This paper explains the steps involved in the proof of the Eichler-Selberg Trace Formula for Hecke operators of level one. It is based on an appendix in Serge Lang’s Introduction to Modular Forms written by Don Zagier, though I also draw heavily from sections of Toshitsune Miyake’s Modular Forms and Xueli Wang’s and Dingyi Pei’sModular Forms with Integral and Half-Integral Weights. Section 2 su...

Large organizations load much of their data into data warehouses for subsequent querying, analysis, and data mining. Extract-Transform-Load (ETL) workflows populate those data warehouses with data from various data sources by specifying and executing a set of transformations forming a directed acyclic transformation graph (DAG). Over time, hundreds of individual ETL workflows evolve as new sour...

Task time is a measure of productivity in an interface. Keystroke Level Modeling (KLM) can predict experienced user task time to within 10 to 30% of actual times. One of the biggest constraints to implementing KLM is the tedious aspect of estimating the low-level motor and cognitive actions of the users. The method proposed here combines common actions in applications into highlevel operators (...

The notion of “atomicity” implies that it is safe to rearrange memory accesses within a transaction. In this paper, we sketch a mechanism for postponing contentious transactional operations until commit time, where they become impervious to aborts. We then contemplate the interplay between such a mechanism and languagelevel semantics. Though preliminary, our algorithms and recommendations shoul...

in this paper, a complete description concerning linear operators of banach spaces with range in lipschitz algebras $lip_al(x)$ is provided. necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. finally, a lower bound for the essential norm of such operators is obtained.

in this paper, we considered composition operators on weighted hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a hilbert-schmidt characterization and characterizes the membership in schatten-class for these operators. also, closed range composition operators  are investigated.

we study interior operators and interior structures in a fuzzy setting.we investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

Recently the distributive equations involving various classes of aggregation operators have aroused widespread attention because of their importance in the theoretic and applied communities of fuzzy set theory. 2-uninorms and semi-t-operators are two special classes of aggregation operators and have been proved to be useful in many areas such as fuzzy decision making, approximate reasoning and ...

Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system...