Mathematics

In contemporary mathematics, a Colombeau algebra of Colombeau generalized functions is an algebra of a certain kind containing the space of Schwartz distributions. While in classical distribution theory a general multiplication of distributions is not possible, Colombeau algebras provide a rigorous framework for this. Remark 1.1.1.Such a multiplication of distributions has been a long time mistakenly believed to be impossible because of Schwartz’ impossibility result, which basically states that there cannot be a differential algebra containing the space of distributions and (...) preserving the product of continuous functions. However, if one only wants to preserve the product of smooth functions instead such a construction becomes possible, as demonstrated first by J.F.Colombeau [1],[2]. As a mathematical tool, Colombeau algebras can be said to combine a treatment of singularities, differentiation and nonlinear operations in one framework, lifting the limitations of distribution theory. These algebras have found numerous applications in the fields of partial differential equations, geophysics, microlocal analysis and general relativity so far. (shrink)

In the paper it is demonstrated that Bell's theorem is unproveable.

CAT4 is proposed as a general method for representing information, enabling a powerful programming method for large-scale information systems. It enables generalised machine learning, software automation and novel AI capabilities. It is based on a special type of relation called CAT4, which is interpreted to provide a semantic representation. This is Part 2 of a five-part introduction. The focus here is on defining key mathematical properties of CAT2, identifying the topology and defining essential functions over a coordinate system. The analysis (...) is from first principles. This develops on from the axioms introduced in Part 1. The interpretation of fact networks is introduced in Part 3, and the full application to semantic theory comes in Part 4, where we introduce general functions, including the language interpretation or linguistic functions. In Part 5, we turn to software design considerations, to show how files, indexes, functions and screens can be defined to implement a CAT4 system efficiently. (shrink)

I have been working for a long time about basic laws which direct existence, and some mathematical problems which are waited for a solution. I can count myself lucky, that I could make some important inferences during this time, and I published them in a few papers partially as some propositions. This work aimed to explain and discuss these inferences all together by relating them one another by some extra additions, corrections and explanations being physical phenomena are prior. There are (...) many motivation instruments for exact physical inferences. (shrink)

The 'Science of Knowing: Mathematics' textbook is the first book to put forward and substantiate the thesis that the mathematical understanding of mathematics, as exemplified in F. William Lawvere's Functorial Semantics, constitutes the science of knowing i.e. cognitive science.

In this paper, I define and study an abstract algebraic structure, the dimensive algebra, which embodies the most general features of the algebra of dimensional physical quantities. I prove some elementary results about dimensive algebras and suggest some directions for future work.

The history of science is polarized by debates over Plato and Aristotle’s holism versus the atomism of Democritus and others. This includes the complementarity of continuous and discrete, one and the many, waves and particles, and analog or digital views of reality. The three-fold method of the Pythagorean paradigm of unity, duality, and harmony enables the calculation of fundamental physical constants required by the forces of nature in the formation of matter; thereby demonstrating Plato’s archetypal viewpoint.

This came into existence when one day (10 -12 years back), all of a sudden I draw a line and divided the line into same segment and draw one more line above the previous line and mark the points on the both lines and magically I got a triangle (while attach all the points with each other), with at point 1 no of points 1 at 2 no of points 3 and at 3 no of points 5. Now an idea (...) born into my mind while I should not expand it more and I got Amazing Result which is in front of All Mathematics Lovers. (shrink)

Motivation -/- God is great, whatever (Air, Water, Earth, Fire & Space) we have it is just because of a Power, which governs the whole universe and more than this Power, it has created human beings, and what we have got or did not get yet, trying to get. The Method, The Principle, The Knowledge or more by which we get or prove in front of World People, basically it is called Science, who GET it, are called Scientists, Mathematicians, Inventors (...) etc i.e. we all breath we all know but in ancient time we don’t know what we breath as the time passes away one man’s curiosity bring out the name of gas which we breathe i.e. Oxygen. There are lot examples or more yet to come. -/- In this regard my little contribution in the field of Mathematics, it starts from my early childhood I used to play with numbers. After a lot of times devoted on numbers one day while squaring 11, 12, 13 so on I found that there is an amazing symmetry of 2 & it’s great. (shrink)

