Vertex algebras and the Landau-Ginzburg/Calabi-Yau correspondence

We construct a spectral sequence that converges to the cohomology of the chiral de Rham complex over a Calabi-Yau hypersurface and whose first term is a vertex algebra closely related to the Landau-Ginburg orbifold. As an application, we prove an explicit orbifold formula for the elliptic genus of Calabi-Yau hypersurfaces.Comment: Latex, 50p. Some typos corrected, the page size may have been fixed. One new result, a theorem on the vertx algebra structure of the Landau-Ginzburg orbifold appears in sect. 5.2.18. This is the final version to appear in the Moscow Mathematical Journa

Deformations of chiral algebras and quantum cohomology of toric varieties

We reproduce the quantum cohomology of toric varieties (and of some hypersurfaces in projective spaces) as the cohomology of certain vertex algebras with differential. The deformation technique allows us to compute the cohomology of the chiral de Rham complex over the projective space.Comment: we use the deformation technique from the earlier version of this note to compute the cohomology of the chiral de Rham complex over the projective space; the two new results, Theorems 2.5A and B, are explained in sect. 2.

The Comparison of Two Calculation Methods of Billets Heating in Furnaces with the Help of Zone and FVM Methods

The comparison of two modelling methods for radiation heat exchange – finite volume and zonal methods – has been provided. The mathematical model of heating concast bars ring furnace has been created. Modelling of different heat modes of this furnace has been completed. In the result of modelling, it is shown that these methods demonstrate similar accuracy of obtained temperature values (not exceeding 50∘C). The calculation time of FVM method is greater than zonal method to 13%, because recalculations of absorption coefficients by EWBM method is needed. Keywords: radiation transfer, mathematical modeling, zonal method, discrete transfer zonal metho

PROBLEMS OF TEACHING HUMAN ANATOMY AT THE MODERN STAGE AND THE WAYS OF THEIR SOLUTIONS

For quality teaching human anatomy to students, it is necessary to emphasize the efficient use and combination of traditional methods with various forms of integration of test control. Through the details of the study of the organs structure on natural preparations, with their wider use, it is necessary to distinguish clinical aspects: introduction to the educational process of acquaintance with the data of various clinical situations using the example of the use of situational tasks «Krok-1». This is precisely the way which is methodically substantiated for the optimization and scientific organization of the modern educational process at the human anatomy departments. Aim and tasksof this work was to reveal the essence and characteristics of teaching human anatomy in modern conditions, identifying the shortcomings and advantages of the updated approaches to teaching, introduced in the educational process, and rethinking the traditional teaching methods with various forms of integration of modern techniques. Methods and results of the study. Efficient use and combination of traditional methods with various forms of integration of test control (but not prevailing) is the methodically substantiated way of optimization and scientific organization of the educational process in the applied study of anatomy as the foundation of medicine. This method of conducting classes and monitoring students knowledge gives them an opportunity to learn as much material as possible and encourages them to process data of all sections of the subject by themselves which is necessary for obtaining the profession of a doctor in the futur

Simulation of the solidification of the melt in the Vanyukov furnace in the case of emergency stoppage

A mathematical model of the Vanyukov furnace, which makes it possible to predict the behavior of an object in the emergency operational mode (upon the disconnection of the oxygen supply) and develop an effective system of additional heating which damps the consequences of the emergency mode and lowers the costs for the renovation of the furnace operation, is created. It is shown how solidification upon cooling the furnace with time is simulated using the enthalpy and porosity method. The mathematical model is adopted for existing production conditions, which are weakly defined. The energy characteristics of the mode for the solidifying furnace bath, which ensures its holding for a long time in the ready state to rapid firing, are found. Thus, the problem of excessively expensive furnace firing after prolonged production stoppage is solved in the conjugated statement with a calculation of the heating system of the overbath space. © 2013 Allerton Press, Inc

View factors for surface zones

Methods of calculating view factors with different surface configurations are compared. A simple approach is proposed for estimating the error in calculating the view factors. An algorithm is formulated for selection of the method and the number of points of integration prior to the calculation. The algorithm significantly reduces the computation time by minimizing the number of integration points required, without loss of precision. © 2013 Allerton Press, Inc