Deterministic Guarantees for Burer-Monteiro Factorizations of Smooth Semidefinite Programs

We consider semidefinite programs (SDPs) with equality constraints. The variable to be optimized is a positive semidefinite matrix X of size n. Following the Burer-Monteiro approach, we optimize a factor Y of size n × p instead, such that X = YY^T. This ensures positive semidefiniteness at no cost and can reduce the dimension of the problem if p is small, but results in a nonconvex optimization problem with a quadratic cost function and quadratic equality constraints in Y. In this paper, we show that if the set of constraints on Y regularly defines a smooth manifold, then, despite nonconvexity, first- and second-order necessary optimality conditions are also sufficient, provided p is large enough. For smaller values of p, we show a similar result holds for almost all (linear) cost functions. Under those conditions, a global optimum Y maps to a global optimum X = YY^T of the SDP. We deduce old and new consequences for SDP relaxations of the generalized eigenvector problem, the trust-region subproblem, and quadratic optimization over several spheres, as well as for the Max-Cut and Orthogonal-Cut SDPs, which are common relaxations in stochastic block modeling and synchronization of rotations. © 2019 Wiley Periodicals, Inc.     

Effects of the photocathode non-uniformity on radon measurements by plastic scintillation spectrometry

Journal of Radioanalytical and Nuclear Chemistry - This work shows a study of the effect of the non-uniformity of photocathode response on the energy resolution of plastic scintillators optimized...     

Spin Transport over Huge Distances in a Magnetized 2D Electron System

Experimental results on the properties of a recently discovered new collective state, the magnetofermionic condensate, are summarized herein. Condensation occurs in a fermionic system, a quantum Hall insulator (filling factor ν = 2), as a result of the formation of a dense ensemble of long‐lived spin cyclotron magnetoexcitons, composite bosons. At temperatures below 1 K, the exciton ensemble exhibits a sharp enhancement in its response to an external electromagnetic field due to the formation of a super‐absorbing state that interacts coherently with the electromagnetic field. Simultaneously, the electrons below the Fermi level rearrange to form a new non‐equilibrium radiative recombination channel. The condensate shows a sharp decrease in viscosity and the ability to spread over macroscopically large distances, on the order of a millimeter, at a speed of $\approx {10}^3\text{cm}{\text{s}}^{?1}$. Due to this rapid long‐distance spin transfer, new opportunities in the field of spintronics have been opened up.     

Synthesis and Characterization of Oxazaborinin Phosphonate for Blue OLED Emitter Applications

A blue-light emitting material based on a boron complex containing heteroaromatic phosphonate ligand is synthesized and characterized. The Phospho-Fries rearrangement is used in the synthesis route of the ligand as a convenient method of introducing phosphonate groups into phenols. Structural, thermal and photophysical properties of the resulting oxazaborinin phosphonate compound have been characterized. DFT geometry optimizations were studied as well as the spatial position and symmetry of the HOMO and LUMO. Good thermal stability up to 250 °C enables vacuum deposition methods next to solution processing. Combining the work function with the optical band gap from UV-Vis measurements shows that band alignment is possible with standard contact materials. Photoluminescence reveals an emission peak at 428 nm, which is suitable for a blue light-emitter.     

The synthesis and cytotoxic activity of N-unsubstituted 3-aryl-4-(trifluoromethyl)-4H-spiro[chromeno[3,4-c]pyrrolidine-1,11'-indeno[1,2-b]quinoxalines]

Chemistry of Heterocyclic Compounds - A method for a regio- and stereoselective synthesis of N-unsubstituted...     

Chemically induced symmetry breaking in the crystal structure of guanidinium uranyl sulfate

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Synthesis of Novel 5,6‐Dihydropyrrolo[2,1‐a]isoquinolines via Grob Reaction between (E)‐1,1,1‐Trifluoro‐3‐nitro‐2‐butene and 3,4‐Dihydroisoquinolines

Uncatalyzed cycloaddition of 3,4‐dihydroisoquinolines to (E)‐1,1,1‐trifluoro‐3‐nitro‐2‐butene via Grob reaction provide a simple one‐step route to the 5,6‐dihydropyrrolo[2,1‐a]isoquinolines, which represent the basic structural framework of the antitumor active alkaloid crispine.     

Vapor pressure of selected aliphatic alcohols by ebulliometry. Part 1

Vapor pressures for liquid 2,2-dimethyl-1-propanol (CAS Registry Number 75-84-3), 1-hexanol (CAS Registry Number 111-27-3), 1-heptanol (CAS Registry Number 111-70-6), 1-octanol (CAS Registry Number 111-87-5) and 1-tetradecanol (CAS Registry Number 112-72-1) were measured by the precision comparative ebulliometry over an approximate pressure range from 8 to 100 kPa. The relative uncertainty in pressure is estimated to be less than or equal to 0.05% of the measured value and the absolute uncertainty in temperature is estimated at less than or equal to 0.01 K on ITS-90. The results are represented by the Antoine equation and compared with available literature data. A new transformation of vapor pressure data, which facilitates the detection of systematic errors, is presented.