Linearization of class C for contractions on Banach spaces

In this work we prove a C¹-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite-dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant manifolds, which can be interesting by itself and that was needed on the proof of our main theorem. Our results essentially generalize some classical results by P. Hartman in finite dimensions, and a result of Mora-Sola-Morales in the infinite-dimensional case. It is shown that the result can be applied to some abstract systems of semilinear damped wave equations.     

Quaternionic Electron Theory: Geometry, Algebra, and Dirac's Spinors

The use of complexified quaternions andi-complex geometry in formulating the Dirac equationallows us to give interesting geometric interpretationshidden in the conventional matrix-basedapproach.     

Analysis of complex samples by solvating gas chromatography (supercritical fluid to gas transition)

The various forms of chromatography are primarily determined by differences in the physical state of the mobile phases. The main chromatographic categories include gas chromatography (GC), liquid chromatography, and supercritical fluid chromatography. Adjusting a temperature and pressure will change the mobile phase from liquid to supercritical fluid to gas, with concomitant changes in their physical properties. In this paper, the technique transition-phase chromatography (TPC) is described. In TPC, different mobile phase conditions exist inside the column. This phase transformation within the column results in huge differences in density, solvating power, viscosity, diffusivity, and, as a consequence, in the chromatographic properties of the mobile phase. TPC experiments using capillary columns packed in our laboratory have shown that when the mobile phase is transformed from supercritical fluid to gas, high column efficiencies can be achieved. The transition from supercritical fluid to gas (also called solvating GC), a particular case of the TPC, is evaluated for the separation of complex real samples (environmental, food, and fuels).     

Real

The famous problem involves applying two maps: and to positive integers. If is even, one applies , if it is odd, one applies . The conjecture states that each trajectory of the system arrives to the periodic orbit . In this paper, instead of choosing each time which map to apply, we allow ourselves more freedom and apply both and independently of . That is, we consider the action of the free semigroup with generators and on the space of positive real numbers. We prove that this action is minimal (each trajectory is dense) and that the periodic points are dense. Moreover, we give a full characterization of the group of transformations of the real line generated by and .

     

Tabu search embedded simulated annealing for the shortest route cut and fill problem

The shortest route cut and fill problem proposed by Henderson et al ¹ is studied in this paper where we extend the model to include multiple vehicles and a makespan objective. A new tabu search embedded simulated annealing algorithm for both models is developed. Computational experiments show that the new approach is robust and achieves better solutions when compared with those found using Henderson et al's algorithm for larger test cases within significantly shorter times.     

Magnetic properties of ferromagnetic quasi-1D copper-peptide compounds: exchange interactions and very low temperature phase transitions

The magnetic properties of the Cu(II)-peptide compounds (L-tyrosyl-L-leucinato)Cu(II) and (L-tryptophyl-glycinato)Cu(II), to be identified as Cu(II)Tyr-Leu and Cu(II)Trp-Gly, respectively, have been investigated by specific heat (0.08 < T < 28 K), dc magnetization (2 < T < 80 K, with B(0) = mu(o)H < or = 9 T), and ac magnetic susceptibility (with B(0) = 0 for 0.03 < T < 3 K and B(0) up to 9 T for 2 < T < 80 K) measurements. Above approximately 1 K, the specific heat and magnetization of both compounds display a ferromagnetic (FM) spin chain behavior sustained by syn-anti carboxylate bridges connecting equatorially Cu(II) ions at about 5 A. To model this behavior, we calculated the eigenvalues of Heisenberg chains with up to 20 spins 1/2 and used the method of Bonner and Fisher. A global fit of the model to the specific heat and magnetization data gives 2J(0)/k(B) = 3.60(5) K and 2.59(5) K for the intrachain exchange interactions in Cu(II)Tyr-Leu and Cu(II)Trp-Gly, respectively (H(ex)(i,j) = -2J(0) S(i).S(j)). These values of 2J(0) are discussed in terms of structural properties of the carboxylate bridges in the two compounds. Using the parameters obtained from the global fit, we calculated isothermal susceptibilities in agreement with the ac susceptibilities measured with small applied dc magnetic fields. However, the ac susceptibility measured with applied dc fields larger than 1 T lie between the values calculated for the isothermal and adiabatic susceptibilities. At 0.16 K for Cu(II)Tyr-Leu and 0.53 K for Cu(II)Trp-Gly, the observed specific heat and magnetic susceptibility display peaks associated to three-dimensional magnetic phase transitions. The interchain exchange couplings 2J(1) producing the 3D magnetic order are ferromagnetic and have magnitudes 2J(1)/k(B) approximately 0.015 and 0.073 K for Cu(II)Tyr-Leu and Cu(II)Trp-Gly, respectively.     

UV/Vis spectra and solubility of some naphthoquinones, and the extraction behavior of plumbagin from Plumbago scandens roots in supercritical CO2

The solubility of 1,4-naphthoquinone, plumbagin, lawsone, and juglone in supercritical carbon dioxide was determined spectroscopically at 40°C, and in the pressure range 8–18 MPa. Their solubilities at 12 MPa were between 0.3 and 10 g L⁻¹. Plumbagin from Plumbago scandens L. roots was extracted at 40°C and 20 MPa. The extracted plumbagin mass fraction was up to 0.2% in fresh roots but down to about 0.006% in aged roots. n-Hexane and chloroform extraction of such aged roots indicates that the older and dryer the roots are, the stronger they bind plumbagin. Reversed-phase HPLC indicated a relatively pure plumbagin extract with supercritical carbon dioxide.