Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations

Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability. Here, we focus on these stability properties in the limit as the timestep tends to zero. Our analysis is motivated by an example of an exponentially almost surely stable nonlinear SDE for which the Euler-Maruyama (EM)method fails to reproduce this behavior for any nonzero timestep. We begin by showing that EM correctly reproduces almost sure and small-moment exponential stability for sufficiently small timesteps on scalar linear SDEs. We then generalize our results to multidimensional nonlinear SDEs. We show that when the SDE obeys a linear growth condition, EM recovers almost surely exponential stability very well. Under the less restrictive condition that the drift coefficient of the SDE obeys a one-sided Lipschitz condition, where EM may break down, we show that the backward Euler method maintains almost surely exponential stability

On the Epochal Strengthening in the Relationship between Rainfall of East Africa and IOD

Abstract Variability of the equatorial East Africa "short rains" (EASR) has intensified significantly since the turn of the twentieth century. This increase toward more extreme rainfall events has not been gradual but is strongly characterized by epochs. The rain gauge–based Global Precipitation Climatology Centre (GPCC) monthly precipitation dataset for the period 1901–2009 is used to demonstrate that the epochal changes were dictated by shifts in the Indian Ocean dipole (IOD) mode. These shifts occurred during 1961 and 1997. In the pre-1961 period, there was virtually no significant linear link between the IOD and the EASR. But a relatively strong coupling between the two occurred abruptly in 1961 and was generally maintained at that level until 1997, when another sudden shift to even a greater level occurred. The first principal component (PC1) extracted from the EASR spatial domain initially merely explained about 50% of the rainfall variability before 1961, and then catapulted to about 73% for the period from 1961 to 1997, before eventually shifting to exceed 82% after 1997. The PC1 for each successive epoch also displayed loadings with notably improved spatial coherence. This systematic pattern of increase was accompanied by both a sharp increase in the frequency of rainfall extremes and spatial coherence of the rainfall events over the region. Therefore, it is most likely that the 1961 and 1997 IOD shifts are responsible for the epochal modulation of the EASR in both the spatial and temporal domain

Object initial languages

From the introduction: The purpose of the present paper is to present some facts that have come to our attention recently concerning a number of Amerindian languages which we believe do exhibit object-initial basic orders. The languages we shall discuss belong to South American Indian groups which are known to have suffered more or less catatrophic decline in numbers due to the onslaught of European settlement in the New World over the past five hundred years (see Hemming 1978). Since the historical accident of European colonial expansionism has had such a devastating effect in this case, linguists might be well advised to reduce henceforth the extent of the trust they place in alleged universals of constituent ordering, and should also be sceptical of the linguistic relevance of claims that certain basic orders are rare or \u27marked\u27. The geographically widespread character of the SVO order shared by English, French, Spanish, Portuguese, and Dutch, for example, may be more directly relatable to the widespread expansion by speakers of those languages through colonization on every habitable continent of the globe than to anything about the naturalness of SVO order

He-isotopic investigation of geothermal gases from the Tabar-Lihir-Tanga-Feni Arc and Rabaul, Papua New Guinea

In order to investigate the behavior of slab-derived volatiles in the subduction environment, helium isotope ratios have been measured in geothermal gases from the Tabar-Lihir-TangaFeni (TLTF) chain in the Bismarck Archipelago of Papua New Guinea. As recorded by several geochemical tracers, these volcanos carry an exceptionally large slab-derived component, and therefore may provide new insights to the old question of volatiles in subduction zones. Geothermal gases from Lihir Island have homogeneous ^3He/^4He ratios of 7.18±0.07 times the atmospheric ratio (R_A), while those from Ambitle Island (Feni Group) have lower ratios of 6.61±0.13 R_A. These ^3He/^4He ratios are within the range defined by more-typical arc volcanos, but lie at the low end of the spectrum observed in arc volcanos erupted through purely oceanic crust. Although a small slab-derived signature (^3He/^4He ratio lower than depleted mantle) exists in the TLTF gases, these data demonstrate that even in volcanos with a comparatively large slab component, He is overwhelmingly derived from the depleted mantle wedge. This observation further confirms the relative insensitivity of He isotopes to the presence of slab fluids. He isotope ratios of 6.25 R_A were measured in geothermal gases from the Rabaul Caldera on New Britain Island. Coincidentally, these samples were taken six months prior to the major 1994 eruption at Rabaul. In conjunction with samples taken from the same locality 8 years earlier, these data allow us to test whether increasing He isotope ratios associated with fresh ascending magmas precede volcanic eruptions. Although some of the 1986 samples had much lower ^3He/^4He ratios (5 R_A than observed in 1994, one did not. We thus find no strong evidence for a systematic rise in the He isotope ratio of the Rabaul fluids between 1986 and 1994. If a ^3He/^4He increase did precede the Rabaul eruption, then it occurred either prior to 1986 or sometime between our 1994 sampling and the eruption

Potentials of ICT-based Business Initiatives for Enterprise Creation In Nigeria

Unemployment among school leavers and graduates of tertiary institutions have been a bane causing death of marketableskills and skills mismatch in Nigeria, besides restiveness and other social vices. Information and communicationtechnologies (ICTs) have been increasingly promoted as a key solution for comprehensive development, poverty alleviationand the empowerment of historically disadvantaged groups. ICT-based business initiatives have been hailed as “potentialgoldmines; hence the need for acquisition of functional and marketable skills, especially in ICT and related modern skills,becomes indisputably imperative. The benefits have far-reaching consequences for the economic and social development ofa country, as ICT businesses can foster new avenues for education, communication and information sharing; increasedproductivity and speed of work; improved accuracy as computers tend to make fewer mistakes than humans; fastercommunication; and savings in labour costs since fewer workers may be required. This paper, motivated by the potentiallypowerful role that ICTs can play in the empowerment of the unemployed, poor and underdeveloped individuals in Nigeria, isan attempt to suggest possible ICT initiatives that can be used to create self-sustainable enterprises and entrepreneurs. It isanticipated that the insights developed in this study would be useful both for purposes of policy formulation and effectiveprogramme- and self- development.Keywords - Enterprise Creation, Training, Skill-Acquisition, Seed-Money and Empowerment

Effect of biweekly shoot tip harvests on the growth and yield of Georgia Jet sweet potato grown hydroponically

Sweet potato shoot tips have been shown to be a nutritious green vegetable. A study was conducted to determine the effect of biweekly shoot tip harvests on the growth and yield of Georgia Jet sweet potato grown in the greenhouse using the nutrient film technique (NFT). The nutrient solution consisted of a modified half Hoagland solution. Biweekly shoot tip harvests, beginning 42 days after planting, provided substantial amounts of vegetable greens and did not affect the fresh and dry foliage weights or the storage root number and fresh and dry storage root weights at final harvest. The rates of anion and cation uptake were not affected by tip harvests