Conformal anomaly in 4D gravity-matter theories non-minimally coupled with a dilaton

The conformal anomaly for 4D gravity-matter theories, which are non-minimally coupled with the dilaton, is systematically studied. Special care is taken of rescaling of fields, treatment of total derivatives, hermiticity of the system operator and the choice of measure. Scalar, spinor and vector fields are taken as the matter quantum fields and their explicit conformal anomalies in the gravity-dilaton background are found. The cohomology analysis is carried out and some new conformal invariants and trivial terms, involving the dilaton, are obtained. The symmetry of the constant shift of the dilaton field plays an important role. The general structure of the conformal anomaly is examined. It is shown that the dilaton affects the conformal anomaly characteristically for each case: (1) [Scalar] The dilaton changes the conformal anomaly only by a new conformal invariant, I₄; (2) [Spinor] The dilaton does not change the conformal anomaly; (3) [Vector] The dilaton changes the conformal anomaly by three new (generalized) conformal invariants, I₄, I₂, I₁. We present some new anomaly formulae which are useful for practical calculations. Finally, the anomaly induced action is calculated for the dilatonic Wess-Zumino model. We point out that the coefficient of the total derivative term in the conformal anomaly for the 2D scalar coupled to a dilaton is ambiguous. This resolves the disagreement between earlier calculations and the result of Hawking and Bousso.     

Precision-optimized single protocol pre-/post-contrast modified-look locker inversion T1 mapping using composite inversion group fitting

BackgroundInvestigation of a simple, precision optimized, identical pre−/post-contrast modified look locker inversion recovery (MOLLI) protocol employing Composite inversion group (IG) fitting in a clinical cardiomyopathy population.MethodsCardiac magnetic resonance imaging (MRI) was performed at 3 Tesla in 36 patients (48.0 years [IQR: 35.7, 58.2 years]) with known/suspicion of hypertrophic cardiomyopathy. T1 mapping was performed pre−/post-contrast (0.15 mmol/kg Gadobutrol) using a standard 3-parameter fit (STANDARD) and an optimized (OPTIMAL) single-protocol Composite-IG fitting MOLLI approach. The OPTIMAL protocol was based on a simulation study (for 11hb acquisitions) with cost metric analysis across the range of expected T1 values (300-1400 ms) and heart rates (50-80 bpm).All maps were generated offline based on motion corrected source images. Based on region of interest analysis, the precision of both approaches was assessed using a previously validated propagation of errors technique for pre−/post-contrast T1 mapping as well as calculated ECV (based on point-of care hematocrit measurements. Furthermore, respective T1 and ECV values were calculated. Statistical methods included Wilcoxon Signed-Rank tests and Student's paired t-test.ResultsA total of ~9000 11hb inversion groupings were simulated with a 4(0)2(0)2(0)2(0)1 grouping providing the optimal precision across the specified T1/heart rate range. In comparison to standard pre-contrast 5(3)3 MOLLI, this OPTIMAL protocol demonstrated a significantly improved pre-contrast precision (9.1 [6.2, 9.9]ms vs. 9.4 [7.3, 10.8]ms; P < 0.001) while no significant differences were found for post-contrast T1 mapping (4.5 [2.6, 5.3]ms vs. 4.2 [2.8, 5.1]ms; P = 0.25) and EVC mapping (0.38 [0.28, 0.45]ms vs. 0.35 [0.25, 0.44]ms; P = 0.07) or reproducibility (0.16 [0.14, 0.19] vs. 0.19 [0.13, 0.23] P = 0.53).Direct comparison of resulting T1/ECV values demonstrated no significant differences between STANDARD and OPTIMAL techniques for pre-contrast T1 (1178 [1158, 1199]ms vs. 1173 [1143, 1195]ms; P = 0.46) and significant differences for post-contrast T1 (466 [446, 506]ms vs. 456 [433, 503]ms; P = 0.04) and ECV (23.1 [20.8, 25.1]% vs. 23.9 [22.3, 26.4]%; P = 0.001).ConclusionsA single optimized Composite-IG fitting protocol for pre−/post-contrast T1 mapping demonstrated improved precision over standard MOLLI techniques. It enables a simplified workflow with reduction of potential sources of error especially with respect to image data co-registration easing advanced post-processing for generation of patient specific ECV maps.     

