Vertex Algebras, Mirror Symmetry, And D-Branes: The Case Of Complex Tori

A vertex algebra is an algebraic counterpart of a two-dimensional conformal field theory. We give a new definition of a vertex algebra which includes chiral algebras as a special case, but allows for fields which are neither meromorphic nor anti-meromorphic. To any complex torus equipped with a flat Kahler metric and a closed 2-form we associate an N=2 superconformal vertex algebra (N=2 SCVA) in the sense of our definition. We find a criterion for two different tori to produce isomorphic N=2 SCVA's. We show that for algebraic tori isomorphism of N=2 SCVA's implies the equivalence of the derived categories of coherent sheaves corresponding to the tori or their noncommutative generalizations (Azumaya algebras over tori). We also find a criterion for two different tori to produce N=2 SCVA's related by a mirror morphism. If the 2-form is of type (1,1), this condition is identical to the one proposed by Golyshev, Lunts, and Orlov, who used an entirely different approach inspired by the Homological Mirror Symmetry Conjecture of Kontsevich. Our results suggest that Kontsevich's conjecture must be modified: coherent sheaves must be replaced with modules over Azumaya algebras, and the Fukaya category must be ``twisted'' by a closed 2-form. We also describe the implications of our results for BPS D-branes on Calabi-Yau manifolds.Comment: 70 pages, AMS Latex. v2: a gap in the reasoning of Appendix B has been filled, and a proof of the "Borcherds formulas" has been adde

Lectures on Mirror Symmetry, Derived Categories, and D-branes

This paper is an introduction to Homological Mirror Symmetry, derived categories, and topological D-branes aimed mainly at a mathematical audience. In the paper we explain the physicists' viewpoint of the Mirror Phenomenon, its relation to derived categories, and the reason why it is necessary to enlarge the Fukaya category with coisotropic A-branes; we discuss how to extend the definition of Floer homology to such objects and describe mirror symmetry for flat tori. The paper consists of four lectures which were given at the Institute for Pure and Applied Mathematics (Los Angeles), March 2003, as part of a program on Symplectic Geometry and Physics.Comment: 30 page

Noncommutative Instantons and Twistor Transform

Recently N.Nekrasov and A.Schwarz proposed a modification of the ADHM construction of instantons which produces instantons on a noncommutative deformation of the 4-dimensional real affine space. In this paper we study the relation between their construction and algebraic bundles on noncommutative projective spaces. We exhibit one-to-one correspondences between three classes of objects: framed bundles on a noncommutative projective plane, certain complexes of sheaves on a noncommutative 3-dimensional projective space, and the modified ADHM data. The modified ADHM construction itself is interpreted in terms of a noncommutative version of the twistor transform. We also prove that the moduli space of framed bundles on the noncommutative projective plane has a natural hyperkahler metric and is isomorphic as a hyperkahler manifold to the moduli space of framed torsion free sheaves on the commutative projective plane. The natural complex structures on the two moduli spaces do not coincide but are related by an SO(3) rotation. Finally, we propose a construction of instantons on a more general noncommutative R^4 than the one considered by Nekrasov and Schwarz (a q-deformed R^4).Comment: 56 pages, AMS-Latex. Dedicated to A.N.Tyurin on his 60th birthday. v2: A section about instantons on a q-deformed R^4 and the corresponding q-deformation of the ADHM construction has been adde

Remarks on A-branes, mirror symmetry, and the Fukaya category

We discuss D-branes of the topological A-model (A-branes), which are believed to be closely related to the Fukaya category. We give string theory arguments which show that A-branes are not necessarily Lagrangian submanifolds in the Calabi–Yau: more general coisotropic branes are also allowed, if the line bundle on the brane is not flat. We show that a coisotropic A-brane has a natural structure of a foliated manifold with a transverse holomorphic structure. We argue that the Fukaya category must be enlarged with such objects for the Homological Mirror Symmetry Conjecture to be true

Better seasonal forecasts for the renewable energy industry

Anomalous seasons such as extremely cold winters or low-wind summers can seriously disrupt renewable energy productivity and reliability. Better seasonal forecasts providing more accurate information tailored to stakeholder needs can help the renewable energy industry prepare for such extremes.The authors acknowledge funding from the EU Horizon 2020 project “Sub-seasonal to seasonal climate forecasting for energy (S2S4E)” (GA776787).Peer ReviewedPostprint (author's final draft

Carbon taxation in Russia : prospects for a double dividend and improved energy efficiency

