Yano Equation Research Articles

Closed conformal Killing–Yano initial data

Through an exhaustive search, we produce a five-parameter family of propagation identities for the closed conformal Killing–Yano (cCYK) equation on two-forms, which hold on an Einstein cosmological vacuum spacetime in any dimension n > 4. It is well-known that spacetimes admitting a non-degenerate two-form of this type are exhausted by the Kerr-NUT-(A)dS family of exact higher dimensional black hole solutions. As a consequence, we identify a set of necessary and sufficient conditions ensuring that the cosmological vacuum development of an initial data set for Einstein’s field equations admits a cCYK two-form. We refer to these conditions as closed conformal Killing–Yano initial data equations. The four-dimensional case is special and is treated separately, where we can also handle the conformal Killing–Yano equation without the closed condition.

Biokinetic aspects for biocatalytic remediation of xenobiotics polluted seawater.

This research was conducted to investigate the biocatalytic remediation of xenobiotics polluted seawater using two biocatalysts; whole bacterial cells of facultative aerobic halotolerant Corynebacterium variabilis Sh42 and its extracted crude enzymes. One-Factor-at-A-Time technique and statistical analysis were applied to study the effect of initial substrate concentrations, pH, temperature, and initial biocatalyst concentrations on the batch biocatalytic degradation of three xenobiotic pollutants (2-hydroxybiphenyl (2-HBP), catechol and benzoic acid) in artificial seawater (salinity 3·1%). HPLC and gas-chromatography mass spectroscopy analyses were utilized to illustrate the quantitative removal of the studied aromatic xenobiotic pollutants and their catabolic pathway. The results revealed that the microbial and enzymatic cultures followed substrate inhibition kinetics. Yano and Koga's equation showed the best fit for the biokinetic degradation rates of 2-HBP and benzoic acid, whereas Haldane biokinetic model adequately expressed the specific biodegradation rate of catechol. The biokinetic results indicated the good efficiency and tolerance of crude enzyme for biocatalytic degradation of extremely high concentrations of aromatic pollutants than whole C. variabilis Sh42 cells. The monitored by-products indicated that the catabolic degradation pathway followed an oxidation mechanism via a site-specific monooxygenase enzyme. Benzoic acid and catechol were identified as major intermediates in the biodegradation pathway of 2-HBP, which were then biodegraded through meta-cleavage to 2-hydroxymuconic semialdehyde. With time elapsed, the semialdehyde product was further biodegraded to acetaldehyde and pyruvic acid, which would be further metabolized via the bacterial TCA cycle. The batch enzymatic bioreactors performed superior-specific biocatalytic degradation rates for all the studied xenobiotic pollutants. The enzymatic system of C. variabilis Sh42 is tolerable for toxic xenobiotics and different physicochemical environmental parameters. Thus, it can be recommended as an effective biocatalyst for biocatalytic remediation of xenobiotics polluted seawater.

Conformal Killing–Yano 2-forms

Riemannian manifolds carrying 2-forms satisfying the Killing–Yano equation and the conformal Killing–Yano equation are natural generalizations of nearly Kähler and Sasakian manifolds. In this article we exhibit new solutions of these equations. We also provide obstructions for their existence on Lie groups, and reduce the study of conformal Killing–Yano 2-forms to a particular class of non degenerate Killing–Yano 2-forms.

The highest inhibition coefficient of phenol biodegradation using an acclimated mixed culture.

In this study a membrane biological reactor (MBR) was operated at 25 ± 1 °C and pH = 7.5 ± 0.5 to treat synthetic wastewater containing high phenol concentrations. Removal efficiencies of phenol and chemical oxygen demand (COD) were evaluated at four various hydraulic retention times (HRTs) of 24, 12, 8, and 4 hours. The removal rate of phenol (5.51 kg-Phenol kg-VSS(-1) d(-1)), observed at HRT of 4 h, was the highest phenol degradation rate in the literature. According to COD tests, there were no significant organic matter in the effluent, and phenol was degraded completely by mixed culture. Substrate inhibition was calculated from experimental growth parameters using the Haldane, Yano, and Edward equations. The results show that the Haldane equation is fitted to the experimental data in an excellent manner. Kinetic parameters were derived by nonlinear regression with a correlation coefficient (R(2)) of 0.974. The values for Haldane constants μmax, Ks, and Ki were 0.3085 h(-1), 416 mg L(-1) and 1,886 mg L(-1), respectively. The Ki value is the highest value obtained for mixed cultures degrading phenol under batch conditions.

Invariant solutions to the conformal Killing–Yano equation on Lie groups

We search for invariant solutions of the conformal Killing–Yano equation on Lie groups equipped with left invariant Riemannian metrics, focusing on 2-forms. We show that when the Lie group is compact equipped with a bi-invariant metric or 2-step nilpotent, the only invariant solutions occur on the 3-dimensional sphere or on a Heisenberg group. We classify the 3-dimensional Lie groups with left invariant metrics carrying invariant conformal Killing–Yano 2-forms.

