Teaching The First American Civilization Recognizing The Moundbuilders as a Great Native-American Civilization

The Moundbuilders are a culture of mystery, little recognized by most Americans, yet they created farms, villages, towns, and cities covering as much as a third of the United States. Social studies teachers have yet to mine the resources left us over thousands of years by the native artisans and builders who preceded the nations European explorers came into contact with after 1492. Several of the Moundbuilder cities grew to sizeable proportions and one in particular, Cahokia, Illinois, not far from East St. Louis became a kind of center for the many peoples inhabiting the surrounding tributaries of the Mississippi river. Some argue that Cahokia was the center of an empire or confederation of native peoples

Minimal periods of periodic solutions of some Lipschitzian differential equations

AbstractA problem of finding lower bounds for periods of periodic solutions of a Lipschitzian differential equation, expressed in the supremum Lipschitz constant, is considered. Such known results are obtained for systems with inner product norms. However, utilizing the supremum norm requires development of a new technique, which is presented in this paper. Consequently, sharp bounds for equations of even order, both without delay and with arbitrary time-varying delay, are found. For both classes of system, the obtained bounds are attained in linear differential equations

Eccentric Black Hole Mergers in Dense Star Clusters: The Role of Binary-Binary Encounters

We present the first systematic study of strong binary-single and binary-binary black hole interactions with the inclusion of general relativity. When including general relativistic effects in strong encounters, dissipation of orbital energy from gravitational waves (GWs) can lead to captures and subsequent inspirals with appreciable eccentricities when entering the sensitive frequency ranges of the LIGO and Virgo GW detectors. In this study, we perform binary-binary and binary-single scattering experiments with general relativistic dynamics up through the 2.5 post-Newtonian order included, both in a controlled setting to gauge the importance of non-dissipative post-Newtonian terms and derive scaling relations for the cross-section of GW captures, as well as experiments tuned to the strong interactions from state-of-the art globular cluster models to assess the relative importance of the binary-binary channel at facilitating GW captures and the resultant eccentricity distributions of inspiral from channel. Although binary-binary interactions are 10-100 times less frequent in globular clusters than binary-single interactions, their longer lifetime and more complex dynamics leads to a higher probability for GW captures to occur during the encounter. We find that binary-binary interactions contribute 25-45% of the eccentric mergers which occur during strong black hole encounters in globular clusters, regardless of the properties of the cluster environment. The inclusion of higher multiplicity encounters in dense star clusters therefore have major implications on the predicted rates of highly eccentric binaries potentially detectable by the LIGO/Virgo network. As gravitational waveforms of eccentric inspirals are distinct from those generated by merging binaries which have circularized, measurements of eccentricity in such systems would highly constrain their formation scenario.Comment: 18 pages, 6 figures. Published in The Astrophysical Journa

Calculation of Indicators of Reliability of Technical Systems by the Typical Structural Scheme Method

A method for calculating the indicators of structural reliability of systems with a large number of elements is presented. The method is based on the use of typical structural schemes, reflecting the concept of connections between elements. It is shown how, by sup-plementing and combining typical structures, one can create graphological structures to perform calculations of reliability indicators.Наведено метод, розроблений для розрахунків показників структурної надійності систем з великим числом елементів. Метод ґрунтується на використанні типових структурних схем, що відбивають принципову схему зв'язків між елементами. Показано, як шляхом поповнення та об'єднання типових структур можна створювати графологічні структури для виконання розрахунків показників надійності.Представлен метод, разработанный для расчетов показателей структурной надежности систем с большим числом элементов. Метод основывается на использовании типовых структурных схем, отражающих принципиальную схему связей между элементами. Показано, как путем пополнения и объединения типовых структур можно создавать графологические структуры для выполнения расчетов показателей надежности