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 paper introduces a novel constraint adaptive filtering algorithm based on a relative logarithmic cost function which is termed as Constrained Least Mean Logarithmic Square (CLMLS). The proposed CLMLS algorithm elegantly adjusts the cost function based on the amount of error thereby achieves better performance compared to the conventional Constrained LMS (CLMS) algorithm. With no assumption...

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 ...

We provide optimal control laws by using tools from stochastic calculus of variations and the mathematical concept of δ−sensitivity. The analysis relies on logarithmic transformations of the value functions and the use of linearly solvable Partial Differential Equations(PDEs). We derive the corresponding optimal control as a function of the δ−sensitivity of the logarithmic transformation of the...

The lift-gas allocation problem with pressure-drop constraints and well-separator routing is a mixed-integer nonlinear program considerably hard to solve. To this end, a mixed-integer linear programming formulation was developed by multidimensional piecewiselinearization of pressure drop functions using standard (CC) and logarithmic (Log) aggregated models. These models were compared by means o...

‎We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives‎ ‎of global normalizing factors associated to intertwining operators for the following reductive groups over number fields‎: ‎inner forms of $operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$‎. ‎This estimate is a key in...

The use of Pearson’s correlation coefficient in Author Cocitation Analysis was compared with Salton’s cosine measure in a number of recent contributions. Unlike the Pearson correlation, the cosine is insensitive to the number of zeros. However, one has the option of applying a logarithmic transformation in correlation analysis. Information calculus is based on both the logarithmic transformatio...

In this paper, we investigate the costs and benefits of implementing memory interleaving in software. As our main contribution, we compare software memory interleaving to row-major allocation and logarithmic broadcasting. Our analysis demonstrates the clear superiority of software interleaving over row-major allocation in the presence of memory contention. Our analysis also indicates that the c...