Fuzzy Cores and Fuzzy Balancedness

We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (1963) and Shapley (1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that any fuzzy game has a non-empty core if and only if it satisfies all (fuzzy) balanced inequalities. We also consider deposit games to illustrate the use of the main result.Cooperative fuzzy games;fuzzy balancedness;fuzzy core

Valley development on Hawaiian volcanoes

Work in progress on Hawaiian drainage evolution indicates an important potential for understanding drainage development on Mars. Similar to Mars, the Hawaiian valleys were initiated by surface runoff, subsequently enlarged by groundwater sapping, and eventually stabilized as aquifers were depleted. Quantitative geomorphic measurements were used to evaluate the following factors in Hawaiian drainage evolution: climate, stream processes, and time. In comparing regions of similar climate, drainage density shows a general increase with the age of the volcani island. With age and climate held constant, sapping dominated valleys, in contrast to runoff-dominated valleys, display the following: lower drainage densities, higher ratios of valley floor width to valley height, and more positive profile concavities. Studies of stream junction angles indicate increasing junction angles with time on the drier leeward sides of the major islands. The quantitative geomorphic studies and earlier field work yielded important insights for Martian geomorphology. The importance of ash mantling in controlling infiltration on Hawaii also seems to apply to Mars. The Hawaiian valley also have implications for the valley networks of Martian heavily cratered terrains

Fluvial valleys on Martian volcanoes

Channels and valleys were known on the Martian volcanoes since their discovery by the Mariner 9 mission. Their analysis has generally centered on interpretation of possible origins by fluvial, lava, or viscous flows. The possible fluvial dissection of Martian volcanoes has received scant attention in comparison to that afforded outflow, runoff, and fretted channels. Photointerpretative, mapping, and morphometric studies of three Martian volcanoes were initiated: Ceraunius Tholus, Hecate Tholus, and Alba Patera. Preliminary morphometric results indicate that, for these three volcanoes, valley junction angles increase with decreasing slope. Drainage densities are quite variable, apparently reflecting complex interactions in the landscape-forming factors described. Ages of the Martian volcanoes were recently reinterpreted. This refined dating provides a time sequence in which to evaluate the degradational forms. An anomaly has appeared from the initial study: fluvial valleys seem to be present on some Martian volcanoes, but not on others of the same age. Volcanic surfaces characterized only by high permeability lava flows may have persisted without fluvial dissection

Examination of Critical Greek Texts of the New Testament Through Word Study of Therapeuo

This project seeks to examine the idea of healthcare within the New Testament of the Bible. A word study of the most prevalent Greek word for healing in the New Testament, therapueo, was done to illuminate the meanings behind these scriptural examples of healing. Five passages that included verses surrounding occurrences of therapeuo were selected to be translated. Four of these passages were from the book of Luke and the fifth was from Acts. The report consists of two parts. The first will discuss the word study conducted on therapeuo exclusively, and the second will expand on some of the portions of the translated passages that stood out regarding healing. The definition and use of therapeuo was found to be a very broad term for healing of many different types, according to the word study. Many other phrases and language used stood out in the translations and these were further examined in the second part of the report. It was concluded that the word study of therapeuo was thorough, but other types of healing, and other words for healing, should be studied in order to gain a more complete depiction of healing in the New Testament

Pie Charts Using Microsoft Word 365

This handout demonstrates how to use Microsoft Word 365 to build pie charts

Conjunctions

This instructional handout offers guidelines for using conjunctions

Tables Using Microsoft Word 365

This handout provides instruction for creating a table using Microsoft Word 365