Cosmological constant—the weight of the vacuum

Recent cosmological observations suggest the existence of a positive cosmological constant Λ with the magnitude Λ(G/c³)≈10⁻¹²³. This review discusses several aspects of the cosmological constant both from the cosmological (Sections 1–6) and field theoretical (Sections 7–11) perspectives. After a brief introduction to the key issues related to cosmological constant and a historical overview, a summary of the kinematics and dynamics of the standard Friedmann model of the universe is provided. The observational evidence for cosmological constant, especially from the supernova results, and the constraints from the age of the universe, structure formation, Cosmic Microwave Background Radiation (CMBR) anisotropies and a few others are described in detail, followed by a discussion of the theoretical models (quintessence, tachyonic scalar field, …) from different perspectives. The latter part of the review (Sections 7–11) concentrates on more conceptual and fundamental aspects of the cosmological constant like some alternative interpretations of the cosmological constant, relaxation mechanisms to reduce the cosmological constant to the currently observed value, the geometrical structure of the de Sitter spacetime, thermodynamics of the de Sitter universe and the role of string theory in the cosmological constant problem.     

No-Go theorem in spacetimes with two commuting spacelike killing vectors

Four-dimensional Riemannian spacetimes with two commuting spacelike Killing vectors are studied in Einstein's theory of gravity, and found that no outer apparent horizons exist, provided that the dominant energy condition holds.     

Schwarzschild and Synge once again

We complete the historical overview about the geometry of a Schwarzschild black hole at its horizon by emphasizing the contribution made by Synge in [6] to its clarification.     

QuEChERS sample preparation followed by ultra-performance liquid chromatography – tandem mass spectrometry for rapid screening of dioctyl sulfosuccinate sodium salt in avian egg tissue

A quantification method was developed for the determination of dioctyl sulfosuccinate sodium salt (DOSS) in avian egg samples based on a QuEChERS extraction technique followed by UPLC-MS/MS analysis. DOSS is an anionic surfactant that is part of the Corexit^® 9500 dispersive mixture that prevents the formation of oil slicks on water bodies. It was extensively used when the Deepwater Horizon rig exploded and a large amount of crude oil was released into the Gulf of Mexico. QuEChERS provided a simple, effective and time saving sample preparation method prior to analysis without reducing analytical sensitivity and became an excellent substitute to lengthy traditional extraction methods. Weak anionic exchange cleanup significantly reduced matrix effects and improved analyte sensitivity. Ultra-performance liquid chromatography provided an effective separation method, while MS/MS provided the necessary selectivity and increased sensitivity. Our method achieved baseline separation of DOSS, surrogate (sodium octyl sulfate – d17) and the internal standard (sodium dioctyl sulfate – d25), with limits of detection (LOD) and limits of quantitation (LOQ) for DOSS being 260 and 500 pg/mL, respectively. Quality control recoveries were 70.5 ± 7.3% (mean ± standard deviation, n = 3) for the laboratory control sample and 72.4 ± 4.9% (n = 3) for the matrix spike. The extraction efficiency was monitored by adding surrogate compound to every sample with recoveries of 104.6 ± 14.1 for SDS-d1 and 81.8 ± 6.8 for SOS-d17. Currently, limited peer reviewed scientific data are reported on the effects of oil dispersants on the environment. Our analytical method for the determination of DOSS in avian egg matrix can be used to provide reliable data on the fate and effects of DOSS in biological systems.     

带交易费用的无限期资产市场预期均衡的存在性

本文通过一个简单的模型证明了带交易费用的无限期资产经济预期均衡存在性,所用条件与已有文献相比更加简明     

Bounding a class of nonconvex linearly-constrained resource allocation problems via the surrogate dual

We consider a class of problems of resource allocation under economies of scale, namely that of minimizing a lower semicontinuous, isotone, and explicitly quasiconcave cost function subject to linear constraints. An important class of algorithms for the linearly constrained minimization of nonconvex cost functions utilize the branch and bound approach, using convex underestimating cost functions to compute the lower bounds.We suggest instead the use of the surrogate dual problem to bound subproblems. We show that the success of the surrogate dual in fathoming subproblems in a branch and bound algorithm may be determined without directly solving the surrogate dual itself, but that a simple test of the feasibility of a certain linear system of inequalities will suffice. This test is interpreted geometrically and used to characterize the extreme points and extreme rays of the optimal value function's level sets.Research partially supported by NSF under grant # ENG77-06555.     

Supply chain design considering economies of scale and transport frequencies

In this paper we consider a 3-echelon, multi-product supply chain design model with economies of scale in transport and warehousing that explicitly takes transport frequencies into consideration. Our model simultaneously optimizes locations and sizes of tank farms, material flows, and transport frequencies within the network. We consider all relevant costs: product cost, transport cost, tank rental cost, tank throughput cost, and inventory cost. The problem is based on a real-life example from a chemical company. We show that considering economies of scale and transport frequencies in the design stage is crucial and failing to do so can lead to substantially higher costs than optimal. We solve a wide variety of problems with branch-and-bound and with the efficient solution heuristics based on iterative linearization techniques we develop. We show that the heuristics are superior to the standard branch-and-bound technique for large problems like the one of the chemical company that motivated our research.