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The Chunochi, Dhamman, Sounchal, Sarsawah and Malhar areas lie along the eastern limb of Hazara-Kashmir Syntaxis. This is an active fold-and-thrust belt in the sub Himalayas of Pakistan. The Early Miocene to Recent sedimentary rock sequence is exposed in the area. The stratigraphic sequence of the study area includes the Early Miocene Murree formation, Early to Middle Miocene Kamlial formation, Middle to Late Miocene Chinji formation, Late Miocene Nagri formation, Late Miocene Dhok Pathan formation, Pliocene Soan formation and Pliestocene Mirpur formation. The Baluch syncline, Panakah anticline and Nainsukh anticline are the major folds. These are open to isoclinal in nature. The Dhamman fault, Tangai fault, Riasi fault, Gali Samiar fault, Godri Badshah- Kotli fault, Chak Nasru fault, Nuhi Sarota fault and Hill Kalan fault are the major faults. The Riasi fault, Godri Badshah-Kotli fault and Chak Nasru fault are active faults. The sedimentary structures observed in the area are cross bedding, load cast and rip ups. The facing of the stratigraphic units is marked on the basis of these structures....

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This analysis takes a didactic approach. It attempts to demystify the aura surrounding operational design by presenting a theoretical framework for comprehending its fundamental precepts. The goals of this analysis are threefold: provide a methodological example for understanding and applying design, show how design enhances decision making and risk analysis, and investigate the major differences between design in major combat operations and design in counterinsurgency (COIN)....

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1 The Process of Operational Design 1 2 Developing an Operational Approach 21 3 Methodology for Understanding and Employing Operational Design 31 4 Establishing the Link between Operational Design and Decision Analysis 59 5 Operational Design and Counterinsurgency 83...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear Fractional Programming Abstract: This paper is concerned with the study of duality conditions to convex-concave generalized multiobjective fuzzy nonlinear fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn-Tucker Saddle and Stationary points are characterized. In addition, some important theorems related to the Kuhn-Tucker problem for saddle and stationary points are established. Moreover, a general dual problem is formulated together with weak; strong and converse duality theorems are proved. Key Words: Generalized multiobjective fractional programming; Disjunctive programming; Convexity; Concavity; fuzzy parameters Duality. ...

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Contents Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear Fractional Programming BY E.E.AMMAR . . . . . . . . . . . . . . . . . . . . 01 Surface Embeddability of Graphs via Joint Trees BY YANPEI LIU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 Plick Graphs with Crossing Number 1 BY B.BASAVANAGOUD AND V.R.KULLI . . . . . . . . . . . . . . . . . . . . . . 21 Effects of Foldings on Free Product of Fundamental Groups BY M.El-GHOUL, A. E.El-AHMADY, H.RAFAT AND M.ABU-SALEEM. . . . . . . 29 Absolutely Harmonious Labeling of Graphs BY M.SEENIVASAN AND A.LOURDUSAMY . . . . . . . . . . . . . . . . . . . . 40 The Toroidal Crossing Number of K4n BY SHENGXIANG LV, TANG LING AND YUANGQIU HUANG . . . . . . . . . . 52 On Pathos Semitotal and Total Block Graph of a Tree BY MUDDEBIHAL M. H. AND SYED BABAJAN. . . . . . . . . . . . . . . . . . 64 Varieties of Groupoids and Quasigroups Generated by Linear-Bivariate Polynomials Over Ring Zn BY E.ILOJIDE, T.G.JAIYEOLA AND O.O.OWOJORI . . . . . 79 New Characterizations for Bertrand Curves in Minkowski 3-Space BY BAHADDIN BUKCU, MURAT K...

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An introduction to moral, political and economic philosophy. Twelve philosophers in each category are featured, their basic theories are examined and provide the basis for discussion....

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PARTI An Introduction to Clearer Thinking Chapter 1 Attitudes: How They Affect Our Thinking 3 Chapter 2 Classifying Viewpoints: Conservative and Liberal 12 Chapter 3 Epistemology and Logic 20 Chapter 4 Fallacies: Errors o f L anguage and Logic 32 PART 2 Moral Philosophy: Ideas of Good and Evil, Right and Wrong Chapter 5 Moral Philosophy: A Brief Introduction 47 Chapter 6 Plato and Aristotle: Idealism and Realism 55 Chapter 7 Epicurus and Epictetus: Pleasure and Apathy 65 Chapter 8 Aquinas and Descartes: Faith and Reason 72 Chapter 9 Hume, Bentham and Mill: Subjectivism and Utilitarianism 82 Chapter 10 Kant and Schopenhauer: Idealism and Pessimism 90 Chapter 11 Nietzsche and Sartre: Naturalism and Existentialism 99 PART 3 Political Theory: The Relationship of Man and the State Chapter 12 Introduction to Political Theory 111 Chapter 13 Law: Understanding the Rule o f Reason 119 Chapter 14 Problems o f Government: Five Great Issues 127 Chapter 15 Plato and Aristotle: Utopia and Polity 138 Chapter 16 Augustine and Aquinas: Platonist and Aristotelian 146 Chapter 17 Machiavelli and Hobbes: The Prince ...

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In The 2nd Conference on Combinatorics and Graph Theory of China (Aug. 16-19, 2006, Tianjing), I formally presented a combinatorial conjecture on mathematical sciences (abbreviated to CC Conjecture), i.e., a mathematical science can be reconstructed from or made by combinatorialization, implicated in the foreword of Chapter 5 of my book Automorphism groups of Maps, Surfaces and Smarandache Geometries (USA, 2005). This conjecture is essentially a philosophic notion for developing mathematical sciences of 21st century, which means that we can combine different fields into a union one and then determines its behavior quantitatively. It is this notion that urges me to research mathematics and physics by combinatorics, i.e., mathematical combinatorics beginning in 2004 when I was a post-doctor of Chinese Academy of Mathematics and System Science. It finally brought about me one self-contained book, the first edition of this book, published by InfoQuest Publisher in 2009. This edition is a revisited edition, also includes the development of a few topics discussed in the first edition....

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1.5 ENUMERATION TECHNIQUES 1.5.1 Enumeration Principle. The enumeration problem on a finite set is to count and find closed formula for elements in this set. A fundamental principle for solving this problem in general is on account of the enumeration principle: For finite sets X and Y , the equality |X| = |Y | holds if and only if there is a bijection f : X → Y . Certainly, if the set Y can be easily countable, then we can find a closed formula for elements in X....

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Contents Preface to the Second Edition . . . . . . . . . . . . . . . . . . . i Chapter 1. Combinatorial Principle with Graphs . . . . . . . . . . 1 1.1 Multi-sets with operations. . . . . . . . . . . . . . . . . . . . .2 1.1.1 Set . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Boolean algebra . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.4 Multi-Set . . . . . . . . . . . . . . . . . . . . . . . . . .8 1.2 Multi-posets . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.1 Partially ordered set . . . . . . . . . . . . . . . . . . . . .11 1.2.2 Multi-Poset . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Countable sets . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.1 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.2 Countable set . . . . . . . . . . . . . . . . . . . . 16 1.4 Graphs . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.1 Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . .18 1.4.2 Subgraph . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4.3 Labeled graph. . . . . . ...

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This is Mill’s first work on economics. It foreshadows his _Political Economy_ which was the standard Anglo-American Economics textbook of the late 19th and early 20th centuries. Mill’s economic theory moved from free market capitalism, to government intervention within the precepts of Utilitarianism, and finally to Socialism. [Summary written by the reader]...

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Philosophy, Economics/Political Economy