scholarly journals Noether-Wald charges in six-dimensional Critical Gravity

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Giorgos Anastasiou ◽  
Ignacio J. Araya ◽  
Cristóbal Corral ◽  
Rodrigo Olea
Keyword(s):  
Weyl Tensor ◽  
Einstein Space ◽  
Gravity Theory ◽  
Compact Form ◽  
Conformal Invariants ◽  
Einstein Manifolds ◽  
Conformal Gravity ◽  
Covariant Derivatives ◽  
The Difference ◽  
Derivatives Of

Abstract It has been recently shown that there is a particular combination of conformal invariants in six dimensions which accepts a generic Einstein space as a solution. The Lagrangian of this Conformal Gravity theory — originally found by Lu, Pang and Pope (LPP) — can be conveniently rewritten in terms of products and covariant derivatives of the Weyl tensor. This allows one to derive the corresponding Noether prepotential and Noether-Wald charges in a compact form. Based on this expression, we calculate the Noether-Wald charges of six-dimensional Critical Gravity at the bicritical point, which is defined by the difference of the actions for Einstein-AdS gravity and the LPP Conformal Gravity. When considering Einstein manifolds, we show the vanishing of the Noether prepotential of Critical Gravity explicitly, which implies the triviality of the Noether-Wald charges. This result shows the equivalence between Einstein-AdS gravity and Conformal Gravity within its Einstein sector not only at the level of the action but also at the level of the charges.

Energy Approximation

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Main Lemma ◽  
The Other ◽  
Coarse Scale ◽  
Continuous Solutions ◽  
Material Derivative ◽  
Energy Variation ◽  
Energy Approximation ◽  
The Difference ◽  
Derivatives Of

This chapter presents the equations and calculations for energy approximation. It establishes the estimates (261) and (262) of the Main Lemma (10.1) for continuous solutions; these estimates state that we are able to accurately prescribe the energy that the correction adds to the solution, as well as bound the difference between the time derivatives of these two quantities. The chapter also introduces the proposition for prescribing energy, followed by the relevant computations. Each integral contributing to the other term can be estimated. Another proposition for estimating control over the rate of energy variation is given. Finally, the coarse scale material derivative is considered.

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

Effects of avertin versus xylazine-ketamine anesthesia on cardiac function in normal mice

2001 ◽  
Vol 281 (5) ◽  
pp. H1938-H1945 ◽  
Author(s):  
Chari Y. T. Hart ◽  
John C. Burnett ◽  
Margaret M. Redfield
Keyword(s):  
Cardiac Function ◽  
Diastolic Pressure ◽  
Systolic Function ◽  
Pressure Rise ◽  
Left Ventricular ◽  
Lv Function ◽  
Ketamine Anesthesia ◽  
The Difference ◽  
And Function ◽  
Derivatives Of

Anesthetic regimens commonly administered during studies that assess cardiac structure and function in mice are xylazine-ketamine (XK) and avertin (AV). While it is known that XK anesthesia produces more bradycardia in the mouse, the effects of XK and AV on cardiac function have not been compared. We anesthetized normal adult male Swiss Webster mice with XK or AV. Transthoracic echocardiography and closed-chest cardiac catheterization were performed to assess heart rate (HR), left ventricular (LV) dimensions at end diastole and end systole (LVDd and LVDs, respectively), fractional shortening (FS), LV end-diastolic pressure (LVEDP), the time constant of isovolumic relaxation (τ), and the first derivatives of LV pressure rise and fall (dP/d t max and dP/d t min, respectively). During echocardiography, HR was lower in XK than AV mice (250 ± 14 beats/min in XK vs. 453 ± 24 beats/min in AV, P < 0.05). Preload was increased in XK mice (LVDd: 4.1 ± 0.08 mm in XK vs. 3.8 ± 0.09 mm in AV, P < 0.05). FS, a load-dependent index of systolic function, was increased in XK mice (45 ± 1.2% in XK vs. 40 ± 0.8% in AV, P < 0.05). At LV catheterization, the difference in HR with AV (453 ± 24 beats/min) and XK (342 ± 30 beats/min, P < 0.05) anesthesia was more variable, and no significant differences in systolic or diastolic function were seen in the group as a whole. However, in XK mice with HR <300 beats/min, LVEDP was increased (28 ± 5 vs. 6.2 ± 2 mmHg in mice with HR >300 beats/min, P < 0.05), whereas systolic (LV dP/d t max: 4,402 ± 798 vs. 8,250 ± 415 mmHg/s in mice with HR >300 beats/min, P < 0.05) and diastolic (τ: 23 ± 2 vs. 14 ± 1 ms in mice with HR >300 beats/min, P < 0.05) function were impaired. Compared with AV, XK produces profound bradycardia with effects on loading conditions and ventricular function. The disparate findings at echocardiography and LV catheterization underscore the importance of comprehensive assessment of LV function in the mouse.