Hierarchy of Chaotic Maps with an Invariant Measure and their Compositions

Abstract

We give a hierarchy of many-parameter families of maps of the interval [0, 1] with an invariant measure and using the measure, we calculate Kolmogorov–Sinai entropy of these maps analytically. In contrary to the usual one-dimensional maps these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor at certain region of parameters space, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at certain values of the parameters.     

No or Infinitely Many A.C.I.P.¶for Piecewise Expanding Cr Maps¶in Higher Dimensions

We modify Tsujii's example [9] to show that in contrast with the one-dimensional case, piecewise uniformly expanding and C ^r maps of the plane may: (1) either have no absolutely continuous invariant probability measures (a.c.i.p. for short) and be such that {\bf every point} is statistically attracted to a fixed repelling point;? (2) or have infinitely many ergodic a.c.i.p. Received: 6 September 2000 / Accepted: 15 May 2001     

Electronic Spectral Studies and Determination of the First Excited Singlet-State Dipole Moments of New Benzo[a]phenothiazine Derivatives

The room temperature (298 K) electronic absorption, and fluorescence excitation and emission spectra of seven new, pharmacologically-important benzo[a]phenothiazines (12H-benzo[a]phenothiazine ( 1 ), 9-methyl-12H-benzo[a] phenothiazine ( 2 ), 10-methyl-12H-benzo[a] phenothiazine ( 3 ), 11-methyl-12H-benzo[a]phenothiazine ( 4 ), 5-oxo-5H-benzo[a]phenothiazine ( 5 ), 6-hydroxy-5-oxo-5H-benzo[a]phenothiazine ( 6 ) and 6-methyl-5-oxo-5H-benzo[a] phenothiazine ( 7 ):) were measured in several solvents of different polarities and hydrogen bonding abilities. In combination with the ground state dipole moments of these benzo[a]phenothiazines, the spectral data were used to determine their first excited singlet-state dipole moments by means of the solvatochromic shift method. These excited singlet-state dipole moments were found to be significantly higher (1.9 to 2.5 Debye units) than their ground-state counterparts.     

Synthesis and Fluorescence Studies of Some New Fluorophores and Their Effect on Hybridization of Oligodeoxyribonucleotides

Some novel fluorophores, viz. 6-(6-isobutyrylamino-1,3-dioxo-1H,3H-benzo[de]isoquinolin-2-yl)-hexanoic acid (1), 6-(6-dimethylamino-1,3-dioxo-1H, 3H-benzo[de]isoquinolin-2-yl)-hexanoic acid (2), 6-(6-benzoylamino-1, 3-dioxo-1H, 3H-benzo[de]isoquinolin-2-yl)-hexanoic acid (3), 6-(6-amino-1-oxo-1H, 3H-benzo[de]isoquinolin-2-yl)-hexanoic acid (4) and 6-(6-amino-1H,3H-benzo[de] isoquinolin-2-yl)-hexanoic acid (5) have been designed, synthesized and characterized. Their comparative fluorescence has been studied in different organic solvents and aqueous solutions containing inorganic ions. Out of these, two fluorophores, 1 and 2 have been used for labelling of nucleosides which were finally converted into their phosphoramidites, and used for labelling of oligodeoxyribonucleotides through covalent attachment. These fluorophores after attachment on oligodeoxyribonucleotides showed good fluorescence signals and higher hybridisation affinity than unlabelled oligodeoxyribonucleotides.     

Monazite (monoclinic LaPO4) slip systems at room temperature

Polycrystalline monazite (monoclinic LaPO₄) was deformed by spherical indentation at room temperature. Slip systems were identified using TEM of thin sections prepared parallel and close to the indented surface. Dislocation Burgers vectors (b) were identified by Burgers circuit closure in high resolution TEM images, supplemented by diffraction contrast where possible. A total of 441 b determinations were made in 97 grains. The most common slip systems were [001]/(010), [100]/(010) and [010]/(100). Slip on (001) was less common. Many other less common slip systems and Burgers vectors were also identified, including b = [101], [101], [011], [110] and [111]. b = [101] dislocations dissociate into ½[101] partials, and b = [101] dislocations are inferred to dissociate to ½[101] partials, with a low energy stacking fault of ～30 mJ/m². b = [100] dislocations may dissociate into ¼[210] + ¼[210] partials. b = [010] may sometimes dissociate to ½[010] + ½[010] partials. Other types of partial dislocations were also observed and discussed. All partial dislocations were climb dissociated. The line energies of monazite dislocations and their partials were calculated, and stacking fault structures for partial dislocations are analyzed. Satisfaction of the Von Mises criterion for full ductility most likely involves [101]/(111) and ?011?/{011} or {111} slip, but other combinations that require both b = [101] and ?011? or ?110? are possible. If deformation twinning is active, slip systems with b = ?011? or ?110? may not be necessary for full ductility.     

