Complete right- and left-sided thoracic ducts associated with aberrant left vertebral artery: unreported case with surgical implications

Anatomy is the keystone to an appropriate understanding of surgical and radiological sciences. Here the authors report on a rare case of complete right- and left-sided thoracic ducts (TDs) associated with aberrant left-vertebral artery (LVA) arising from the aortic arch. The TDs originated from right and left cisterna chyli and terminated separately close to the left venous angle. Superior to the aortic arch, the TDs showed different relationships to the LVA; the right TD was ventral, while the left was dorsal in position. This report is associated with other variations detailed below, and may have important implications in cervicothoracic surgery. (Folia Morphol 2018; 77, 1: 156–160)

Aplikasi Kamus Istilah Kebudayaan Indonesia Berbasis Desktop Menggunakan Metode Fisher-yates

Semakin maju arus globalisasi, rasa cinta terhadap budaya semakin berkurang, dan ini sangat berdampak tidak baik bagi masyarakat asli Indonesia. Perlu diketahui bersama bahawa tidak sedikit dari kebudayaan kita yang sudah mulai punah. Budaya asing saat ini banyak mewarnai budaya Indonesia. Di Jakarta Kebudayan asli betawi saat ini sudah tidak ada lagi terdengar Tanjidor alat musik khas dari tanah Betawi. Pembelajaran berbasis multimedia merupakan salah satu alternatif pembelajaran yang dapat dilakukan di dalam kelas dengan menggunakan metode Multimedia Development Life Cycle (MDLC) dengan menggunakan 6 tahap pengembangan mulimedia dan di tambah dengan Algoritma Fisher-Yates yang diterapkan di menu Kuis pada aplikasi, untuk pengacakan soal dan jawaban. Dengan melalui pembelajaran berbasis multimedia, contoh dalam sekolah, guru dapat membantu mengantarkan siswa untuk mendapatkan situasi pembelajaran yang sedemikian rupa guna memberikan pemahaman secara konkret terhadap materi yang disampaikan. Aplikasi ini dapat bermanfaat membantu masyarakat umum mengenal kebudayaan Jawa Timur, dan menggunakan Algortima Fisher-Yates. Berdasarkan hasil uji coba user, menunjukkan responden sangat baik, rata-rata dari nilai yang didapatkan adalah sebesar 82%, yaitu sangat baik Aplikasi ini menggunakan Adobe Flash CS5 berbasis Dekstop dan diakses secara offline. Kata kunci— Kamus Kebudayaan, Fisher Yates, Jawa Timu

Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as introduced and studied in previous papers in the series) but this paper is largely independent of that theory. We obtain a characterization, on a large family of projective bundles, of those `admissible' Kaehler classes (i.e., the ones compatible with the bundle structure in a way we make precise) which contain an extremal Kaehler metric. In many cases, such as on geometrically ruled surfaces, every Kaehler class is admissible. In particular, our results complete the classification of extremal Kaehler metrics on geometrically ruled surfaces, answering several long-standing questions. We also find that our characterization agrees with a notion of K-stability for admissible Kaehler classes. Our examples and nonexistence results therefore provide a fertile testing ground for the rapidly developing theory of stability for projective varieties, and we discuss some of the ramifications. In particular we obtain examples of projective varieties which are destabilized by a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely self-contained; partially replaces and extends math.DG/050151

Uniqueness and examples of compact toric Sasaki-Einstein metrics

In [11] it was proved that, given a compact toric Sasaki manifold of positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed Sasaki structure on which a Sasaki-Einstein metric exists. In the present paper we first prove the uniqueness of such Einstein metrics on compact toric Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure, and secondly remark that the result of [11] implies the existence of compatible Einstein metrics on all compact Sasaki manifolds obtained from the toric diagrams with any height, or equivalently on all compact toric Sasaki manifolds whose cones have flat canonical bundle. We further show that there exists an infinite family of inequivalent toric Sasaki-Einstein metrics on $S^5 \sharp k(S^2 \times S^3)$ for each positive integer $k$.Comment: Statements of the results are modifie

Exceptional del Pezzo hypersurfaces

We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$. As a corollary we obtain the existence of orbifold K\"ahler--Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$.Comment: 149 pages, one reference adde

Energy properness and Sasakian-Einstein metrics

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type inequality. At the end of this paper, we also obtain a Miyaoka-Yau type inequality in Sasakian geometry.Comment: 27 page

New Results in Sasaki-Einstein Geometry

This article is a summary of some of the author's work on Sasaki-Einstein geometry. A rather general conjecture in string theory known as the AdS/CFT correspondence relates Sasaki-Einstein geometry, in low dimensions, to superconformal field theory; properties of the latter are therefore reflected in the former, and vice versa. Despite this physical motivation, many recent results are of independent geometrical interest, and are described here in purely mathematical terms: explicit constructions of infinite families of both quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry; an extremal problem that determines the Reeb vector field for, and hence also the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the existence of Sasaki-Einstein metrics. Some of these results also provide new insights into Kahler geometry, and in particular new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.Comment: 31 pages, no figures. Invited contribution to the proceedings of the conference "Riemannian Topology: Geometric Structures on Manifolds"; minor typos corrected, reference added; published version; Riemannian Topology and Geometric Structures on Manifolds (Progress in Mathematics), Birkhauser (Nov 2008

Obstructions to the Existence of Sasaki-Einstein Metrics

We describe two simple obstructions to the existence of Ricci-flat Kahler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kahler-Einstein metrics on Fano orbifolds. We present several families of hypersurface singularities that are obstructed, including 3-fold and 4-fold singularities of ADE type that have been studied previously in the physics literature. We show that the AdS/CFT dual of one obstruction is that the R-charge of a gauge invariant chiral primary operator violates the unitarity bound.Comment: 35 pages, 1 figure; references and a footnote adde