The elasto-damage theory of the components assembling model

The potential energy in materials is well approximated by pair functional which is composed of pair potentials and embedding energy. During calculating material potential energy, the orientational component and the volumetric component are derived respectively from pair potentials and embedding energy. The sum of energy of all these two kinds of components is the material potential. No matter how microstructures change, damage or fracture, at the most level, they are all the changing and breaking atomic bonds. As an abstract of atomic bonds, these components change their stiffness during damaging. Material constitutive equations have been formulated by means of assembling all components' response functions. This material model is called the component assembling model. Theoretical analysis and numerical computing indicate that the proposed model has the capacity of reproducing some results satisfactorily, with the advantages of great conceptual simplicity, physical explicitness, and intrinsic induced anisotropy, etc.

Utilization of agro-industrial wastes as fish feedstuffs in Nigeria

Fish feeding accounts for a substantial amount in the variable expenditure of a fish farming enterprises. There is a need to examine closely the potentials and advantages of locally available agro-industrial by-products, as possible substitutes for the conventional feedstuffs which are dwindling in supply, and escalating in their cost. A wide range of by products from plant, animal and industrial processes have been studied and posses nutrient composition which can be exploited as dietary ingredients for warm water species as the Tilapia and Clarias sp. Such useful by-products include poultry feathers, rice bran, soybean hulls and cocoa husks which are discarded as wastes. However, some processing treatments might be required to alleviate the toxic effects of possible anti-nutritional factors in the by-products, for the achievement of optimum benefit

Utilization of waste waters in fish production: preliminary results from fish culture studies in floating cages in a sewage pond, New Bussa, Nigeria

The utilization of waste waters in aquaculture were briefly reviewed. At the National Institute for Freshwater Fisheries Research (NIFFR), stocking density (20 to 160 fish/m super(3)) experiments using Sarotherodon galilaeus (without supplementary feeding) in floating cages were carried out in a sewage pond (0.4ha surface area). Cage culture of S. galilaeus was observed to have potentials in waste waters aquaculture. Recommendations were made on the execution of an intergrated waste water management and utilization.

Modern aquaculture practices for increased fish production in Nigeria

Various modern aquaculture practices applied in fish production especially in Asia are reviewed. The vast Nigerian aquatic medium of numerous water bodies like rivers, streams, lakes reservoirs, flood plains, irrigation canals, coastal swamps offer great potentials for aquaculture production, if optimally utilized. Constraints to modernization of aquaculture in Nigeria among other factors are: 1) a serious shortage of trained manpower; 2) lack of knowledge on profitability of aquaculture as an industry; 3) limited availability of fund (or capital); 4) non-recognition of indigenous trained aquaculture personnel; 5) inadequate data base on the biology and ecological requirements of endemic fish species with aquaculture potentials; 6) insufficient data on production and management techniques; and 7) lack of rational aquaculture development planning. Recommendations are made towards combating these constraints

Investment prospects in marine capture fisheries

An examination is made of investment prospects in the Nigerian marine fisheries, considering the following sectors: inshore demersal fishery; inshore pelagic fishery; and the offshore pelagic fishery. The marine fisheries resources of countries with which Nigeria has bilateral fishing rights agreements are discussed, considering Equatorial Guinea, Guinea Conakry, Guinea Bissau, Senegal and Mauritania. Fishing gear and methods for the marine fishery sectors are outlined. Market potentials for fish products and profitability are also examined

Investment prospects in inshore trawling in Nigeria

Commercial trawling for finfish in Nigeria's inshore water is a recent activity. Intensive industrial trawling started when the Federal Government distributed trawlers to viable fishermen cooperatives during the Third National Development Plan Period (1975-80). Hitherto, industrial fisheries development in the country focused on the assessment of the potential fish stock on Nigeria's continental shelf and measures to increase artisanal production. As a result of increasing demand for fish and shortage of foreign exchange to import fish, measures to increase fish supply leaned towards industrial exploitation of the fisheries potentials of Nigeria's continental shelf. Based on this background, this paper examines the investment prospects of trawling for fish in inshore waters. The fisheries potentials of the inshore zone of Nigeria are identified. Catch efficiency and profitability of inshore trawling are estimated. Measures that can safeguard the longterm interest of the trawling industry are recommended

An evaluation of the artisanal fisheries resources of the Cross River State of Nigeria

The Cross River State (Nigeria) marine and freshwater artisanal capture fisheries are divided into 4 categories according to the type of resources being exploited. Schaefer's production model is applied to each of the fisheries to estimate the maximum sustainable yields (Ymax). The total potential yield for all the fisheries in natural waters is 178,650 tonnes/year. This potential is unlikely to be achieved as more fishermen are abandoning the occupation due to the scarcity of boats, outboard engines and nets. Even if the full potentials were realized the production would still be short of what the State should produce by about 30.5%. Investment opportunities which, if effected can help to narrow the gap between the available and the desired level of production are enumerated

