Abnormal effect of hydroxyl on the longest wavelength maximum in ultraviolet absorption spectra for bis‐aryl Schiff bases

Two sets of bis‐aryl Schiff bases that contain 4(or 4′)‐OH and 2(or 2′)‐OH were synthesized. The first set consists of 4‐HOArCH=NArY and XArCH=NArOH‐4′, and the second set consists of 2‐HOArCH=NArY and XArCH=NArOH‐2′. Their ultraviolet absorption spectra were measured and investigated. A very interesting phenomenon was observed by analyzing their wave number ν_max (cm^?1) of longest wavelength maximum λ_max (nm) of ultraviolet. Compared with the change regularity of the ν_max of XArCH=NArY (where the X and Y excluded OH), the 4′‐position hydroxyl (4′‐OH) and 2′‐position hydroxyl (2′‐OH) have abnormal performance. The details are the following: the 4′‐OH contributes an additional red shift to the ν_max of XArCH=NArOH‐4′ (λ_max increase), whereas the 2′‐OH contributes an additional blue shift to the ν_max of XArCH=NArOH‐2′ (λ_max decrease). In addition, there are ortho steric effects of all 2‐OH and 2′‐OH on the ν_max for 2‐HOArCH=NArY and XArCH=NArOH‐2′, and the ortho steric effect contributes a red shift to their ν_max. These experimental facts can provide an important theoretical reference for us using aryl Schiff base compounds as optical materials and performing the molecular design.     

Strong duality and minimal representations for cone optimization

The elegant theoretical results for strong duality and strict complementarity for linear programming, LP, lie behind the success of current algorithms. In addition, preprocessing is an essential step for efficiency in both simplex type and interior-point methods. However, the theory and preprocessing techniques can fail for cone programming over nonpolyhedral cones. We take a fresh look at known and new results for duality, optimality, constraint qualifications, CQ, and strict complementarity, for linear cone optimization problems in finite dimensions. One theme is the notion of minimal representation of the cone and the constraints. This provides a framework for preprocessing cone optimization problems in order to avoid both the theoretical and numerical difficulties that arise due to the (near) loss of the strong CQ, strict feasibility. We include results and examples on the surprising theoretical connection between duality gaps in the original primal-dual pair and lack of strict complementarity in their homogeneous counterpart. Our emphasis is on results that deal with Semidefinite Programming, SDP.     

Calculation of ion and fast atom contributions to the sputtering non-uniformity of the target with a surface relief in glow discharge

The energy spectra of ion and fast atom flows at the target with a periodical surface relief of small amplitude in glow discharge are calculated. Distributions of the effective sputtering yield of the target and the sputtered atom flow density along its surface are found. It is shown that contributions of the fast atom flow non-uniformity in them are much less than that of the ion flow non-uniformity and may not be taken into account in the simulation of target sputtering in glow discharge when its surface relief element dimensions are small in comparison with the discharge cathode sheath length.     

Generalization of Primal—Dual Interior-Point Methods to Convex Optimization Problems in Conic Form

We generalize primal—dual interior-point methods for linear programming (LP) problems to the convex optimization problems in conic form. Previously, the most comprehensive theory of symmetric primal—dual interior-point algorithms was given by Nesterov and Todd for feasible regions expressed as the intersection of a symmetric cone with an affine subspace. In our setting, we allow an arbitrary convex cone in place of the symmetric cone. Even though some of the impressive properties attained by Nesterov—Todd algorithms are impossible in this general setting of convex optimization problems, we show that essentially all primal—dual interior-point algorithms for LP can be extended easily to the general setting. We provide three frameworks for primal—dual algorithms, each framework corresponding to a different level of sophistication in the algorithms. As the level of sophistication increases, we demand better formulations of the feasible solution sets. Our algorithms, in return, attain provably better theoretical properties. We also make a very strong connection to quasi-Newton methods by expressing the square of the symmetric primal—dual linear transformation (the so-called scaling) as a quasi-Newton update in the case of the least sophisticated framework. August 25, 1999. Final version received: March 7, 2001.     

Geometry of homogeneous convex cones,duality mapping,and optimal self-concordant barriers

We study homogeneous convex cones. We first characterize the extreme rays of such cones in the context of their primal construction (due to Vinberg) and also in the context of their dual construction (due to Rothaus). Then, using these results, we prove that every homogeneous cone is facially exposed. We provide an alternative proof of a result of Güler and Tunç el that the Siegel rank of a symmetric cone is equal to its Carathéodory number. Our proof does not use the Jordan-von Neumann-Wigner characterization of the symmetric cones but it easily follows from the primal construction of the homogeneous cones and our results on the geometry of homogeneous cones in primal and dual forms. We study optimal self-concordant barriers in this context. We briefly discuss the duality mapping in the context of automorphisms of convex cones and prove, using numerical integration, that the duality mapping is not an involution on certain self-dual cones.Research of this author was supported in part by a Summer Undergraduate Research Assistantship Award from NSERC (Summer 2001) and a research grant from NSERC while she was an undergraduate student at Faculty of Mathematics, University of Waterloo.Research of this author was supported in part by a PREA from Ontario, Canada and research grants from NSERC. Corresponding author.Mathematics Subject Classification (2000): 90C25, 90C51, 90C60, 90C05, 65Y20, 52A41, 49M37, 90C30     

