Papers by Dr Haradhan K U M A R Mohajan
Over alcoholic consumption for a long-time is the most common cause of alcoholic hepatitis (AH) t... more Over alcoholic consumption for a long-time is the most common cause of alcoholic hepatitis (AH) that has significant short-term and long-term morbidity and mortality due to chronic liver disease. Alcoholic hepatitis is the most elaborate indicator of alcoholic liver disease (ALD). It is a devastating acute condition of the disease that needs early detection, diagnosis, and proper treatment. It is characterized by inflammation, fibrosis, and ultimately cirrhosis for the continual excessive drinking. It is an acute hepatic inflammation associated with an injury of the liver with the clinical syndrome of acute jaundice and coagulopathy. If it is not treated appropriately, may transform to life-threatening acute liver failure, such as hepatocellular carcinoma (HCC) and liver cirrhosis. Complete alcohol abstinence is the cornerstone therapy for AH to decrease short-term mortality and most of the patients recover for at least six months after abstinence. This review paper tries to discuss the diagnosis and treatment procedures of the AH in brief for the benefit of the patients.
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The aim of this study is to discuss the increase in risk for obesity-related disorders. It is bel... more The aim of this study is to discuss the increase in risk for obesity-related disorders. It is believed that such complications arise due to store of visceral fat. The visceral fat is considered as an independent predictor of all-cause of mortality among type 2 diabetes (T2D) patients. Higher visceral fat is associated with an adverse lipid and glucose profile. Accumulation of visceral fat is located inside the abdominal cavity and surrounds internal organs, such as in the liver, stomach, kidneys, pancreas, intestines, and heart. Store of visceral adipose tissue (VAT) is characterized as pro-inflammatory, metabolically active, and susceptible to lipolysis. This study tries to present briefly the harmful activities of visceral fat in human body.
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Type 2 diabetes (T2D) is a progressive disease, and most patients need to treat with monotherapy ... more Type 2 diabetes (T2D) is a progressive disease, and most patients need to treat with monotherapy and combinations of oral hypoglycaemic drugs. At present about 500 million people worldwide are suffering from T2D. Sodium-glucose cotransporter-2 (SGLT-2) inhibitors are a novel antidiabetic drug class that mediates epithelial glucose transport at the renal proximal tubules, inhibiting glucose absorption that result in glycosuria, modest weight loss and improve glycaemic control with a low risk of hypoglycaemia. These are used by T2D patients together with diet and exercise, either alone or in combination with other diabetes medicines. The main side-effects of SGLT-2 inhibitors are urinary tract and genital infections, as well as euglycemic diabetic ketoacidosis. Some other probable adverse effects are lower limb amputations, risk of bone fractures, Fournier gangrene, male bladder cancer, female breast cancer, orthostatic hypotension, and acute kidney injury. This mini review explains aspects of SGLT-2 inhibitors with treatment procedures and side-effects.
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In this paper economic predictions among commodity prices and Lagrange multipliers are deliberate... more In this paper economic predictions among commodity prices and Lagrange multipliers are deliberated, where utility maximization policy is examined with sufficient mathematical investigation. In mathematical economics, utility reflects the propensity of an activity, which of course increases or decreases complete happiness of the individual/society. The system of Lagrange multiplier is a strongly valuable method in advanced calculus that is applied in this paper with a pair of constraints. This paper also tries to show the economic results of optimization precisely but elaborately.
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Type 2 diabetes (T2D) is a metabolic disorder characterized by hyperglycaemia, insulin resistance... more Type 2 diabetes (T2D) is a metabolic disorder characterized by hyperglycaemia, insulin resistance at peripheral target tissues, and pancreatic β-cell dysfunction. It is a global health problem with epidemic proportions and a huge economic burden. The dipeptidyl peptidase (DPP-4) inhibitors are a new class of antihyperglycaemic agents that are developed for the treatment of T2D. Many clinical studies have suggested that DPP-4 inhibitors (gliptins) are safe from cardiovascular perspective, and may also possess cardioprotective effect. These are regulators of inflammation and metabolism, and also prevent the proteolytic breakdown. These reduce postprandial glucose with minimal risk of hypoglycaemia and gastrointestinal adverse effects. These increase biologically intact forms of glucose-dependent insulinotropic polypeptide (GIP) and glucagon-like peptide-1 (GLP-1), both of which enhance glucose-induced insulin secretion from pancreatic β-cells. These medications become popular and are widely used worldwide for their efficacy, safety, weight neutrality, and tolerability. This article reviews basic studies of the DPP-4 inhibitors in briefly for the management of T2D.
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The peroxisome proliferator-activated receptors (PPARs) are three members of the nuclear receptor... more The peroxisome proliferator-activated receptors (PPARs) are three members of the nuclear receptor prearranged by separate genes as PPARα, PPARβ/δ, and PPARγ that differ in tissue distribution and specific function. PPARγ is a nuclear receptor highly expressed in the colon, and plays a key role in bacterial induced inflammation. It is a mediator of adipocyte differentiation that regulates transcription of several genes involved in fatty acid and energy metabolism. It is known as the glitazone reverse insulin resistance receptor or nuclear receptor subfamily 1, group C, member 3 (NR1C3). It is activated by anti-diabetic Thiazolidinedione (TZD) drugs and is used as insulin sensitizers and also a favorite option for the treatment of T2D patients. It is used as monotherapy or in combination with other oral hypoglycaemic agents, which are generally safe and well-tolerated. The aim of this mini review is to discuss the potential roles of PPARγ for the prevention and treatment of T2D.
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Diabetes mellitus (DM) is a group of metabolic disorders in which there are high levels of glucos... more Diabetes mellitus (DM) is a group of metabolic disorders in which there are high levels of glucose in the blood. The effects of DM are long-term damage, dysfunction and failure of various organs. Metformin is a common first-line treatment for type 2 diabetes (T2D) patients. It is one of the oldest treatments for diabetes, dating back to the 1960s. Some scholars in their studies have found that Metformin used by mothers is safe for their breastfeed infants. Most T2D breastfeeding mothers choice Metformin for their initial treatment of diabetes. Sometimes Metformin is found in low levels in the serum of breastfed infants. But no adverse effects are seen when breastfeeding women use Metformin as an oral medication. Although metformin does not lower plasma glucose, it should be used by breastfeeding mothers very carefully and should stop immediately if any side effect is observable.
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Diabetes mellitus (DM) is a fast growing epidemic and a public health concern all over the world ... more Diabetes mellitus (DM) is a fast growing epidemic and a public health concern all over the world due to its increased incidence and its devastating complications. Sulfonylureas (SUs) are oral glucose-lowering agents that are characterized by efficient glycemic control with cardiovascular safety and renal benefits, and use as the second-line drugs for the management of type 2 diabetes (T2D). Although SUs have some side-effects, its glucose-lowering effect is immediate and stimulates the pancreas to release more insulin. It contributes to the development and progression of hypoglycaemia. It is used as an alternative or a complement to Metformin. SUs should be avoided by the elderly weak patients who are at high risk of hypoglycaemia. In this mini review the basic and clinical pharmacology of SUs are described.