Killing–Yano symmetry of Kaluza–Klein black holes in five dimensions

Using a generalized Killing–Yano equation in the presence of torsion, spacetime metrics admitting a rank-2 generalized Killing–Yano tensor are investigated in five dimensions under the assumption that its eigenvector associated with the zero eigenvalue is a Killing vector field. It is shown that such metrics are classified into three types and the corresponding local expressions are given explicitly. It is also shown that they cover some classes of charged, rotating Kaluza–Klein black hole solutions of minimal supergravity and Abelian heterotic supergravity.

Killing–Yano equations with torsion, worldline actions and G-structures

We determine the geometry of the target spaces of supersymmetric non-relativistic particles with torsion and magnetic couplings, and with symmetries generated by the fundamental forms of G-structures for G = U(n), SU(n), Sp(n), Sp(n) · Sp(1), G2 and Spin(7). We find that the Killing–Yano equation, which arises as a condition for the invariance of the worldline action, does not always determine the torsion coupling uniquely in terms of the metric and fundamental forms. We show that there are several connections with skew-symmetric torsion for G = U(n), SU(n) and G2 that solve the invariance conditions. We describe all these compatible connections for each of the G-structures and explain the geometric nature of the couplings.

The Killing–Yano equation on Lie groups

In this paper we study 2-forms which are solutions of the Killing–Yano equation on Lie groups endowed with a left invariant metric having various curvature properties. We prove a general result for 2-step nilpotent Lie groups and as a corollary we obtain a nondegenerate solution of the Killing–Yano equation on the Iwasawa manifold with its half-flat metric.

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 ) 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.

Killing–Yano tensors and multi-Hermitian structures

We show that the Euclidean Kerr–NUT-(A)dS metric in 2 m dimensions locally admits 2 m Hermitian complex structures. These are derived from the existence of a non-degenerate closed conformal Killing–Yano tensor with distinct eigenvalues. More generally, a conformal Killing–Yano tensor, provided its exterior derivative satisfies a certain condition, algebraically determines 2 m almost complex structures that turn out to be integrable as a consequence of the conformal Killing–Yano equations. In the complexification, these lead to 2 m maximal isotropic foliations of the manifold and, in Lorentz signature, these lead to two congruences of null geodesics. These are not shear-free, but satisfy a weaker condition that also generalises the shear-free condition from four dimensions to higher dimensions. In odd dimensions, a conformal Killing–Yano tensor leads to similar integrable distributions in the complexification. We show that the recently discovered five-dimensional solution of Lü, Mei and Pope also admits such integrable distributions, although this does not quite fit into the story as the obvious associated two-form is not conformal Killing–Yano. We give conditions on the Weyl curvature tensor imposed by the existence of a non-degenerate conformal Killing–Yano tensor; these give an appropriate generalisation of the type D condition on a Weyl tensor from four dimensions.

Generalized Killing–Yano equations in [formula omitted] gauged supergravity

We propose a generalization of the (conformal) Killing–Yano equations relevant to D=5 minimal gauged supergravity. The generalization stems from the fact that the dual of the Maxwell flux, the 3-form ∗F, couples naturally to particles in the background as a ‘torsion’. Killing–Yano tensors in the presence of torsion preserve most of the properties of the standard Killing–Yano tensors — exploited recently for the higher-dimensional rotating black holes of vacuum gravity with cosmological constant. In particular, the generalized closed conformal Killing–Yano 2-form gives rise to the tower of generalized closed conformal Killing–Yano tensors of increasing rank which in turn generate the tower of Killing tensors. An example of a generalized Killing–Yano tensor is found for the Chong–Cvetič–Lü–Pope black hole spacetime [Z.W. Chong, M. Cvetic, H. Lu, C.N. Pope, hep-th/0506029]. Such a tensor stands behind the separability of the Hamilton–Jacobi, Klein–Gordon, and Dirac equations in this background.

Killing–Yano equations and G structures

We solve the Killing–Yano equation on manifolds with a G structure for G = SO(n), U(n), SU(n), Sp(n) ⋅ Sp(1), Sp(n), G2 and Spin(7). Solutions include nearly-Kähler, weak holonomy G2, balanced SU(n) and holonomy G manifolds. As an application, we find that particle probes on AdS4 × X compactifications of type IIA and 11-dimensional supergravity admit a type of symmetry generated by the fundamental forms. We also explore the symmetries of string and particle actions in heterotic and common sector supersymmetric backgrounds. In the heterotic case, the generators of the symmetries completely characterize the solutions of the gravitino Killing spinor equation, and the structure constants of the symmetry algebra depend on the solution of the dilatino Killing spinor equation.

