From the Farkas Lemma to the Hahn–Banach Theorem

This paper provides new versions of the Farkas lemma characterizing those inequalities of the form f(x) ≥ 0 which are consequences of a composite convex inequality (S ◦ g)(x) ≤ 0 on a closed convex subset of a given locally convex topological vector space X, where f is a proper lower semicontinuous convex function defined on X, S is an extended sublinear function, and g is a vector-valued S-convex function. In parallel, associated versions of a stable Farkas lemma, considering arbitrary linear perturbations of f, are also given. These new versions of the Farkas lemma, and their corresponding stable forms, are established under the weakest constraint qualification conditions (the so-called closedness conditions), and they are actually equivalent to each other, as well as equivalent to an extended version of the so-called Hahn–Banach–Lagrange theorem, and its stable version, correspondingly. It is shown that any of them implies analytic and algebraic versions of the Hahn–Banach theorem and the Mazur–Orlicz theorem for extended sublinear functions.

Application of Text Summarization techniques to the Geographical Information Retrieval task

Automatic Text Summarization has been shown to be useful for Natural Language Processing tasks such as Question Answering or Text Classification and other related fields of computer science such as Information Retrieval. Since Geographical Information Retrieval can be considered as an extension of the Information Retrieval field, the generation of summaries could be integrated into these systems by acting as an intermediate stage, with the purpose of reducing the document length. In this manner, the access time for information searching will be improved, while at the same time relevant documents will be also retrieved. Therefore, in this paper we propose the generation of two types of summaries (generic and geographical) applying several compression rates in order to evaluate their effectiveness in the Geographical Information Retrieval task. The evaluation has been carried out using GeoCLEF as evaluation framework and following an Information Retrieval perspective without considering the geo-reranking phase commonly used in these systems. Although single-document summarization has not performed well in general, the slight improvements obtained for some types of the proposed summaries, particularly for those based on geographical information, made us believe that the integration of Text Summarization with Geographical Information Retrieval may be beneficial, and consequently, the experimental set-up developed in this research work serves as a basis for further investigations in this field.

New methodology for describing the equilibrium beach profile applied to the Valencia's beaches

Mathematical models used for the understanding of coastal seabed morphology play a key role in beach nourishment projects. These projects have become the fundamental strategy for coastal maintenance during the last few years. Accordingly, the accuracy of these models is vital to optimize the costs of coastal regeneration projects. Planning of such interventions requires methodologies that do not generate uncertainties in their interpretation. A study and comparison of mathematical simulation models of the coastline is carried out in this paper, as well as elements that are part of the model that are a source of uncertainty. The equilibrium profile (EP) and the offshore limit corresponding to the depth of closure (DoC) have been analyzed taking into account different timescale ranges. The results have thus been compared using data sets from three different periods which are identified as present, past and future. Accuracy in data collection for the beach profiles and the definition of the median grain size calculation using collected samples are the two main factors that have been taken into account in this paper. These data can generate high uncertainties and can produce a lack of accuracy in nourishment projects. Together they can generate excessive costs due to possible excess or shortage of sand used for the nourishment. The main goal of this paper is the development of a new methodology to increase the accuracy of the existing equilibrium beach profile models, providing an improvement to the inputs used in such models and in the fitting of the formulae used to obtain seabed shape. This new methodology has been applied and tested on Valencia's beaches.

Sea-floor images from during POLARSTERN cruise ANT-XV/3 to the Weddell Sea, Antarctica

