The earliest known record of California Indian numbers

The earliest written record of a numeral system for any California Indian tribe has been ascribed to Padre José Señán, O.F.M., missionary at Mission San Buenaventura. It is now known that the earliest is in The First Spanish Entry Into San Francisco Bay 1775, the diary of Fr. Vicente Maria, O.F.M., chaplain of a Spanish expedition. He recorded the Indian words for the numbers one to fourteen. The first eight of these correspond with the same numbers used by the Costanoans of Mission Santa Clara. The differences are credited to the influence of other tribes who visited Angel Island in San Francisco Bay where Padre Vicente made his record.     

The basis automaton for the given regular language

A new problem of the theory of finite automata (Rabin-Scott’s automata) is considered. So called basis automaton for the given regular languageL is defined. This automaton is unique for the givenL, it is defined by two automata of canonical form: forL and for its inverse languageL ^R. Some properties of basis automata are considered. Such properties make these automata most convenient for using in some special tasks, dealing with the given regular language.     

The improved screening curve method regarding existing units

In this study, a new method is developed to determine the least cost capacity expansion of a power system by using the screening curve method. The proposed methodology differs from the previous studies by its geometrical solution process to evaluate a capacity expansion problem considering both existing and candidate power plants. The algorithms are computationally more efficient and simple than the ones in previous studies for the same improvement. Further, the interpretation of the optimal capacity expansion plan is enhanced by explicitly exhibiting the results of all considered capacity expansion alternatives. The solution process can be interpreted as minimizing the long run marginal cost of supplying 1 megawatt of capacity during the whole year by finding the optimal combination of units. The developed method calculates and finds the cost polygon with the minimum area by moving along the intersection points of the screening curves to form trapezoids and then joining them to form cost polygons. The intersection points, which are needed to calculate the areas of the cost polygons, are found by using the Karush–Kuhn–Tucker conditions in a recursive manner. The last unit in the merit order of dispatching is determined by scenarios to yield an optimal capacity expansion plan. The scenarios are primarily based on a tradeoff between incurring investment costs by commissioning candidate units or taking online existing units with relatively higher variable costs compared to the candidate units.     

Three-dimensional numerical modeling of thermohaline and wind-driven circulations in the Persian Gulf

The Persian Gulf circulation is investigated with respect to the relevant forcing mechanism including wind stress and thermohaline surface fluxes by using a three-dimensional numerical hydrodynamic model. The model results show a correlation between the strength of the bottom layer outflow of the Persian Gulf and that of the Indian Ocean Surface Water (IOSW) inflow into the Gulf. The inflow of IOSW into the Gulf attain maximum values in May–June in conjunction with peak bottom outflow through the Hormuz Strait. The results of sensitivity experiment indicate that circulation is dominated by thermohaline flows at almost all parts of the Gulf. The heat fluxes play an essential role on the general circulation of the Persian Gulf. In spring and summer, the wind stress generates southeast-flowing surface currents of magnitude about 5 cm/s along the Saudi Arabia and Iranian coasts on the northern Gulf. In winter and autumn, due to weak static stability, the wind produces mesoscale eddies in most parts of the Gulf. In winter and spring the wind stress acts to reinforce the thermohaline circulation of deep outflow. Conversely, in summer and autumn the wind forcing acts in opposition to the thermohaline forcing and causes a bottom inflow from Oman Sea into the Gulf.     

Mathematical books for and in India in the nineteenth century

This paper investigates mathematical books published in England especially for India, and books translated in India, in the nineteenth century. The survey has been carried out at the Oriental and India Office of the British Library and does not claim to be exhaustive. I have discussed the contents of those written in Hindi and have listed those in other languages for others to translate if they wish.     

Karl M. Peterson: The earliest derivation of the Mainardi-Codazzi equations and the fundamental theorem of surface theory

In 1853 Karl M. Peterson, a young Latvian student at the University of Dorpat [Tartu], submitted a candidates' dissertation [a requirement for obtaining a degree] containing a derivation of the Gauss-Mainardi-Codazzi equations and a proof of the Fundamental Theorem of Surface Theory. This predates the publications of equivalent equations derived by G. Mainardi [1856] and D. Codazzi [1860 and 1868–1869], as well as O. Bonnet's proof of the Fundamental Theorem. Although Peterson later [1865–1881] played a major role in the formation of a school of differential geometry at Moscow University, this early work remained virtually unknown until its translation [into Russian] and its publication in 1952. The contents of the dissertation and the probable sources of Peterson's ideas and techniques are discussed.     

Henselianity in the language of rings

We consider four properties of a field K related to the existence of (definable) henselian valuations on K and on elementarily equivalent fields and study the implications between them. Surprisingly, the full pictures look very different in equicharacteristic and mixed characteristic.     

Sentences in the language of reasoning

In the present paper we investigate a few grammatical aspects of texts in which a reasoning has been expressed. We are mainly interested in text units (called sentences) that are constituent parts of a reasoning.

Firstly we discuss the full conceptual framework reflected in the reasoning: its under lying form. Next we divide sentences into two main classes: fundamental and informative sentences. Each of these main classes will thereupon be subdivided. In classifying we are guided by the manner in which sentences function in a reasoning. The nature of each class is elucidated by a discussion and examples.

We subsequently deal with compound sentences and sentence groups. Finally we analyse two texts according to the grammatical classification principles explained in the paper.     

The mirror image of the language of 2-synchronizing words

Aword w over a finite alphabet Σ is said to be n-synchronizing if for each deterministic finite automaton $ \overleftarrow w $ \overleftarrow w = a _t ...a ₂ a ₁.     

The language of geodesics for Garside groups

We prove that the language of all geodesics of any Garside group, with respect to the generating set of divisors of the Garside element, forms a regular language. In particular, the braid groups admit generating sets where the associated language of geodesics is regular.in final form: 28 October 2003Charney was partially supported by NSF grant DMS-0104026. Meier thanks the AMS for the support of a Centennial Research Fellowship.     

The first Chinese translation of the last nine books of Euclid's Elements and its source

Books VII to XV of the Elements (Books VII to XIII by Euclid and Books XIV and XV by Hypsicles of Alexandria) were first translated into Chinese by the British missionary Alexander Wylie and the Chinese mathematician Li Shanlan between the years 1852 and 1856. The translation was subsequently published in 1857. Neither of the translators in their prefaces to the translation or in their other writings mentioned the specific original source. Accordingly, historians have pondered this question ever since. Some took a bold guess that its source was Isaac Barrow's English translation. This article provides solid evidence to show that the guess is wrong, and argues that the first English translation of Euclid's Elements of 1570 by Henry Billingsley was the actual source.