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Management of type 1 diabetes (T1D) is a great challenge for the healthcare professionals and at ... more Management of type 1 diabetes (T1D) is a great challenge for the healthcare professionals and at present there is no known strategy to prevent it. The common symptoms of T1D are polyuria, polydipsia, weight loss, hypoglycaemia, marked hyperglycaemia, ketonemia, and insulin deficiency with nonresponsive to oral agents. It is a life-threatening multifactorial autoimmune disease with progressive β-cell destruction that leads to severe endogenous insulin deficiency. The scientists are not sure why these β-cells are damaged. T1D is incurable and usually treated with lifelong insulin injections and careful attention to diet and physical activity. As a result, ultimately the patients become physiological dependence on exogenous insulin. The purpose of this study is to provide various information and treatment strategy of type 1 diabetes (T1D).
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Diabetes mellitus (DM) is a chronic but non-contagious metabolic disease that is characterized by... more Diabetes mellitus (DM) is a chronic but non-contagious metabolic disease that is characterized by elevated levels of blood sugar. In pregnancy it increases various risk factors, such as adverse maternal, fetal, obstetric, and neonatal consequences. Gestational diabetes (GD) is associated with abnormalities in placental development including impairments in trophoblastic differentiation. Insulin therapy is the best treatment for both mother and fetus. On the other hand, Metformin is an oral anti-hyperglycaemia agent that is commonly used to treat type 2 diabetes (T2D) pregnant and non-pregnant women worldwide. But its role in gestational diabetes management remains controversial. It prevents the production of hepatic glucose, increases fatty acid oxidation, enhances insulin sensitivity, decreases lipid synthesis, and impedes gluconeogenesis. From the scientific researches of scientists obtained that hypoglycaemia is not a concern of Metformin. In this review article the benefits and possible negative impacts of Metformin use during pregnancy are discussed in briefly.
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Hyperglycaemia is a presence of too much high glucose (sugar) in the bloodstream if it is not wel... more Hyperglycaemia is a presence of too much high glucose (sugar) in the bloodstream if it is not well-controlled. When the blood glucose level (BGL) is above 15 mmol/l, the situation is considered as hyperglycaemia. Long-term uncontrolled hyperglycaemia can affect type 1 diabetes (T1D) and type 2 diabetes (T2D) patients, as well as pregnant women with gestational diabetes. If it is not treated for a long-time, different vital organs of the body, such as the eyes, nerves, kidneys, and blood vessels may permanently damage. Diabetic ketoacidosis (DKA) and hyperosmolar hyperglycemic state (HHS) are diabetes emergencies and life-threatening complications in hyperglycaemia. Prevention and treatment of hyperglycaemia and its related complications are necessary for a healthy life of diabetes patients. This study tries to discuss the causes, symptoms, prevention, and treatment of hyperglycaemia with highlights on DKA and HHS.
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Metformin is one of the safest and most effective first-line glucose-lowering oral drug therapies... more Metformin is one of the safest and most effective first-line glucose-lowering oral drug therapies for overweight and obese type 2 diabetes (T2D) patients, and those with normal kidney function. It is one of the drugs of Biguanide class of anti-diabetic compounds. It prevents the production of hepatic glucose, increases fatty acid oxidation, enhances insulin sensitivity, decreases lipid synthesis, and impedes gluconeogenesis. Sometimes it is used in combination with insulin or other oral medications. It should be used very carefully who have surgery, trauma, heart failure, severe kidney disease, and impaired liver functions. Some patients face side effects of Metformin and they should take it considering possible side effects of it. In this study aspect of Metformin is discussed as a guideline for the proper treatment T2D patients.
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During profit maximization procedure an industry faces various difficulties; and increase of cost... more During profit maximization procedure an industry faces various difficulties; and increase of cost of principal raw material is one of them that happen frequently. In this study an attempt is taken to discuss economic effects on various inputs when the cost of principal raw material is increased. The economic sensitivity analysis of various inputs on the basis of principal raw material is an essential step for an industry when the industry is on the profit maximization track. This article deals with four variable inputs, such as capital, labor, principal raw materials, and irregular inputs of an industry, where nonlinear budget constraint is considered. This study stresses on mathematical formalities to show the economic predictions scientifically.
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Hyperosmolar hyperglycaemic state (HHS) is a life-threatening complication of type 2 diabetes (T2... more Hyperosmolar hyperglycaemic state (HHS) is a life-threatening complication of type 2 diabetes (T2D), but it is preventable. There is no precise definition of HHS. It is characterized by severe hyperglycaemia with blood glucose levels greater than 600 mg/dl (33.3 mmol/l), a marked increase in serum osmolality greater than 320 mOsm/kg, and severe dehydration without significant ketoacidosis (<3 mmol/l). Early clinical diagnosis and prompt treatment, such as insulin therapy, restoration of electrolyte disturbances and management of concurrent illnesses may improve the outcome. Intravenous insulin and fluid replacement with careful monitoring are the main treatment policy of HHS. In this study an attempt has been taken to discuss various effects of HHS with prevention and treatment of this complication of diabetes.
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Hypoglycaemia is a low blood glucose concentration and an indicator of diabetes mellitus, and are... more Hypoglycaemia is a low blood glucose concentration and an indicator of diabetes mellitus, and are associated with physical and psychological morbidity. It is a common, potentially avoidable consequence of diabetes treatment, and a major barrier to better metabolic control in diabetes. It is due to overtreatment of diabetes patients with insulin or sulfonylureas or glinides or also consumption of too little food or unplanned excessive exercise or physical activity. It is the acute complication of diabetes and is associated with considerable morbidity and mortality. It is important of the early recognition, treatment, and prevention of hypoglycaemia. Immediate treatment of severe hypoglycaemia is needed to avoid life threatening complications of the diabetic patients. In this study an attempt has been taken to discuss the aspects of hypoglycaemia of diabetes mellitus patients.
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At present panniculus morbidus becomes a cause of various physical complications, such as chronic... more At present panniculus morbidus becomes a cause of various physical complications, such as chronic cellulitis, skin rashes, intertriginous dermatitis, subcutaneous abscesses, folliculitis, skin ulcerations, fistulas, and ischemic panniculitis. Panniculus is seemed as an apron of an extremely large fold of excess skin, tissue, and fat hanging from the abdomen below the waistline and even down to the groin. It is extremely unsightly, painful, and susceptible to various infections. It is found in people who are severely obese, after extreme weight loss (usually 100 pounds or more) through the diet, fasting, and exercise or following gastric restrictive surgery. Medicine, exercise, diet or any other mechanism cannot cure panniculus morbidus; and in this stage, bariatric surgery is needed for the welfare of the panniculus patients.
