Around Taylor’s Theorem on the Convergence of Sequences of Functions

Egoroff’s classical theorem shows that from a pointwise convergence we can get a uniform convergence outside the set of an arbitrary small measure. Taylor’s theorem shows the possibility of controlling the convergence of the sequences of functions on the set of the full measure. Namely, for every sequence of real-valued measurable factions |fn } n∈ℕ pointwise converging to a function f on a measurable set E, there exist a decreasing sequence |δn } n∈ℕ of positive reals converging to 0 and a set A ⊆ E such that E \ A is a nullset and lim n → + ∞ | f n ( x ) − f ( x ) | δ n = 0 for all x ∈ A . Let J ( A , { f n } ) {\lim _{n \to + \infty }}\frac{{|{f_n}(x) - f(x)|}}{{{\delta _n}}} = 0\,{\rm{for}}\,{\rm{all}}\,x \in A.\,{\rm{Let}}\,J(A,\,\{ {f_n}\} ) denote the set of all such sequences |δn } n∈ℕ. The main results of the paper concern basic properties of sets of all such sequences for a given set A and a given sequence of functions. A relationship between pointwise convergence, uniform convergence and the Taylor’s type of convergence is considered.

What can we know about the future? Epistemology and the credibility of claims about the world ahead

Purpose The purpose of this paper is to examine whether the results of futures studies are knowledge or if not, what it is that futures studies actually produce. Five types of representations of the future are the result of these studies. As the value of futures studies depends on no small measure of their credibility, the standards for carrying out and reporting these studies are identified along with a description of how Toulmin’s model of informal logic can be used to best improve their credibility. Design/methodology/approach This paper is based on a multi-disciplinary literature review and integrative analysis. Findings Using epistemological criteria for knowledge as truth, belief and rationale, the results of futures studies are not and cannot be knowledge. Instead, futures studies produce five kinds of “representations of the future”: predictions, projections and forecasts, scenarios, visions and structures for action. Six standards for conducting and reporting the results of futures studies are provided which will increase the credibility of these studies. Toulmin’s informal logic format will provide the foundation for the most persuasive basis of such studies. Practical implications Futurists will understand that the products of their studies are not knowledge and why this is the case. They will also understand that the type of futures studies they are conducting are either conditional, contingent propositions or normative prescriptions in nature. There are six guidelines for carrying out and reporting futures studies which can also be used to assess the quality of published studies. They will see how the use of a certain kind of informal logic can establish the most credible foundations for their studies. Originality/value As an integrative literature review, it incorporates and simplifies widely disparate existing contributions to the topic of the nature of knowledge regarding futures studies and the criteria for making such studies as credible as possible.

Surface and Ground Water Pollution: Causes and Effects of Urbanization and Industrialization in South Asia

Water pollution in South Asia is an alarming issue that has immersed recently. Developing countries, particularly those in South Asia, are fast adopting industrial pollution control standards similar to those in developed countries. So both surface and groundwater are already scarce however, individuals and industries continue to pollute the already limited supply of water. On the other hand, the pollution of rivers is more severe and critical near urban stretches due to huge amounts of pollution load discharged by urban activities. Unplanned urbanization and industrialization occurring in these countries like Bangladesh, India, Nepal and Sri Lanka, etc. may be largely responsible for this grave situation. Therefore these human activities including industrialization and urbanization contributed immensely in no small measure to the degradation and pollution of the environment which adversely has an effect on the water resources such as surface and groundwater that is a necessity for life. This paper tries to discuss basically the causes and effects of urbanization and industrialization in surface and groundwater pollution and equally to address the controlling issues and challenges in South Asia.

The intercultural city: real estate markets, migratory trends and social dynamics [La città interculturale: dinamiche immobiliari, migratorie e sociali]

New ethnicities and new cultures are taking up residence in our cities: for years the flow of foreign people has been compensating the decreasing rates of natural growth and population ageing. This trend comes along with several consequences in the real estate market, and the scientific literature has shown up events in common with many countries. Spatial segregation, as a consequence of real estate dynamics, has to be critically evaluated: it is by no means a neutral mechanism, yet it contributes in no small measure to the spatial segregation of the smaller communities. Nuove etnie e nuove culture abitano le nostre città: da anni il flusso di persone straniere compensa il decrescente saldo naturale e l’invecchiamento della popolazione. Ciò non è senza conseguenze sul mercato immobiliare e la letteratura scientifica mette in luce fenomeni comuni a molti paesi. La segregazione spaziale effetto di dinamiche di mercato va considerata criticamente: quest’ultimo non è dispositivo neutrale, ma concorre attivamente alla segregazione spaziale delle comunità.

Oil and Global Insecurity: Lessons from Asia, Latin America and African Oil Producing Countries

This paper critically digs into history to examine the role oil played in generating war among nations. It also examines conflicts and agitations within nations as well as regime-change in the global system with their attendant consequences on global security. The discovery of oil as a major source of energy for the running of military and civilian complexes the world over, has been a blessing and a curse. Oil as a commodity has contributed in no small measure to growth and development as it helps in turning the wheels necessary for industrialization. However, the search for oil over the years by nations of the world has engendered conflicts and full-fletched wars within and among nations due to antagonistic encounter of interests. Asian and African oil producing countries are the worst hit, as established powers sponsor proxy wars, change unfriendly regimes in the name of accessing abundant oil resources with all the security implications these portend. Within the oil producing states, agitations and rebellion are commonplace in oil producing regions. The governing elites see oil revenue as opportunity for primitive accumulation leaving the people in oil producing regions in extreme poverty and deprivation in the midst of abundant wealth. The frustration and agony of the people find expression in violence and counter violence by the state reducing the oil regions to theaters of conflicts and security crises. The paper however, concluded and recommended that; oil search by the established and emerging powers should be carried out within the confines of the law. Oil producing states deserve to be respected by the international community to utilize their resources for the development of their people. There must not be interference in their internal affairs. Again, the governing elites should develop strategies for equitably distributing oil wealth among the various stake holders within the oil producing states so as to nib rebellion in the bud for the sake of international peace and security.

