70,459 research outputs found
SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization
In this paper, we introduce a new class of nonsmooth convex functions called
SOS-convex semialgebraic functions extending the recently proposed notion of
SOS-convex polynomials. This class of nonsmooth convex functions covers many
common nonsmooth functions arising in the applications such as the Euclidean
norm, the maximum eigenvalue function and the least squares functions with
-regularization or elastic net regularization used in statistics and
compressed sensing. We show that, under commonly used strict feasibility
conditions, the optimal value and an optimal solution of SOS-convex
semi-algebraic programs can be found by solving a single semi-definite
programming problem (SDP). We achieve the results by using tools from
semi-algebraic geometry, convex-concave minimax theorem and a recently
established Jensen inequality type result for SOS-convex polynomials. As an
application, we outline how the derived results can be applied to show that
robust SOS-convex optimization problems under restricted spectrahedron data
uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP
relaxation result for restricted ellipsoidal data uncertainty and answers the
open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a
robust solution from the semi-definite programming relaxation in this broader
setting
Stabilized hot electron bolometer heterodyne receiver at 2.5 THz
We report on a method to stabilize a hot electron bolometer (HEB) mixer at 2.5 THz. The technique utilizes feedback control of the local oscillator (LO) laser power by means of a swing-arm actuator placed in the optical beam path. We demonstrate that this technique yields a factor of 50 improvement in the spectroscopic Allan variance time which is shown to be over 30 s in a 12 MHz noise fluctuation bandwidth. Furthermore, broadband signal direct detection effects may be minimized by this technique. The technique is versatile and can be applied to practically any local oscillator at any frequency
On the Triality Theory for a Quartic Polynomial Optimization Problem
This paper presents a detailed proof of the triality theorem for a class of
fourth-order polynomial optimization problems. The method is based on linear
algebra but it solves an open problem on the double-min duality left in 2003.
Results show that the triality theory holds strongly in a tri-duality form if
the primal problem and its canonical dual have the same dimension; otherwise,
both the canonical min-max duality and the double-max duality still hold
strongly, but the double-min duality holds weakly in a symmetrical form. Four
numerical examples are presented to illustrate that this theory can be used to
identify not only the global minimum, but also the largest local minimum and
local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011.
arXiv admin note: substantial text overlap with arXiv:1104.297
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China's building stock estimation and energy intensity analysis
Reliable and objective data regarding building stock is essential for predicting and analyzing energy demand and carbon emission. However, China's building stock data is lacking. This study proposes a set of China building floor space estimation method (CBFSM) based on the improved building stock turnover model. Then it measures China's building stocks by vintage and type from 2000 to 2015, as well as building energy intensity (national level and provincial level) and energy-efficient buildings. Results showed that total building stocks increased significantly, rising from 35.2 billion m2 in 2000 to 63.6 billion m2 in 2015, with the average growth rate 4.0%. The deviations were well below 10% by comparing with China Population Census, which validated the reliability of CBFSM and the results. As for energy intensity, urban dwellings and rural dwellings showed relatively stable and increasing trend respectively. The commercial building energy intensity saw a downward trend during “12th Five Year Plan” period. This indicated the effectiveness of building energy efficiency work for commercial buildings since 2005.38.6 billion m2 residential dwellings and 5.7 billion m2 commercial buildings still need to be retrofitted in future. CBFSM can overcome shortages in previous studies. It can also provide Chinese government with technical support and data evidence to promote the building energy efficiency work
Realizing quantum controlled phase-flip gate through quantum dot in silicon slow-light photonic crystal waveguide
We propose a scheme to realize controlled phase gate between two single
photons through a single quantum dot in slow-light silicon photonic crystal
waveguide. Enhanced Purcell factor and beta factor lead to high gate fidelity
over broadband frequencies compared to cavity-assisted system. The excellent
physical integration of this silicon photonic crystal waveguide system provides
tremendous potential for large-scale quantum information processing.Comment: 9 pages, 3 figure
A general maximum entropy principle for self-gravitating perfect fluid
We consider a self-gravitating system consisting of perfect fluid with
spherical symmetry. Using the general expression of entropy density, we
extremize the total entropy under the constraint that the total number of
particles is fixed. We show that extrema of coincides precisely with the
relativistic Tolman-Oppenheimer-Volkoff (TOV) equation of hydrostatic
equilibrium. Furthermore, we apply the maximum entropy principle to a charged
perfect fluid and derive the generalized TOV equation. Our work provides a
strong evidence for the fundamental relationship between general relativity and
ordinary thermodynamics.Comment: 13 pages, no figure. The arguments have been improved so that the
assumption p=p(\rho) is no longer neede
Microwave Slow-Wave Structure and Phase-Compensation Technique for Microwave Power Divider
In this paper, T-shaped electromagnetic bandgap is loaded on a coupled transmission line itself and its electric performance is studied. Results show that microwave slow-wave effect can be enhanced and therefore, size reduction of a transmission-line-based circuit is possible. However, the transmission-line-based circuits characterize varied phase responses against frequency, which becomes a disadvantage where constant phase response is required. Consequently, a phase-compensation technique is further presented and studied. For demonstration purpose, an 8-way coupled-line power divider with 22.5 degree phase shifts between adjacent output ports, based on the studied slow-wave structure and phase-compensation technique, is developed. Results show both compact circuit architecture and improved phase imbalance are realized, confirming the investigated circuit structures and analyzing methodologies
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