Coevolution of Black Holes and Galaxies,edited by Luis C. Ho

Surface Science [Vol. 1] Lectures at an International Course, Trieste, 1974. (International Atomic Energy Agency, Vienna) [Pp. 505] £14.00; $31.00. Scope: Postgraduate course.

Simple Dielectric Liquids By T. J. Gallagher (Clarendon Press: Oxford University Press 1975) [Pp. vi+154] £6.00. Scope: Treatise/textbook. Level: Undergraduate to postgraduate.

Real Solids and Radiation By A. E. Hughes and D. Pooley (Wykeham Publications 1975) [Pp. xii+196] £3.00. Scope: General introduction. Level: Undergraduate, school.

New Uses for Ion Accelerators Editor: J. F. Ziegler (Plenum Press, 1975) [Pp. xii+482] $33.60.

Electrical Measurement Systems for Biological and Physical Scientists By L. J. Weber and D. L. McLean (Addison Wesley, 1975) [Pp. xiv+399] £8.25. Scope: Textbook. Level: undergraduate.

Temperature Measurement 1975 (Conference Series No. 26.) Edited by B. F. Billings and T. J. Quinn (The Institute of Physics 1975.) [Pp. xiv+454.] £20.00. Scope: Survey. Level: Specialist/postgraduate.

Theory and Application of the Boltzmann Equation By C. Cercignani (Scottish Academic Press x1975) [Pp. xii+415] £10.50. Scope: Textbook. Level: Undergraduate/postgraduate.

The Use of Physics Literature. Edited by H. Coblans. (Butterworths, 1976.) [Pp. vi+290.] £6.00. Scope: Survey; library (reference). Level: Specialist/post-graduate; undergraduate.

Authenticity in Art. By S. J. Fleming. (The Institute of Physics, 1975.) [Pp. 164.] £6.50. Level: Specialist/post-graduate; undergraduate; general reader.     

FTIR Spectral Study of Intramolecular Hydrogen Bonding in Thromboxane A2 Receptor Antagonist S-145 and Related Compounds. Part 4

Abstract

An N-methylated compound of S-145, (±)-(5Z)-7-[3-endo-[N-methyl)phenylsulphonyl)amino]bicyclo [2.2.1]hept-2-exo-yl]heptenoic acid 1, its chain analogue 12-[N-methyl(phenylsulphonyl)amino]dodecanoic acid 3, (±)-(5Z)-7-[3-endo-(benzoylamino)bicyclo[2.2.1]hept-2-exo-yl] heptenoic acid 5 and related compounds were synthesized in order to study the formation of a new class of intramolecular hydrogen bond IX (cis-CO₂H…O = Y). Their FTIR spectra were measured in dilute CCl₄ solution and subjected to curve analysis in order to separate overlapping absorption bands. For compounds 1,3 and 5, the intramolecular hydrogen bonds of the IX type involving 14-, 17- and 14-membered rings were found between a carboxyl group, which takes a cis-structure IV, and an oxygen atom of a sulphonyl or benzoylamino group, respectively. The C[dbnd]O stretching vibration bands of these carboxyl groups shifted to lower wavenumbers (ca. 19 cm^?1). The direction of these shifts was contrary to that found for α-keto and α-alkoxycarboxylic acids in which carboxyl groups take a trans-structure III due to the formation of intramolecular hydrogen bonds I and II, respectively.     