A well-ordered society faces a crisis whenever a sufficient number of noncompliers enter into the political system. This has the potential to destabilize liberal democratic political order. This article provides a formal analysis of two competing solutions to the problem of political stability offered in the public reason liberalism literature—namely, using public reason or using convergence discourse to restore liberal democratic political order in the well-ordered society. The formal analyses offered in this article show that using public reason fails completely, (...) and using convergent discourse, although doing better, has its own critical limitations that have not been previously recognized properly. (shrink)

The goal of this paper is to explain the nature of philosophy as a distinct science with its own subject-matter. This is achieved through a comparative analysis of mathematical and philosophical knowledge that reveals a profound similarity between mathematics and philosophy as mutually complementary sciences exploring the field of abstract entities that can be comprehended only by purely a priori theoretical inquiry. By considering this complementarity, a general definition of philosophy can be obtained by dualizing the traditional Aristotelian definition of (...) mathematics as the “science of quantity”. Philosophy should thus be interpreted as an a priori science of the pure qualitative attributes of being. (shrink)

Całość rozpoczyna teoretyczny rozdział matematyczno-statystyczny. Jego istota i charakter jest odmienny, od pozostałych dziewięciu rozdziałów praktyczno-specjalistycznych. Prezentuje on aparat matematyczno-statystyczny niezbędny do zrozumienia treści kolejnych kierunkowych już rozdziałów monografii. Treści merytoryczne tego rozdziału nie są zaprezentowane w formie systematycznego wykładu, czy prezentacji, ale przedstawiają jedynie sygnalnie i syntetycznie pojęcia, definicje, twierdzenia oraz zasady i metody, które stanowią fundament ich zastosowań w naukach ekonomicznych, finansach oraz informatyce. Rozdziały: od drugiego do dziesiątego są kierunkowymi rozdziałami specjalistycznymi i prezentują różne kierunki praktycznych zastosowań (...) metod matematycznych i statystycznych, czyli ilościowych. Rozdziały: drugi i trzeci dotyczą zarządzania finansami. Przy czym pierwszy z nich dotyczy naliczania odsetek w banku od dyspozytorów kredytów i obligacji. Kolejny zaś traktuje o metodach oceny ekonomicznej efektywności projektów inwestycyjnych i produkcyjnych oraz zawiera analizę wrażliwości wybranych wskaźników finansowych na zmiany czynników je tworzących. Rozdział czwarty prezentuje podstawowe informacje i zasady korzystania z arkusza kalkulacyjnego na przykładzie programu MS Excel wraz z omówieniem wybranych funkcji finansowych. W rozdziale piątym omówione są wybrane narzędzia wspomagające przetwarzanie danych informacji, jakimi są systemy SAS wykorzystywane przede wszystkim w interakcjach gospodarczych oraz w procesie dydaktycznym na uczelniach wyższych. Modele zachowań konsumenta, idea aproksymacji oraz wybrane mikroekonomiczne funkcje popytu zostały – wraz z przykładami – omówione w rozdziale szóstym. W rozdziale siódmym czytelnik znajdzie opis działań podejmowanych przez firmę w celu optymalizacji jej finansowego i gospodarczego funkcjonowania w okresie niepewności rynkowej na przykładzie pandemii COVID 19 i konkretnego przdsiębiorstwa. Dwa kolejne rozdziały: ósmy i dziewiąty są ze sobą ściśle zintegrowane. Oba one dotyczą niedookreślonych układów równań liniowych. Pierwszy z nich – o charakterze teoretycznym – poświęcony jest rozważaniom dotyczącym wykorzystywaniu rachunku macierzowego do rozwiązywania niedookreślonych układów równań liniowych. Kolejny zaś przedstawia praktyczne zastosowanie teoretycznych kwestii rozdziału poprzedniego do określenia wyceny wartości rynkowej nieruchomości. Monografię kończy rozdział dziesiąty dotyczący wybranych narzędzi wspierających proces sprzedaży usług finansowych wraz z prezentacją prognoz służących zminimalizowaniu ryzyka i błędów w procesie planowania sprzedaży w organizacji. W większości rozdziałów zawarte są rozwiązane przykładowo zadania z wyczerpującym komentarzem objaśniającym. Niniejsza monografia składa się z dziesięciu rozdziałów, jednak – zdaniem autorów – tematyka zastosowania metod ilościowych nie została w niej wyczerpana. Toteż planowana jest kolejna część tej publikacji zawierająca kontynuację podjętego i aktualnie rozpoczętego tematu. (shrink)