Prosecutorial Independence in Lesotho: A Critique of the Model

The Constitution of Lesotho is substantially cast on the Westminster prototype. As such, its institutions, by and large, reflect the structure of similar institutions at Westminster. The institution of the Director of Public Prosecutions (DPP) is no different: it has been designed to mirror its namesake under the British constitutional design. The underlying feature of classic British-based constitutions is the weak separation of powers and the predominance and condescending nature of the executive branch of government, as incarnated by the office of the Prime Minister. As such, most institutions within the design are beholden to the executive in general and to the Prime Minister in particular. The institution of the DPP is integral in the administration of criminal justice. Hence, its independence and its accountability in the discharge of this important constitutional mandate are of paramount importance. This notwithstanding, the Constitution of Lesotho is generally weak on safeguarding the independence of the office of the DPP and ensuring its corresponding duty of accountability. The purpose of this article is to critique the constitutional design in relation to the office of the DPP and to expose the deficiency of the constitutional clause establishing the Lesotho DPP office. The article contends that while the Constitution, under section 141, provides for some small measure of independence of this office, the broader schematisation of the Constitution is feeble on the independence and accountability of the office. The article analyses the constitutional design of the Lesotho DPP office in comparison with international developments.

UNHOLY PRACTICES AMONG YOUTHS IN NIGERIA: VENOMS BREEDING TO A DISJOINTED SOCIETY

Before the year 1990 and up to the late 1990s, Nigeria was ravaged by what was known then as “Advanced Free Fraud” christened (419) and “Trades of Narcotic Drugs”. After more than two decades, a new set of unholy practices have found its way into the fabric of the society and have consistently proven to be worse than the duo of “419” and “trades of narcotic drugs”. This set of practices though not narrowed to the youths but majorly driven and made to flourish by the attendant number of youths who are in haste not only to make a living but flamboyant, thriftless and profligate lives detrimental to norms, values and society itself. Premised on the danger they herald for the society, the paper appraised the numerous unholy practices rampant among youths in Nigeria and their impacts on the society. Exploratory method was made use of; secondary source was employed and inferences were drawn via qualitative analysis. Findings revealed that exponential decadence among youths is directly proportional to the culture of prostitution, regime of internet fraud (yahoo-yahoo), kidnapping for ransom, social revolution of gambling etcetera. The paper concludes that unholy practices among youths have constituted a nuisance in no small measure to the society. The paper however advocates that the government at all levels should up their game in training youths in the vocation that would make them engage and reduce the surge in such practices in the society.

1837

Historians often think of Russia before the 1860s in terms of conservative stasis, when the ‘gendarme of Europe’ secured order beyond the country’s borders and entrenched the autocratic system at home. This book offers a profoundly different vision of Russia under Nicholas I. Drawing on an extensive array of sources, it reveals that many of modern Russia’s most distinctive and outstanding features can be traced back to an inconspicuous but exceptional year. Russia became what it did, in no small measure, because of 1837. The catalogue of the year’s noteworthy occurrences extends from the realms of culture, religion, and ideas to those of empire, politics, and industry. Exploring these diverse issues and connecting seemingly divergent historical actors, Paul W. Werth reveals that the 1830s in Russia were a period of striking dynamism and consequence, and that 1837 was pivotal for the country’s entry into the modern age. From the romantic death of Russia’s greatest poet, Alexander Pushkin, in January to a colossal fire at the Winter Palace in December, Russia experienced much that was astonishing in 1837: the railway and provincial press appeared, Russian opera made its debut, Orthodoxy pushed westward, the first Romanov visited Siberia—and much else besides. The cumulative effect was profound. The country’s integration accelerated, and a Russian nation began to emerge, embodied in new institutions and practices, within the larger empire. The result was a quiet revolution, after which Russia would never be the same.

Introduction

To know Russia, you really have to understand 1837. That is the main message of this intriguing and unusual book. In ten chapters ranging from culture and ideas to empire and industry, it paints a rich and vivid portrait of the world’s largest country at a critical moment, when modern Russia acquired many of its most distinctive and outstanding features. Composers and poets, engineers and imperialists, philosophers and grand princes, peasants and camels, beards and potatoes—all make their appearance, and together they helped to forge the quiet revolution that changed Russia forever. Indeed, Russia is what it is today, in no small measure, because of 1837.

RANDOM REAL BRANCHED COVERINGS OF THE PROJECTIVE LINE

In this paper, we construct a natural probability measure on the space of real branched coverings from a real projective algebraic curve $(X,c_X)$ to the projective line $(\mathbb{C} \mathbb {P}^1,\textit{conj} )$ . We prove that the space of degree d real branched coverings having “many” real branched points (for example, more than $\sqrt {d}^{1+\alpha }$ , for any $\alpha>0$ ) has exponentially small measure. In particular, maximal real branched coverings – that is, real branched coverings such that all the branched points are real – are exponentially rare.