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Diabetic ketoacidosis (DKA) is a life-threatening medical emergency that requires immediate evalu... more Diabetic ketoacidosis (DKA) is a life-threatening medical emergency that requires immediate evaluation and treatment. It remains a significant complication of diabetes and is increasing alarmingly worldwide. It is an endocrine complication that involves hyperglycemia, anion gap metabolic acidosis, and ketosis. It is characterized by hyperglycaemia with glucose is greater than 11 mmol/l (200 mg/dl), capillary/venous pH is less than 7.3, bicarbonate (HCO3-) is less than 15 mEq/l, serum anion gap is greater than 16 mmol/l, moderate to severe dehydration is seen and creatinine ratio is increased, and ketones (ketonemia and ketonuria ≥3 mmol/l) are present. It occurs in patients with type 1 diabetes (T1D), and type 2 diabetes (T2D); and early diagnosis, monitoring, and treatment are necessary for the welfare of the patients. Treatment of DKA involves volume expansion, insulin replacement, and prevention of hypokalemia. DKA can be prevented through the earlier recognition and initiation of insulin therapy. An attempt has been taken here to discuss the aspects of DKA in some detail.
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In medical science, hemochromatosis is a genetic disorder that is commonly known as bronze diabet... more In medical science, hemochromatosis is a genetic disorder that is commonly known as bronze diabetes, which is due to continuously over-absorbed of excess iron from the gastrointestinal tract for hepcidin deficiency, and deposited in the liver, pancreas, heart, skin, gonads, pituitary gland, and other organs. Hepcidin regulates the activity of ferroportin, the only identified cellular iron exporter. Hemochromatosis is a relatively new term to common people, and it is named bronze diabetes because of the brown color of the skin due to the accumulation of huge iron in the body. Symptoms and expressions of this disease are hepatic fibrosis, fatigue, arthralgia, cirrhosis, diabetes mellitus, arthropathy, pigmentation, cardiomyopathy, and hepatomegaly. Hemochromatosis is more prevalence among Northern European populations, and five to ten times more common among males than females. Phlebotomy is the popular treatment of this disease to remove iron, and ensures normal survival if applied early, and has been shown recently to reverse hepatic fibrosis but not cirrhosis.
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Every organization expects to achieve maximum profit for its survival economic environment. To de... more Every organization expects to achieve maximum profit for its survival economic environment. To develop profit maximization strategy an organization must be sincere in economic sensitivity analysis. In this study sensitivity analysis is inspected to predict about the economic situation for the efficient production of the organization. Here scientific based production policy is indicated subject to a budget constraint, using Lagrange multiplier technique.
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Papers by Dr Haradhan K U M A R Mohajan
Cosmology is a branch of a science, which explains the universe as a whole its history, the origin, present state, and future. In 1915, Albert Einstein inrtoduced the General Relativity, which uniquely determines the evolution of the universe. At present, General Relativity is the best theory to describe gravitational processes. In the standard cosmological picture, the universe is modeled by the spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) solution of General Relativity. The purpose of this the book is to describe elaborately some basic results and applications of global aspects in gravitation and cosmology, and the singularities therein.
Finally , if we can really create a sound and efficient capital market, which is an efficient tool for resources mobilization and allocation, greater dependence on the banking sector can be reduced, medium and large projects of both public and private sectors can be financed through raising funds from the capital market, excessive borrowing of the government from banking sectors, foreign countries and multi-lateral development partners (such as World Bank (WB), International Monetary Fund (IMF) and Asian Development Bank (ADB)) on tight caution can be avoided, and dynamism in the economy can be injected exploiting all the investment opportunities. This will result in higher economic growth, such as 7-8% growth of the gross domestic product (GDP).
According to International Energy Agency data, the United States of America (USA) and China together emit approximately 40% of global CO2 emissions, and about 35% of total greenhouse gases. This book stresses the greenhouse gas emissions of the USA and China, and shows various ways to decrease greenhouse gas emissions. The Kyoto Protocol is introduced in 1997 but developed countries and some industrialized developing countries are not implementing this Protocol. In December, COP/CMP7, United Nations (UN) Climate Change Consensus 2011, Durban, South Africa, all the nations of UN do not agree to reduce GHGs according to Kyoto Protocol agreement but Kyoto Protocol is extended up to 2015. The USA is searching for the advanced technologies to develop both vehicles and fuels. Recently the USA, Brazil and some other countries are producing biofuels, electric and solar cells and are using them in vehicles to reduce stress on gasoline and are trying to develop them.
Methane is present in the atmosphere very low compared to carbon dioxide but it is dangerous greenhouse gas, since it is 21 times more global warming potential than carbon dioxide. In the pre-industrial period methane was 715 ppb (parts per billion) but in 2005 it increased 148% to reach 1,774 ppb. This book discusses the effects of methane gas which causes severe global warming in the atmosphere.
In the 1990s the unconventional shale gas extraction increases in the USA due to national and global demand of energy. The expansion of shale gas production will provide low carbon economy, therefore it is a positive side of low greenhouse gas emissions in the atmosphere and considering the benefit sides it has been referred to as a bridging fuel. Horizontal drilling and hydraulic fracturing are the two technologies by the combination with one another; provide the potential to unlock tighter shale gas formations. The conventional natural gas reserves declining globally, so that shale gas extraction emerged as a potentially significant new source of unconventional gas in the USA, the United Kingdom (UK) and elsewhere. This book discusses the procedure of extraction, benefits and disadvantages of unconventional shale gas.
In this book very simple calculations are presented to estimate three greenhouse gases, carbon dioxide, methane, and nitrous oxide emissions from small industries which cause the global warming in the atmosphere. Emissions from combined heat and power plants are allocated in this book by using ‘The World Resources Institute and World Business Council for Sustainable Development Efficiency’ method.
This book analyzes the price or quantity controls of greenhouse gases in the presence of uncertain costs. The greenhouse gases are a stock pollutant in the environment. Hence, the marginal benefit curve must be relatively flat which indicates to establish the preference of a price control over a quantity control. In the case of permanent shocks, the traditional comparison of marginal benefits versus marginal costs cannot be measured accurately. The choice between quantity and price controls becomes ambiguous and depends upon a more difficult measurement of marginal costs and benefits. The book advises to impose taxes to reduce greenhouse gas emissions.
As the temperature of the world is increasing, hence immediate steps are to be taken to reduce greenhouse gas emissions to safe the future generations and keep the planet environment friendly. This book emphasizes on the affects of global warming and discusses different ways to reduce greenhouse gas emissions.
