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A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its function and role in mathematics are widely accepted by mathematicians today. On the last century, many works are concentrated on the combinatorial properties of maps. The main trend is the enumeration of maps, particularly the rooted maps, pioneered by W. Tutte, and today, this kind of papers are still appeared on the journals frequently today. All of those is surveyed in Liu’s book [33]. To determine the embedding of a graph on surfaces, including coloring a map on surfaces is another trend in map theory. Its object is combinatorialization of surfaces, see Gross and Tucker [22], Mohar and Thomassen [53] and White [70], especially the [53] for detail. The construction of regular maps on surfaces, related maps with groups and geometry is a glimmer of the map theory with other mathematics....

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Thrilling narratives of voyages, discoveries, adventures, battles, darings and sufferings of the heroic characters, bold explorers and dauntless spirits who have made ocean history and established christian supremacy over the most savage lands of the earth. Reciting astonishing incidents and perilous undertakings among wild beasts and savage people in heroic efforts for a reclamation of all lands to civilization, and recording a description of the riot of murder, pillage and inhumanity which characterized the pirates, marooners and buccaneers who ravaged the spanish main and for centuries bid defiance to the armed fleets of all nations....

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The Rolling Stone of History. -- Surprising revelations -- Ancient Cities that are now no more -- Effects of Cataclysms upon the human race -- The rise and fall of nations -- Cave dwellers who became masters of the world -- The first boats -- Building a strong nation -- The earliest navigators -- Evolution of the ship -- Discoveries of the ancients -- Islands of the long ago -- Changes in the earth's surface -- Commerce of Troy with India -- Expeditions sent out by Menelaus and Neco -- The circumnavigation of Africa by the ancients -- Solomon's navy -- Discovery of the West Indies by Carthaginians -- Hamilcar's voyage to the North seas -- Wonderful lands and fountains -- Astounding adventures of Hanuo -- Weird sights on the shores of ancient Africa -- Witches and Snake charmers -- Among the mermaids -- Voyage of Pytheas, the philosopher -- Tears of sorrowing sea-birds -- Discovery of a new world -- A wondrously profitable commerce -- A northwest passage -- The Romans pass to China by a north route -- Destruction of the Roman empire....

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Twenty years ago when Margaret Titcomb was finishing her manuscript for this book there was little concern that the oceans of the earth might be endangered. Without doubt contamination of the seas was occurring, but there was no real public awarenessno sense of threat. A deleterious mercury content had not yet been detected in the great billfish and tunas. There were fewer oil despoliations, and the dumping of chemicals and radioactive wastes had not yet reached a level which would, in the next two decades, cause great submarine areas to be laid waste. Nor had commercial fisheries yet developed their omnivorous technical expertise to efficiency levels which, unless curbed, could wipe out whole species. There was another difference. Then, there were “a few Hawaiian fishermen still living who were trained in the Hawaiian knowledge” (p. 54), and who could supplement the prodigious fund of information of Mary Kawena Pukui, with whose collaboration this book was written. Now, as the Hawaiian fishermen pass from the scene, there goes with them much of the ancient lore of the sea. There is today an encouraging awareness on the part of sc...

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FISH, including shellfish, were the main protein-giving elements of the Hawaiian diet. Pig, dog, chicken and wild birds furnished some additional proteins but the comparatively small supply marked them more for the chiefs than the commoners use. Daily life was one of fishing and cultivating the plantations. Fishing required a search of the sea, from the areas within the reefs to the sea scarcely within sight of land. By salting, drying, impounding, the supply was made somewhat independent of weather conditions. Care was taken to avoid waste....

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The following collection of archival and oral historical-consultation records pertaining to Waikamoi Preserve and the greater watershed of the Haleakala mountain lands on the island of Maui, was compiled by Kumu Pono Associates LLC, at the request of The Nature Conservancy-Hawaii. This study provides The Nature Conservancy and its partners in management of the Waikamoi Preserve, with a cultural assessment of the Waikamoi Preserve, as required by State review laws governing The Nature Conservancys stewardship of the preserves natural resources. The primary documentation (both archival and oral historical), was collected by the authors over the period of six years, and provides readers with access to a rich and diverse collection of cultural- historical narratives from the island of Maui. The study focuses on lands situated on the eastern slopes of Haleakala, a region traditionally called Maui Hikina, with particular emphasis on those lands which make up and adjoin “Waikamoi Preserve.” These lands represent some of the most significant native forest resources remaining in the Hawaiian Islands, and are part of a unique cultural landsc...

