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### Arithmetic

 Arithmetic or arithmetics (from the Greek word ????µ?? = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers. Professional mathematicians sometimes use the term (higher) arithmetic when referring to more advanced results related to number theory, but this should not be confused with elementary arithmetic.

### Vplx Program Documentation Volume 1: Introduction

##### By: Robert E. Fay

Statistical Reference Document

Excerpt: History. This documentation describes VPLX, a general program for variance estimation from complex samples. VPLX was begun in 1989. The initial and continuing objective is to develop a general purpose program for the analysis of survey data generally and Census Bureau products specifically. The program has been used for a number of purposes at the Census Bureau. It is the production system for the variance calculations for the Current Population Survey (CPS), th...

### Interaction of Ice Sheets and Climate During the Past 800 000 Year...

##### By: B. De Boer; R. Bintanja; R. S. W. Van De Wal; L. J. Lourens; L. B. Stap

Description: Institute for Marine and Atmospheric research Utrecht, Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlands. During the Cenozoic, land ice and climate interacted on many different timescales. On long timescales, the effect of land ice on global climate and sea level is mainly set by large ice sheets in North America, Eurasia, Greenland and Antarctica. The climatic forcing of these ice sheets is largely determined by the meridional ...

Abe-Ouchi, A., Saito, F., Kawamura, K., Raymo, M. E., Okuno, J., Takahashi, K., and Blatter, H.: Insolation-driven 100 000-year glacial cycles and hysteresis of ice-sheet volume, Nature, 500, 190–193, 2013.; Annan, J. D. and Hargreaves, J. C.: A new global reconstruction of temperature changes at the Last Glacial Maximum, Clim. Past, 9, 367–376, doi:10.5194/cp-9-367-2013, 2013.; Bahr, D. B., Meier, M. F., and Peckham, S...

### Can We Predict the Duration of an Interglacial? : Volume 8, Issue ...

##### By: L. C. Skinner; J. F. McManus; E. W. Wolff; V. Brovkin; P. C. Tzedakis; D. Raynaud; D. A. Hodell

Description: Environmental Change Research Centre, Department of Geography, University College London, London WC1E 6BT, UK. Differences in the duration of interglacials have long been apparent in palaeoclimate records of the Late and Middle Pleistocene. However, a systematic evaluation of such differences has been hampered by the lack of a metric that can be applied consistently through time and by difficulties in separating the local from the global component in var...

American Commission on Stratigraphic Nomenclature: Code of stratigraphic nomenclature, Am. Assoc. Petr. Geol. B., 45, 645–660, 1961.; Archer, D. and Ganopolski, A.: A movable trigger: Fossil fuel CO2 and the onset of the next glaciation, Geochem. Geophys. Geosyst. 6, Q05003, doi:10.1029/2004GC000891, 2005.; Bard, E., Hamelin, B., and Delanghe-Sabatier, D.: Deglacial meltwater Pulse 1B and Younger Dryas sea lev...

### Improving Computational Efficiency in Large Linear Inverse Problem...

##### By: A. M. Michalak; V. Yadav

Description: Department of Global Ecology, Carnegie Institution for Science, Stanford, California, 94305, USA. Addressing a variety of questions within Earth science disciplines entails the inference of the spatiotemporal distribution of parameters of interest based on observations of related quantities. Such estimation problems often represent inverse problems that are formulated as linear optimization problems. Computational limitations arise when the number of obs...

Aster, R. C., Borchers, B., and Thurber, C. H.: Parameter estimation and inverse problems, Academic Press, 376 pp., 2013.; Atmadja, J. and Bagtzoglou, A. C.: State of the art report on mathematical methods for groundwater pollution source identification, Environ. Forensics, 2, 205–214, 2001.; Bennett, A. F.: Inverse modeling of the ocean and atmosphere, Cambridge University Press, Cambridge, UK, 2002.; Golub, G. H. and Van Loan, C. F.: Matrix Computations, 3rd ed., The J...

### Data Compression to Define Information Content of Hydrological Tim...

##### By: M. B. Parlange; N. Van De Giesen; S. V. Weijs

Description: Environmental fluid mechanics and Hydrology Lab, ENAC, Ecole Polytechnique Fédérale de Lausanne, Station 2, 1015 Lausanne, Switzerland. When inferring models from hydrological data or calibrating hydrological models, we might be interested in the information content of those data to quantify how much can potentially be learned from them. In this work we take a perspective from (algorithmic) information theory (AIT) to discuss some underlying issues regar...