Optimization is an inessential part of the economics and business. Every firm wants output maximization, cost minimization, utility maximization and social welfare. The techniques to predict the future performance vary from an educated guess based on an appropriate analogy to very complex analytical and numerical calculations and approximations. However, what they all have in common is that they analyze the performance in the past to say something to obtain constrained optimal output in the future.
John V. Baxley and John C. Moorhouse (1984) have analyzed an example in utility maximization in their paper, “Lagrange Multipliers Problems in Economics”, using Lagrange multipliers, and provided a formulation for nontrivial constrained optimization problems with special reference to application in economics. They consider implicit functions with assumed characteristic qualitative features and provide illustration of an example, generating meaningful economic behavior. At the end of their paper, they have suggested several similar types of problems and leave them unsolved. In this book we mainly attempt to study and extend their paper and solve those suggested optimization problems, and discuss optimization of social welfare subject to maximization constraints.
In this book an attempt has been made to maximize an output subject to a budget constraint to maximize utility function subject to multiple constraint and minimization of cost in three variables subject to output function as a constraint, studying the behavior of the firm. We extended the work of Islam (2008) to by using Lagrange multipliers technique, as well as necessary and sufficient conditions for optimal value have been applied. We gave interpretation of Lagrange multiplier in this specific illustration, showing its positive value, and examined the behavior of an agency. We consider theoretically a variation of the problem by assuming that a government agency is allocated an annual budget and required to maximize and make available some sort of services to the community.
We deal with formulating mathematical model for the problem, considering Cobb-Douglas production function in three variables (factors: capital, labor, and other inputs). Considering an explicit form of production function, we apply necessary conditions to this output maximization problem, and find stationary points as well as optimal value of the production function. We give a reasonable interpretation of the Lagrange multiplier in the context of this particular illustration. We analyze the comparative static results and examine the behavior of the agency; that is, how a change in the input costs will affect the situation, or if the budget for the services undergoes some changes.
Typically, during some emergencies, such as in the times of a war or a natural disaster, governments intervene and legislate a maximum ceiling prices of certain basic consumer goods, as there is inadequate supply, and the civilian populations are subject to some form of rationing. This occurred in Pakistan in the 1970s because of political disturbances, and the results were relevant. Initially, this is done through a “first come first served” approach, with or without limiting sales to each consumer. Lines are formed, and much time is spent foraging for those rationed goods. Eventually, some kind of non-price rationing mechanism is evolved.
Usually, the method of rationing is through the use of redeemable coupons used by government agencies. The government agencies supply each consumer with an allotment of coupons each month. Under rationing goods, each consumer must have enough number of coupons as well as money to buy rationed goods. In turn, each consumer pays money and redeems a certain number of coupons at the times of purchase of rationed good. This effectively means that the consumer pays two prices at the time of purchase of a rationed good. She pays both the coupon price and the monetary price of a rationed good. This requires the consumer to have both sufficient funds and sufficient coupons in order to buy a unit of a rationed good. In result, there are two kinds of money involved to buy a rationed good, and hence consumer faces two constraints: budget constraint, and the ration coupon constraint. This situation develops a problem of utility maximization subject to multiple constraints, in these particular cases two constraints.
It is quite common to receive a discount when ordering in larger quantities, or in some markets, the prices vary depending on quantity of commodity purchased. Also firms offer a lower per unit price if a consumer is willing to purchase larger quantity of a commodity. Such quantity discounts alter the linear budget constraint, and result in a nonlinear (convex type) budget constraint.
To get intuitive ideas and understanding of the problem at hand, we here consider explicitly a simple algebraic function in three variables, and examine the behavior of the agency, that is, how a change in the costs of input will affect the situation, or if the demand of the services undergoes some changes. We also give suitable interpretation of the Lagrange multiplier in the context of this specific situation, besides using it as a device for transforming a constrained problem into a higher dimensional unconstrained problem.
The optimal environmental tax should be less than the marginal environmental damages; since the presence of pre-existing distortionary taxes, increasing the welfare costs is associated with the overall tax code. The reduction of pollution causes the benefits of health by supplying maximum labors to create benefit-side tax interactions, which will tend to reduce the optimal environmental taxes. This book also shows that the existence of social security system preserves the gross wage of labors during sick days and grants subsidies to medical treatments. An attempt is made to confirm that health effects labor supply, which results in an additional impact, the benefit-side tax-interaction effect.
The book also investigates some policies that would influence people to drive fewer miles and to buy smaller cars, use better pollution control equipment, and cleaner fuel. An attempt has been taken to quote the vehicle tax rates of Bangladesh. Despite technological advances, the emissions of cars’ still cannot be measured reliably enough to impose a Pigovian tax. Literature review reveals that the gas tax depends on fuel type, engine size and pollution control equipment. A vehicle tax depends on mileage or a combination of uniform tax rates on gasoline and engine size with a subsidy to pollution control equipment. We suggested two models, which first considers homogenous consumers and then considers for heterogeneous consumers that differ by income and two taste parameters, one for miles and other for vehicle size. Yet Bangladesh has not imposed emission taxes on vehicles properly; as a result the air pollutions in large cities are increasing dangerously. Dhaka, the capital of Bangladesh, is one of the dangerously polluted cities of the world. The government of Bangladesh should take immediate steps to impose emission taxes on vehicles according to guidelines of this book to apply the taxes on vehicles.
Green Accounting contains a beneficial economic model where government pursues optimal economic policies. The aim of it is to serve as an indicator of wealth changes, performance of environment policy and sustainable use of natural capital. All the services are outputs from natural capital, the change of values of natural wealth. It also indicates the present and future production, and use of ecosystem services to indicate the sustainability of natural resources. Accounting prices of goods and services are constructed and are shown to reflect social securities.
Environmental Accounting (EA) is an inclusive field of accounting, management and economics. By increasing social focus on the environment, accounting fills an expectation role to measure environmental performance. A business firm’s strategy includes responding to capital and operating of pollution control equipment. The partial aim of this book is to derive Green Accounting systems related with economics where the value of changes in natural capital is derived from their production of ecosystem services. Here we have related wealth to society’s capital asset, which include all types of capital. The literature on income and wealth has congregated to a common agreement on the natural capital stock as the basis for obtaining appropriate welfare measures.
This book deals with Borda count which is sincere voting system and originally proposed by French mathematician and philosopher Jeans-Charles Borda. In Borda count a defeated candidate can manipulate the election result in his favor in sincere way by introducing a candidate which is a clone of him and voters ranked this clone candidate immediately below him. In this situation Borda rule is strictly follows but manipulation is possible. The book shows that this type of manipulation is vulnerable. Both single and simultaneous vulnerabilities of cloning manipulations are discussed with detail calculations and easier ways.
