Anatomy of production functions: a technological menu and a choice of the best technology

Jones (2005) proposed microfoundations for the Cobb-Douglas production function. We show that Jones' technological menu is a special case of a concept of support set discussed by Matveenko (1997) and Rubinov, Glover (1998) by use of a duality approach. We use this approach to clarify the relation between different production functions and technological menus. Also we construct an "ideas model" generating CES production function.Production function, technological menu, Leontief function, Cobb-Douglas function, CES function, duality, support set

Area distribution of two-dimensional random walks and non Hermitian Hofstadter quantum mechanics

When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non hermitian Hofstadter-like quantum model where a charged particle on a square lattice coupled to a perpendicular magnetic field hopps only to the right. In the commensurate case when the magnetic flux per unit cell is rational, an exact solution of the quantum model is obtained. Periodicity on the lattice allows to relate traces of the Nth power of the Hamiltonian to probability distribution generating functions of biased walks of length N.Comment: 14 pages, 7 figure

Correlation functions in the Calogero-Sutherland model with open boundaries

Calogero-Sutherland models of type $BC_N$ are known to be relevant to the physics of one-dimensional quantum impurity effects. Here we represent certain correlation functions of these models in terms of generalized hypergeometric functions. Their asymptotic behaviour supports the predictions of (boundary) conformal field theory for the orthogonality catastrophy and Friedel oscillations.Comment: LaTeX, 11 pages, 1 eps-figur

Dimensional reduction on a sphere

The question of the dimensional reduction of two-dimensional (2d) quantum models on a sphere to one-dimensional (1d) models on a circle is adressed. A possible application is to look at a relation between the 2d anyon model and the 1d Calogero-Sutherland model, which would allow for a better understanding of the connection between 2d anyon exchange statistics and Haldane exclusion statistics. The latter is realized microscopically in the 2d LLL anyon model and in the 1d Calogero model. In a harmonic well of strength \omega or on a circle of radius R - both parameters \omega and R have to be viewed as long distance regulators - the Calogero spectrum is discrete. It is well known that by confining the anyon model in a 2d harmonic well and projecting it on a particular basis of the harmonic well eigenstates, one obtains the Calogero-Moser model. It is then natural to consider the anyon model on a sphere of radius R and look for a possible dimensional reduction to the Calogero-Sutherland model on a circle of the same radius. First, the free one-body case is considered, where a mapping from the 2d sphere to the 1d chiral circle is established by projection on a special class of spherical harmonics. Second, the N-body interacting anyon model is considered : it happens that the standard anyon model on the sphere is not adequate for dimensional reduction. One is thus lead to define a new spherical anyon-like model deduced from the Aharonov-Bohm problem on the sphere where each flux line pierces the sphere at one point and exits it at its antipode.Comment: 10 pages, 1 figur

Vortex structures of rotating Bose-Einstein condensates in anisotropic harmonic potential

We found an analytical solution for the vortex structure in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level approximation. This solution is exact in the limit of a large number of vortices and is obtained for the case of anisotropic harmonic potential. For the case of symmetric harmonic trap when the rotation frequency is equal to the trapping frequency, the solution coincides with the Abrikosov triangle vortex lattice in type-II superconductors. In a general case the coarse grained density is found to be close to the Thomas-Fermi profile, except the vicinity of edges of a condensate cloud.Comment: 7 pages, 3 figure

Księgi Metamorphoseon В. Отвиновского как источник для русских переводов Метаморфоз Овидия начала XVIII века: номинация святилищ

The article examines the translation of lexemes nominating shrines in Polish Ovid’s Metamorphoses adaptation Księgi Metamorphoseon, to jest, Przemian od Publiusa Owidiusza Nasona Wierszami opisane made by Walerian Otwinowski in 1638. From this Polish verse translation in early 18th century was made both Russian translations of Metamorphoses. Thus the results of present study can be considered also as starting point for further examination of Russian translations. It is determined that in Otwinowski’s version lexeme kościół was chosen as a unified neutral equivalent for some different Latin nominations of pagan sanctuaries. Comparison with another Polish translation of Metamorphoses, Jakob Żebrowski’s Metamorphoseon, to jest Przeobrażenia ksiąg piętnaście (1636), shows that Otwinowski’s decision to translate different Latin lexical equivalents by unified lexical item is a distinctive feature of his translation. For further study in translation techniques in both Russian translations it is important that the Polish origin (Otwinowski’s translation) itself doesn’t represent a field for a variety of translation correspondences within considered lexemes.В статье исследуются принципы перевода наименований сакральных построек в польской комментированной версии Метаморфоз Овидия Księgi Metamorphoseon, to jest, Przemian od Publiusa Owidiusza Nasona Wierszami opisane, изданной Валерианом Отвиновским в Кракове в 1638 г. Именно с этого польского текста в начале XVIII в. были выполнены первые полные русские переводы Метаморфоз. Устанавливается, что в абсолютном большинстве случаев В. Отвиновский выбрал единый нейтральный вариант для перевода разных латинских наименований языческих святилищ – лексему kościół. Сравнение перевода В. Отвиновского с переводом Я. Жебровского, изданным в 1636 г., показывает, что унификация вариантов перевода была сознательным выбором В. Отвиновского. Проведённое исследование может стать точкой отсчёта для дальнейшего анализа обращения с наименованиями святилищ в русских переводах. W. Otwinowskio „Księgi Metamorphoseon“ kaip XVIII amžiaus pradžios Ovidijaus „Metamorfozės“ vertimų į rusų kalbą šaltinis: šventovių pavadinimai Santrauka. Straipsnyje nagrinėjami sakralinių pastatų pavadinimų vertimo principai Valerijano Otwinowskio lenkiškoje komentuotoje Ovidijaus Metamorphoses versijoje Księgi Metamorphoseon, to jest, Przemian od Publiusa Owidiusza Nasona Wierszami opisane, išleistoje 1638 m. Krokuvoje. Būtent iš šio lenkiško teksto XVIII a. pradžioje buvo padaryti pirmieji pilni Metamorfozių vertimai į rusų kalbą. Nustatyta, kad daugeliu atvejų W. Otwinowskis įvairiems lotyniškiems pagoniškų šventovių pavadinimams versti pasirinko vieną neutralų variantą ‒ leksemą kościół. Otwinowskio vertimo gretinimas su J. Žebrovskio vertimu, išleistu 1636 m., parodo, kad vertimo variantų suvienodinimas buvo sąmoningas V. Otwinowskio pasirinkimas. Atliktas tyrimas gali tapti atspirties tašku tolesniam šventovių pavadinimų traktavimo rusų vertimuose nagrinėjime. Reikšminiai žodžiai: Ovidijaus Metamorfozės, vertimo technika, lenkų-lotynų kalbos vertimai, šventovių pavadinimai, W. Otwinowski