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1848, Kamehameha III granted fee-simple interest of Kalialinui to a chiefly steward, Kamaikaaloa (Kamaikaaloa), who held the land through the remainder of his lifetime, and subsequently conveyed it to his heirs. Kalalawalu—daughter of Kamaikaaloa and Kealohaaukai—and her husband, Douglas Panee, sold the land of Kalialinui to Haleakala Ranch in 1888. Most of Kalialinui, including the land that became the Waikamoi Preserve, has been held by Haleakala Ranch since that time. In the later 1800s and early 1900s, cowboys of the Haleakala Ranch traveled from the lower Kula lands to the mountain lands of Haleakala via the “Aina Hou Trail,” passing Halemau (Halemauu) and Leleiwi, and through Kalialinui, towards the Koolau Gap lands. The Aina Hou Trail passes along the contour at about the 6300-6400 foot elevation to a place known as the “Aina Hou Bowl.” The Aina Hou Bowl is generally situated between the 6300 to 5600 foot elevation, and noted for a spring which was tapped to feed a historic ranch trough. Lands in this area were used as mountain pasturage by the ranch. The 5,230-acre Waikamoi Preserve was established in 1983 through...

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Na Kamalei-K. E. E. P. – Koolauloa Early Education Program is a Native Hawaiian nonprofit organization that includes Ho‘ala Na Pua, a parent-child interaction and family education program that services the families of Ko‘olauloa, O‘ahu, Hawai‘i. The Houlu Hou Project: Stories Told By Us is a project of Na Kamalei that is funded in part by the Administration for Native Americans. The project goal is to provide families with services and opportunities that foster culturally appropriate and healthy development of a balanced child. The oral legacy within our community strengthens our families and produces stories that bring meaning to our lives and that help identify who we are and where we are from. Our resource partners are Ko‘olauloa community organizations that support the advancement of Native Hawaiian children and their families through the creation of children’s books. Stories of history, geography, language and culture are born and shared in the context of the community. Kupuna (elders) now encourage the sharing of these stories so that future generations will benefit from this legacy. This serie...

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R. S. Kuykendall spent four decades of his life writing the history of Hawaii. He came to the Islands in 1922 as executive secretary of the newly formed Historical Commission of the Territory of Hawaii. The Commission planned, among other projects, to publish a large-scale history: a general narrative of a thousand pages or more, sufficiently documented to ensure "authoritativeness. " Working to this mandate, Kuykendall brought to bear on his task everything he could muster in the way of personal and professional resources. He was well suited to the sort of pioneer labor that faced him. He had a great appetite and aptitude for spadework of an archival kind, locating, acquiring, and organizing collections of documents. His use of materials was marked by a quite outstanding scrupulosity with regard to matters of fact. Whatever industriousness and commonsensical perceptiveness could wring from often inadequate, often intransigent sources, Kuykendall set himself to extract. Though the Historical Commission itself did not survive the Great Depression, Kuykendall, continuing his researches as a faculty member of the University o...

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This volume is one of the fruits of a project undertaken more than a dozen years ago by the Historical Commission of the Territory of Hawaii and carried on since 1932 by the University of Hawaii. The project called for the preparation of a comprehensive general history of Hawaii based upon a thorough study of original sources. The first phase of the undertaking was to discover the source material not already available in Honolulu and to obtain copies of as much of it as possible, particularly of documents which shed new light on the history of the islands. For this purpose, extensive research has been carried on in the national archives of the United States, Great Britain, and France, and minor investigations have been made in the archives of Belgium and Mexico and in a number of libraries and collections in the United States. Many thousand pages of transcripts have been obtained from these places, supplementing at many points and in many important respects the materials previously available in Honolulu. Independently of this project, a large quantity of new material has been added to collections in the Territory, and there has...

