Dual Pole Indicatrix Curve and Surface

In this paper, the vectorial moment vector of the unit Darboux vector, which consists of the motion of the Frenet vectors on any curve, is reexpressed in the form of Frenet vectors. According to the new version of this vector, the parametric equation of the ruled surface corresponding to the unit dual pole indicatrix curve is given. The integral invariants of this surface are rederived and illustrated by presenting with examples

Smarandache Curves in Terms of Sabban Frame of Spherical Indicatrix Curves

In this paper, we investigate special Smarandache curves in terms of Sabban frame of spherical indicatrix curves and we give some characterization of Smarandache curves. Besides, we illustrate examples of our results

Coccygectomy as a Surgical Option in the Treatment of Chronic Traumatic Coccygodynia: A Single-Center Experience and Literature Review

Study DesignRetrospective cohort study.PurposeTrauma is the most common cause for chronic coccygodynia. The present study aims at presenting our results after complete removal of the coccyx for refractory traumatic coccygodynia in terms of pain level, complication rates, and patients' overall satisfaction.Overview of LiteratureThere is limited extant literature describing the success rate and complications in refractory isolated traumatic coccygodynia.MethodsFrom January 2011 to January 2012, 10 consecutive patients with posttraumatic coccygodynia (six males and four females; mean age, 42 years) were enrolled in our study. Conservative treatment of the condition had failed in all patients. The same surgeon performed a complete coccygectomy on all patients. Postoperative outcomes included measurements of pain relief and degree of patient satisfaction with the procedure's results.ResultsIn our selected cohort, all patients indicated complete pain relief or significant pain improvement in follow up-care and would recommend this procedure. One patient developed a subcutaneous hematoma that required surgical intervention.ConclusionsOur results suggest that complete removal of the coccyx relieves pain in patients with refractory chronic traumatic coccygodyniaand is therefore a reasonable treatment option after conservative treatment failure

The first horse herders and the impact of early Bronze Age steppe expansions into Asia

This is the author accepted manuscript. The final version is available from AAAS via the DOI in this recordThe file includes the article, supplementary material and additional supplementary materialThe published version of the supplementary materials are at http://science.sciencemag.org/content/suppl/2018/05/08/science.aar7711.DC1Part of the additional supplementary materials for this article are in ORE at http://hdl.handle.net/10871/32792The Yamnaya expansions from the western steppe into Europe and Asia during the Early Bronze Age (~3000 BCE) are believed to have brought with them Indo-European languages and possibly horse husbandry. We analyze 74 ancient whole-genome sequences from across Inner Asia and Anatolia and show that the Botai people associated with the earliest horse husbandry derived from a hunter-gatherer population deeply diverged from the Yamnaya. Our results also suggest distinct migrations bringing West Eurasian ancestry into South Asia before and after but not at the time of Yamnaya culture. We find no evidence of steppe ancestry in Bronze Age Anatolia from when Indo-European languages are attested there. Thus, in contrast to Europe, Early Bronze Age Yamnaya-related migrations had limited direct genetic impact in Asia.The study was supported by the Lundbeck Foundation (EW), the Danish National Research Foundation (EW), and KU2016 (EW). Research at the Sanger Institute was supported by the Wellcome Trust (grant 206194). RM was supported by an EMBO Long-Term Fellowship (ALTF 133-2017). JK was supported by the Human Frontiers Science Program (LT000402/2017). Botai fieldwork was supported by University of Exeter, Archeology Exploration Fund and Niobe Thompson, Clearwater Documentary. AB was supported by NIH grant 5T32GM007197-43. GK was funded by Riksbankens Jubileumsfond and European Research Council. MP was funded by Netherlands Organization for Scientific Research (NWO), project number 276-70-028, IU was funded by the Higher education commission of Pakistan. Archaeological materials from Sholpan and Grigorievka were obtained with partial financial support of the budget program of the Ministry of Education and Science of the Republic of Kazakhstan “Grant financing of scientific research for 2018-2020” No. AP05133498 “Early Bronze Age of the Upper Irtysh”

The first horse herders and the impact of early Bronze Age steppe expansions into Asia.

The Yamnaya expansions from the western steppe into Europe and Asia during the Early Bronze Age (~3000 BCE) are believed to have brought with them Indo-European languages and possibly horse husbandry. We analyzed 74 ancient whole-genome sequences from across Inner Asia and Anatolia and show that the Botai people associated with the earliest horse husbandry derived from a hunter-gatherer population deeply diverged from the Yamnaya. Our results also suggest distinct migrations bringing West Eurasian ancestry into South Asia before and after, but not at the time of, Yamnaya culture. We find no evidence of steppe ancestry in Bronze Age Anatolia from when Indo-European languages are attested there. Thus, in contrast to Europe, Early Bronze Age Yamnaya-related migrations had limited direct genetic impact in Asia