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Bello-Cruz Yunier Li Guoyin Nghia Tran Thai An 《Journal of Optimization Theory and Applications》2022,194(1):167-190
Journal of Optimization Theory and Applications - In the previous paper Bello-Cruz et al. (J Optim Theory Appl 188:378–401, 2021), we showed that the quadratic growth condition plays a key... 相似文献
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Foundations of Computational Mathematics - Kurdyka–Łojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In... 相似文献
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Badro J Fiquet G Struzhkin VV Somayazulu M Mao HK Shen G Le Bihan T 《Physical review letters》2002,89(20):205504
We present a new method to separate the crystallographic and electronic phase transitions in hematite using x-ray emission spectroscopy and x-ray diffraction. Our observations, based on the behavior of a metastable high-pressure phase in the stability domain of the low-pressure phase, show that the electronic transition is preempted by the crystallographic transition. The former occurs only afterwards in the high-pressure phase, possibly as a result of a Mott transition. The idea that the electronic transition drives the transition in hematite is therefore invalidated. Such methods should help elucidate the mechanics and the driving forces behind a number of first-order high-pressure phase transitions. 相似文献
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Swamy V Kuznetsov A Dubrovinsky LS McMillan PF Prakapenka VB Shen G Muddle BC 《Physical review letters》2006,96(13):135702
We investigated the size-dependent high-pressure phase transition behavior of nanocrystalline anatase TiO2 with synchrotron x-ray diffraction and Raman spectroscopy to 45 GPa at ambient temperature. Pressure-induced amorphization results in a high-density amorphous (HDA) form when the starting crystallite size is < 10 mm. The HDA-TiO2 transforms to a low-density amorphous form at lower pressures. Harnessing the nanometer length scale thus provides a new window for experimental investigation of amorphization in poor glass formers and a synthesis route for new amorphous materials. 相似文献
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Guoyin Li 《Mathematical Programming》2013,137(1-2):37-64
In this paper, by examining the recession properties of convex polynomials, we provide a necessary and sufficient condition for a piecewise convex polynomial to have a Hölder-type global error bound with an explicit Hölder exponent. Our result extends the corresponding results of Li (SIAM J Control Optim 33(5):1510–1529, 1995) from piecewise convex quadratic functions to piecewise convex polynomials. 相似文献
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ABSTRACTA new opposed type double-stage large volume cell has been developed to compress large volume samples to more than 100?GPa (Mbar) pressure. A pair of second-stage diamond anvils is introduced into the first-stage Paris–Edinburgh press. The double-stage large volume cell allows the generation of ultrahigh pressures using a large culet diameter of the second-stage diamond anvils (diameters of 0.5–1.2?mm). Pressure generation up to 131?GPa has been achieved by using the culet diameter of 0.5?mm. Sample volume of the double-stage large volume cell can be more than ~100 times larger than that of conventional Mbar experiment using a diamond anvil cell. The double-stage large volume cell has a large opening in the horizontal plane for X-ray measurements, which is particularly suited for the multi-angle energy dispersive X-ray diffraction measurement, thus opening a new way of in situ structural determinations of amorphous materials at Mbar pressures. 相似文献