Kinetic parameters of hexose transport in hybrids between malignant and nonmalignant cells

1983 ◽  
Vol 62 (1) ◽  
pp. 49-80
Author(s):  
M.K. White ◽  
M.E. Bramwell ◽  
H. Harris
Keyword(s):  
Kinetic Parameters ◽  
Malignant Cell ◽  
Hexose Transport ◽  
Hybrid Cells ◽  
Michaelis Constant ◽  
Independent Measurement ◽  
The Difference ◽  
Hexose Uptake ◽  
Derivatives Of

Matched pairs of isogeneic hybrid cells, in which one member of the pair was malignant and the other not, were used to examine the linkage between malignancy and functional alterations in hexose transport. The kinetic parameters of uptake of 2-deoxy-D-glucose were measured in a range of such hybrids, both human and murine. Some other malignant cell lines were also examined and were compared with non-tumorigenic derivatives of tumour cells selected by exposure to the lectin, wheat-germ agglutinin. In every case, malignancy, as defined by the ability of cells to grow progressively in vivo, was found to be linked to a decrease in the Michaelis constant of hexose uptake. Independent measurement of the transport and phosphorylation reactions involved in hexose uptake revealed that this decrease was determined by the membrane transport system. The difference in Michaelis constant between malignant and non-malignant cells was observed with 3-O-methylglucose, a hexose that is transported into the cell but not further metabolized. The activity of hexokinase in cell homogenates was higher than the level that would be required to cope with transport and showed no correlation with tumorigenicity. Measurement of the uptake of D-glucose itself, by a rapid filtration centrifugation method, gave results similar to those obtained with 2-deoxy-D-glucose.

Conformai Curvature Tensors

2011 ◽  
Author(s):  
Charles Fefferman ◽  
C. Robin Graham
Keyword(s):  
Normal Form ◽  
Curvature Tensor ◽  
Riemannian Metric ◽  
Conformal Group ◽  
Conformal Change ◽  
Conformal Curvature ◽  
Covariant Derivatives ◽  
Curvature Tensors ◽  
Derivatives Of

This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to g. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group O(p + 1, q + 1) on tensors. It is assumed throughout this chapter that n ≥ 3.

scholarly journals Unusual Regularity in GC Retention of Simple Amino Acid Derivatives

2019 ◽  
Vol 6 (1) ◽  
pp. 3-14 ◽  
Author(s):  
Igor G. Zenkevich ◽  
Nino G. Todua ◽  
Anzor I. Mikaia
Keyword(s):  
Gas Chromatography ◽  
Retention Index ◽  
Methyl Esters ◽  
Elution Order ◽  
Alkyl Esters ◽  
Methyl Group ◽  
The Difference ◽  
Direct Use ◽  
Derivatives Of

Background: Application of simple regularities and general principles along with direct use of reference gas chromatography retention index data for reliable structure determination of compounds can be enhanced by determination of new regularities that are specific to certain structural elements. Objective: Revelation and interpretation of an anomaly in the elution order of alkyl esters of alkoxycarbonyl derivatives of glycine and alanine on standard and semi-standard non-polar phases. Method: Preliminary derivatization of amino acids to alkyl esters of N-alkoxycarbonyl analogs and interpretation of their gas chromatographic characteristics. Results: Alkyl esters of N-alkoxycarbonyl derivatives of alanine (Alkyl = C2H5, n- and iso-C3H7) elute prior to the same derivatives of glycine, despite the presence of an additional methyl group at C(2) in the molecule. Elution order is reversed for methyl esters of N-methoxycarbonyl derivatives. Conclusion: It is established that the peculiar behavior of alkyl esters of N-alkoxycarbonyl derivatives of glycine and alanine agrees with the concepts of gas chromatography and the known retention index regularities of organic compounds. A decrease of retention index values is a result of an introduction of an additional methyl group to a carbon atom connected to two polar fragments in a molecule like CH2XY. The dependence of the difference of retention index values for homologs of the types of CH3-CHXY and CH2XY vs. the total mass of fragments (X + Y) is similar to those for other sub-groups of analytes.

scholarly journals On higher covariant derivatives of the curvature tensors of Kählerian C-spaces

