A refined energy bound for perpendicular bisectors
Let $\mathcal{P}$ be a set of $n$ points in the Euclidean plane. We prove that, for any $ε> 0$, either a single line or circle contains $n/2$ points of $\mathcal{P}$, or the number of distinct perpendicular bisectors determined by pairs of points in $\mathcal{P}$ is $Ω(n^{52/35 - ε})$, where the constant implied by the $Ω$ notation depends on ...
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New Theorem on Perpendicular Bisectors of Focal Radii of an Ellipse
Ellipse is one of the conic sections,it is sort of elongated circle. It is the locus of a point that moves in such a way that the ratio of its distance from a fixed point to its distance from a fixed point to its distance from a fixed line equals to constant 'e'.
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Abstract Arhinolemur scalabrinii† Ameghino, 1898 was originally described as a strepsirrhine primate (Mammalia) but has been recognized as an anostomid fish since 2012. It remains the only extinct anostomid species known from complete cranial material.
Karen M. Panzeri +8 more
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Redescription of the Triassic cynodont Cistecynodon parvus and reassessment of its phylogeny
Abstract Cynodontia is an important subclade of Therapsida that first occurred in the late Permian. It includes extinct subclades which are the non‐mammaliaform cynodonts and Mammaliaformes, with the latter ultimately giving rise to crown mammals. The systematics of non‐mammaliaform cynodonts has been extensively studied and is relatively well‐resolved,
Erin S. Lund +4 more
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72. A variable parallel is drawn to the base of a triangle ABC, meeting AB, AC in Q, R; BM, CN are perpendicular to the bisector of the vertical angle. If QM, RN meet at P, it is required to prove that the circumcircle of PQR touches the inscribed circle of ABC and also one of the exscribed circles [PDF]
n ...
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The mechanism of labor in nonhuman primates: A look inside
Abstract While in humans, the flexed position of the fetus and its rotating course down the birth canal are well documented, in other primates the mechanism of labor is unknown. Despite the lack of comparative data, it is commonly assumed that the human obstetric mechanism is unique, and anthropologists have disputed when and why the transition to the ...
Melissa K. Stoller
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Abstract Prozostrodon brasiliensis, a probainognathian cynodont of the clade Prozostrodontia, is recognized as a key taxon for understanding the origin of Mammaliaformes and mammals. Despite detailed investigations of its cranial anatomy, the postcranial skeleton has received comparatively less attention.
Iasmim M. Michelotti +4 more
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Fascicle measurement methods do result in lengths that are significantly different
A recent comparison of the most prevalent methods for measuring fascicles, in situ measurement versus chemical digestion, concluded that the measurements are indistinguishable based on data from different conspecific individuals. However, our study of contralateral muscles of the same individuals shows that the methods clearly result in statistically ...
Katherine M. Clark +5 more
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Grooved Surface of the Obturator Internus Muscle With Two Distinct Adjacent Parts
ABSTRACT The specific anatomical features of the obturator internus, particularly those of its medial surface, remain insufficiently characterized. This study investigated the morphology of the obturator internus muscle by focusing on the shape of its medial surface and potential age‐related changes.
Satoru Muro +4 more
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Anatomy of the Soft Palate and Its Role in Upper Airway Function: A Narrative Review
ABSTRACT The soft palate is a complex anatomical structure, located at the posterior aspect of the oral and nasal cavities, able to dynamically create valve closure of the nasal and the oral cavities. Its precise movement is critical for speech, swallowing, and respiration. Despite its functional importance, detailed characterization of its constituent
James C. D. Miller +4 more
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