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest in (...) exploring the foundations of multialgebras applied to the study of logic systems. -/- It is well known from universal algebra that, for every signature Sigma, there exist algebras over Sigma which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of Sigma-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms (or propositional formulas, in the context of logic). Equivalently, the forgetful functor, from the category of Sigma-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor U, from the category of Sigma-multialgebras to Set, does not have a left adjoint. -/- In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices (which selects how a homomorphism approaches indeterminacies), there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that U does not have a left adjoint. (shrink)

La siguiente ponencia-taller tiene por finalidad explicar cómo podría aplicarse el Método de George Polya para resolver problemas (matemáticos) en el contexto de la Lógica Matemática, especialmente en la lógica Matemática elemental (la lógica de primer orden con identidad). Es una propuesta pedagógica experimental (además de las ya existentes) que tal vez pueda ser útil para la enseñanza de la lógica matemática en ciencias o en humanidades. Dicha ponencia se presentó (vía web) con motivo de la celebración del Día Mundial (...) de Lógica 2022 en dos ocasiones: En la Universidad Central de Venezuela (Venezuela) y en la Universidad Mayor de San Andrés (Logic & Analytics Group - La Paz y La Sociedad Científica de Filosofía de la UMSA, Bolivia). Es un proyecto pedagógico en construcción. (shrink)

The New Collection is a peer-reviewed interdisciplinary academic journal published by the Middle Common Room of New College, University of Oxford.

3rd ed, 2021. A circumscription of the classical theory of computation building up from the Chomsky hierarchy. With the usual topics in formal language and automata theory.

Book Review Luck, logic, and white lies: the mathematics of games, second edition by Jörg Bewersdorff, New York, Taylor & Francis, CRC Press, 2021, 568 pp., GBP 42.99 (paperback), ISBN 9780367548414, Number of chapters 51.

Book Review Mathematics of casino carnival games by Mark Bollman, New York: CRC Press 2021, 318 pp., GBP 48.99 (hardback), ISBN 9780367348656.

This is the first in a series of math books intended for those who have completed at least secondary school mathematics and have acquired 1) certain calculating skills, and 2) dissatisfaction with their understanding of what they are calculating. We will start our journey with numbers. Numbers are the oldest mathematical idea, but still also the most important one. We will go through the basics of numbers in a way that will give you the confidence to really understand numbers and (...) really know how to apply them. You will also learn all the essential elements of mathematics through the example of the world of numbers. The example of numbers will be used to illustrate what mathematical objects are and how they are applied, and what mathematical tools we use in their description and application. (shrink)

For an arbitrary forcing class Γ, the Γ-fragment of Todorčević’s strong reflection principle SRPis isolated in such a way that the forcing axiom for Γ implies the Γ-fragment of SRP, the sta...

We study the notion of ????-MAD families where ???? is a Borel ideal on ω. We show that if ???? is any finite or countably iterated Fubini product of the ideal of finite sets Fin, then there are no analytic...

We consider existentially closed fields with several orderings, valuations, and p-valuations. We show that these structures are NTP2 of finite burden, but usually have the independence property. Mo...

‘Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.’ Along this line, in The Open World, Hermann Weyl contrasted the desire to make the infinite accessible through finite processes, which underlies any theoretical investigation of reality, with the intuitive feeling for the infinite ‘peculiar to the Orient,’ which remains ‘indifferent to the concrete manifold of reality.’ But a critical analysis may acknowledge a valuable dialectical opposition. Struggling to spell (...) out the infinity of real numbers mathematicians come to see the active role of emptiness. Pondering over the essence of self-awareness, the Japanese philosopher Nishida Kitarō comes to see the ‘place’ where it abides as absolute nothingness. Thus, the two ways of seeing coalesce into a perspective in which infinity and nothingness mirror each other. (shrink)

The aim of this volume is to open up new perspectives and to raise new research questions about a unified approach to truth, modalities, and propositional attitudes. The volume's essays are grouped thematically around different research questions. The first theme concerns the tension between the theoretical role of the truth predicate in semantics and its expressive function in language. The second theme of the volume concerns the interaction of truth with modal and doxastic notions. The third theme covers higher-order solutions (...) to the semantic and modal paradoxes, providing an alternative to first-order solutions embraced in the first two themes. This book will be of interest to researchers working in epistemology, logic, philosophy of logic, philosophy of language, philosophy of mathematics, and semantics. (shrink)

Rosłanowski and Shelah [Small-large subgroups of the reals, Math. Slov. 68 473–484] asked whether every locally compact non-discrete group has a null but non-meager subgroup, and converse...

