have proposed three classes of mixture ratio estimators for estimating population mean by using information on auxiliary variables and attributes simultaneously in two-phase sampling under full, partial and no information cases and analyzed the properties of the estimators. A simulated study was carried out to compare the performance of the proposed estimators with the existing estimators of finite population mean. It has been found that the mixture ratio estimator in full information case using multiple auxiliary variables and attributes is more efficient than mean per unit, ratio estimator using one auxiliary variable and one attribute, ratio estimator using multiple auxiliary variable and multiple auxiliary attributes and mixture ratio estimators in both partial and no information case in two-phase sampling. A mixture ratio estimator in partial information case is more efficient than mixture ratio estimators in no information case.

Abstract:
Quadratic theory of gravity is a complicated constraint system. We investigate some consequences of treating quadratic terms perturbatively (higher derivative version of backreaction effects). This approach is shown to overcome some well known problems associated with higher derivative theories, i.e., the physical gravitational degree of freedom remains unchanged from those of Einstein gravity. Using such an interpretation of $R + \beta R^2$ gravity, we investigate a classical and Wheeler DeWitt evolution of $R + \beta R^2$ gravity for a particular sign of $\beta$, corresponding to non- tachyon case. Matter is described by a phenomenological $\rho \propto a(t)^{-n}$. It is concluded that both the Friedmann potential $U(a)$ ($ {\dot a}^2 + 2U(a) = 0 $) and the Wheeler DeWitt potential $W(a)$ ($\left[-{\partial^2\over \partial a^2} + 2W(a)\right]\psi (a) =0 $) develop repulsive barriers near $a\approx 0$ for $n>4$ (i.e., $ p > {1\over 3}\rho $). The interpretations is clear. Repulsive barrier in $U(a)$ implies that a contracting FRW universe ($k>0, k=0, k<0$) will bounce to an expansion phase without a total gravitational collapse. Repulsive barrier in $W(a)$ means that $a \approx 0$ is a classically forbidden region. Therefore, probability of finding a universe with the big bang singularity ($a=0$ ) is exponentially suppressed.

Abstract:
In this paper, we study Raychaudhuri's equation in the background of $R + \beta R^2$ gravity with a phenomenological matter ($\rho \propto a(t)^{-n}$). We conclude that even though the Strong Energy Condition (S.E.C.) for Einstein's gravity, which guarantees singularity, is $n\geq 2$ for $\rho \propto a(t)^{-n}$, a perturbative analysis of Raychaudhuri's equation in the background of $R + \beta R^2$ gravity reveals that the big bang singularity may not be guaranteed for $n > 4$. We derive the following Strong Energy Conditions for $R + \beta R^2$ ($\beta \not= 0$): 1) For $k<0$ FRW metric, S.E.C. is ($0\leq n\leq 4$) i.e., $-\rho_n \leq p_n \leq {1\over 3}\rho_n$. 2) For $k=0$ FRW metric, S.E.C. is ( $1\leq n\leq 4$) i.e., $-{2\over 3}\rho_n \leq p_n \leq {1\over 3}\rho_n$. 3) For $k>0$ FRW metric, S.E.C. is ($2\leq n\leq 4$) i.e., $-{1\over 3}\rho_n \leq p_n \leq {1\over 3}\rho_n$.

Abstract:
Low soil fertility is a major constraint to maize production in the small holder farms of Meru South District. This is mainly attributed to the mining of nutrients due to cropping without external addition of adequate nutrients. Mineral fertilizers are expensive hence un affordable by most small holder farmers. The use of organic matter to increase and maintain soil fertility is being considered as a solution to help the low-income small holder farmers. A study was conducted in Mucwa location, Meru South District to determine the levels of complementarity between organic and mineral N amendments on maize yields and their influence on soil chemical properties. The experiment was set in a complete randomized block design (CRBD) with three replicates. The treatments were compared with the response obtained from control. The general soil fertility parameters changed slightly with Calcium, Magnesium and Potassium increasing in all treatments. The organic Carbon and total Nitrogen was higher in treatments that received sole organic N sources than in sole mineral N and a combination of organic and mineral N sources. The highest maize grain yield of 4.8 t·ha^{-1} and 4.2 t·ha^{-1} were realized from sole application of calliandra during the 2005 Short rains and 2006 Long rains cropping seasons. Generally the maize grain yields were lower in treatments with mineral N alone compared to the treatments with organics. Treatments with sole calliandra and sole tithonia had the highest benefit cost ratio (BCR), followed closely by manure treatment. More so, integration of organic and mineral N sources resulted to higher net benefit and BCR than the application of the recommended rate of mineral fertilizers. Results obtained indicated that the use of either organic or combined organic/mineral N soil amendment appear to be superior to using mineral amendment sources alone.

Abstract:
This paper investigates the incremental effects of corporate ownership structure on earnings conservatism, examining data of Chinese listed companies. We employ the concept of conditional conservatism to define earnings conservatism and adopt empirical models developed by Basu (1997) and Ball and Shivakumar (2005) to measure the degree of earnings conservatism. Our empirical results show that the earnings of companies with higher non-tradable shares have lower earnings conservatism. Consistent with prior studies, this point demonstrates that the companies with state and concentrated ownership structures are more likely to depend on private communication to reduce information asymmetry and to resolve agency problems internally, thereby creating a low demand for earnings conservatism. The results of this study contribute to our understanding of how companies’ ownership structures affect the properties of earnings in emerging markets and post-Communist markets. Keywords: earnings conservatism, non-tradable shares, ownership structure, post-Communist studies, split-share structure, state ownership JEL Classifications: M40, M41, M49

Abstract:
Plant regeneration for efficient vegetative propagation in white dasheen has been developed. Meristem cultured on Murashige and Skoog medium supplemented with 6-Benzyladenine (BA) and Indole-3-acetic acid (IAA) gave the best explants establishment and development. This in vitro system provides for a uniform production system which is easily managed and yields high quality cornels for commercial production.