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 $\ell_1$-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$^{51}$ 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 μg/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.Al–Mg–Si 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 Al–Mg–Si 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 Al–Mg–Si–Mn–Fe and Al–Mg–Si–Fe 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 Al–Mg–Si–Mn 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 α-AlFeMnSi phase with typical composition of Al24(Fe,Mn)6Si2. With increased Fe content, β-AlFe was found in the microstructure with a long needle-shaped morphology, which was identified as Al13(Fe,Mn)4Si0.25. In the Al–Mg–Si alloy, the identified Fe-rich intermetallics included the compact α-AlFeSi phase with typical composition of Al8Fe2Si and the needle-shaped β-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 α-AlFeMnSi intermetallics and suppresses the formation of β-AlFe phase in the Al–Mg–Si 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.Al–Mg–Si 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 Al–Mg–Si 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 Al–Mg–Si–Mn–Fe and Al–Mg–Si–Fe 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 Al–Mg–Si–Mn 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 α-AlFeMnSi phase with typical composition of Al24(Fe,Mn)6Si2. With increased Fe content, β-AlFe was found in the microstructure with a long needle-shaped morphology, which was identified as Al13(Fe,Mn)4Si0.25. In the Al–Mg–Si alloy, the identified Fe-rich intermetallics included the compact α-AlFeSi phase with typical composition of Al8Fe2Si and the needle-shaped β-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 α-AlFeMnSi intermetallics and suppresses the formation of β-AlFe phase in the Al–Mg–Si 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 $S$ under the constraint that the total number of particles is fixed. We show that extrema of $S$ 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 $s^a$. Let $k^a$ be any null vector along $L$ and $s\equiv -k^a s_a$. Then the generalized bound can be derived from the following conditions: (i) $s'\leq 2\pi T_{ab}k^ak^b$, where s'=k^a\grad_a s and $T_{ab}$ is the stress energy tensor; (ii) on the initial 2-surface $B$, $s(0)\leq -{1/4}\theta(0)$, where $\theta$ is the expansion of $k^a$. 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 $s<-{1/4}\theta$ and fails for those in the region where $s>-{1/4}\theta$. 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