The euclidean distance degree of orthogonally invariant matrix varieties

The Euclidean distance degree of a real variety is an important invariant arising in distance minimization problems. We show that the Euclidean distance degree of an orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in concrete circumstances.     

Bound states of string networks and D-branes

We show the existence of nonthreshold bound states of (p,q) string networks and D3-branes, preserving 1/4 of the full type-IIB supersymmetry, interpreted as string networks "dissolved" in D3-branes. We also explicitly write down the expression for the mass density of the system and discuss the extension of the construction to other Dp-branes. Differences in our construction of string networks with the ones interpreted as dyons in N = 4 gauge theories are also pointed out.     

Gomory integer programs

 The set of all group relaxations of an integer program contains certain special members called Gomory relaxations. A family of integer programs with a fixed coefficient matrix and cost vector but varying right hand sides is a Gomory family if every program in the family can be solved by one of its Gomory relaxations. In this paper, we characterize Gomory families. Every TDI system gives a Gomory family, and we construct Gomory families from matrices whose columns form a Hilbert basis for the cone they generate. The existence of Gomory families is related to the Hilbert covering problems that arose from the conjectures of Seb?. Connections to commutative algebra are outlined at the end. Received: May 17, 2001 / Accepted: February 7, 2002 Published online: April 24, 2003 RID="⋆" ID="⋆" Research partially supported by NSF grant DMS-0100141.     

Erratum to: Solution behavior of aqueous mixtures of low and high molecular weight hydrophobic amphiphiles

Mixtures of a hydrophobic triblock copolymer (L121, PEO₅PPO₆₈PEO₅) and a hydrophobic anionic surfactant (AOT, Sodium bis(2-ethylhexyl)sulfosuccinate), each alone forming turbid vesicular solutions in water, aggregate to produce a thermodynamically stable, transparent and isotropic solution. Mixed AOT/L121 aggregates could be confirmed by fluorescence, surface tension, differential scanning calorimetry (DSC) and isothermal titration calorimetry (ITC). In an isotropic region, where mixed aggregates are formed, there is a synergistic interaction between monomers of AOT and L121 in the mixture. In addition, Small Angle Neutron Scattering (SANS) experiments provided evidence that mixed aggregates have the shape of either spheres (with a certain polydispersity) or very short ellipsoids (axial ratio below 2), confirming a transition from giant multilamellar vesicles to small aggregates upon mixing the two hydrophobic amphiphiles. Upon dilution, the morphology changes to disk-like. From an examination of the results of all the methods the peculiar behavior of the mixed AOT/L121 system is explained.     

Tuning photosensitized singlet oxygen generation efficiency of novel aza-BODIPY dyes

Novel aza-BODIPY derivatives substituted with heavy atoms such as bromine and iodine were synthesized, and their triplet and singlet oxygen generation efficiencies have been investigated. These derivatives showed absorption in the NIR region with high molar extinction coefficients. The dye substituted with four iodine atoms showed yields of Φ(T) = 0.78 and Φ((1)O(2)) = 0.70, which are the highest values so far obtained for the aza-BODIPY derivatives.     

Determination of molybdenum(VI) by differential pulse polarographic technique using 4-(2-hydroxy phenyl ethaminodiol), benzene-1,3-diol(4-2-HPEDB-1,3,D)

A novel analytical reagent 4-(2-hydroxy phenyl ethaminodiol), benzene-1,3-diol(4-2-HPEDB-1,3,D) was synthesized for the determination of molybdenum(VI). The present paper reveals the detailed study of electroanalytical behaviour for [Mo-(4-2-HPEDB-1,3,D)] complex under optimized conditions. The peak obtained for [Mo-(4-2-HPEDB-1,3,D)] prevent the interference of foreign ions which shows the sensitivity of the proposed method. The linearity was maintained at the concentration range of 0.5–200 μg/mL at pH 4.5 with correlation factor 0.9997. The present method was successfully applied for the analysis of molybdenum(VI) in biological fluids and plant material. The results obtained from the proposed method show good agreement with reference method.     

Strings in some Bianchi type cosmologies

Some Bianchi type cosmological models-two in four and one in higher dimensions-are here studied in the context of cosmic strings. The physical implications of the models are briefly discussed. It is interesting to note that cosmic strings do not occur in Bianchi type V cosmology.     

Unsymmetrically substituted 9,10-dihydro-9,10-diboraanthracenes as versatile building blocks for boron-doped π-conjugated systems

The targeted hydrolysis of the 9,10-dihydro-9,10-diboraanthracene adduct (Me(2)S)HB(C(6)H(4))(2)BH(SMe(2)) (1) with 0.5 equiv of H(2)O leads to formation of the borinic acid anhydride [(Me(2)S)HB(C(6)H(4))(2)B](2)O (2) and thereby provides access to the field of unsymmetrically substituted 9,10-dihydro-9,10-diboraanthracenes. Compound 2 reacts with tBuC≡CH to give the corresponding vinyl derivative in an essentially quantitative conversion. Subsequent cleavage of the B-O-B bridge by LiAlH(4) with formation of hydridoborate functionalities is possible but is accompanied by partial B-C(vinyl) bond degradation. This situation changes when the related mesityl derivative [MesB(C(6)H(4))(2)B](2)O (7) is employed, which can be synthesized from BrB(C(6)H(4))(2)BBr (6) by treatment with 1 equiv of MesMgBr and subsequent hydrolysis. The reaction of 7 with LiAlH(4) in tetrahydrofuran (THF) furnishes Li[MesB(C(6)H(4))(2)BH(2)] (8); hydride elimination with Me(3)SiCl leads to formation of the THF adduct MesB(C(6)H(4))(2)BH(THF) (9·THF). Alternatively, 7 can be transformed into the bromoborane MesB(C(6)H(4))(2)BBr (10) by treatment with BBr(3). A Br/H-exchange reaction between 10 and Et(3)SiH yields the donor-free borane MesB(C(6)H(4))(2)BH (9), which forms B-H-B bridged dimers (9)(2) in the solid state. The vinyl borane MesB(C(6)H(4))(2)BC(H)=C(H)Mes (14) is accessible from MesC≡CH and either 9·THF or 9. Compared with the related compound Mes(2)BC(H)=C(H)Mes, the electronic absorption and emission spectra of 14 reveal bathochromic shifts of Δλ(abs)=17 nm and Δλ(em)=74 nm, which can be attributed to the rigid, fully delocalized π framework of the [MesB(C(6)H(4))(2)B] chromophore.     

Laser produced plasma: A pumping source for cadmium photo-ionization laser

We report laser oscillations in Cd II on 4d ⁹5s ^{2 2} D _5/2 − 4d ¹⁰5p ² P _3/2 transition at 441.6 nm using laser produced tungsten plasma as a pumping source. Mach Zehnder interferometer is used to measure electron density. Design and working of the crossed heat pipe used in the studies is discussed.     

Graph splicing systems

In this paper, extended graph splicing systems are defined. It is shown that when strings are represented as linear graphs, any recursively enumerable set can be generated by an extended graph splicing system. It is also shown that the computational completeness of extended graph splicing systems can be proved under some constraints too.