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Preface. xi -- List of Abbreviations. xiii -- Introduction: A Glimpse of Ancient Hawaii. 1 -- Coming of the Foreigners. 12 -- Kamehameha and the Founding of the Kingdom. 29 -- 1819. 61 -- Kamehameha II. 71 -- Early Commercial Development. 82 -- New Religion and New Learning. 100 -- The Early Years of the Reign of Kamehameha III: Regency of Kaahumanu. 117 -- The Troubled Thirties. 133 -- The Birth of Constitutional Government. 153 -- Industry, Agriculture, Manufactures. 170 -- The Recognition of Hawaii's Independence. 185 -- The Paulet Episode. 206 -- Governmental Reorganization in the Midst of Difficulties. 227 -- The Land Revolution. 269 -- Commercial and Agricultural Progress, 1830-1854. 299 -- Religious and Educational Development, 1840-1854. 335 -- The Struggle for Equitable Treaties. 368 -- The Shadow of Destiny. 383 -- On the Date of the Birth of Kamehameha. 429 -- On the Regency, 1823-1833. 430 -- On the Origin of the Hawaiian Sandalwood Trade. 434 -- On the Debt Settlement of 1826. 434 -- Index. 437 --...

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In this latest book, John Clark, author of the highly regarded "Beaches of Hawaii" series, gives us the many captivating stories behind the hundreds of Hawaii place names associated with the ocean—the names of shores, beaches, and other sites where people fish, swim, dive, surf, and paddle. Significant features and landmarks on or near shores, such as fishponds, monuments, shrines, reefs, and small islands, are also included. The names of surfing sites are the most numerous and among the most colorful: from the purely descriptive (Black Rock, Blue Hole) to the humorous (No Can Tell, Pray for Sex). Clark began gathering information for the "Beaches" series in 1972, and during the years that followed interviewed hundreds of informants, many of them native Hawaiians, and consulted dozens of Hawaiian reference books, newspapers, and maps. A significant amount of the oral history he collected was unrecorded and remained only in his notebooks and memory. Hawaii Place Names: Shores, Beaches, and Surf Sites is the final product of those years of research, and like its popular predecessors, it benefits substantially from Clark's ...

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In 1966 the University of Hawaii Press published the first edition of Place Names of Hawaii. Written by Mary Kawena Pukui and Samuel H. Elbert, it contained 1,125 entries, all of which were place names in the Hawaiian language. In 1974 the press published the second edition by Pukui, Elbert, and Esther T. Mookini. It contained some four thousand entries, and this time it included place names in English and other languages. This edition, in the words of the authors, provided "a glossary of important place names in the State, including names of valleys, streams, mountains, land sections, surfing areas, towns, villages, and Honolulu streets and buildings." During the years that have followed its publication, the second edition of Place Names of Hawaii has become a standard reference in the literature of Hawaii....

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The cartographic history of Hawaii began with the arrival of Captain James Cook, the famous explorer and chartmaker, in 1778. Between then and the mid-19th century, visitors to HawaiI produced a rich assortment of charts and maps depicting the shores, harbors, towns, and volcanoes of the various islands. This volume traces the story of the mapping of HawaiI during the pivotal years in which the indigenous society was radically transformed by the peoples and ideas imported from the West. Foreigners introduced the concept of mapmaking to HawaiI, and they made maps of the islands to satisfy the needs of maritime commerce, missionary endeavors, and scientific investigations. Nearly seventy maps, complemented by more than twenty views, portraits, and illustrations, are reproduced here. Included are many charts and harbor plans produced by such famous figures of naval history as James Cook, William Bligh, George Vancouver, Otto von Kotzebue, Urey Lisiansky, Jean Francois de la Pérouse, Louis Duperrey, and Charles Wilkes. These richly reproduced charts document the early geography of Honolulu, Lahaina, Hilo, and Kailua—the most...

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The Early Mapping of Hawaii is an overview of the history of the mapping of Hawaii from the time of European discovery in 1778 through the mid-19th century. Mapmaking was not an art indigenous to Hawaii; foreigners were responsible for the introduction of mapmaking in the islands. For well over seventy years, mapping in Hawaii was largely carried out by Europeans or Americans, and the early maps of Hawaii were mostly made to serve the needs of those foreigners....

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The Rosetta Stone, in Hieroglyphics and Greek; with Translations, and an explanation of the hieroglyphical character; and followed by an appendix of kings names....

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There have been some significant changes in this edition. A new Geography section has replaced the former Land and Water sections. Entries in the new section include area (total and land), comparative area, land boundaries, coastline, maritime claims, boundary disputes, climate, terrain, land use, environment, and special notes. In the Government section, a new entry on dependent areas has also been added....

