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Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with convex quadratic constraints. Firstly, based on our existing results, the problem is reconstructed as an equivalent problem with a simple concave quadratic objective function in the result space, with a convex feasible domain. A global optimization algorithm for solving equivalent problems is proposed based on a branch and bound framework that can ensure the global optimality of the solution. This algorithm combines effective relaxation processes with branching processes related to new external approximation techniques. Finally, the theoretical feasibility of the algorithm was analyzed., Comment: arXiv admin note: text overlap with arXiv:2312.15384

High pressure plays a crucial role in the field of superconductivity. Compressed hydride superconductors are leaders in the race for a material that can conduct electricity without resistance at high or even room temperature. In the present work, we have discovered new lanthanum superhydride, cubic A15-type La$_4$H$_{23}$, with lower stabilization pressure compared to the reported $\textit{fcc}$ LaH$_{10}$. Superconducting La$_4$H$_{23}$ was obtained by laser heating of LaH$_3$ with ammonia borane at about 120 GPa. Transport measurements reveal the maximum critical temperature $\textit{T}$$_{C}$(onset) = 105 K and the critical field $\textit{H}$$_{C2}$(0) = 32 T at 118 GPa, as evidenced by the sharp drop of electrical resistance and the displacement of superconducting transitions in applied magnetic fields. Moreover, we provide evidence for unconventional transport associated with a pseudogap phase in La$_4$H$_{23}$ using pulsed magnetic fields up to 68 T. A large negative magnetoresistance in the non-superconducting state below 40 K, quasi $\textit{T}$-linear electrical resistance, and a sign-change of its temperature dependence mark the emergence of pseudogap in this hydride. Discovered lanthanum hydride is a new member of the A15 family of superconductors with $\textit{T}$$_C$ exceeding the boiling point of liquid nitrogen., Comment: A mistake in Figure 3(a) was fixed

Polyhydride superconductors have been shown to possess metallic properties with a Bardeen-Cooper-Schrieffer-type superconducting ground state. Here, we provide evidence for unconventional transport associated with a pseudogap phase in cubic cerium superhydride CeH$_{10}$ ($\textit{T}$$_C$ = 116 K) at pressure of 115-125 GPa. A large negative magnetoresistance in the non-superconducting state below 90 K, quasi $\textit{T}$-linear electrical resistance, and a sign-change of its temperature dependence mark the emergence of this phase. We studied the magnetic phase diagrams and the upper critical fields $\textit{B}$$_{C2}$(T) of CeH$_{10}$, CeH$_9$, and CeD$_9$ in pulsed fields up to 70 T. $\textit{B}$$_{C2}$(T) of CeH$_9$ and CeD$_9$ exhibits pronounced saturation at low temperatures in accordance with the Werthamer-Helfand-Hohenberg model, whereas CeH$_{10}$ stands out in particular, as it does not obey this model. Our observations, therefore, reveal the unconventional nature of non-superconducting state of cerium superhydride CeH$_{10}$., Comment: The discussion part has been improved

By directly altering microscopic interactions, pressure provides a powerful tuning knob for the exploration of condensed phases and geophysical phenomena. The megabar regime represents an exciting frontier, where recent discoveries include novel high-temperature superconductors, as well as structural and valence phase transitions. However, at such high pressures, many conventional measurement techniques fail. Here, we demonstrate the ability to perform local magnetometry inside of a diamond anvil cell with sub-micron spatial resolution at megabar pressures. Our approach utilizes a shallow layer of Nitrogen-Vacancy (NV) color centers implanted directly within the anvil; crucially, we choose a crystal cut compatible with the intrinsic symmetries of the NV center to enable functionality at megabar pressures. We apply our technique to characterize a recently discovered hydride superconductor, CeH$_9$. By performing simultaneous magnetometry and electrical transport measurements, we observe the dual signatures of superconductivity: local diamagnetism characteristic of the Meissner effect and a sharp drop of the resistance to near zero. By locally mapping the Meissner effect and flux trapping, we directly image the geometry of superconducting regions, revealing significant inhomogeneities at the micron scale. Our work brings quantum sensing to the megabar frontier and enables the closed loop optimization of superhydride materials synthesis.

Covalent and ionic polyhydrides have become the two main camps in searching for the high-temperature superconductors under pressure. They have been considered as important platforms for exploring ternary or multiple hydrides in order to further increase the Tc or decrease the stabilization pressure. In this work, we successfully synthesized ternary hexagonal La-Ce polyhydrides stable in the pressure range of 95-130 GPa by laser-heating the La-Ce alloy (initial ratio La:Ce=2.5-3.5) in ammonia borane. Superconductivity at 176 K was strikingly preserved to about 100 GPa. The extrapolated upper critical field Hc2(0) reached 216 T at 100 GPa, the highest value among the synthesized polyhydrides. We also performed the contrast experiments and stabilized binary high-temperature superconducting LaHx with Tc-103 K at 78 GPa. In the pressure range of 95-130 GPa, the ternary hexagonal La-Ce-H system exhibits higher Tc than the binary La-H system, with the maximum difference of 100 K, and the compounds of both systems were synthesized at the same pressure and temperature conditions. These results clearly indicate that the discovered La-Ce-H system not only enriches the high-temperature superconducting hydrides but also realizes high-Tc at moderate pressures.

Recently, several research groups announced reaching the point of metallization of hydrogen above 400 GPa. Following the mainstream of extensive investigations of compressed polyhydrides, in this work we demonstrate that small (4 atom %) doping of molecular hydrogen by strontium leads to a dramatic reduction in the metallization pressure to about 200 GPa. Studying the high-pressure chemistry of the Sr-H system at 56-180 GPa, we observed the formation of several previously unknown compounds: C2/m-Sr$_3$H$_{13}$, pseudocubic SrH$_6$, SrH$_9$ with cubic F-43m Sr sublattice, and pseudotetragonal P1-SrH$_{22}$, the metal hydride with the highest hydrogen content discovered so far. Unlike Ca and Y, strontium forms molecular semiconducting polyhydrides, whereas calcium and yttrium polyhydrides are high-Tc superconductors with an atomic H sublattice. The latter phase, SrH$_{22}$ or Sr$_{0.04}$H$_{0.96}$, may be considered as a convenient model of the consistent bandgap closure and metallization of hydrogen. Using the impedance measurements in diamond anvil cells at 300-440 K, we estimated the direct bandgap of the Pm-3n-like compound P1-SrH$_6$ to be 0.44-0.51 eV at 150 GPa, and its metallization pressure to be 220 GPa. Together with the machine learning interatomic potentials, the impedance spectroscopy allowed us to estimate the diffusion coefficients of hydrogen D$_H$ = 1.0-2.8 E-10 m$^2$/s in SrH$_6$ and 1.2-2.1 E-9 m$^2$/s in P1-SrH$_{22}$ at 500-600 K., Comment: Supporting information was compressed and reduced by 2 times to 36 figures