59,338 research outputs found
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
Generic dark matter signature for gamma-ray telescopes
We describe a characteristic signature of dark matter (DM) annihilation or
decay into gamma-rays. We show that if the total angular momentum of the
initial DM particle(s) vanishes, and helicity suppression operates to prevent
annihilation/decay into light fermion pairs, then the amplitude for the
dominant 3-body final state f^+f^-\gamma has a unique form dictated by gauge
invariance. This amplitude and the corresponding energy spectra hold for
annihilation of DM Majorana fermions or self-conjugate scalars, and for decay
of DM scalars, thus encompassing a variety of possibilities. Within this
scenario, we analyze Fermi LAT, PAMELA and HESS data, and predict a hint in
future Fermi gamma-ray data that portends a striking signal at atmospheric
Cherenkov telescopes (ACTs).Comment: 9 pages, 4 figures. Version to appear in PR
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
Can the Bump be Observed in the Early Afterglow of GRBS with X-Ray Line Emission Features?
Extremely powerful emission lines are observed in the X-ray afterglow of
several GRBs. The energy contained in the illuminating continuum which is
responsible for the line production exceeds 10 erg, much higher than
that of the collimated GRBs. It constrains the models which explain the
production of X-ray emission lines. In this paper, We argue that this energy
can come from a continuous postburst outflow. Focusing on a central engine of
highly magnetized millisecond pulsar or magnetar we find that afterglow can be
affected by the illuminating continuum, and therefore a distinct achromatic
bump may be observed in the early afterglow lightcurves. With the luminosity of
the continuous outflow which produces the line emission, we define the upper
limit of the time when the bump feature appears. We argue that the reason why
the achromatic bumps have not been detected so far is that the bumps should
appear at the time too early to be observed.Comment: 13 pags, 2 tables, appear in v603 n1 pt1 ApJ March 1, 2004 issu
Contribution of the antibiotic chloramphenicol and its analogues as precursors of dichloroacetamide and other disinfection byproducts in drinking water
Dichloroacetamide (DCAcAm), a disinfection byproduct, has been detected in drinking water. Previous research showed that amino acids may be DCAcAm precursors. However, other precursors may be present. This study explored the contribution of the antibiotic chloramphenicol (CAP) and two of its analogues (thiamphenicol, TAP; florfenicol, FF) (referred to collectively as CAPs), which occur in wastewater-impacted source waters, to the formation of DCAcAm. Their formation yields were compared to free and combined amino acids, and they were investigated in filtered waters from drinking-water-treatment plants, heavily wastewater-impacted natural waters, and secondary effluents from wastewater treatment plants. CAPs had greater DCAcAm formation potential than two representative amino acid precursors. However, in drinking waters with ng/L levels of CAPs, they will not contribute as much to DCAcAm formation as the Ī¼g/L levels of amino acids. Also, the effect of advanced oxidation processes (AOPs) on DCAcAm formation from CAPs in real water samples during subsequent chlorination was evaluated. Preoxidation of CAPs with AOPs reduced the formation of DCAcAm during postchlorination. The results of this study suggest that CAPs should be considered as possible precursors of DCAcAm, especially in heavily wastewater-impacted waters
Effect of iron on the microstructure and mechanical property of Al-Mg-Si-Mn and Al-Mg-Si diecast alloys
This article is made available through the Brunel Open Access Publishing Fund. Copyright @ 2012 Elsevier B.V.This article has been made available through the Brunel Open Access Publishing Fund.AlāMgāSi based alloys can provide super ductility to satisfy the demands of thin wall castings in the application of automotive structure. In this work, the effect of iron on the microstructure and mechanical properties of the AlāMgāSi diecast alloys with different Mn concentrations is investigated. The CALPHAD (acronym of Calculation of Phase Diagrams) modelling with the thermodynamic properties of the multi-component AlāMgāSiāMnāFe and AlāMgāSiāFe systems is carried out to understand the role of alloying on the formation of different primary Fe-rich intermetallic compounds. The results showed that the Fe-rich intermetallic phases precipitate in two solidification stages in the high pressure die casting process: one is in the shot sleeve and the other is in the die cavity, resulting in the different morphologies and