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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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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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x4: Radio labeling of P3n for n is less than or equal to 5 or n = 7 In this section we determine radio numbers of cube path of small order as a special case....

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LOW-INTENSITY CONFLICT: WHAT IS IT AND WHY SHOULD IT CONCERN THE USAF? . . . . . 1 Low-Intensity Conflict Defined . . . . . . . . . . .1 Special Characteristics of Low-Intensity Conflict . . . . . . . . . . . . . 7 Operational Terms Relating to Low-Intensity Conflict . . . . . . . 8 Future Conflicts . . . . . . . . . . . . . . . . . . . . 11 Dealing with Future Conflict. . . . . . . . . . . . .13 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 AIR POWER IN SMALL WARS : THE BRITISH AIR CONTROL EXPERIENCE . . . . . . . . . . . . 19 Air Control's Genesis . . . . . . . . . . . . . . . . .19 Air Control: From Concept to Doctrine . . . . .22 The Requirements of British Air Control . . . .24 Air Control and Today's US Air Force . . . . . . 25 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . .27 3 THE MOROCCO-POLISARIO WAR: A CASE STUDY OF A MODERN LOW-INTENSITY CONFLICT . . . . . . . . . . . . . . . . . . . . 29 Resources and Topography of Western Sahara . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 Moroccan Claims and Stakes in Western Sahara . . . . . . . . . . . . . . . . . . ....

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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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Contents Tangent Space and Derivative Mapping on Time Scale BY EMIN ¨OZYILMAZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Basic Properties Of Second Smarandache Bol Loops BY T.G.JA´IY´E O. L´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Smarandachely Precontinuous maps and Preopen Sets in Topological Vector Spaces BY SAYED ELAGAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Path Double Covering Number of Product Graphs BY A. NAGARAJAN, V. MAHESWARI, S. NAVANEETHAKRISHNAN. . . . . . 27 Some Remarks on Fuzzy N-Normed Spaces BY SAYED ELAGAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 σ-Coloring of the Monohedral Tiling BY M. E. BASHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 The Forcing Domination Number of Hamiltonian Cubic Graphs BY H.ABDOLLAHZADEH AHANGAR AND PUSHPALATHA L. . . . . . . . . . 53 Permutation Polynomials modulo n, n 6= 2w and Latin Squares BY VADIRAJA BHATTA G. R. and SHANKAR B. R. . . . . . . . . . . . . . . . . 58 Graphoidal Tree d - Cover BY S.SOMASUNDARAM, A.NAGARAJAN AND G.MA...

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This book aims to assist social scientists to analyze their problems using fuzzy models. The basic and essential fuzzy matrix theory is given. The book does not promise to give the complete properties of basic fuzzy theory or basic fuzzy matrices. Instead, the authors have only tried to give those essential basically needed to develop the fuzzy model. The authors do not present elaborate mathematical theories to work with fuzzy matrices; instead they have given only the needed properties by way of examples. The authors feel that the book should mainly help social scientists who are interested in finding out ways to emancipate the society. Everything is kept at the simplest level and even difficult definitions have been omitted. Another main feature of this book is the description of each fuzzy model using examples from real-world problems. Further, this book gives lots of references so that the interested reader can make use of them. This book has two chapters. In Chapter One, basic concepts about fuzzy matrices are introduced. Basic notions of matrices are given in section one in order to make the book self contained. Section two g...

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Preface 4 Dedication 6 Chapter One BASIC MATRIX THEORY AND FUZZY MATRIX THEORY 7 1.1 Basic Matrix Theory 7 1.2 Basic Concepts on Fuzzy Matrices 33 1.3 Basic Concepts on Graphs 47 Chapter Two DESCRIPTION OF SIMPLE FUZZY MODELS AND THEIR APPLICATIONS TO REAL WORLD PROBLEMS 71 2.1 Description of Simple Fuzzy Matrix Model 72 2.2 Definition of Fuzzy Cognitive Maps with real world model representation 146 2.3 Definition and Illustration of Fuzzy Relational Maps 205 2.4 Introduction to Bidirectional Associative Memories (BAM) Model and their Application 238 2.5 Description of Fuzzy Associative Memories (FAM) model and their illustrations 264 2.6 Fuzzy Relational Equations (FRE) and their application 277 REFERENCE 317 INDEX 345 ABOUT THE AUTHORS 352...