We show that Weak Vopěnka’s Principle, which is the statement that the opposite category of ordinals cannot be fully embedded into the category of graphs, is equivalent to the large cardinal princi...

Hermann Weyl was one of the greatest mathematicians of the 20th century, with contributions to many branches of mathematics and physics. In 1918 he wrote a famous book, “Das Kontinuum”, on the foundations of mathematics. In that book he described mathematical analysis as a ‘house built on sand’, and tried to ‘replace this shifting foundation with pillars of enduring strength’. In this paper we reexamine and explain the philosophical and mathematical ideas that underly Weyl’s system in “Das Kontinuum”, and show (...) that they are still useful and relevant. We propose a precise formalization of that system, which is the first to be completely faithful to what is written in the book. Finally, we suggest that a certain set-theoretical modern system reflects better Weyl’s ideas than previous attempts (most notably by Feferman) of achieving this goal. (shrink)

In this dissertation we explore projective Fraïssé theory and its applications, as well as limitations, to the study of compact metrizable spaces. The goal of projective Fraïssé theory is to approximate spaces via classes of finite structures and glean topological or dynamical properties of a space by relating them to combinatorial features of the associated class of structures. Using the framework of compact metrixable structures, we establish general results which expand and help contextualize previous works in the field. Many proofs (...) in the domain of projective Fraïssé theory are carried out in a context dependent fashion and have thus far eluded clean generalizations. A reason is to be found in the lack of a clear understanding of which spaces are amenable to be studied via projective Fraïssé limits. We give both positive and negative results in this direction. We isolate a combinatorial condition which entails a correspondence between finite structures and regular quasi-partitions of compact metrizable spaces. This correspondence greatly aids the combinatorial-toplogical translation. We apply this machinery to study a class of one-dimensional compact metrizable spaces, which we call smooth fences. To this end, we isolate a class of finite structures—finite partial orders whose Hasse diagram is a forest—whose projective Fraïssé limit approximates a distinctive smooth fence with remarkable properties. We call it the Fraïssé fence and characterize it topologically by carefully exploiting the bridge between the combinatorial and topological worlds. We explore homogeneity and universality features of the Fraïssé fence and the properties of its spaces and endpoints, and provide some results on the dynamics of its group of homeomorphisms. The dissertation is partially based on [1, 2]. (shrink)

The number of bricks in a ziggurat is a sum of consecutive squares.

Sticking to elementary mathematics, this text is a short introduction to understanding historical and comparative counting systems. It gives a brief historical and contextual overview, along with showing how to read and count in a number of ancient systems including Egyptian, Babylonian, Mayan, Roman, Hebrew, Intuit, binary, Quipu and abacus.

This paper sought to investigate the fundamental differences in mathematics education through a comparison of curriculum of 2 countries—Singapore and Canada (as represented by Ontario)—in order to discover what the Ontario education system may learn from Singapore in terms of mathematics education. Mathematics curriculum were collected for Grades 1 to 8 for Ontario, and the equivalent in Singapore. The 2 curriculums were textually analyzed based on both the original and the revised Bloom’s taxonomy to expose their foci. The difference in (...) focus was then compared and discussed to find the best ways to improve the Ontario mathematics curriculum. With one of the best education systems in North America, the Ontario mathematics curriculum would only need to refocus its attention towards a more balanced approach, with greater focus on understanding through practices. Ontario would benefit greatly from a deeper research into the Singaporean math curriculum. (shrink)

This paper reconstructs Steel’s multiverse project in his ‘Gödel’s program’ (Steel [2014]), first by comparing it to those of Hamkins [2012] and Woodin [2011], then by detailed analysis what’s presented in Steel’s brief text. In particular, we reconstruct his notion of a ‘natural’ theory, describe his multiverse axioms and his translation function, and assess the resulting status of the Continuum Hypothesis. In the end, we reconceptualize the defect that Steel thinks CH might suffer from and isolate what it would take (...) to remove it while working within his framework. As our goal is to present as coherent and compelling a philosophical and mathematical story as we can, we allow ourselves to augment Steel’s story in places (e.g., in the treatment of Amalgamation) and to depart from it in others (e.g., the removal of ‘meaning’ from the account). The relevant mathematics is laid out in the appendices. (shrink)

Answering one of the main questions of [S.-D. Friedman, T. Hyttinen and V. Kulikov, Generalized descriptive set theory and classification theory, Mem. Amer. Math. Soc. 230 80, Chap. 7]...

