Stability of coulomb systems with magnetic fields

The ground state energy of an atom in the presence of an external magnetic filedB (with the electron spin-field interaction included) can be arbitrarity negative whenB is arbitrarily large. We inquire whether stability can be restored by adding the self energy of the field, B ². For a hydrogenic like atom we prove that there is a critical nuclear charge,z _c , such that the atom is stable forz<z _c and unstable forz>z _c .Work partically supported by U.S. National Scinece Foundation grant DMS-8405264 during the author's stay at the Institute for Advanced Study, Princeton, NJ, USAWork partially supported by U.S. National Science Foundation grant PHY-8116101-A03Work partially supported by U.S. and Swiss National Science Foundation Cooperative Science Program INT-8503858. Current address: Institut f. Mathematik, FU Berlin, Arnimallee 3, D-1000 Berlin 33     

Synthetic and Spectral Studies of Some Nickel Complexes Involving the Iminoquinolinone-Type Ligand

In this study we prepared N,O-bidentate ligands, sodium salt of 5-(4′-hydroxyphenylimino)quinolin-8-one, and sodium salt of 5,8-quinolinequinone-5-(8-hydroxy-5-quinolylimide) [indoöxine]. According to experimental results, formation of nickel complexes causes a large bathochromic shift of the absorption bands; in addition, these absorption bands appear in the near-infrared region at 678-812 nm. Also, EA, ¹³C NMR, UV, and IR were performed to characterize these complexes. The above results suggest that coordination occurs via the oxygen atom of the quinoneimine moiety and the nitrogen atom of the pyridine moiety.     

New results on the geometry of the moduli space of Riemann surfaces

We briefly survey our recent results about the Mumford goodness of several canonical metrics on the moduli spaces of Riemann surfaces,including the Weil-Petersson metric,the Ricci metric, the Perturbed Ricci metric and the Kahler-Einstein metric.We prove the dual Nakano negativity of the Weil-Petersson metric.As applications of these results we deduce certain important results about the L~2-cohomology groups of the logarithmic tangent bundle over the compactifled moduli spaces.     

Excimer Formation in a Confined Space: Photophysics of Ladderphanes with Tetraarylethylene Linkers

Communication between chromophores is vital for both natural and non‐natural photophysical processes. Spatial confinements offer unique conditions to scrutinize such interactions. Polynorbornene‐ and polycyclobutene‐based ladderphanes are ideal model compounds in which all tetraarylethylene (TAE) linkers are aligned coherently. The spans for each of the monomeric units in these ladderphanes are 4.5–5.5 Å. Monomers do not exhibit emission, because bond rotation in TAE can quench the excited‐state energy. However, polymers emit at 493 nm (Φ=0.015) with large Stokes shift under ambient conditions and exhibit dual emission at 450 and 493 nm at 150 K. When the temperature is lowered, the emission intensity at 450 nm increases, whereas that at 493 nm decreases. At 100 K, both monomers and polymers emit only at 450 nm. This shorter‐wavelength emission arises from the intrinsic emission of TAE chromophore, and the emission at 493 nm could be attributed to the excimer emission in the confined space of ladderphanes. The fast kinetics suggest diffusion‐controlled formation of the excimer.     

Passive Q-switch and mode-locking modulators for Nd:hosted lasers

Four kinds of currently available Nd:hosted laser passive Q-switch and mode-locking modulators: plastic dye sheet, LiF:F₂⁻ color center crystal, Cr⁺⁴ :YAG crystal and RG1000 colored glass filter were investigated in detail and summarized for comparison for the first time. The LiF:F₂⁻ crystal with outstanding annealability, long lifetime, low cost and operability at high repetition rates is highly recommended.     

Computing Harmonic Maps and Conformal Maps on Point Clouds

We use a narrow-band approach to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a point cloud approximation, we simply use the standard cubic lattice to approximate its $\epsilon$-neighborhood. Then the harmonic map of the surface can be approximated by discrete harmonic maps on lattices. The conformal map, or the surface uniformization, is achieved by minimizing the Dirichlet energy of the harmonic map while deforming the target surface of constant curvature. We propose algorithms and numerical examples for closed surfaces and topological disks. To the best of the authors' knowledge, our approach provides the first meshless method for computing harmonic maps and uniformizations of higher genus surfaces.     

Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients

Using canonical 1-parameter family of Hermitian connections on the tangent bundle, we provide invariant solutions to the Strominger system on certain complex Lie groups and their quotients. Both flat and non-flat cases are discussed in detail. This paper answers a question proposed by Andreas and Garcia-Fernandez in Comm Math Phys 332(3):1381–1383, 2014.     

A sharp polynomial estimate of positive integral points in a 4‐dimensional tetrahedron and a sharp estimate of the Dickman‐de Bruijn function

The estimate of integral points in right‐angled simplices has many applications in number theory, complex geometry, toric variety and tropical geometry. In [24], [25], [27], the second author and other coworkers gave a sharp upper estimate that counts the number of positive integral points in n dimensional () real right‐angled simplices with vertices whose distance to the origin are at least . A natural problem is how to form a new sharp estimate without the minimal distance assumption. In this paper, we formulate the Number Theoretic Conjecture which is a direct correspondence of the Yau Geometry conjecture. We have proved this conjecture for . This paper gives hope to prove the new conjecture in general. As an application, we give a sharp estimate of the Dickman‐de Bruijn function for .     

In situ scanning tunneling microscopy imaging of mercury film electrodeposited on Ir(1 1 1)

In situ scanning tunneling microscopy (STM) was used to examine multilayer Hg film electrodeposited on a well-ordered Ir(1 1 1) single crystal electrode in 0.1 M HClO₄ + 1 mM Hg(ClO₄)₂. Topography STM scans showed that the Ir(1 1 1) – supported Hg film electrode contained well-defined terraces separated by monatomic steps (Δz = 2.3 Å). The STM’s tip could be used to induce local dissolution of the Hg deposit under proper operating conditions and the depth of the etched pit informed directly the thickness of Hg deposit. Although in situ STM imaging with a tungsten tip could not result in atomic structure of bare Hg film in 0.1 M HClO₄, it discerned highly ordered iodine adlayers, represented by a (2 × 8√3)rect – I structure, on the Hg film in solution containing potassium iodide. These STM results suggested that the Hg substrate could have an ordered atomic structure.