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In this book for the first time we have ventured into the total analysis of migrant labourers in rural Tamil Nadu who are victims of HIV/AIDS using FCM, BAM and Neutrosophic Cognitive Maps. As in our study and analysis we felt several of the factors related with the psycho, socio, economic problems of these HIV/AIDS patients from rural Tamil Nadu (a southernmost state in India) remain indeterminate apart from the data being an unsupervised one. At the outset, we first emphasize that the study and analysis (and there by the conclusions and suggestions) pertain only to migrant labourers from rural Tamil Nadu who are poor and uneducated and who are HIV/AIDS infected. So this study cannot be extended to urban people or rich/ sophisticated/ educated populations of Tamil Nadu....

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Migration acquires great significance in the study of peoples and populations, for it not only involves the merely mathematical spatial redistribution of people, but also because it has enormous impact on livelihood, life-styles, employment, socioeconomic and political stability; or in other words, it influences the entire society. When used in the geographical context, the term ‘migration’ refers to the ‘permanent or semipermanent change in the residence of an individual person or group of people.’ Traditional studies classify migrants under two broad heads: voluntary migrants and involuntary migrants....

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In the following index of the islands of the Territory of Hawaii and vicinity and the geographical features of those islands, the aríchipelago is divided into three groups, namely: (1) the Main Group, comprising all islands from Hawaii to Niihau, including islets lying offshore from the main islands; (2) the Leeward Islands from Ni-lioa. to kure, consisting of a chain of islands, atolls, and shoals, exítending from beyond Kauai west-north-west for 1,100 miles; and (8) Other Islands, being certain islands scattered in the North Paícific Ocean and generally acknowledged to have been under Haíwaiian sovereignty, or to which Hawaii had some claim and to which claim the United States has succeeded....

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In collecting the names from the primary source, the thirty-three maps and quadrangles of the islands, except those of the re-survey of Oahu, were marked in rectangles, the sides of which were one minute long, and the named geographic features located to the nearíest minute of latitude and longitude. The names are'listed exactly as they are spelled on the quadrangles and maps. No decisions have been made as to whether the names are correct. However, the Haíwaiian place names which appear in the Sixth Report of the United States Geographic Board have been compared with the same names in the gazetteer, and where the spelling is different, the nomenclaíture of that Board is given in parentheses with the letters U.S.G.B. Names which appear in that report of the United States Geographic Board and which do not appear on maps are also included....

Table of Contents Details
Introduction -- 7 -- Areas of main Hawaiian islands and highest point on each island -- 10 -- Abbreviations -- 11 -- The Gazetteer: -- Main Islands -- Hawaii -- 13 -- Kahoolawe -- 75 -- Kauai -- 79 -- Lanai -- 103 -- Maui -- 111 -- Molokai -- 143 -- Niihau -- 159 -- Oahu -- 163 -- Leeward Islands -- 197 -- Other Islands -- 199 -- Sources of Place-Names in the Gazetteer: - Maps of the United States Geological Survey -- 200 -- Maps and Charts of the Territorial, the Royal Hawaiian, and the United States Governments -- 202 -- Miscellaneous maps - Key to Identification Symbols -- 205 -- Hawaiian Words Used in Naming Lands and Features, by Robert D King -- 206 -- Hawaiian Topographic Survey and Associated Matters, by Walter F Frear -- -- 209 -- Districts in the Hawaiian Islands, by Robert D King -- 214 -- Hawaiian Toponymy, by John Wesley Coulter -- 231 -- References on Hawaiian Place-Names -- 238 -- Advisory Committee on Hawaiian Geographic Names, by John Wesley Coulter – 240 -- MAPS-Maps For Use with the Gazetteer: -- Hawaii, Territory of, Fig 1 -- 6 -- Hawaii (island) Fig 2 -- 12 -- Kahoolawe, Fig 4 -- 102 -- Kauai, Fig 3 -- 78 -- L...

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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...

Excerpt Details
On (∈ vq)-Fuzzy Bigroup Abstract: In this paper, we introduce the concept of fuzzy singleton to bigroup, and uses it to define (∈ v q)- fuzzy bigroup and discuss its properties. We investigate whether or not the fuzzy point of a bigroup will belong to or quasi coincident with its fuzzy set if the constituent fuzzy points of the constituting subgroups both belong to or quasi coincident with their respective fuzzy sets, and vise versa. We also prove that a fuzzy bisubset μ is an (∈ vq)-fuzzy subbigroup of the bigroup G if its constituent fuzzy subsets are (∈ vq)-fuzzy subgroups of their respective subgroups among others. Key Words: Bigroups, fuzzy bigroups, fuzzy singleton on bigroup, (∈ vq)- fuzzy subgroups, (∈ vq)- fuzzy bigroup ...

