Real-time Optimal Monetary Policy with Undistinguishable Model Parameters and Shock Processes Uncertainty

This paper studies optimal real-time monetary policy when the central bank takes the exogenous volatility of the output gap and inflation as proxy of the undistinguishable uncertainty on the exogenous disturbances and the parameters of its model. The paper shows that when the exogenous volatility surrounding a specific state variable increases, the optimal policy response to that variable should increase too, while the optimal response to the remaining state variables should attenuate or be unaffected. In this way the central bank moves preemptively to reduce the risk of large deviations of the economy from the steady state that would deteriorate the distribution forecasts of the output gap and inflation. When an empirical test is carried out on the US economy the model predictions tend to be consistent with the data

Ramanujan's "Lost Notebook" and the Virasoro Algebra

By using the theory of vertex operator algebras, we gave a new proof of the famous Ramanujan's modulus 5 modular equation from his "Lost Notebook" (p.139 in \cite{R}). Furthermore, we obtained an infinite list of $q$-identities for all odd moduli; thus, we generalized the result of Ramanujan.Comment: To appear in Comm. Math. Phy

Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, II: higher level case

We give an a priori proof of the known presentations of (that is, completeness of families of relations for) the principal subspaces of all the standard A_1^(1)-modules. These presentations had been used by Capparelli, Lepowsky and Milas for the purpose of obtaining the classical Rogers-Selberg recursions for the graded dimensions of the principal subspaces. This paper generalizes our previous paper.Comment: 26 pages; v2: minor revisions, to appear in Journal of Pure and Applied Algebr

The N=1 triplet vertex operator superalgebras

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, important in logarithmic conformal field theory. We classify irreducible SW(m)-modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible SW(m) characters. Finally, we contemplate possible connections between the category of SW(m)-modules and the category of modules for the quantum group U^{small}_q(sl_2), q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily on properties of characters and the Zhu's algebra A(SW(m)). This paper is a continuation of arXiv:0707.1857.Comment: 53 pages; v2: references added; v3: a few changes; v4: final version, to appear in CM

Structure of and ion segregation to an alumina grain boundary: implications for growth and creep

Using periodic density-functional theory (DFT), we investigated the structure and cohesive properties of the �-alumina �11 tilt grain boundary, with and without segregated elements, as a model for the thermally grown oxide in jet engine thermal barrier coatings. We identified a new low-energy structure different from what was proposed previously based on electron microscopy and classical potential simulations. We explored the structure and energy landscape at the grain boundary for segregated Al, O, and early transition metals (TMs) Y and Hf. We predict that the TMs preferentially adsorb at the same sites as Al, while some adsites favored by O remain unblocked by TMs. All segregated atoms have a limited effect on grain boundary adhesion, suggesting that adhesion energies alone cannot be used for predictions of creep inhibition. These findings provide some new insights into how TM dopants affect alumina growth and creep kinetics. I

Higher depth false modular forms

False theta functions are functions that are closely related to classical theta functions and mock theta functions. In this paper, we study their modular properties at all ranks by forming modular completions analogous to modular completions of indefinite theta functions of any signature and thereby develop a structure parallel to the recently developed theory of higher depth mock modular forms. We then demonstrate this theoretical base on a number of examples up to depth three coming from characters of modules for the vertex algebra $W^0(p)_{A_n}$, $1 \leq n \leq 3$, and from $\hat{Z}$-invariants of $3$-manifolds associated with gauge group $\mathrm{SU}(3)$

Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case

This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine Lie algebras. A key idea is to prove suitable presentations of principal subspaces, without using bases or even ``small'' spanning sets of these spaces. In this paper we prove presentations of the principal subspaces of the basic A_1^(1)-modules. These convenient presentations were previously used in work of Capparelli-Lepowsky-Milas for the purpose of obtaining the classical Rogers-Ramanujan recursion for the graded dimensions of the principal subspaces.Comment: 20 pages. To appear in International J. of Mat

Logarithmic intertwining operators and vertex operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra $M(1)_a$, of central charge $1-12a^2$. We classify these operators in terms of {\em depth} and provide explicit constructions in all cases. Furthermore, for $a=0$ we focus on the vertex operator subalgebra L(1,0) of $M(1)_0$ and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of {\em hidden} logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1,0)-module.Comment: 32 pages. To appear in CM