In recent decades, the development of sciences and technologies had a significant impact in society. This impact has been object of analysis from several standpoints, i.e., scientific, communication, historical and anthropological. Consequently, serious changes were required by the society. One of these has been the emerging relationship science in society and its foundations of applied sciences. A related foundational challenging is the educational process, which was and still is an unlimited challenge for teachers and professors: i.e., levels of understanding, curricula, (...) activing critical engagement, transfer knowledge—and—skills, management, classroom and subsequently pre-service teachers need special teacher education. Taking into account Joule’s bicentenary commemoration in physics and Nature of Science teaching this paper introduces to a level of inquiring within historical and NoS approaches in the pre-service teachers, typically science, technology, engineering and mathematics. In particular, history and historiography of Joule’s physics are dealt with. (shrink)

Abstract: The dynamic viscoelastic properties of Polyvinylacetate with molecular weight 83000g/mol (PVA 83K ) were determined by using a Rheometer operated in the dynamic mode and 8 mm parallel plate over a wide range of temperature as a function of frequency. The measurements were performed successively in the parallel plate geometry using 8 mm plate instead of 25 mm. The glass plateau regime is clearly observed because we could measure PVA 83K sample successively under its glass temperature. The rheological properties (...) of polydisperse PVA 83K were completely studied. The storage and loss compliance and the relaxation spectrum are evaluated. (shrink)

We propose a novel type of low distortion radial embedding which focuses on one specific entity and its closest neighbors. Our embedding preserves near-exact distances to the focus entity and aims to minimize distortion between the other entities. We present an interactive exploration tool SolarView which places the focus entity at the center of a "solar system" and embeds its neighbors guided by concentric circles. SolarView provides an implementation of our novel embedding and several state-of-the-art dimensionality reduction and embedding techniques, (...) which we adapted to our setting in various ways. We experimentally evaluated our embedding and compared it to these state-of-the-art techniques. The results show that our embedding competes with these techniques and achieves low distortion in practice. Our method performs particularly well when the visualization, and hence the embedding, adheres to the solar system design principle of our application. Nonetheless - as with all dimensionality reduction techniques - the distortion may be high. We leverage interaction techniques to give clear visual cues that allow users to accurately judge distortion. We illustrate the use of SolarView by exploring the high-dimensional metric space of bibliographic entity similarities. (shrink)

In his constructive and well-informed commentary, Andrei Khrennikov acknowledges a privileged status of classical probability theory with respect to statistical analysis. He also sees advantages offered by the Contextuality-by-Default theory, notably, that it “demystifies quantum mechanics by highlighting the role of contextuality,” and that it can detect and measure contextuality in inconsistently connected systems. He argues, however, that classical probability theory may have difficulties in describing empirical phenomena if they are described entirely in terms of observable events. We disagree: contexts (...) in which random variables are recorded are as observable as the variables’ values. Khrennikov also argues that the Contextuality-by-Default theory suffers the problem of non-uniqueness of couplings. We disagree that this is a problem: couplings are all possible ways of imposing counterfactual joint distributions on random variables that de facto are not jointly distributed. The uniqueness of modeling experiments by means of quantum formalisms brought up by Khrennikov is achieved for the price of additional, substantive assumptions. This is consistent with our view of quantum theory as a special-purpose generator of classical probabilities. Khrennikov raises the issue of “mental signaling,” by which he means inconsistent connectedness in behavioral systems. Our position is that it is as inherent to behavioral systems as their stochasticity. (shrink)

Abstract: The main purpose of this paper is to find Artin's characters table of the group (Q2n×D3)when n=p_1.p_2….p_n,and p_1,p_2,…,p_n are primes number, which is denoted by Ar(Q2n×D3) where Q2m is denoted to Quaternion group and D3 is the Dihedral group of order 6 .

Annotation: This article shows the main problems and financial decadences of universities. And also, some effective solutions are provided.