The majority judgment is a method of election which is a new theory in social choice where voters judge candidates instead of ranking them. Here emphasize is imposed on the works of Michel Balinski and Rida Laraki majority judgment in an election. In Arrow’s impossibility theorem of social choice theory, the voters have to give a strictly preference ordering over the alternatives and hence they cannot express indifference of the candidates. In the process of majority judgment the voters can express much more information than the Arrow’s process does but it is not free from counter-intuitive results. The Borda majority count avoids some counter-intuitive results and an attempt has been taken here to highlight them. The book discusses both the advantages and drawbacks of the majority judgment in an election. Sometimes tie arises in majority judgment and different processes of tie-breaking are discussed with theoretical and mathematical calculations.
The single transferable vote (STV) is a system of preferential voting designed to minimize wasted votes. In STV, a constituency elects two or more representatives per electorate. As a result the constituency is proportionally larger than a single member constituency from each party. Political parties tend to offer as many candidates as they most optimistically could expect to win; the major parties may nominate almost as many candidates as there are seats, while the minor parties and independents rather fewer. STV initially allocates an elector’s vote for her most preferred candidate and then, after candidate have been either elected or eliminated, transfers surplus or unused votes according to the voter’s stated preferences (ties disallowed). The book deals with different STV counting methods so that one can compare among them and analyze advantages and drawbacks of them. Since in STV ties are disallowed, so that tie-breaking in STV is important and are discussed in some details. In STV manipulation of voting is sometimes possible and this book has taken an attempt to give a clear concept of STV manipulation.
This book deals with approval voting (AV) and its critical strategy profile. Approval voting is a single winner voting system used for multi-candidate elections. In this method each voter may vote for as many of the candidates as she wishes that is the voter votes for all candidates of whom the voter approves. In Approval voting no ranking is involved, so all the votes have equal weight. Some scientific and engineering societies adopted approval voting but unfortunately yet has not adopted in any public election, despite efforts to institute it, so its success should be judge as mixed. The book also discusses aspects of approval voting and compares with some other voting rules. Approval voting may elect Condorcet winners or Condorcet losers.
The median voter theorem is one of the most prominent results of formal political theory and economics, and is widely used to study interactions between them. The median voter is the person in the middle of the distribution on the single dimension and is a more accurate predictor of decision outcomes under simple majority voting system. Politicians believe that elections are logically imperfect. Median voting model has such imperfections less than the other models and an attempt has been taken to explore these in some details. Although the median voting model plays a pioneer role in modern democracy but it cannot solve all the problems of voting system, and the book deals where the median voter theorem fails.
In this book voting methods are discussed in very simple but in a detailed manner. Mathematical calculations are presented here in easier ways, so that the readers can realized every chapter with full satisfaction.
Keywords: Condorcet winner, Borda scores, voting system, voting paradox, majority voting, single transferable vote, tie-breaking in STV, AV outcomes, median voter, manipulation of voting, dictatorship.
This book discusses the theory of green national accounting and, emphasizes on social welfare and sustainable accounting. Weitzman provides a foundation for net national product as the stationary equivalent of a wealth maximizing path when there is a constant interest rate and no exogenous technological progress. An attempt has been taken here to make the relationship with different incomes and green net national product, under no exogenous technological progress and a constant utility discount rate. The book shows that green net national product measures the gross social profit rather than net social profit.
It is observed that the world economy following an egalitarian path, the aggregate capital gains being positive is equivalent to the interest rate tending to decrease. This is important for the concept of net national product in open economies. Martin Weitzman gives a foundation for net national product as the stationary equivalent of a wealth maximizing path when there is a constant interest rate and no exogenous technological progress. The NNP should equal the maximum consumption level that can be sustained. The ordinary Hartwick rule gives a sufficient condition for constant consumption in a closed economy with constant population and stationary technology. An attempt has been taken in this book to discuss the net national product and sustainability in open economy. The book also highlights the recent world economy and the open economy of Bangladesh.
In 1742, Leonhard Euler developed the generating function for P(n). Godfrey Harold Hardy said Srinivasa Ramanujan was the first, and up to now the only, mathematician to discover any such properties of P(n). We have showed how to find the number of partition of n by using MacMahon’s table. In 1742, Euler also stated the series in the enumeration of partitions. In 1952, Percy Alexander MacMahon also quoted the self-conjugate partitions of n. We prove the Euler’s theorems with the help of Euler’s device of the introduction of a second parameter z. In mathematics, a generating function is a formal power series in one intermediate, whose coefficients encode information about a sequence of numbers that is indexed by the natural numbers. Generating functions were first introduced by Abraham de Moivre in 1730 in order to solve the general linear recurrence problem. H. S. Wilf defined the generating function as “A generating function is a clothesline on which we hang up a sequence of numbers for display.” Generating functions were introduced in 1748 by Euler in Introductio in Analysin Infnitorum. He used generating functions as a tool to discover a number of interesting properties concerning partitions.
In 1995, R. Fokkink, W. Fokkink and Z. B. Wang defined the in terms of , where is the smallest part of partition . In 2008, George E. Andrews obtained the generating function for . In 2013, Andrews, Frank G. Garvan and Jie Liang extended the FFW-function and obtained the similar expressions for the spt-function and then defined the spt-crank generating functions. They also defined the generating function for FFW (z, n) in various ways. In 1894, L. J. Rogers found the two identities for the first time. In 1913, Ramanujan found the two identities later and then the two identities are known as the Rogers-Ramanujan Identities. In 1982, R. J. Baxter used the two identities in solving the Hard Hexagon Model in statistical mechanics. In 1829, C. G. J. Jacobi proved his triple product identity; it is used in proving The Rogers-Ramanujan Identities. In 1921, Ramanujan used Jacobi’s triple product identity to prove his famous partition congruences.
The rank of a partition of an integer is a certain integer associated with the partition. The term has first introduced by Freeman S. Dyson in a paper published in Eureka in 1944. He discussed his conjectures related to the partitions empirically some Ramanujan’s famous partition congruences. In this chapter we prove the Dyson’s conjectures with rank of partitions. In 1921, S. Ramanujan proved his famous partition congruences: The number of partitions of numbers 5n+4, 7n+5 and 11n +6 are divisible by 5, 7 and 11 respectively in another way. In 1944, Dyson defined the relations related to the rank of partitions. These are later proved by A. O. L. Atkin and H. P. F. Swinnerton-Dyer in 1954. In 1920, Srinivasa Ramanujan defined the Mock Theta functions in his Lost Notebook and unpublished papers. We prove the Mock Theta Conjectures with the help of Dyson’s rank and S. Ramanujan’s Mock Theta functions.