Table of Contents Details
Contents On (∈ vq)- Fuzzy Bigroup BY AKINOLA L.S. and AGBOOLA A.A.A. . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Connectivity of Smarandachely Line Splitting Graphs BY B.BASAVANAGOUD and VEENA MATHAD . . . . . . . . . . . . . . . . . . . . . . 08 Separation for Triple-Harmonic Di?erential Operator in Hilbert Space BY E.M.E.ZAYED and S.A.OMRAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Classification of Differentiable Graph BY A. El-Abed . . . . . . . . . . . . . . . . . 24 On Equitable Coloring of Helm Graph and Gear Graph BY KALIRAJ.K and VERNOLD VIVIN.J . . . . . . . . . . . . . . . . . . . . . . . . . . 32 On the Roman Edge Domination Number of a Graph BY K. EBADI, E. KHODADADI and L. PUSHPALATHA. . . . . . . . . . . . . . . . . . 38 The Upper Monophonic Number of a Graph BY J.JOHN and S.PANCHALI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Some Results on Pair Sum Labeling of Graphs BY R. PONRAJ, J.VIJAYA XAVIER PARTHIPAN and R.KALA . . . . . . . . . . . . . . 53 Weierstrass Formula for Minimal Surface in the Special Three-Dimensional Kenmotsu Manifold K with _-...

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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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Extending Homomorphism Theorem to Multi-Systems Abstract: The multi-laterality of WORLD implies multi-systems to be its best candidate model for ones cognition on nature, which is also included in an ancient book of China, TAO TEH KING written by Lao Zi, an ancient philosopher of China. Then how it works to mathematics, not suspended in thought? This paper explains this action by mathematical logic on mathematical systems generalized to Smarandache systems, or such systems with combinatorial structures, i.e., combinatorial systems, and shows how to extend the homomorphism theorem in abstract algebra to multi-systems or combinatorial systems. All works in this paper are motivated by a combinatorial speculation of mine which is reformed on combinatorial systems and can be also applied to geometry. Key Words: Homomorphism theorem, multi-system, combinatorial system. ...

Table of Contents Details
Contents Extending Homomorphism Theorem to Multi-Systems BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 A Double Cryptography Using the Smarandache Keedwell Cross Inverse Quasigroup BY T. G. JA´IY´EOL´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 On the Time-like Curves of Constant Breadth in Minkowski 3-Space BY SUHA YILMAZ AND MELIH TURGUT. . . . . . . . . . . . . . . . . . . . . 34 On the Basis Number of the Strong Product of Theta Graphs with Cycles BY M.M.M. JARADAT, M.F. JANEM AND A.J. ALAWNEH. . . . . . . . . . . .40 Smarandache Curves in Minkowski Space-time BY MELIH TURGUT AND S¨UHA YILMAZ . . . . . . . . . . . . . . . . . . . . . 51 The Characterization of Symmetric Primitive Matrices with exponent n − 3 BY LICHAO, HUANGFU AND JUNLIANG CAI . . . . . . . . . . . . . . . . . . 56 The Crossing Number of the Circulant Graph C(3k − 1; {1, k}) BY JING WANG AND YUANQIU HUANG. . . . . . . . . . . . . . . . . . . .79 On the Edge Geodetic and k-Edge Geodetic Number of a Graph BY A.P. SANTHAKUMARAN AND S.V. ULLAS CHANDRAN. . . . . . . . . .85 Simple Path Cove...

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In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of Neutrosophy, and its connected logic, Neutrosophic Logic. Neutrosophy is a new branch of philosophy that studies the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. This was introduced by one of the authors, Florentin Smarandache. A few of the mentionable characteristics of this mode of thinking are [90-94]: It proposes new philosophical theses, principles, laws, methods, formulas and movements; it reveals that the world is full of indeterminacy; it interprets the uninterpretable; regards, from many different angles, old concepts, systems and proves that an idea which is true in a given referential system, may be false in another, and vice versa; attempts to make peace in the war of ideas, and to make w...