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

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

M2-Branes and Fano 3-folds

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.Comment: 128 pages, 39 figures, 42 table

Randomizing world trade. II. A weighted network analysis

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed/undirected, aggregated/disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243 [physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011

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

Calabi-Yau Volumes and Reflexive Polytopes

We study various geometrical quantities for Calabi–Yau varieties realized as cones over Gorenstein Fano varieties, obtained as toric varieties from reflexive polytopes in various dimensions. Focus is made on reflexive polytopes up to dimension 4 and the minimized volumes of the Sasaki–Einstein base of the corresponding Calabi–Yau cone are calculated. By doing so, we conjecture new bounds for the Sasaki–Einstein volume with respect to various topological quantities of the corresponding toric varieties. We give interpretations about these volume bounds in the context of associated field theories via the AdS/CFT correspondence

K\"{a}hler-Einstein metrics on strictly pseudoconvex domains

The metrics of S. Y. Cheng and S.-T. Yau are considered on a strictly pseudoconvex domains in a complex manifold. Such a manifold carries a complete K\"{a}hler-Einstein metric if and only if its canonical bundle is positive. We consider the restricted case in which the CR structure on $\partial M$ is normal. In this case M must be a domain in a resolution of the Sasaki cone over $\partial M$. We give a condition on a normal CR manifold which it cannot satisfy if it is a CR infinity of a K\"{a}hler-Einstein manifold. We are able to mostly determine those normal CR 3-manifolds which can be CR infinities. Many examples are given of K\"{a}hler-Einstein strictly pseudoconvex manifolds on bundles and resolutions.Comment: 30 pages, 1 figure, couple corrections, improved a couple example

PERTANGGUNGJAWABAN PERUSAHAAN TERHADAP PEMOTONGAN UPAH KARYAWAN KONTRAK PADA PENUNDAAN KEWAJIBAN PEMBAYARAN UTANG

Perusahaan dapat melakukan Penundaan Kewajiban Pembayaran Utang (PKPU) agar tetap dapat melanjutkan usahanya sembari mengamankan aset dan kekayaannya sehingga memberikan jaminan bagi pelunasan utang-utang bagi para kreditur. Kondisi tersebut kadangkala berdampak kepada para pekerja terkait pemotongan upah yang seharusnya dibayarkan termasuk bagi karyawan kontrak. Bentuk perlindungan hukum serta upaya hukum yang dapat dilakukan oleh karyawan kontrak atas tindakan perusahaan yang melakukan pemotongan upah dalam masa PKPU tetap. Perusahaan bertanggungjawab atas penundaan pembayaran upah kepada karyawan kontrak pada masa PKPU apabila karyawan menempuh upaya hukum. Dalam penelitian yuridis normatif ini diperoleh kesimpulan bahwa upaya hukum yang dapat dilakukan oleh karyawan kontrak atas pemotongan upah oleh perusahaan dalam masa PKPU-Tetap tidak terakomodasi secara penuh oleh peraturan perundang-undangan yang berlaku saat ini. Perlindungan terhadap kepentingan karyawan kontrak dalam kondisi sebaiknya didasarkan pada perjanjian kerja antara karyawan dengan pihak perusahaan dimana upaya hukum dapat ditempuh melalui gugatan maupun kesepakatan perdamaian selama tidak diatur lain dalam perjanjian kerja.Companies can defer debt payment obligations (PKPU) so that they can continue their business while securing their assets and assets to provide guarantees for the repayment of debts for creditors. This condition sometimes has an impact on workers about wage deductions that should be paid, including for contract employees. Forms of legal protection and legal remedies can be taken by contract employees for the actions of companies that cut wages during the permanent PKPU period. The company is responsible for delaying payment of wages to contract employees during the PKPU period if the employee takes legal action. In this normative juridical research, it is concluded that the legal remedies that can be taken by contract employees for deductions from wages by the company during the PKPU-Permanent period are not fully accommodated by the current laws and regulations. Protection of the interests of contract employees under conditions should be based on a work agreement between the employee and the company where legal remedies can be taken through a lawsuit or a peace agreement as long as it is not regulated otherwise in the work agreement

A high-throughput synthetic platform enables the discovery of proteomimetic cell penetrating peptides and bioportides

Collectively, cell penetrating peptide (CPP) vectors and intrinsically active bioportides possess tremendous potential for drug delivery applications and the discrete modulation of intracellular targets including the sites of protein–protein interactions (PPIs). Such sequences are usually relatively short (< 25 AA), polycationic in nature and able to access the various intracellular compartments of eukaryotic cells without detrimental influences upon cellular biology. The high-throughput platform for bioportide discovery described herein exploits the discovery that many human proteins are an abundant source of potential CPP sequences which are reliably predicted using QSAR algorithms or other methods. Subsequently, microwave-enhanced solid phase peptides synthesis provides a high-throughput source of novel proteomimetic CPPs for screening purposes. By focussing upon cationic helical domains, often located within the molecular interfaces that facilitate PPIs, bioportides which act by a dominant-negative mechanism at such sites can be reliably identified within small number libraries of CPPs. Protocols that employ fluorescent peptides, routinely prepared by N-terminal acylation with carboxytetramethylrhodamine, further enable both the quantification of cellular uptake kinetics and the identification of specific site(s) of intracellular accretion. Chemical modifications of linear peptides, including strategies to promote and stabilise helicity, are compatible with the synthesis of second-generation bioportides with improved drug-like properties to further exploit the inherent selectivity of biologics

Stability of vector bundles and extremal metrics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46622/1/222_2005_Article_BF01404460.pd