In 1944, Freeman Dyson conjectured the existence of a “crank” function for partitions that would provide a combinatorial result of Ramanujan’s congruence modulo 11. In 1988, Andrews and Garvan stated such functions and described the celebrated result that the crank simultaneously explains the three Ramanujan congruences modulo 5, 7 and 11. Dyson wrote the article, titled “Some Guesses in the Theory of Partitions”, for Eureka, the undergraduate mathematics journal of Cambridge. He discovered many conjectures in this article by attempting to find a combinatorial explanation of Ramanujan’s famous congruences for P(n), the number of partitions of n indeed, Ramanujan’s formulas lay unread until 1976 when Dyson found in the Trainty College Library of Cambridge University among papers from the estate of the late G. N. Watson. In 1986, Garvan wrote his Pennsylvania state PhD thesis precisely on the formulas of Ramanujan relation to the crank. In view of this theoretical description, the story of the crank is a long romantic tale and the crank functions are intimately connected to all partitions congruences. In 2005, K. Mahlburg stated that the crank functions themselves obey Ramanujan type congruences.
In 2013, Andrews, Garvan and Liang defined Self-conjugate S-partitions. In 2011, Andrews stated the definition of spt(n). Let spt (n) denote the total number of appearances of the smallest part in each partition of n. In 1988, Garvan gave new combinatorial interpretations of Ramanujan’s partition congruences mod 5, 7 and 11 in terms of a crank for weighted vector partitions. In 2008, Andrews stated Ramanujan-type congruences for the spt-function mod 5, 7 and 13. The new combinatorial interpretations of the spt-congruences mod 5 and 7 are given and these are in terms of the spt-crank but for a restricted set of vector partitions.
In 2008, J. Lovejoy and R. Osburn defined the generating function for , the number of overpartitions of an integer n. In 2009, Byungchan Kim defined the generating function for . He also defined with increasing relation and overpartition congruences mod 4, 8 and 64. In 2009, Bingmann, Lovejoy and Osburn defined the generating function for . In 2012, Andrews, Garvan, and Liang defined the in terms of partition pairs. In this chapter the number of smallest parts in the overpartitions of n with smallest part not overlined is discussed, and the vector partitions and -partitions with 4 components, each a partition with certain restrictions are also discussed. In 2014, Garvan and Jennings-Shaffer able to define the for marked overpartitions. In 2009, Bingmann, Lovejoy and Osburn showed the generating function for . In 2009, Bingmann, Lovejoy and Osburn have shown the generating function for .
In this book we have tried to introduce recent development of partition and generating functions. We have developed theorems and have provided remarks and have added examples and tables. We have established some remarks and try to make easier the concepts of theorems and remarks with introducing examples and definitions where necessary.
The microfinance system of Grameen Bank (GB) is a revolutionary tool to eradicate poverty of the rural people especially the women of Bangladesh. At present GB is the largest microfinance bank in Bangladesh and probably the biggest microcredit organization in the world. It provides loans to assetless and landless poor people whom no commercial bank give loan. Microcredit is the most useful and popular financial system in the world to face financial crisis of the poor people. GB loan distribution has risk of default and sometimes the loans are used even dowry which is crime against women right. The rate of interest in GB is very high and due to high interest rate the poor women cannot use the loan in a high profitable business to bear this burden, so some of the borrowers lose lands and assets to pay the loan. The book discusses both advantages and drawbacks of GB with mathematical calculations in some details.
Green finance is part of a broader occurrence; from the incorporation of various non-financial or ethical concerns onto the financial universe. Generally green finance is considered as the financial support for green growth which reduces greenhouse gas emissions and air pollutant emissions significantly. Green finance in agriculture, green buildings and other green projects should increase for the economic development of the country. In this book an attempt has been made to describe green financing in a boarder sense.
This study presents a review of major capital structure fiction. Capital structure decision is important for companies because it helps to increase firm value by ensuring that the company has enough resources to carry out planned investments using as much as possible the cheapest cost of capital. It therefore involves choices between the different sources of capital such as debt, equity and hybrid capital. The different sources of finance available to companies are also influenced by the quality and maturity of the financial system and the overall risk of operating in that environment. The paper identified a host of capital structure theories that are key contemplation in the financing structure of firms around the world. This review will help companies in emerging and underdeveloped economies identify the peculiarities in the choosing the appropriate blend of capital.
The emergence of e-commerce and development of information and technology plays a significant role in the nature of work as well as their attitude towards the organization. We have been experiencing a tremendous growth in banking sector of Bangladesh during the last decade of the twentieth century. Private commercial bank plays a vital role in the overall development of our economy. Though it is a challenging profession, people working in this sector have increased notably during last few years. In recent time banking sectors have become the first choice for career development. In consideration of that factor, this study investigates job satisfaction among employees of all public and private commercial bank limited. The research method used an anonymous survey that was voluntarily completed and returned to the researcher. The study determined that morale and job satisfaction plays a vital role in overall performance of the employees in the workplace. The study also determined that social status, supportive colleagues and feeling secure about the job were the top three best reasons for working in the banks. It was also determined that pay, decision making authority, and promotional policy were the three top priorities for improving the work environment.
This book aims at developing a taxonomy, which uses both institutional and functional criteria. Departing from the assumption that there are several evolutionary stages in the development of university-industry collaboration, which embrace unstructured to fully structured and complex modes, the paper identifies five stages: (i) ad hoc collaboration at an individual level, (ii) development of internal support structures, (iii) creation of autonomous support structures, (iv) setting up of individual enterprises and (v) national and transnational networking. These five development stages include organizational forms, such as Industrial Liaison Offices, University-Industry Research Centers, Trading Companies, Foundations, and, Affiliate programs and Consortia. Each of these organizational models is reviewed in terms of its objectives, functioning and predominance in different regions of the world. Without attempting to be exhaustive specific case examples are included from the African, Western European and Latin American countries. These case examples draw particular attention to some of the crucial management aspects in the development of university-industry collaboration. These lessons will refer to the choice of an appropriate organizational model. It will provide also some guidelines for the strategic and operational management of these relations.
Shortage of electricity and gas supplies, poor infrastructure of roads, bridges and ports, political instability are major problems in national production and economic development. Other obstacles of development are illiteracy and unskilled manpower and non-proper utilization of the manpower. Natural calamities and non-planned urbanizations are also effect economic development.
Bangladesh is considered as one of the major labor exporting countries of the world. Since independence over 7.4 million labors went abroad. The migrant labors send the remittance, which is a driver of growth of the economy of Bangladesh. The major portion of the remittance spends to buy food and basic consumption goods, housing, children’s education and health care. As a result remittance is not contributed directly for the economic development.
