We introduce and study the notion of a logarithmic vertex algebra, which is algebra with singularities in operator product expansion quantum fields; thus providing rigorous formulation algebraic properties fields conformal field theory. develop framework that allows many results about algebras to be extended algebras, including particular Borcherds identity Kac Existence Theorem. Several exampl...

This is the second part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part II), we develop logarithmic formal calculus and study logarithmic intertwining operators. In this paper, Part II of a series of eight papers on logarithmic tensor category theory, we develop ...

Some physical parameters, that are positive by definition, appear often as reciprocal pairs, like an electrical resistivity ρ and the electrical conductivity σ = 1/ρ , or a frequency ν and the period T = 1/ν . Theoretical arguments suggest that behind these pairs there are more natural parameters: their logarithms. This paper suggests a terminology that could bring those logarithmic units into ...

background: cutaneous leishmaniasis is one of the most important parasitic diseases in humans. in this disease, one of the responsible organisms is leishmania major, which is transmitted by sandfly vector. there are specific differences in biochemical profiles and metabolite pathways in logarithmic and stationary phases of leishmania parasites. in the present study, 1h nmr spectroscopy was used...

for all $a,b>0$, the following two optimal inequalities are presented: $h^{alpha}(a,b)l^{1-alpha}(a,b)geq m_{frac{1-4alpha}{3}}(a,b)$ for $alphain[frac{1}{4},1)$, and $ h^{alpha}(a,b)l^{1-alpha}(a,b)leq m_{frac{1-4alpha}{3}}(a,b)$ for $alphain(0,frac{3sqrt{5}-5}{40}]$. here, $h(a,b)$, $l(a,b)$, and $m_p(a,b)$ denote the harmonic, logarithmic, and power means of order $p$ of two positive numbers...

LetX be a complex analytic manifold, D ⊂ X a Koszul free divisor with jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor), j : U = X −D →֒ X the corresponding open inclusion, E an integrable logarithmic connection with respect to D and L the local system of the horizontal sections of E on U . In this paper we prove that the canonical morphisms ΩX(logD)(E(kD)) −→ Rj∗L, j...

We show that the monotone analogue of logspace computation is more powerful than monotone log-depth circuits: monotone bounded fanin circuits for a certain function in monotone logspace require depth (lg 2 n).