1983 ◽  
Vol 91 ◽  
pp. 1-18 ◽  
Author(s):  
Ryoichi Takagi
Keyword(s):  
Symmetric Spaces ◽  
Compact Type ◽  
Hermitian Symmetric Spaces ◽  
Covariant Derivatives ◽  
Higher Covariant Derivatives ◽  
Group Of Isometries ◽  
Complex Homogeneous Manifold ◽  
Curvature Tensors ◽  
Simply Connected ◽  
Derivatives Of

A compact simply connected complex homogeneous manifold is said briefly a C-space, which was completely classified by H. C. Wang [12]. A C-space is called to be Kählerian if it admits a Kählerian metric such that a group of isometries acts transitively on it. Hermitian symmetric spaces of compact type are typical examples of a Kählerian C-space. Let M be an arbitrary Kählerian C-space and R its curvature tensor. M. Itoh [6] expressed R in the language of Lie algebra and investigated various properties of R. In this paper, we study higher covariant derivatives of R.

scholarly journals Minimal coupling in presence of non-metricity and torsion

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Adrià Delhom
Keyword(s):  
Riemannian Space ◽  
Field Equations ◽  
Lagrange Equations ◽  
Minimal Coupling ◽  
Covariant Derivatives ◽  
Derivatives Of ◽  
Matter Fields

Abstract We deal with the question of what it means to define a minimal coupling prescription in presence of torsion and/or non-metricity, carefully explaining while the naive substitution $$\partial \rightarrow \nabla $$∂→∇ introduces extra couplings between the matter fields and the connection that can be regarded as non-minimal in presence of torsion and/or non-metricity. We will also investigate whether minimal coupling prescriptions at the level of the action (MCPL) or at the level of field equations (MCPF) lead to different dynamics. To that end, we will first write the Euler–Lagrange equations for matter fields in terms of the covariant derivatives of a general non-Riemannian space, and derivate the form of the associated Noether currents and charges. Then we will see that if the minimal coupling prescriptions is applied as we discuss, for spin 0 and 1 fields the results of MCPL and MCPF are equivalent, while for spin 1/2 fields there is a difference if one applies the MCPF or the MCPL, since the former leads to charge violation.

BEZIEHUNGEN ZWISCHEN SUBSTITUTION IM RING A UND ABBAU IM STOFFWECHSEL BEI VERWANDTEN DES TESTOSTERONS

1962 ◽  
Vol 41 (4) ◽  
pp. 494-506 ◽  
Author(s):  
H. Langecker
Keyword(s):  
Double Bond ◽  
Ring System ◽  
Keto Group ◽  
Hydroxyl Group ◽  
Methyl Group ◽  
Structural Peculiarities ◽  
Metabolic Degradation ◽  
The Difference ◽  
Testosterone Metabolites ◽  
Derivatives Of

ABSTRACT Judging from the metabolites found in the urine, 1-methyl-androst-1-en-17β-ol-3-one (methenolone) and testosterone are metabolized in a different manner. For further clarification, other derivatives of testosterone with modifications in Ring A were investigated with regard to the oxidation of the 17-hydroxyl group. The production of urinary 17-ketosteroids decreased in the following sequence: testosterone; 1α-methyltestosterone and androstan-17β-ol-3-one; 1β-methyl-androstan-17β-ol-3-one; 2α-methyl-androstan-17β-ol-3-one and androst-1-en-17β-ol-3-one; 1α-methyl-androstan-17β-ol-3-one; 1-methyl-androsta-1,4-dien-17β-ol-3-one; 1,17α-dimethyl-androst-1-en-17β-ol-3-one and 1 -methyl-androst-1 -en-17β-ol-3-one (methenolone). The difference in metabolic degradation is also demonstrated in the fractionation of the urinary ketones. While after the administration of testosterone practically only hydrogenated 17-ketones are observed in the urine, the unchanged compound is still traceable in remarkable quantities after the administration of methenolone, along with minor quantities of the corresponding diketone. Testosterone-metabolites here are absent, whereas they represent the major substances present after the administration of androst-1-en-17β-ol-3-on. Following the administration of 1α-methyltestosterone only hydrogenated 17-ketones are detected which are still partly methylated. The 1-methyl-group and the Δ 1-double-bond seem to be responsible for the inhibition of the oxidation of methenolone in the 17-position. In addition, the hydrogenation of the double-bond and the reduction of the 3-keto-group are inhibited, obviously on account of the same structural peculiarities. The demethylation of methenolone is also inhibited. Any change in the steroid ring system forms a new substrate, thus producing new conditions for the enzymatic attack in the metabolic degradation.

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