Comparative Study on Pantothenic Acid Separation by Reactive Extraction with Tri-n-octylamine and Di-(2-ethylhexyl) Phosphoric Acid

The mechanism of reactive extraction of pantothenic acid with tri-n-octylamine and di-(2-ethylhexyl) phosphoric acid was analysed for three solvents in the presence or absence of 1-octanol. In the absence of 1-octanol, the stoichiometric ratio between the solute and tri-n-octylamine was 1:1 for dichloromethane, 1:2 for butyl acetate, and 1:4 for n-heptane. In the presence of 1-octanol, the formation of aminic adducts was restricted, the stoichiometries for the interfacial reaction between the acid and tri-n-octylamine becoming 1:1 for dichloromethane and butyl acetate, 1:2 for n-heptane. A similar effect has been observed for extraction with di-(2-ethylhexyl) phosphoric acid, the structure of the interfacial compound being changed for n-heptane and butyl acetate from HAE2 in the absence of 1-octanol to HAE by addition of this alcohol. The highest extraction constants were obtained when extractant associates were formed. However, when the extraction mechanism was the same, the increase in organic phase polarity influenced positively the value of extraction constant

Particle Collisions on Stringy Black Hole Background

The collision of two particles in the background of a Sen black hole is studied. With the equations of motion of the particles, the center-of-mass energy is investigated when the collision takes place at the horizon of a Sen black hole. For an extremal Sen black hole, we find that the center-of-mass energy will be arbitrarily high with two conditions: (1) spin $a\neq 0$ and (2) one of the colliding particles has the critical angular momentum $l_{\text{c}}=2$. For a nonextremal Sen black hole, we show that, in order to obtain an unlimited center-of-mass energy, one of the colliding particles should have the critical angular momentum $l'_{\text{c}}=2 r_{+}/a$ ($r_{+}$ is the radius of the outer horizon for a nonextremal black hole). However, a particle with the angular momentum $l=l'_{\text{c}}$ could not approach the black hole from outside of the horizon through free fall, which implies that the collision with arbitrarily high center-of-mass energy could not take place. Thus, there is an upper bound of the center-of-mass energy for the nonextremal black hole. We also obtain the maximal center-of-mass energy for a near-extremal black hole and the result implies that the Planck-scale energy is hard to be approached. Furthermore, we also consider the back-reaction effects. The result shows that, neglecting the gravitational radiation, it has a weak effect on the center-of-mass energy. However, we argue that the maximum allowed center-of-mass energy will be greatly reduced to below the Planck-scale when the gravitational radiation is included.Comment: 17 pages, 4 figures, published versio

Irreducible holonomy algebras of Riemannian supermanifolds

Possible irreducible holonomy algebras \g\subset\osp(p,q|2m) of Riemannian supermanifolds under the assumption that \g is a direct sum of simple Lie superalgebras of classical type and possibly of a one-dimensional center are classified. This generalizes the classical result of Marcel Berger about the classification of irreducible holonomy algebras of pseudo-Riemannian manifolds.Comment: 27 pages, the final versio

Nonlinear stability analysis of the Emden-Fowler equation

In this paper we qualitatively study radial solutions of the semilinear elliptic equation $\Delta u + u^n = 0$ with $u(0)=1$ and $u'(0)=0$ on the positive real line, called the Emden-Fowler or Lane-Emden equation. This equation is of great importance in Newtonian astrophysics and the constant $n$ is called the polytropic index. By introducing a set of new variables, the Emden-Fowler equation can be written as an autonomous system of two ordinary differential equations which can be analyzed using linear and nonlinear stability analysis. We perform the study of stability by using linear stability analysis, the Jacobi stability analysis (Kosambi-Cartan-Chern theory) and the Lyapunov function method. Depending on the values of $n$ these different methods yield different results. We identify a parameter range for $n$ where all three methods imply stability.Comment: 12 pages; new reference added; 3 new references added; fully revised versio

Algebraic structure of gravity in Ashtekar variables

The BRST transformations for gravity in Ashtekar variables are obtained by using the Maurer-Cartan horizontality conditions. The BRST cohomology in Ashtekar variables is calculated with the help of an operator $\delta$ introduced by S.P. Sorella, which allows to decompose the exterior derivative as a BRST commutator. This BRST cohomology leads to the differential invariants for four-dimensional manifolds.Comment: 19 pages, report REF. TUW 94-1

Hidden Symmetries for Ellipsoid-Solitonic Deformations of Kerr-Sen Black Holes and Quantum Anomalies