Russia is not only one of the world?s major sources of carbon based energy ? coal, oil and gas ? but is also one the most intensive users of energy. Furthermore, Russia accounts for a disproportionately large share of global carbon dioxide emissions ? some 5% to 6% of global carbon dioxide emissions (EIA, 2011a). It has been estimated (World Bank, 2008) that Russia could reduce its use of primary energy use by 45% with consequent economic and environmental benefits. High energy and carbon intensity of the Russia economy is, inter alia, explained by low energy prices due to high export taxes as well as administrative regulation of domestic prices of gas and electricity and low environmental taxes. Carbon taxes are one such Pigouvian tax and they would address concerns on several fronts simultaneously. In the short to medium term they would, inter alia, lead to lower GHG emissions and encourage the diffusion of more energy efficient technologies. In the longer term, the increased cost of energy inputs is expected to induce technological progress. In this analysis, the macroeconomic and sectoral effects of carbon taxes on the Russia economy are examined. This analysis addresses the following objectives: i) to test the double dividend hypothesis under perfect and imperfect competition in output markets, to analyse ii) the incidence of carbon taxes, iii) impacts on sectoral competitiveness, iv) effects on income equity, and v) interactions of carbon taxes with other taxes. A computable single-country multi-sector comparative static CGE model is employed.Russland verfügt nicht nur über einen der größten Vorräte an kohlenstoffbasierter Energie wie Kohle, Rohöl und Gas, sondern ist auch einer der größten Energieverbraucher. Darüber hinaus ist Russland für einen überproportional großen Anteil von Kohlendioxid-Emission - etwa 5% bis 6% ? der weltweiten Kohlendioxidemission verantwortlich. Mit der Einführung einer Kohlendioxidsteuer könnten gleichzeitig unterschiedliche Wirkungen erzielt werden. Kurz- und mittelfristig würden Kohlenstoffsteuern sowohl zu einer Reduzierung von Treibhausgasemissionen als auch zur Einführung von energieeffizienteren Technologien führen. Langfristig wird erwartet, dass hohe Energiekosten den Anreiz zur Entwicklung und zur Investition in energiesparenden technischen Fortschritt erhöhen. Die vorliegende Arbeit analysiert und bewertet die makroökonomischen und sektoralen Auswirkungen einer Einführung von Kohlenstoffsteuern auf die russische Wirtschaft. Die Ziele der Arbeit bestehen darin, die Hypothese der doppelten Dividende für den Fall des vollkommenen und des unvollkommenen Wettbewerbs auf Gütermärkten zu überprüfen und die Inzidenz einer Kohlenstoffsteuer, ihre Auswirkungen auf die sektorale Wettbewerbsfähigkeit, ihre Auswirkungen auf die Einkommensverteilung und die Interaktion von Kohlenstoffsteuern mit anderen Steuern zu analysieren und zu bewerten. Als methodischer Ansatz wurde ein Single-Country und Multi-Sektor Model gewählt

Mathematical model of nonstationary hydraulic processes in gas centrifuge cascade for separation of multicomponent isotope mixtures

The article presents results of development of a mathematical model of nonstationary hydraulic processes in gas centrifuge cascade for separation of multicomponent isotope mixtures. This model was used for the calculation parameters of gas centrifuge cascade for separation of silicon isotopes. Comparison of obtained values with results of other authors revealed that developed mathematical model is adequate to describe nonstationary hydraulic processes in gas centrifuge cascades for separation of multicomponent isotope mixtures

Modeling of filling gas centrifuge cascade for nickel isotope separation by feed flow input to different stages

The article presents results of research filling gas centrifuge cascade by process gas fed into different stages. The modeling of filling cascade was done for nickel isotope separation. Analysis of the research results shows that nickel isotope concentrations of light and heavy fraction flows after filling cascade depend on feed stage number

АNALYSIS OF OPTICAL METHODS FOR MONITORING THE WORKING SURFACE STATE OF THE GRINDING WHEEL

The article describes an analysis of non-contact optical methods for monitoring linear wear and the working surface condition of the grinding wheel during dry grinding. The presented methods are based on computer processing of photo and video materials, 3D models surface construction of the grinding wheel, the machine vision and using of the optical equipment. The advantages and disadvantages of this methods were analyzed. As a result of the conducted research, it was concluded that the usable area of the considered methods depends on the circle material, cutting parameters, control objectives, including the requirement for on-line control, and also the available material and technical equipment

Ellipsis and zeugma in Portuguese

In this article such a figure of speech as ellipsis in Portuguese is considered. An analysis of ellipsis, its functions, properties and features is conducted. Four types of ellipsis in Portuguese are described, with an analysis of their examples. Additionally, zeugma and its essence are considered, along with its relevance to ellipsis and their differences