Investment prospects of fish farming in the Jos-Plateau, Nigeria

The investment prospects of fish farming in the Jos-Plateau, Nigeria, strategically located in about the centre of the country are discussed with special reference to its numerous abandoned mine lakes and the tripartite role of government, universities and individuals. In the Jos-Plateau, about 17.0 km super(2) is covered by these disused mine lakes, making up about 20-30% of the area covered. In such enterprise, problems commonly encountered, like population growth and government planning policies, fish demand and supply, manpower, feed and seed availability, preservation, processing and marketing are discussed. Inspite of these, prospects still abound with regards to land-use of these numerous disused mine lakes and feed availability based on the principles of using both industrial and farm by-products for fish culture, processing and marketing. These potentials, if properly harnessed, will help to supplement the protein insufficiency in the diet of the populace. In this regard, proposals on the economics of production and sales, strategies for achieving these development goals, cost-benefit analysis and their implications in further development of fish culture are discussed

Fish farming in Anambra State: economic criteria

The paper is based on the premise that an understanding of the role and potentials of fish farming entrepreneurs in terms of their activities and expectations would enhance fish production and productivity. To this end, the present paper investigates the activities of 24 fish farmers in Anambra State, Nigeria. Based on the fish farmers' experience, the paper presents fish farming investments, budgets and recommendations that could ensure fish farming development as a profitable business venture and at the same time ensure greater fish production in the country

Harnessing the fishery potential of man-made lakes for the partial commercialisation of Niger River Basin Development Authority, Minna, Nigeria

Niger River Basin Development Authority Minna (NRBDA) is one of the eleven river basins in Nigeria now undergoing transition towards partial commercialisation. In the light of this the need to be self-sustaining through exploration and exploitation of every possible areas along their operation to yield revenue cannot be over-emphasized. Therefore it is most pertinent to consider fisheries activities along their water bodies as one of the major sources of revenue by organising the local fishermen operating along the water into cooperative bodies and made to pay for fishing rights. Strategies to accomplish this objective is highlighted. The need to embark on aquaculture projects by construction of fish ponds at suitable sites along the reservoirs and developing the recreational potentials of their water bodies as sources of revenue is also stressed

Practical suggestions for the commercialisation of fishery production in Ondo State

The paper examines the fisheries resources and activities in Ondo State, Nigeria. As a result of the geographical advantage via location along the Atlantic coast the potentials and constraints of coastal artisanal fisheries in Ondo State are assessed. Practical suggestions and approaches for a successful commercialisation of fishery production are given. These include: (a) Identification of useful and reliable fisheries institutions, (b) Inauguration establishment and coordination of a fishery development agency, (c) establishment of aquaculture technology centres (ATC), (d) provision of fishery development fund, (e) Standardisation of fishery consultancy units, etc

Integrating cultural, economic and environmental requirements for fish production in Borno State

The study examines the integration of cultural, economic and environmental requirements for fish production in Borno State, Nigeria. A reconnaissance survey was conducted transferring some selected Local Government Areas. 60 questionnaires were administered in the six Local Governments representing Southern Borno State with Biu and Shani, central Borno with Konduga & Jere and Northern Borno with Gubia and Kukawa respectively. There is no cultural constraint to fish production but about 63% prefers to invest in other farming activities than in fish farming. 33% are not aware that fish can be cultured apart from getting it from the wild. 35% have the impression that fish farming ventures can be handled by government only. The economic earnings for fish production are high especially in some parts of Northern Borno, but the Local market potentials throughout the state are great. Nigeria has suitable soil for ponds apart from few locations at the central and Northern Borno that are made by sandy soil. Numerous perennial and seasonal rivers, streams, lakes, pools and flood plains adequate for fish culture especially in Southern Borno exist. The mean annual rainfall can result in some water storage in ponds. In areas where the annual precipitation is less than 550mm, exist few flow boreholes with potentials for fish production. The temperature regime may support growth and survival of fish even during the hottest months of the year (March, April and May). With the understanding and manipulation of these requirements, fish production in Nigeria can be greatly enhanced

Re-emphasizing the importance of Lake Chad fisheries in Nigerian economy: Borno State experience