Abstract: The research findings summarized in the paper include data on the radioecological conditions of the canal located in Jambay region of Uzbekistan. The focus of the study was on the determination of accumulation of radionuclides in molluscs depending on the content of radionuclides in aqueous sediments and water by the help of the scintillation gamma spectrometry method.

This paper explores whether there is any relation between mathematical proofs that specify the grounds of the theorem being proved and mathematical proofs that explain why the theorem obtains. The paper argues that a mathematical fact’s grounds do not, simply by virtue of grounding it, thereby explain why that fact obtains. It argues that oftentimes, a proof specifying a mathematical fact’s grounds fails to explain why that fact obtains whereas any explanation of the fact does not specify its ground. The (...) paper offers several examples from mathematical practice to illustrate these points. These examples suggest several reasons why explaining and grounding tend to come apart, including that explanatory proofs need not exhibit purity, tend not to be brute force, and often unify separate cases by identifying common reasons behind them even when those cases have distinct grounds. The paper sketches an account of what makes a proof explanatory and uses that account to defend the morals drawn from the examples already given. (shrink)

Abstract: The main aim of this work is to introduce acceleration methods called a hyperbolic acceleration methods which are of series of numerated methods. In general, these methods named as AL-Tememe’s acceleration methods of first kind discovered by (Ali Hassan Mohammed). These are very beneficial to acceleration the numerical results for definite integrations with continuous integrands which are of 2nd order main error, with respect to the accuracy and the number of the used subintervals and the fasting obtaining results. Especially, (...) for acceleration the results which are obviously obtained by trapezoidal and midpoint methods. Moreover, these methods could be enhancing the results of the ordinary differential equations numerically which are of 2nd order main error. (shrink)

Abstract: The study sought to establish Tanzanian`s financial inclusion level, its determinant and whether the country`s financial inclusion levels have influence on the access to basic income, food, heath, employment and education service. Among the major determinants of financial inclusion are income, financial literacy and the geographical presence of financial institutions. With regard to the link between financial inclusion and livelihood indicators, it is found that greater financial inclusion promotes access to basic income, food, health and education for households for (...) the country, with differential effect of inclusion becoming wider when banking instead of total inclusion considered. The purpose of this paper is to assess the contribution of financial inclusion to the rural livelihood households. This has been analyzed with the theoretical background on financial access and livelihood, and by analyzing the primary data collected from five wards, Named; Pawaga, Kalenga, Ismani, Nduli and Kibebe in Iringa district. The results show that, there is a significant positive relationship between Financial Inclusion and the Rural Livelihood households in Tanzania. Access to, availing of formal banking services pave the way to positive changes in the rural livelihood status of households. With regard to rural households in Tanzania the country needs aggressive financial inclusion strategies to reduce access vulnerabilities and poverty. (shrink)

Abstract: This article is dedicated to prevent the challenges that are occurring in the sphere of education. And also, some effective solutions are provided.

Abstract: Efficient law enforcement depends on the quality and outlook of the institutions and personnel saddled with this responsibility. There are several agencies in Nigeria created for the purpose of law enforcement. Despite the multiplicity of these agencies, however, the country is still far from being a reflection of a society where security and orderliness are being maintained. The essence of this paper is to explore the law-enforcement terrain of the country with a view to ascertaining the state of affairs (...) vis-a-vis the existing law enforcement agencies, their functional relevance, and general impact on the society in terms of maintenance of law and order. Findings reveal that the state of security and maintenance of law and order is still abysmally low in spite of the fact that there exist several law enforcement agencies within the country. The main recommendation is that instead of placing emphasis on creating more and more law enforcement agencies, which sometimes amount to duplication of functions, efforts should be made to reorganize, streamline and strengthen the existing institutions. (shrink)

Abstract: When in 1846, Euhemerus, a Greek philosopher propounded a theory that all Greek gods were once men who were deified in their life time and worshipped as a god after their death. The Greeks never take the assertion kindly. Euphemerus was accused of sacrilege. Later findings by anthropologists proved Euphemerus correct. Heroes and deification of heroes are found in different parts of the world. The writer is aware that deification of a hero is a symbiotic venture. This means that (...) the hero might have worked so hard in solving the people’s problems, the people in return deifies him. In this write up, the writer is looking for the significance of this deification. The writer through oral interviews, visit to library and reading relevant books on the topic is able to arrive at the answer as stated in the write up. (shrink)