Transects of a Remotely Operated Vehicle (ROV) providing sea-bed videos and photographs were carried out during POLARSTERN expedition ANT-XV/3 focussing on the ecology of benthic assemblages on the Antarctic shelf in the South-Eastern Weddell Sea. The ROV-system sprint 103 was equiped with two video- and one still camera, lights, flash-lights, compass, and parallel lasers providing a scale in the images, a tether-management system (TMS), a winch, and the board units. All cameras used the same main lense and could be tilted. Videos were recorded in Betacam-format and (film-)slides were made by decision of the scientific pilot. The latter were mainly made under the aspect to improve the identification of organisms depicted in the videos because the still photographs have a much higher optical resolution than the videos. In the photographs species larger than 3 mm, in the videos larger than 1 cm are recognisable and countable. Under optimum conditions the transects were strait; the speed and direction of the ROV were determined by the drift of the ship in the coastal current, since both, the ship and the ROV were used as a drifting system; the option to operate the vehicle actively was only used to avoide obstacles and to reach at best a distance of only approximately 30 cm to the sea-floor. As a consequence the width of the photographs in the foreground is approximately 50 cm. Deviations from this strategy resulted mainly from difficult ice- and weather conditions but also from high current velocity and local up-welling close to the sea-bed. The sea-bed images provide insights into the general composition of key species, higher systematic groups and ecological guilds. Within interdisciplinary approaches distributions of assemblages can be attributed to environmental conditions such as bathymetry, sediment characteristics, water masses and current regimes. The images also contain valuable information on how benthic species are associated to each other. Along the transects, small- to intermediate-scaled disturbances, e.g. by grounding icebergs were analysed and further impact to the entire benthic system by local succession of recolonisation was studied. This information can be used for models predicting the impact of climate change to benthic life in the Southern Ocean. All these approaches contribute to a better understanding of the fiunctioning of the benthic system and related components of the entire Antarctic marine ecosystem. Despite their scientific value the imaging methods meet concerns about the protection of sensitive Antarctic benthic systems since they are non-invasive and they also provide valuable material for education and outreach purposes.

A collection of millennial hymns : adapted to the present order of the church.

Includes index.

Reply (grounded upon records) to the pamphlet published by Wm. Hutt ... in the year 1839; entitled "The Stade duties considered" ...

Text of "The Stade duties considered" and "Reply" in parallel columns.

Prices of corn in Oxford in the beginning of the fourteenth century, also from the year 1853 to the present time; to which are added some miscellaneous notices of prices in other places /

Includes tables.

Foreign direct investment in the United States : report of the Secretary of Commerce to the Congress in compliance with the Foreign investment study act of 1974, Public law 93-479.

Vol. 1 includes full text of the Foreign investment study act of 1974.

An introduction to Latin syntax, or, An exemplification of the rules of construction, as delivered in Mr. Ruddiman's Rudiments : without anticipating posterior rules ... to which is subjoined an epitome of ancient history, from the creation to the birth of Christ ... to which is added, a proper collection of historical and chronological questions : with a copious index /

English and Latin in parallel columns.

The epistle to the Hebrews in Greek and English, with an analysis and exegetical commentary /

Greek and English in parallel columns.

Three letters to the editor of the Maidstone gazette, relative to a free trade in corn, in Great Britain, with some prefatory remarks. Also an appendix, upon the state of wool and woollen trades,

Mode of access: Internet.

Calculating tables, giving the products of every two numbers from one to one thousand and their application to the multiplication and division of all numbers above one thousand.

Added t.-p. in French and German. 9. ed 1904. p. III-X in French and German in parallel columns.

A new and easy method of learning Hebrew without points. : To which is annex'd, by way of praxis, The book of Proverbs, divided according to the metre: with the masoretical reading in Roman letters, the interlinear version of Santes Pagninus, &c. A grammatical analysis, and short notes critical and explanatory ... /

Errata: p. [2]-[3] at end.

Management audit : regulation of grain dealers and warehousemen and the administration of the Grain Insurance Fund : Illinois Department of Agriculture and the Grain Insurance Corporation.

"The audit was conducted pursuant to Legislative Audit Commission Resolution Number 125, which was adopted December 11, 2002. This audit was conducted in accordance with generally accepted government auditing standards and the audit standards promulgated by the Office of the Auditor General at 74 Ill. Adm. Code 420.310. This audit report is transmitted in conformance with Section 3-14 of the Illinois State Auditing Act."--Cover letter.

Llyfr gweddi gyffredin = The Book of common prayer, and administration of the sacraments and other rites and ceremonies of the church, according to the use of the United Church of England and Ireland : together with the Psalter or Psalms of David, pointed as they are to be sung or said in churches.

Preliminary and closing material in Welsh.