In Bangladesh debt burden is increasing rapidly over time due to increase in the budget deficit. Both the internal and external debts of the government are increasing every year. In Bangladesh, during 2000 to 2005, income poverty reduced from 48.9% to 40% and 2005 to 2010 reduced from 40% to 31.50%. The present government has targeted to reduce poverty rate to 25% and 15% by 2013 and 2021 respectively. Various microfinance programmes also help the poor to reduce the poverty of the country.
In this book we have also discussed the poverty and economic development of three countries of Africa: Zambia, Kenya and Ethiopia. Finally we have developed the global effect of food price hike.
Zambia is a landlocked country located in southern central Africa. It is one of the poorest countries in the world and is considered a least developed country. Malnutrition is a chronic and difficult problem in this country. Agriculture is the main occupation of it and maize is the main staple food. About 90% farmers of the country are smallholders, dependent on rain fed agriculture. After independent it was rich in food and can export maize but since 2002 it has to import maize every year. Literacy rate is low and women are less literate than men. HIV/AIDS, tuberculosis and malaria are fatal diseases in Zambia and mortality rates are among the highest in the world. The rural transportation network is largely undeveloped and communication costs are very high and foreign direct investment is also very low. Main export item of the country is copper. According to the Food and Agriculture Organization, 49% of the Zambian population is undernourished and unable to manage minimum energy requirement.
The economy of Kenya has been continued to be the largest in the East African region and third largest in Sub-Saharan Africa after South Africa and Nigeria respectively. At present Kenya is one of the most highly literate countries in sub-Saharan Africa. But more than 60% people of Kenya live below the poverty line. Rapid increases in inflation could reduce economic growth and worsen the poverty levels of the citizens of Kenya. In Kenya economic development is dependent on agricultural improvement. Kenya is the largest food and agricultural products importer in east Africa. About 82% of the total land in Kenya is classified as arid and semi-arid. Agricultural products depend on proper rainfall. Main staple food of Kenya is maize, which accounted about 65% of total staple food caloric intake and 36% of total food caloric intake. The cash income of the rural people of Kenya comes from the selling of agricultural products. At present the government of the country is trying to reduce poverty. An attempt has been taken here to discuss the food and economic situation and the development of these sectors of the country.
Ethiopia is considered to be one of the oldest nations in the world. It is the second most populous country in Sub-Saharan Africa. It is rated the poorest and most heavily indebted countries of the world, ranked last out of 208 countries. About 26% of the population of the country, mostly women and rural residents, is living below the poverty line. In terms of health and welfare, it ranks among Africa’s and the world’s poorest nations and the infant mortality rate is among the highest in the world. In Ethiopia at least 80 languages are spoken as mother tongues among 70 ethnic groups. Political instability is another major problem of Ethiopia for the overall development. However, it is enriched with several agricultural, minerals and other natural resources.
The book also discusses the global food price hike and the effects of it among the poor of developing countries. Increase of food price became severe during 2007 and 2008, which was high in the last fifty years and more than half of the populations of the world affected due to this price hike. Biofuels production is one of the main causes of food price increase. Rapid increase of world population is another cause of food price rise. Soaring food prices have generated global concern about threats to food security, shaking the satisfaction created by many years of comparatively low commodity prices. Right of food is a fundamental right of every citizen of the state; unfortunately citizens of the most countries are deprived from this right. In the last decade the food and nutrition crisis has extended due to increased food price. Many developing countries use food price subsidies or price controls to improve the nutrition of the poor but this is not a permanent solution to control food price hike.
Chapter-I is introductory but it includes the core concept of the thesis. We have discussed some definitions, mathematical calculations and diagrams where necessary. These are used in subsequent chapters of the thesis.
In chapter-II we use the technique of the method of Lagrange multipliers which is a very useful and powerful technique in multivariable calculus and has been used to facilitate the determination of necessary conditions; normally, this method was considered as device for transferring a constrained problem to a higher dimensional unconstrained problem. Using this technique, John V. Baxley and John C. Moorhouse (1984) have analyzed an example of utility maximization in their paper, “Lagrange Multipliers Problems in Economics” using Lagrange multipliers, and provided a formulation for nontrivial constrained optimization problem with special reference to application in economics (Moolio, Islam, and Mohajan 2009). They considered implicit functions with assumed characteristic qualitative features and provided illustration of an example, generating meaningful economic behavior. This approach and formulation may enable one to view optimization problems in economics from a somewhat wider perspective. In this chapter an attempt has been made to maximize an output subject to a budget constraint (Moolio, Islam, and Mohajan 2009), to maximize utility function subject to multiple constraint (Islam, Mohajan and Moolio 2010) and minimization of cost in three variables subject to output function as a constraint (Islam and Moolio 2008), studying the behavior of the firm. We extended the work of Islam (2008) to by using Lagrange multipliers technique, as well as necessary and sufficient conditions for optimal value have been applied. We gave interpretation of Lagrange multiplier in this specific illustration, showing its positive value, and examined the behavior of an agency. In this chapter, we consider theoretically a variation of the problem by assuming that a government agency is allocated an annual budget and required to maximize and make available some sort of services to the community. We deal with formulating mathematical model for the problem, considering Cobb-Douglas production function in three variables (factors: capital, labor, and other inputs). Considering an explicit form of production function, we apply necessary conditions to this output maximization problem, and find stationary points as well as optimal value of the production function (Moolio, Islam and Mohajan 2009). We give a reasonable interpretation of the Lagrange multiplier in the context of this particular illustration. We analyze the comparative static results (Chiang 1984) and examine the behavior of the agency; that is, how a change in the input costs will affect the situation, or if the budget for the services undergoes some changes. Typically, during some emergencies, such as in the times of a war or a natural disaster, governments intervene and legislate a maximum ceiling prices of certain basic consumer goods, as there is inadequate supply, and the civilian populations are subject to some form of rationing. This occurred in Pakistan in the 1970s because of political disturbances, and the results were relevant. Initially, this is done through a “first come first served” approach, with or without limiting sales to each consumer. Lines are formed, and much time is spent foraging for those rationed goods. Eventually, some kind of non-price rationing mechanism is evolved (Samuelson and Nordhaus 2001). Usually, the method of rationing is through the use of redeemable coupons used by government agencies. The government agencies supply each consumer with an allotment of coupons each month. Under rationing goods, each consumer must have enough number of coupons as well as money to buy rationed goods. In turn, each consumer pays money and redeems a certain number of coupons at the times of purchase of rationed good. This effectively means that the consumer pays two prices at the time of purchase of a rationed good. She pays both the coupon price and the monetary price of a rationed good. This requires the consumer to have both sufficient funds and sufficient coupons in order to buy a unit of a rationed good. In result, there are two kinds of money involved to buy a rationed good, and hence consumer faces two constraints: budget constraint, and the ration coupon constraint. This situation develops a problem of utility maximization subject to multiple constraints, in these particular cases two constraints. It is quite common to receive a discount when ordering in larger quantities, or in some markets, the prices vary depending on quantity of commodity purchased. Also firms offer a lower per unit price if a consumer is willing to purchase larger quantity of a commodity. Such quantity discounts alter the linear budget constraint, and result in a nonlinear (convex type) budget constraint (Islam, Mohajan and Moolio 2011c). To get intuitive ideas and understanding of the problem at hand, we here consider explicitly a simple algebraic function in three variables, and examine the behavior of the agency, that is, how a change in the costs of input will affect the situation, or if the demand of the services undergoes some changes. We also give suitable interpretation of the Lagrange multiplier in the context of this specific situation, besides using it as a device for transforming a constrained problem into a higher dimensional unconstrained problem.