Nigeria with an estimated population of about 120 million people requires about 2.3 million metric tonnes of fish and fisheries product for good health at the recommended 19 kg/caput/year by FAO. Lake Chad fisheries resource of Borno State is a blessing in disguise to the Nigerian economy. It has potential to produce over 300,000 metric tonnes of fish protein annually, representing about 12.2% of the total fish demand of Nigerians. In spite of this laudable potential Lake Chad fisheries resources of Borno State declined in the past two decades due, largely, to lack of/or inadequate attention by the government, private and commercial organization, lack of social economics and infra-structural facilities for rational exploitations and management of its resources. This paper re-emphasizes the importance of Lake Chad Fisheries of Borno State in the Nigerian economy. The fisheries resources, the environment, the exploitation, the potential marketing, the role of law enforcement and foreign agencies, the constraints and potentials are discussed. Nigeria can derive a substantial proportion of its fish demand from Lake Chad fisheries of Borno State alone just with the adoption of some proffered strategies including combined efforts of the private and public sectors in the rational management of the fisheries resource of Lake Chad

Invariants, Lie-Bäcklund operators and Bäcklund transformations

This thesis is mainly concerned with the application of groups of transformations to differential equations and in particular with the connection between the group structure of a given equation and the existence of exact solutions and conservation laws. In this respect the Lie-Bäcklund groups of tangent transformations, particular cases of which are the Lie tangent and the Lie point groups, are extensively used.

In Chapter I we first review the classical results of Lie, Bäcklund and Bianchi as well as the more recent ones due mainly to Ovsjannikov. We then concentrate on the Lie-Bäcklund groups (or more precisely on the corresponding Lie-Bäcklund operators), as introduced by Ibragimov and Anderson, and prove some lemmas about them which are useful for the following chapters. Finally we introduce the concept of a conditionally admissible operator (as opposed to an admissible one) and show how this can be used to generate exact solutions.

In Chapter II we establish the group nature of all separable solutions and conserved quantities in classical mechanics by analyzing the group structure of the Hamilton-Jacobi equation. It is shown that consideration of only Lie point groups is insufficient. For this purpose a special type of Lie-Bäcklund groups, those equivalent to Lie tangent groups, is used. It is also shown how these generalized groups induce Lie point groups on Hamilton's equations. The generalization of the above results to any first order equation, where the dependent variable does not appear explicitly, is obvious. In the second part of this chapter we investigate admissible operators (or equivalently constants of motion) of the Hamilton-Jacobi equation with polynornial dependence on the momenta. The form of the most general constant of motion linear, quadratic and cubic in the momenta is explicitly found. Emphasis is given to the quadratic case, where the particular case of a fixed (say zero) energy state is also considered; it is shown that in the latter case additional symmetries may appear. Finally, some potentials of physical interest admitting higher symmetries are considered. These include potentials due to two centers and limiting cases thereof. The most general two-center potential admitting a quadratic constant of motion is obtained, as well as the corresponding invariant. Also some new cubic invariants are found.

In Chapter III we first establish the group nature of all separable solutions of any linear, homogeneous equation. We then concentrate on the Schrodinger equation and look for an algorithm which generates a quantum invariant from a classical one. The problem of an isomorphism between functions in classical observables and quantum observables is studied concretely and constructively. For functions at most quadratic in the momenta an isomorphism is possible which agrees with Weyl' s transform and which takes invariants into invariants. It is not possible to extend the isomorphism indefinitely. The requirement that an invariant goes into an invariant may necessitate variants of Weyl' s transform. This is illustrated for the case of cubic invariants. Finally, the case of a specific value of energy is considered; in this case Weyl's transform does not yield an isomorphism even for the quadratic case. However, for this case a correspondence mapping a classical invariant to a quantum orie is explicitly found.

Chapters IV and V are concerned with the general group structure of evolution equations. In Chapter IV we establish a one to one correspondence between admissible Lie-Bäcklund operators of evolution equations (derivable from a variational principle) and conservation laws of these equations. This correspondence takes the form of a simple algorithm.

In Chapter V we first establish the group nature of all Bäcklund transformations (BT) by proving that any solution generated by a BT is invariant under the action of some conditionally admissible operator. We then use an algorithm based on invariance criteria to rederive many known BT and to derive some new ones. Finally, we propose a generalization of BT which, among other advantages, clarifies the connection between the wave-train solution and a BT in the sense that, a BT may be thought of as a variation of parameters of some. special case of the wave-train solution (usually the solitary wave one). Some open problems are indicated.

Most of the material of Chapters II and III is contained in [I], [II], [III] and [IV] and the first part of Chapter V in [V].

Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

Various families of exact solutions to the Einstein and Einstein-Maxwell field equations of General Relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations.

The physical situations in which such equations arise include: a) the external gravitational field of an axisymmetric, uncharged steadily rotating body, b) cylindrical gravitational waves with two degrees of freedom, c) colliding plane gravitational waves, d) the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and e) colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein-Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa.

The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables.