We give the construction of a line bundle over the based Brownian bridge, as well as the construction of spinor fields over the based and the free Brownian bridge. Introduction The Dirac operator over the free loop space is a very important object for the algebraic topology [24]; its index gives the Witten genus and it can predict the rigidity theorem of Witten: the index of some classical oper...

surge is one of the two destructive factors in compressors. surge is the stream instability phenomenon in compressor that imposes severe damages to the compressors. nowadays, suppressingsurge phenomenon is one of the most important issues in oil and gas industries, especially when flow reduction or gas reflux is considered. according to moore-greitzer compressor model, this paper designs an act...

in trading electrical energy in deregulated power systems, violation of operation constraints such as transmission lines flow limits is possible. these conditions have been called “congestion”. one of the most important responsibility of independent system operator (iso) is congestion management in a manner that all the system equipments be operated in their nominal ranges. in this paper, usi...

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

The aim of this paper is to show some examples of matrix-valued orthogonal functions on the real line which are simultaneously eigenfunctions of a second-order differential operator of Schrödinger type and an integral operator of Fourier type. As a consequence we derive integral representations of these functions as well as other useful structural formulas. Some of these functions are plotted t...

We continue Mizar formalization of General Topology according to the book [19] by Engelking. In the article the formalization of Section 1.2 is almost completed. Namely, we formalize theorems on introduction of topologies by bases, neighborhood systems, closed sets, closure operator, and interior operator. The Sorgenfrey line is defined by a basis. It is proved that the weight of it is continuu...

As a tool to carry out the quantization of gauge theory on a noncommutative space, we present a Dirac operator that behaves as a line element of the canonical noncommutative space. Utilizing this operator, we construct the Dixmier trace, which is the regularized trace for infinite-dimensional matrices. We propose the possibility of solving the cosmological constant problem by applying our gauge...

We review the detailed structure of the large N = 4 superconformal algebra, and construct its BRST operator which constitutes the main object for analyzing N = 4 strings. We then derive the general condition for the nilpotency of the BRST operator and show that there exists a line of critical N = 4 string theories. e-mail address: [email protected] e-mail address: [email protected], ohta@...