Domination in Isosceles Triangular Chessboard

In this article, we are interested in the domination problem in isosceles triangular chessboard. In our study we take in account one type of piece of rooks, bishops and kings, and two different types of pieces together, kings with rooks, kings with bishops and rooks with bishops. The chessboard in this work is isosceles triangular with square cells. Also in most cases we determine the possible number of different methods of domination (total solution). Keywords: domination, Isosceles triangle chessboard, Kings, Bishops and Rooks

Introduction to the prisoners and guards game

We study the half-dependent problem for the king graph Kn. We give proofs to establish the values h(Kn) for n ∈ {1, 2, 3, 4, 5, 6} and an upper bound for h(Kn) in general. These proofs are independent of computer assisted results. Also, we introduce a two-player game whose winning strategy is tightly related with the values h(Kn). This strategy is analyzed here for n = 3 and some facts are given for the case n = 4. Although the rules of the game are very simple, the winning strategy is highly complex even for n = 4

Domination and Independence in Cubic Chessboard

In this paper, we are interested in some problems on cubic chessboard with square cells (domination and independence numbers). At the beginning, these problemsare examined with one type of the chess pieces. In certain technique, studying these problemswill continue with two different types. In the case of one type of chess pieces which have been dealt with in this article, the typeis rookor king. The pieces of the two different types in our study are: kings with rooks togethe

The maximum queen’s problem with pawns

The classic n-queens problem asks for placements of just n mutually non-attacking queens on an n × n board. By adding enough pawns, we can arrange to fill roughly one-quarter of the board with mutually non-attacking queens. How many pawns do we need? We discuss that question for square boards as well as rectangular m × n boards

Domination and Independence on Square Chessboard

In this paper, new idea for the problems of independence and domination on chessboard is introduced. Two classical chessboard problems of independence and domination on square chessboard with square cells of siz

Population continuity or replacement at ancient Lachish? A dental affinity analysis in the Levant

Thesis (M.A.) University of Alaska Fairbanks, 2012Are material culture changes between late Bronze and early Iron Age inhabitants of Lachish, in modern day Israel, the result of immigrants settling the region, or an in situ evolution of practices by the same indigenous peoples? The research objectives are to: 1) assess dental affinity of an Iron Age Lachish sample relative to its Bronze Age predecessor, and 2) compare data in both groups with European and North African comparative samples to estimate biological affinity within the Mediterranean area. In the process, two competing hypotheses are tested; one postulates continuity and the other population replacement between the Bronze and Iron Age. Using the Arizona State University Dental Anthropology System, dental trait frequencies were compared to determine inter-sample phonetic affinities. The results suggest: 1) biological continuity between the Lachish Bronze and Iron Ages, and 2) a marked level of heterogeneity with closer affinity to some Egyptian and Phoenician groups within the Mediterranean Diaspora. These findings lend support to one of many competing theories identifying the ancient Lachish peoples, while providing an increased understanding of the Bronze and Iron Age transition in the Levant, which is often considered one of the most intriguing and volatile periods in the Near East.1. Introduction -- Research problem and project development -- Methodological approach -- Objectives and goals of the study -- Research questions -- Hypothesis -- Significance -- Organization of thesis -- 2. Bronze and iron ages in Palestine -- Terminology -- Chronology -- Background: pottery and chronology -- Philistine pottery -- The chronological debate -- The modified conventional chronology -- The low chronology -- Geographic setting of Palestinian settlements -- The Bronze Age in Palestine -- Settlement and burial patterns -- Subsistence patterns -- The Iron Age in Palestine -- The Canaanites -- The Philistines -- The Israelites -- 3. Lachish -- Archaeological background -- Stratigraphy -- Archaeology: early Bronze (EB- ca. 3300-2300 B.C.E.) -- Middle Bronze (MB- ca. 2000-1550 B.C.E.) -- Late Bronze (LB- ca. 1550-1200/1098 B.C.E.) -- Construction -- Foreign relations -- Trade -- Industry -- Agriculture -- Philistine pottery and Lachish -- The end of the Bronze Age at Lachish -- The Iron Age (ca. 1200/1109-586/520 B.C.E.) -- Level V -- Level IV -- Level III -- Level II -- Who are the peoples of ancient Lachish? -- Affinity studies in Lachish and surrounding regions -- 4. Methodological background -- Dental anthropology -- Microevolutionary research and dental analysis -- Dental morphological study -- Advantages of using teeth as a research tool -- Disadvantages of using teeth as a research tool -- Current dental morphological methods -- 5. Materials and methods -- Materials : samples used in study -- Iron age skeletons -- Bronze age skeletons -- Comparative samples -- Methods -- Data collection -- Quantitative MMD -- Isolation-by-distance -- 6. Results -- Traits frequencies -- MMD -- Lachish bronze age sample (LCB) -- Lachish Iron Age sample (LCI) -- Isolation-by-distance -- 7. Discussion -- Egypt and Lachish -- Nubia and Lachish -- Isolation-by-distance -- Who are the peoples of ancient Lachish? -- 8. Conclusions and future research -- Literature cited -- Appendix

Distance-2 Domatic Numbers of Graphs

The distance d(u, v) between two vertices u and v in a graph G equals the length of a shortest path from u to v. A set S of vertices is called a distance-2 dominating set if every vertex in V \S is within distance-2 of at least one vertex in S. The distance-2 domatic number is the maximum number of sets in a partition of the vertices of G into distance-2 dominating sets. We give bounds on the distance-2 domatic number of a graph and determine the distance-2 domatic number of selected classes of graphs

The Distribution and Dating of Egyptian False Doors and Funerary Stelae of the First Intermediate Period: A Preliminary Analysis

The false door, later replaced by the stele, can be traced in the archaeological record from the end of the Old Kingdom to the beginning of the Middle Kingdom. It can be found throughout sites in Upper and Lower Egypt and across each of the major phases of rule, from the Memphites to the Herakleopolitans and the Thebans. However, studies to date have only considered the false door and stele within the parameters of individual sites or localised regions, for example: Dunham and Brovarski's studies at Naga ed-Deir (Brovarski 1989; Dunham 1937), Daoud's study at Memphis (2005) and Fischer's studies at Dendera (1968). There has been little attempt to date false doors and stelae across both time and place. To do so might make it possible to determine a benchmark for dating other events and material culture of the First Intermediate Period, as well as clearer patterns in artistic, administrative and social changes. The purpose of this paper, therefore, is twofold: (1) to present the preliminary findings from a site distribution of 562 Egyptian false doors and funerary stelae currently known from the First Intermediate Period (reigns of King Pepy II - Nebhepetre Mentuhotep II) and (2) to explore the results of a set of dating criteria applied to a representative group of 'well-dated' examples

On the Domination Chain of m by n Chess Graphs

A survey of the six domination chain parameters for both square and rectangular chess boards are discussed