sizes. In the AlāMgāSiāMn alloys, the Fe-rich intermetallic phase formed in the shot sleeve exhibited coarse compact morphology and those formed in the die cavity were fine compact particles. Although with different morphologies, the compact intermetallics were identified as the same Ī±-AlFeMnSi phase with typical composition of Al24(Fe,Mn)6Si2. With increased Fe content, Ī²-AlFe was found in the microstructure with a long needle-shaped morphology, which was identified as Al13(Fe,Mn)4Si0.25. In the AlāMgāSi alloy, the identified Fe-rich intermetallics included the compact Ī±-AlFeSi phase with typical composition of Al8Fe2Si and the needle-shaped Ī²-AlFe phase with typical composition of Al13Fe4. Generally, the existence of iron in the alloy slightly increases the yield strength, but significantly reduces the elongation. The ultimate tensile strength maintains at similar levels when Fe contents is less than 0.5 wt%, but decreases significantly with the further increased Fe concentration in the alloys. CALPHAD modelling shows that the addition of Mn enlarges the Fe tolerance for the formation of Ī±-AlFeMnSi intermetallics and suppresses the formation of Ī²-AlFe phase in the AlāMgāSi alloys, and thus improves their mechanical properties.EPSRC and JL
Effect of iron on the microstructure and mechanical property of Al-Mg-Si-Mn and Al-Mg-Si diecast alloys
This article is made available through the Brunel Open Access Publishing Fund. Copyright @ 2012 Elsevier B.V.This article has been made available through the Brunel Open Access Publishing Fund.AlāMgāSi based alloys can provide super ductility to satisfy the demands of thin wall castings in the application of automotive structure. In this work, the effect of iron on the microstructure and mechanical properties of the AlāMgāSi diecast alloys with different Mn concentrations is investigated. The CALPHAD (acronym of Calculation of Phase Diagrams) modelling with the thermodynamic properties of the multi-component AlāMgāSiāMnāFe and AlāMgāSiāFe systems is carried out to understand the role of alloying on the formation of different primary Fe-rich intermetallic compounds. The results showed that the Fe-rich intermetallic phases precipitate in two solidification stages in the high pressure die casting process: one is in the shot sleeve and the other is in the die cavity, resulting in the different morphologies and sizes. In the AlāMgāSiāMn alloys, the Fe-rich intermetallic phase formed in the shot sleeve exhibited coarse compact morphology and those formed in the die cavity were fine compact particles. Although with different morphologies, the compact intermetallics were identified as the same Ī±-AlFeMnSi phase with typical composition of Al24(Fe,Mn)6Si2. With increased Fe content, Ī²-AlFe was found in the microstructure with a long needle-shaped morphology, which was identified as Al13(Fe,Mn)4Si0.25. In the AlāMgāSi alloy, the identified Fe-rich intermetallics included the compact Ī±-AlFeSi phase with typical composition of Al8Fe2Si and the needle-shaped Ī²-AlFe phase with typical composition of Al13Fe4. Generally, the existence of iron in the alloy slightly increases the yield strength, but significantly reduces the elongation. The ultimate tensile strength maintains at similar levels when Fe contents is less than 0.5 wt%, but decreases significantly with the further increased Fe concentration in the alloys. CALPHAD modelling shows that the addition of Mn enlarges the Fe tolerance for the formation of Ī±-AlFeMnSi intermetallics and suppresses the formation of Ī²-AlFe phase in the AlāMgāSi alloys, and thus improves their mechanical properties.EPSRC and JL
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
Local conditions for the generalized covariant entropy bound
A set of sufficient conditions for the generalized covariant entropy bound
given by Strominger and Thompson is as follows: Suppose that the entropy of
matter can be described by an entropy current . Let be any null
vector along and . Then the generalized bound can be
derived from the following conditions: (i) , where
s'=k^a\grad_a s and is the stress energy tensor; (ii) on the initial
2-surface , , where is the expansion of
. We prove that condition (ii) alone can be used to divide a spacetime
into two regions: The generalized entropy bound holds for all light sheets
residing in the region where and fails for those in the region
where . We check the validity of these conditions in FRW flat
universe and a scalar field spacetime. Some apparent violations of the entropy
bounds in the two spacetimes are discussed. These holographic bounds are
important in the formulation of the holographic principle.Comment: 10 pages, 7 figure
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