Study of the positive muon Knight shift in : Evidence for a tetravalent -state and crystalline electric field splitting

We report on transverse field (TF) Muon Spin Rotation (μSR) measurements on a single crystal of the hexagonal heavy fermion superconductor UNi₂Al₃ between 5 K and 300 K. From the measured muon Knight shift (KS) in the easy ( a , b )-plane and along the c-axis we extracted the local magnetic susceptibility tensor [0pt] , which arises from the nearest U-neighbors. By comparison with the bulk susceptibility [0pt] it is found that [0pt] and [0pt] agree well above 150 K but deviate considerably in the basal plane below 150 K, due to the disturbance introduced by the . We succeed in reproducing both [0pt] and [0pt] on the basis of a crystalline electric field (CEF)-approach assuming U to be in the tetravalent state. The disturbance introduced by the affects the CEF-Hamiltonian in an expected manner, suggesting strongly that a CEF-picture implying a rather local 5 f-electron wave function is indeed valid. Reanalyzing older data on UPd₂Al₃ we arrive at the same conclusion. A necessary condition for extracting the local susceptibility was the knowledge of the -site, this information was derived from the analysis of the TF-relaxation rates. At low temperatures we found about 30% of the implanted at the d-site and none at this site above 200 K. The majority fraction was found to be in a tunneling state over six m (or k)-sites around the b-site. No long range diffusion was seen up to room temperature. Received 20 April 1999     

Stochastic Evolutions in Superspace and Superconformal Field Theory

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss how this may be extended to superconformal maps of N=1 superspace with links to superconformal field theory and singular vectors of the N=1 superconformal algebra in the Neveu–Schwarz sector.     

Orthosymplectic unification of the Galilei group and BRST

The inclusion of BRST generators into the Poincarè group in D dimensions is known to lead IOsp[D,2|2]. Similarly, conformal symmetry gets extended into Osp[D×1,3|2]. For the non-relativistic case we find that the Galilei symmetry gets extended, by inclusion of the BRST generators, into an orthosymplectic symmetry possessing Osp[D,1|2] as a subgroup. All such extensions express the possibility of formulating the classical theories in reparametrization invariant ways. They include besides the generators of the initial kinematical symmetry (Poincarè, or conformal, or Galilei), the generators of Parisi-Sourlas transformations. The extended symmetries follow directly through BRST quantization.     

OSp[D+1,3 | 2] unifies the conformal symmetry and BRST

We show that the conformal transformations on the invariant metric of OSp[D,2 | 2], which is the group unifying Lorentz and BRST symmetries, are generated by OSp[D+1, 3 | 2], which thus unifies the conformal and BRST symmetries. We explicitly construct the generators for the scalar and for the spinning particle. We express the generators in terms of the energy-momentum tensor and study their action on the fields. We also study the linear realization of OSp[D+1, 3 | 2] on a space of D+4 bosonic and 2 fermionic variables. Field quantization is also examined.     

Hidden symmetry in the presence of fluxes

We derive the most general first-order symmetry operator for the Dirac equation coupled to arbitrary fluxes. Such an operator is given in terms of an inhomogeneous form ω   which is a solution to a coupled system of first-order partial differential equations which we call the generalized conformal Killing–Yano system. Except trivial fluxes, solutions of this system are subject to additional constraints. We discuss various special cases of physical interest. In particular, we demonstrate that in the case of a Dirac operator coupled to the skew symmetric torsion and U(1)$U(1)$ field, the system of generalized conformal Killing–Yano equations decouples into the homogeneous conformal Killing–Yano equations with torsion introduced in D. Kubiznak et al. (2009) [8] and the symmetry operator is essentially the one derived in T. Houri et al. (2010) [9]. We also discuss the Dirac field coupled to a scalar potential and in the presence of 5-form and 7-form fluxes.     

Reply to criticisms of theB (3) field

The confusion and self-contradiction among recent critics of theB ⁽³⁾ (Evans-Vigier) field are analysed. Barron [17] and Buckingham [18] assert that the field is zero by symmetry. Grimes [21] asserts that the field isnon-zero butfortuitous. Lakhtakia in one paper [19] asserts thatB ⁽³⁾ isnon-zero butnot fundamental, and in a second paper that it isunknowlable and therefore may as well be zero. A rebuttal is given of each the individual papers, and it is shown that the Evans-Vigier field is the fundamental magnetizing field of electromagnetic radiation.     