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and studied hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.Comment: latex2e, 11pt, 34 pages, the variant accepted by EPJC, with additional explanations, modifications and new references requested by refere

Ultraintense X-Ray Induced Ionization, Dissociation, and Frustrated Absorption in Molecular Nitrogen

Sequential multiple photoionization of the prototypical molecule N_2 is studied with femtosecond time resolution using the Linac Coherent Light Source (LCLS). A detailed picture of intense x-ray induced ionization and dissociation dynamics is revealed, including a molecular mechanism of frustrated absorption that suppresses the formation of high charge states at short pulse durations. The inverse scaling of the average target charge state with x-ray peak brightness has possible implications for single-pulse imaging applications

On Some Geometric Structures Associated to a k-Symplectic Manifold

A canonical connection is attached to any k-symplectic manifold. We study the properties of this connection and its geometric applications to k-symplectic manifolds. In particular we prove that, under some natural assumption, any ksymplectic manifold admits an Ehresmann connection, discussing some corollaries of this result, and we find vanishing theorems for characteristic classes on a k-symplectic manifold.Comment: To appear on J. Phys. A: Math. Theo

Revised calibration of the mbt-cbt paleotemperature proxy based on branched tetraether membrane lipids in surface soils

The MBT-CBT proxy for the reconstruction of paleotemperatures and past soil pH is based on the distribution of branched glycerol dialkyl glycerol tetraether (brGDGT) membrane lipids. The Methylation of Branched Tetraether (MBT) and the Cyclisation of Branched Tetraether (CBT) indices were developed to quantify these distributions, and significant empirical relations between these indices and annual mean air temperature (MAT) and/or soil pH were found in a large data set of soils. In this study, we extended this soil dataset to 278 globally distributed surface soils. Of these soils, 26% contains all nine brGDGTs, while in 63% of the soils the seven most common brGDGTs were detected, and the latter were selected for calibration purposes. This resulted in new transfer functions for the reconstruction of pH based on the CBT index: pH = 7.90-1.97 x CBT (r(2) = 0.70; RMSE = 0.8; n = 176), as well as for MAT based on the CBT index and methylation index based on the seven most abundant GDGTs (defined as MBT'): MAT = 0.81-5.67 x CBT + 31.0 x MBT' (r(2) = 0.59; RMSE = 5.0 degrees C; n = 176). The new transfer function for MAT has a substantially lower correlation coefficient than the original equation (r(2) = 0.77). To investigate possible improvement of the correlation, we used our extended global surface soil dataset to statistically derive the indices that best describe the relations of brGDGT composition with MAT and soil pH. These new indices, however, resulted in only a relatively minor increase in correlation coefficients, while they cannot be explained straightforwardly by physiological mechanisms. The large scatter in the calibration cannot be fully explained by local factors or by seasonality, but MAT for soils from arid regions are generally substantially (up to 20 degrees C) underestimated, suggesting that absolute brGDGT-based temperature records for these areas should be interpreted with caution.<br>The applicability of the new MBT'-CBT calibration function was tested using previously published MBT-CBT-derived paleotemperature records covering the last deglaciation in Central Africa and East Asia, the Eocene-Oligocene boundary and the Paleocene-Eocene thermal maximum. The results show that trends remain similar in all records, but that absolute temperature estimates and the amplitude of temperature changes are lower for most records, and generally in better agreement with independent proxy data

Clocking Auger Electrons

Intense X-ray free-electron lasers (XFELs) can rapidly excite matter, leaving it in inherently unstable states that decay on femtosecond timescales. As the relaxation occurs primarily via Auger emission, excited state observations are constrained by Auger decay. In situ measurement of this process is therefore crucial, yet it has thus far remained elusive at XFELs due to inherent timing and phase jitter, which can be orders of magnitude larger than the timescale of Auger decay. Here, we develop a new approach termed self-referenced attosecond streaking, based upon simultaneous measurements of streaked photo- and Auger electrons. Our technique enables sub-femtosecond resolution in spite of jitter. We exploit this method to make the first XFEL time-domain measurement of the Auger decay lifetime in atomic neon, and, by using a fully quantum-mechanical description, retrieve a lifetime of $2.2^{ + 0.2}_{ - 0.3}$ fs for the KLL decay channel. Importantly, our technique can be generalised to permit the extension of attosecond time-resolved experiments to all current and future FEL facilities.Comment: Main text: 20 pages, 3 figures. Supplementary information: 17 pages, 6 figure