Lovász–Schrijver SDP-operator,near-perfect graphs and near-bipartite graphs

We study the Lovász–Schrijver lift-and-project operator (\({{\mathrm{\text {LS}}}}_+\)) based on the cone of symmetric, positive semidefinite matrices, applied to the fractional stable set polytope of graphs. The problem of obtaining a combinatorial characterization of graphs for which the \({{\mathrm{\text {LS}}}}_+\)-operator generates the stable set polytope in one step has been open since 1990. We call these graphs \({{{\mathrm{\text {LS}}}}}_+\)-perfect. In the current contribution, we pursue a full combinatorial characterization of \({{{\mathrm{\text {LS}}}}}_+\)-perfect graphs and make progress towards such a characterization by establishing a new, close relationship among \({{{\mathrm{\text {LS}}}}}_+\)-perfect graphs, near-bipartite graphs and a newly introduced concept of full-support-perfect graphs.     

Spectrophotometric determination of some pesticides in water samples after preconcentration with Saccharomyces cerevisiae immobilized on sepiolite

A sensitive and selective method for the preconcentration and determination of carbaryl, chlorpyrifos, linuron, and thiram was developed. The column sorption method was used for the preconcentration studies. Several parameters, such as amount of sorbent, pH, flow rate, volume of elution solution, and interferences, that can influence the retention of pesticides on Saccharomyces cerevisiae immobilized on sepiolite were investigated. Results showed that it was possible to achieve quantitative analysis when the sample pH was in the range 4-6 for carbaryl and thiram, 4-8 for linuron and 6 for chlorpyrifos using 100 mL of sample solution containing 20 microg of pesticide and 5 mL of eluent. Recoveries of carbaryl, chlorpyrifos, linuron, and thiram were 93.2 +/- 0.4%, 97.1 -/+ 0.3%, 98.5 +/- 0.4%, and 96.1 +/- 0.2%, respectively, at 95% confidence level under optimum conditions. The capacity of the sorbent was found to be 41, 28, 35, and 46 mg g(-1) for carbaryl, chlorpyrifos, linuron, and thiram, respectively. Saccharomyces cerevisiae immobilized on sepiolite is suitable for repeated use without loss of capacity up to twenty five cycles. The pesticides studied have been determined in river water with high precision and accuracy.     

Global Aromaticity in Macrocyclic Cyclopenta‐Fused Tetraphenanthrenylene Tetraradicaloid and Its Charged Species

A stable cyclopenta‐fused tetraphenanthrenylene macrocycle, CPTP‐M , was synthesized, and the structure was confirmed by X‐ray crystallographic analysis. It exhibits a large radical character (number of unpaired electron, N_U=3.52) and a small singlet–triplet energy gap (ΔE_S‐T=?2.8 kcal mol^?1 by SQUID). Its backbone contains 60 ([4n]) conjugated π electrons and is globally antiaromatic. NMR measurements and theoretical calculations revealed that its dication/dianion is globally aromatic owing to the existence of [4n?2]/[4n+2] π‐conjugated electrons. Remarkably, the ring‐current map of the tetraanion shows a unique ring‐in‐ring structure, with a diamagnetic outer ring and a paramagnetic inner ring. Accordingly, both the inner‐rim and outer‐rim protons are deshielded in its ¹H NMR spectrum. The tetraanion can be regarded as an isoelectronic structure of the known octulene, which shows similar electronic properties.     

Stable Expanded Porphycene‐Based Diradicaloid and Tetraradicaloid

The synthesis of a bithiophene‐bridged 34π conjugated aromatic expanded porphycene 1 and a cyclopentabithiophene bridged 32π conjugated anti‐aromatic expanded porphycene 2 by a McMurry coupling strategy is presented. Magnetic measurements and theoretical calculations reveal that both 1 and 2 exhibit an open‐shell singlet ground state with significant radical character (y₀=0.63 for 1 ; y₀=0.68, y₁=0.18 for 2 ; y₀: diradical character, y₁: tetraradical character) and a small singlet–triplet energy gap (ΔE_S‐T=?3.25 kcal mol^?1 for 1 and ΔE_S‐T=?0.92 kcal mol^?1 for 2 ). Despite the open‐shell radical character, both compounds display exceptional stability under ambient air and light conditions owing to effective delocalization of unpaired electrons in the extended cyclic π‐conjugation pathway.     

A new glycoside from Polygala tenuifolia Willd

A new tdterpenoid glycoside, 3-β-O-β-D-glucopyranosyl presenegenin 28-O-α-L-arabipyranosyl（1 → 3）-6-β- xylopyranosyl（1 → 4）-[β-D-apiofuranosyl（1 → 3）]-Ct-L-rhamnopyranosyl（1 → 2）-[α-L-rhamnopyranosyl（1 → 3）]-β-D-fucopyranosyl ester （1） was isolated from the Polygala tenuifolia Willd., together with two known saponins, including polygalasaponinXXIV （2） and polygalasaponinXXVIII （3）. The structure of new compound was elucidated by spectroscopic methods.