Spectrophotometric Characteristics of New Pyridylindolizine Derivatives Solutions

Three new pyridylindolizine derivatives, 1, 2, 3-tricarbometoxi-7-(4-pyridyl)-pyrrolo[1, 2-a]pyridine (I), 1,2-dicarboethoxy-3-(4-bromobenzoyl)-7-(4-pyridyl)-pyrrolo[1,2-a]pyridine (II) and its isomer 1,2-dicarboethoxy-3- (4-bromobenzoyl) -5- (2-pyridyl) -pyrrolo[1, 2-a]pyridine (III) have been investigated in different solutions by UV-VIS absorption, steady-state, and time-resolved fluorescence methods. The effects of the substituent and solvent on the spectroscopic properties have been demonstrated. The fluorescence decay data could be fitted to a single-exponential function. The lifetime values are higher in protic polar than in aprotic apolar solvents for compound I. In the case of compounds II and III the fluorescence intensities and lifetimes are very low, with the exception of III in aprotic solvents. The absorption and fluorescence properties of the compounds showed a solvent dependence.     

Fluorescence Properties and Dipole Moments of Novel Fused Thienobenzofurans. Solvent and Structural Effects

The electronic absorption, fluorescence excitation and emission spectra, and fluorescence quantum yields of novel fused thienobenzofurans, including thieno[3,2-b][1]benzofuran (1), [1]benzothieno[3,2-b]furan (2), and [1]benzothieno[3,2-b][1]benzofuran (3), were recorded in fourteen solvents of different polarities at room temperature. Compound 2 was not fluorescent. Experimental ground-state dipole moments of compounds 1–3 were measured in benzene at 298 K and compared with the corresponding theoretical dipole moment values. The solvent effects on the electronic absorption and fluorescence spectra of these thienobenzofurans were quantitatively investigated by means of solvatochromic correlations based on the Kawski-Chamma-Viallet and McRae equations. A weak negative solvatochromic behavior was found for these compounds, showing that their dipole moments are slightly lower in the excited singlet-state than in the ground-state. Kamlet-Abboud-Taft multiparameter relationships were also established for electronic absorption and fluorescence wavenumbers, and fluorescence quantum yields in most solvents, demonstrating the occurrence of specific solute-solvent interactions.     

A Cosmological Model with Negative Constant Deceleration Parameter in Brans-Dicke Theory

Bermann (1983) [Nuovo Cimento B, 74, 182] obtained a cosmological model with the help of special law of variation for Hubble's parameter that yields constant deceleration parameter models of the universe. Here, we present Bianchi-I model with negative constant deceleration parameter in Brans-Dicke (1961) [Phys. Rev., 124, 925] theory in the presence of perfect fluid source with disordered radiation. Some physical properties of the model are also discussed. PACS numbers: 98-90.     

Theoretical investigation on structures,stability and properties of [P,X, Y] (X=C,Si; Y = O,S) isomers

The structures, energetics and stability of the [P, X, Y] (X?=?C, Si; Y?=?O, S) radicals are explored by means of the density functional theory and ab initio levels. Seventeen [P, X, Y] isomers and 14 interconversion transition states are obtained at the B3LYP/6-311G(d) level. At the CCSD(T)/6-311?+?G(2df)//QCISD/6-311G(d)?+?ZPVE level, the lowest-lying isomers are the linear PCO 1a (0.0?kcal/mol), PCS 1b (0.0) and the three-membered ring cPSiO 1c (0.0), cPSiS 1d (0.0) on their respective potential energy surfaces. These four isomers exhibit considerably not only thermodynamic but also kinetic stabilities. Additionally, the cyclic cPCS 2b (32.8) and linear PSiS 2d (18.6) possess also high kinetic stability. All of six isomers 1a, 1b, 2b, 1c, 1d and 2d are considerably stabilized by a barrier of at least 20?kcal/mol, and may be detected in the laboratory or interstellar space. Their valence bond structures and possible formation strategies in the laboratory and space are discussed in detail. Finally, the similarities and discrepancies on structures and stabilities between [P, X, Y] (X?=?C, Si; Y?=?O, S) isomers are compared. These predicted results are highly expected to be informative for the future identification of [P, X, Y] (X?=?C, Si; Y?=?O, S) in the laboratory and space.