General relativity models the physical universe as a four dimensional space-time manifold (M, g) which is differentiable, space-time orientable, connected, paracompact, Hausdorff and without boundary. It was realized that though locally the laws of physics are those of special relativity and space-time is very nearly flat rise to a non-flat, curved continuum which would also admit a suitable differential structure. The universe is not simply a random collection of irregular distributed matter, but it is a single entity, all parts of which are connected. When considering the large scale structure of the universe, the basic constituents are galaxies, which are congregation of more than 1010 stars bound together by their mutual gravitational attraction. The universe is the totality of galaxies which are causally connected.
Soon after the Einstein’s field equations were discovered, Friedmann showed that the universe must have originated a finite time ago from an epoch of infinite density and curvatures where all the known physical laws break down which we call ‘big bang’. So we cannot predict what was happened in the period of big bang and before big bang. Therefore, we can say that it is a singularity in space-time topology.
The Schwarzschild exterior solution of Einstein’s field equations describes the gravitational fields outside a spherically symmetric star where there is no matter present and space-time is empty. The space-time distance ds for gravitating mass m in coordinates between two infinitesimally separated events is given by the metric;
. (1)
The above space-time has an apparent singularity at r = 2m as seen by the divergence of metric components of equation (1). It was thought initially that the above represents a singularity in the space-time itself and that physics goes seriously wrong at r = 2m. After some efforts it is realized that this is not a genuine space-time singularity but merely a coordinate defect, and what was really needed was an extension of the Schwarzschild manifold. Such an extension of the space-time was obtained by Kruskal (1960) and Szekeres (1960) and this may be regarded as an important insight involving a global approach (Chapter–III). However at r = 0 there is a genuine curvature singularity where the Kretschman scalar i.e., space-time curvature components tend to infinity.
A rigorous analysis of global properties of a general space-time was done by Hawking, Penrose and Geroch, who showed that under certain very general and physically reasonable conditions such as the positivity of energy, occurrence of trapped surface and suitable causality condition the space-time singularities must occur as an inevitable feature, as far as a wide range of gravitation theories describing the gravitational forces are concerned (Hawking and Ellis 1973).
The existence of space-time singularities follows in the form of future or past incomplete non-spacelike geodesics in the space-time. Such a singularity would arise either in the cosmological scenarios, where it provides the origin of the universe or as the end state of the gravitational collapse of a massive star which has exhausted its nuclear fuel providing the pressure gradient against the inwards pull of gravity. Several global features for space-times were understood during this phase work, which resulted in the development of singularity theorems, which have been applied to further work on the Einstein’s equations, asymptotic structure of space-time and such other areas.
While the above developments represent a notable advance towards understanding the global structure of space-time, most of the problems remain unsolved. Apart from the existence of space-time singularities we presently know very little about the global structure of Einstein’s equations. The theorems establish the existence of singularities in the form of either future or past incomplete non-spacelike geodesics for a very wide class of space-times. The theorems provide particularly no information on the nature or the physical significance of the singularities predicted. It is not known if the densities and curvatures will necessarily tend towards infinity along the non-spacelike trajectories falling into such singularities predicted by the singularity theorems.
Thus, the possibility cannot be ruled out that in many cases the singularity theorems would predict physically genuine singularities; though it is not clear at all under what conditions the theorems must give rise to such curvature singularities. In the case of naked singularities it may be possible to communicate with outside observers far away to affect the dynamics of the outside universe. Hence, no causal effects from the singularity can reach any outside observer for whom the singularity is totally hidden within a black hole which is invisible apart from its possible gravitational effects.
In the approximation of the star composed of homogeneous dust without any pressure, the curvature singularity forming as the end state of collapse will be completely covered by the event horizon and would be invisible to any external observer. The hypothesis that the above phenomenon is gravitationally true, that is the singularities forming in general gravitational collapse should always be covered by the event horizon of the gravity, and remains invisible to any external observer is called the cosmic censorship hypothesis. This hypothesis, originally proposed by Penrose, remain unproved as yet in the general case; despite many attempts towards a proof, and has been recognized as one of the most important open problems in general relativity and gravitational physics. However, this throws the black hole dynamics into serious doubt.
Our aim is to discuss the global aspects of gravity, and also to discuss some applications of the results which are already available on the global structure of space-time. We have made every effort to give a basic idea about these throughout the thesis.
This chapter introduces the research strategy and the empirical methods for the general approach, and specific techniques to address the objectives for the research. It also presents the research design and the methods used in the selection of the research participants, and for data collection. Research methodology indicates the logic of development of the process used to generate theory that is procedural framework within which the research is conducted (Remenyi et al. 1998). It provides the principles for organizing, planning, designing, and conducting research. Methodological decisions are determined by the research paradigm that a researcher is following. The research paradigm not only guides the selection of data gathering and analysis methods but also the choice of competing methods of theorizing (Sayer 1992).
This study is based on both primary and secondary data that are collected from various sources. Primary data have been collected from the 500 female garment workers of the slum areas of Chittagong City Corporation (CCC) of Bangladesh by random sampling technique through open-ended questionnaire. The open-ended response questions are most beneficial when a researcher conducts exploratory research, especially if the range of respondents is not known. The open-ended questions can be used to learn what words and phrases people spontaneously give to the free-response questions. The secondary data are collected from the websites, books and e-books, previous published articles, theses, conference papers, case studies, magazines, and various research reports.
Here we have tried to discuss in brief, and clarify how evidence in this study was collected and analyzed, as well as to introduce the research strategy and the empirical techniques applied in this research. The research strategy adopted was face-to-face interview of the garments workers. The mathematical and theoretical data are collected and developed to make this empirical research fruitful.
The purpose of this chapter is to introduce the research instruments that we have developed and utilized in the pursuit of our research goals. This chapter presents an overview of issues related to the procedures involved in the study which include research approaches, focus of research, data collection, research design, two criteria for good measurement, ethical reflections, and conclusion.