Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.

A Natural Orbital Functional Based on an Explicit Approach of the Two-Electron Cumulant

Abstract: The cumulant expansion gives rise to an useful decomposition of the two-matrix in which the pair correlated matrix (cumulant) is disconnected from the antisymmetric product of the onematrices. The cumulant can be approximated in terms of two matrices, � and � , which are explicit functions of the occupation numbers of the natural orbitals. It produces a natural orbital functional (NOF) that reduces to the exact expression for the total energy in two-electron systems.The N-representability positivity necessaryconditionsofthetwo-matriximposeseveralboundson

Multiple Fano Resonances Based on Different Waveguide Modes in a Symmetry Breaking Plasmonic System

Abstract: Multiple Fano resonances are numerically investigated based on different waveguide modes in a nanoscale plasmonic waveguide resonator system, which consists of two grooves coupled with a metal–insulator–metal (MIM) waveguide. Simulation results show that by introducing a small structural breaking in the plasmonic resonator, both symmetric and antisymmetric waveguide modes can be excited. Due to the interaction of the symmetric and antisymmetric waveguide modes, the transmission spectra possess a sharp asymmetrical profile. Because of different origins, these Fano resonances exhibit different dependence on the parameters of the structure and can be easily tuned. These characteristics offer flexibility to design the device. This nanosensor yields a sensitivity of $\sim$ 820 nm/RIU and a figure-of-merit of $\sim\! 3.2\times 10^{5}$ . The utilization of the antisymmetric mode in the MIM waveguide provides a new possibility for designing high-performance plasmonic devices.

An analytical least square solution to the design problem of two-dimensional FIR filters with quadrantally symmetric or antisymmetric frequency response

Abstract: A closed-form least-squares solution to the design problem of two-dimensional real zero-phase finite-impulse-response (FIR) filters with quadrantally symmetric or antisymmetric frequency response is obtained. An in-depth study of the matrices involved in the development of the design technique reveals a number of useful properties. It is shown that these properties lead to an optimal analytical solution for the filter coefficients, making it unnecessary to use the time-consuming methods of optimization, matrix inversion, and iteration. Because of the reduced order of the matrices involved, their specific characteristics, and the analytical approach, the computational complexity is greatly reduced. Simplicity and efficiency of the design technique is illustrated through examples. The results in terms of error in frequency response compare favorably with those obtained by using other techniques. It is shown that the design time using the proposed technique is significantly smaller than that required by the I/sub p/-optimization technique or weighted least-squares technique using Harris' ascent algorithm or modified Lawson's algorithm. >

A remark on gauge transformations and the moving frame method

Abstract: In this note we give a shorter proof of recent regularity results on elliptic partial differential equations with antisymmetric structure presented in Riviere (2007) [23] , Riviere and Struwe (2008) [24] . We differ from the mentioned articles in using the direct method of Helein's moving frame, i.e. minimizing a certain variational energy-functional, in order to construct a suitable gauge transformation. Though this is neither new nor surprising, it enables us to describe a proof of regularity using elementary arguments of calculus of variations and algebraic identities. Moreover, we remark that in order to prove Hildebrandt's conjecture on regularity of critical points of 2D-conformally invariant variational problems one can avoid the application of the Nash–Moser imbedding theorem.

Multiwavelet Frames from Refinable Function Vectors

Abstract: Starting from any two compactly supported d-refinable function vectors in (L2(R))r with multiplicity r and dilation factor d, we show that it is always possible to construct 2rd wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R) and they achieve the best possible orders of vanishing moments. When all the components of the two real-valued d-refinable function vectors are either symmetric or antisymmetric with their symmetry centers differing by half integers, such 2rd wavelet functions, which generate a pair of dual d-wavelet frames, can be real-valued and be either symmetric or antisymmetric with the same symmetry center. Wavelet frames from any d-refinable function vector are also considered. This paper generalizes the work in [5,12,13] on constructing dual wavelet frames from scalar refinable functions to the multiwavelet case. Examples are provided to illustrate the construction in this paper.