McMillan, B.: Two inequalities implied by unique decipherability, IEEE T. Inform. Theory, 2, 115–116, 1956.; Alfonso, L., Lobbrecht, A., and Price, R.: Information theory–based approach for location of monitoring water level gauges in polders, Water Resour. Res., 46, W03528, doi:10.1029/2009WR008101, 2010{a}.; Alfonso, L., Lobbrecht, A., and Price, R.: Optimization of water level monitoring network in polder systems usin...

### Multivariate Localization Methods for Ensemble Kalman Filtering : ...

##### By: I. Szunyogh; M. G. Genton; M. Jun; S. Roh

Description: Department of Statistics, Texas A&M University, College Station, TX, USA. In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performan...

Anderson, J. L.: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter, Physica D, 230, 99–111, 2007.; Anderson, J. and Lei, L.: Empirical localization of observation impact in ensemble kalman filters, Mon. Weather Rev., 142, 739–754, 2013.; Askey, R.: Radial Characteristic Functions, technical report no. 1262, Mathematical Research Center, University of Wisconsin-Madison, Madison, 1973.; Bishop, C. H. and Hodyss, D.: Flow...

### The Pig and the Whitle

##### By: George Robert Gissing, 1857-1903

'I possess a capital of thirty thousand pounds. One third of this is invested in railway shares, which bear interest at three and a half per cent.; another third is in Government stock, and produces two and three-quarters per cent.; the rest is lent on mortgages, at three per cent. Calculate my income for the present year.' This kind of problem was constantly being given out by Mr. Ruddiman, assistant master at Longmeadows School. Mr. Ruddiman, who had reached the age of...

### Geometric Models for Noncommutative Algebras

##### By: Ana Cannas Da Silva

Mathematics document containing theorems and formulas.

Excerpt: Poisson Maps; Characterization of Poisson Maps; Complete Poisson Maps; Symplectic Realizations; Coisotropic Calculus; Poisson Quotients; and Poisson Submanifolds.

### Epitaph on the Earl of Strafford

##### By: John Cleveland

Poetry

Excerpt: HERE lies wise and valiant dust // Huddled up 'twixt fit and just, // Strafford, who was hurried hence // 'Twixt treason and convenience. // He spent his time here in a mist, // A Papist, yet a Calvinist; // His Prince's nearest joy and grief, // He had, yet wanted all relief; // The prop and ruin of the state; // The people's violent love and hate; // One in extremes loved and abhorred. // Riddles lie here, or in a word - // Here lies blood; and let it lie // S...

### Maximus in Minimis : Aphlorisms in Unistiches

##### By: Florentin Smarandache

Etymologically, aphorism + floral = aph(L)orism, which is a short reflection written on a floral design, or a short poetry accompanied by an artistic background. They are colorful contemplations. Maximus in minimis (Lat.) means very much in very little [max in min], or condensed thought, or ideating essence. They are actually maxims, adages, sayings mostly in one line (uni-stich) with a title, as a metaphoric statement, a breathing momentum that oils our soul.

Nonchalantly : The wind with its mantle steps lightly. Skin Condition : The Sun has spots too. At what time? When it rains, God cries. Atmosphere : Blue, as the sky dirtied by clouds. Bright : A balcony full of Sun. Natural disaster : The swans look drunk on the fetid lake. Surprisingly : The crow is a beautiful black. Elegant woman : A bird high on her legs. Most powerful chess piece : You are a queen but only in the dark. Medicinal plant : You’re a flower but ...

### Mathematical Economics and Finance

##### By: Michael Harrison

Mathematics document containing theorems and formulas.

Excerpt: Sign conditions for inequality constrained optimization; Payoffs for Call Options on the Aggregate Consumption; The effect of an interest rate of 10% per annum at different frequencies of compounding; and Notation for portfolio choice problem.

### World Health Organization ; World Health Organization Offeset Publ...

##### By: World Health Organization

Medical Reference Publication

FOREWORD If properly designed, any basic air monitoring programme can provide the data required to develop an air pollution control programme. Analyses of the data collected should relate directly to the purpose, or purposes, of the monitoring programme, the three most common being: (1) to observe trends; (2) to judge compliance with air quality standards and to evaluate control strategies; and (3) to evaluate risk to human health. Other analyses may also be important fo...

### Language, Proof and Logic

##### By: John G. Kemeny

Mathematics document containing theorems and formulas.

Excerpt: The special role of logic in rational inquiry. What do the fields of astronomy, economics, finance, law, mathematics, medicine, physics, and sociology have in common? Not much in the way of subject matter, that's for sure. And not all that much in the way of methodology. What they do have in common, with each other and with many other fields, is their dependence on a certain standard of rationality. In each of these fields, it is assumed that the participants ca...

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