l1 solution of linear inequalities

The numerical solution of a possible inconsistent system oflinear inequalities in the l₁ sense is considered. The non-differentiablel₁ norm minimization problem is approximated by a piecewisequadratic Huber smooth function. A continuation algorithm isdesigned to find an l₁ solution of the inequality system. Inthe case where the linear inequality system is consistent, asolution is obtained by solving any smoothed problem. Otherwise,the algorithm is shown to terminate in a finite number of iterations.We also consider an alternative smoothing scheme which sharessimilar properties with the first one, but results in an improvedcomputational performance of the continuation algorithm on inconsistentsystems. Numerical experiments are conducted to test the efficiencyof the algorithm.     

Structures of transition and alkaline earth metal salts of 5-aminonaphthalene-2-sulfonate and 6-aminonaphthalene-1, 3-disulfonate: Some unusual coordination behaviors

Salts of 5-aminonaphthalene-2-sulfonate with divalent Mg, Mn, Co, and Ni cations have been crystallized and their structures determined by single crystal X-ray methods. The Mg, Mn, and Co salts are isostructural. Crystal data for hexaaquamagnesium(II) 5-aminonaphthalene-2-sulfonate hexahydrate, [Mg(H₂O)₆](H₂NC₁₀H₆SO₃)₂·6H₂O: monoclinic, P2₁/c, Z=2, a=14.1329(18) ?, b=8.5789(11) ?, c=12.4880(17) ?, β=93.374(3)°, V=1511.5(3) ?³; hexaaquamanganese(II) 5-aminonaphthalene-2-sulfonate hexahydrate, [Mn(H₂O)₆](H₂NC₁₀H₆SO₃)₂·6H₂O: monoclinic, P2₁/c, Z=2, a=14.249(3) ?, b=8.5940(17) ?, c=12.505(3) ?, β=93.30(3)°, V=1528.8(6) ?³; hexaaquacobalt(II) 5-aminonaphthalene-2-sulfonate hexahydrate, [Co(H₂O)₆](H₂NC₁₀H₆SO₃)₂·6H₂O: monoclinic, P2₁/c, Z=2, a=14.1406(18) ?, b=8.5674(11) ?, c=12.4960(16) ?, β=93.297(2)°, V=1511.4(3) ?³. The structures are composed of alternating layers of octahedral metal–aqua complexes and sulfonate anions linked by hydrogen bonds. The three water molecules of crystallization are associated with the hexaaquametal cations and sulfonate O atoms. The repeat unit along the a-axis is a single layer. The Ni salt [crystal data for tetraaquabis(5-aminonaphthalene-2-sulfonato-N)nickel(II) dihydrate, [Ni(H₂O)₄(H₂NC₁₀H₆SO₃)₂]·2H₂O: triclinic, , Z=1, a=6.8524(10) ?, b=8.3094(12) ?, c=11.4832(17) ?, α=69.003(2)°, β=76.570(3)°, γ=83.952(2)°, V=593.56(15) ?³] has a very different structure with direct coordination of the amine N atom to Ni, a modified stacking pattern, and fewer free water molecules. Ag and Ni salts of an amine-substituted naphthalenedisulfonate have also been characterized. Crystal data for diaqua(6-ammonionaphthalene-1,3-disulfonato-O)silver(I) hydrate,[Ag(H₂O)₂(H₃NC₁₀H₅(SO₃)₂)]·0.42H₂O: monoclinic, P2₁/c, Z=2, a=9.099(3) ?, b=21.406(6) ?, c=7.629(2) ?, β=110.178(4)°, V=1394.9(7) ?³; tetraaquabis (6-ammonionaphthalene-1,3-disulfonato-O)nickel(II)tetrahydrate, [Ni(H₂O)₄(H₂NC₁₀H₅ (SO₃)₂)₂]·4H₂O: triclinic,, Z=1, a=6.7971(17) ?, b=10.661(3) ?, c=11.165(3) ?, α=68.308(4)°, β=88.292(5)°, γ=84.896(5)°, V=748.8(3) ?³. The silver salt contains six coordinate metal centers each of which bonds to four sulfonate O atoms from three different anions and two water molecules. The nickel salt contains octahedral cations with four water molecules and two trans sulfonate O atoms. Both structures are layered, but differently from each other and from those of the monofunctional naphthalenesulfonate salts.Unusual coordination of a sulfonate group to a transition metal and coordination of an amine group to nickel but not to cobalt or manganese have been observed in a series of metal aminonaphthalenesulfonate salts     

Nonresonant quadrupolar second-harmonic generation in isotropic solids by use of two orthogonally polarized laser beams

We demonstrate an experimental technique for isolating and enhancing quadrupolar second-harmonic generation in isotropic materials by using two orthogonally polarized laser beams that create wavelength-scale, forward-radiating gradients in the second-harmonic polarization.     

Single-shot measurement of temporal phase shifts by frequency-domain holography

Frequency-domain holography is used to measure ultrafast phase shifts induced either by the nonlinear susceptibility ?(3) of fused silica or by ionization fronts in air over a temporal region of 1 ps with 70-fs resolution in a single shot. The use of an imaging spectrometer adds one-dimensional spatial resolution to the single-shot temporal measurements.     

Dead Ends and Detours En Route to Total Syntheses of the 1990s A list of abbreviations can be found at the end of the article

From the very beginning organic chemistry and total synthesis have been intimately joined. In fact, one of the first things that freshmen in organic chemistry learn is how to join two molecules together to obtain a more complex one. Of course they still have a long way to go to become fully mature synthetic chemists, but they must have the primary instinct to build molecules, as synthesis is the essence of organic chemistry. With the different points of view that actually coexist in the chemical community about the maturity of the science (art, or both) of organic synthesis, it is clear that nowadays we know how to make almost all of the most complex molecules ever isolated. The primary question is how easy is it to accomplish? For the readers of papers describing the total synthesis of either simple or complex molecules, it appears that the routes followed are, most of the time, smooth and free of troubles. The synthetic scheme written on paper is, apparently, done in the laboratory with few, if any, modifications and these, essentially, seem to be based on finding the optimal experimental conditions to effect the desired reaction. Failures in the planned synthetic scheme to achieve the goal, detours imposed by unexpected reactivity, or the absence of reactivity are almost never discussed, since they may diminish the value of the work reported. This review attempts to look at total synthesis from a different side; it will focus on troubles found during the synthetic work that cause detours from the original synthetic plan, or on the dead ends that eventually may force redesign. From there, the evolution from the original route to the final successful one that achieves the synthetic target will be presented. The syntheses discussed in this paper have been selected because they contain explicit information about the failures of the original synthetic plan, together with the evolution of the final route to the target molecule. Therefore, they contain a lot of useful negative information that may otherwise be lost.