Inhibition Kinetics of Phenol Degradation by Pseudomonas aeruginosa from Continuous Culture and Washout Data

ABSTRACT Steady states of a continuous culture with an inhibitory substrate were used to estimate kinetic parameters under substrate limitation (chemostat operation). Pure cultures of an indigenous Pseudomonas aeruginosa were grown in continuous culture on phenol, the sole source of carbon and energy, at dilution rates of 0.010 to 0.20 h− 1. Using different dilution rates, several steady states were investigated and the specific phenol consumption rates were calculated. In addition, phenol degradation was investigated by increasing the dilution rate above the critical dilution rate (washout cultivation). The results showed that the specific phenol consumption rate increased with increased dilution rate at steady state and that the degradation by Pseudomonas aeruginosa can be described by simple substrate inhibition kinetics under substrate limitation but cannot be described by simple substrate inhibition kinetics under washout cultivation. Fitting of the steady-state data from continuous cultivation to various inhibition models resulted in the best fit for the Yano and Koga kinetic inhibition model. The r s max value of 0.278 mg/mg/h obtained from the Yano and Koga equation was comparable to the experimentally calculated r s max value of 0.283 mg/mg/h obtained under washout cultivation.

Modeling Biodegradation of Nonylphenol

Nonylphenol is the primary breakdown product of nonylphenol ethoxylates, a certain class of nonionic surfactants. Nonylphenol has been found to be toxic to aquatic organisms and has been suspected of being harmful to humans due to its xenoestrogenic properties. Although there are known releases of nonylphenol to the environment, there is a lack of data describing the extent of biodegradation. This study thus focuses on much needed information on the biodegradation kinetics of nonylphenol. Oxygen uptake, cell growth and nonylphenol removal data were collected using batch reactors in an electrolytic respirometer. Nonylphenol removal, cell growth and substrate removal rates were modeled by the Monod, Haldane, Aiba, Webb, and Yano equations. The differential equations were solved by numerical integration to simulate cell growth, substrate removal, and oxygen uptake as a function of time. All models provided similar results with the Haldane model providing the best fit. The values of the kinetic parameters and the activation energy for nonylphenol were determined. These values can be used for predicting fate and transport of nonylphenol in the environment. The validity of applying each model to the biodegradation of nonylphenol was analyzed by computing the R 2 values of each equation.

KINETICS OF PHENOL AND BENZOATE BIODEGRADATION IN STATIC CULTIVATION SYSTEM BY Burkholderia cepacia G4.

Kinetics of phenol and benzoate degradation by Burkholderia cepacia G4 in classical batch mode of static culture were investigated over a wide range of initial substrate concentrations applied as single substrates. Due to better adaptation to changing conditions, faster degradation of both phenol and benzoate was observed when higher concentrations were used. The results show decrease of the biomass yield coefficient, YX/S, from 0.83 to 0.31 g g-1 when the initial phenol concentration was increased from 0.54 to 0.73 g L-1, supporting the well known inhibitory effect of phenol. On the other hand, linear increasing of the yield coefficient was observed with increasing benzoate concentration. During all experiments, maximum specific substrate consumption rates, rSmax, were reached to 0.27 g g-1h-1 for phenol and to 0.40 g g-1h-1 when benzoate was the sole source of carbon in the bioreactor. In the present study, minor inhibitory effect of benzoate was observed during their investigated concentration range. To explain their degradation modelling, experimental data of both phenol and benzoate biodegradation were fitted using various kinetic models. The results demonstrated that the Yano and Koga equation gave the best fit, compared with the other models. It means that biodegradation of phenol and benzoate can be described by the same kinetic model. Based on the kinetic data, all experiments were not sensitive to change in the saturation constant, KS; therefore, KS-value was fixed at 0.042 and 0.068 g L-1 for phenol and benzoate, respectively. After that, rSmax and the inhibition constant, Ki, parameters were re-fitted in all experiments. In general, the kinetic parameters of both phenol and benzoate degradation were influenced by the initial substrate and bacterial cell mass concentrations, in addition to adaptation with changing in the culture conditions.

Quantum mechanics of Yano tensors: Dirac equation in curved spacetime

In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors.

Debye potentials for Maxwell and Dirac fields from a generalization of the Killing–Yano equation

By using conformal Killing–Yano tensors, and their generalizations, we obtain scalar potentials for both the source-free Maxwell and massless Dirac equations. For each of these equations we construct, from conformal Killing–Yano tensors, symmetry operators that map any solution to another.

Inhibition kinetics of phenol degradation from unstable steady-state data

Multiplicity of steady states of a continuous culture with an inhibitory substrate was used to estimate kinetic parameters under steady-state conditions. A continuous culture of Pseudomonas cepacia G4, using phenol as the sole source of carbon and energy, was overloaded by increasing the dilution rate above the critical dilution rate. The culture was then stabilized in the inhibitory branch by a proportional controller using the carbon dioxide concentration in the reactor exhaust gas as the controlled variable and the dilution rate as the manipulated variable. By variation of the set point, several unstable steady states in the inhibitory branch were investigated and the specific phenol conversion rates calculated. In addition, phenol degradation was investigated under substrate limitation (chemostat operation).The results show that the phenol degradation by P. cepacia can be described by the same set of inhibition parameters under substrate limitation and under high substrate concentrations in the inhibitory branch. Biomass yield and maintenance coefficients were identical. Fitting of the data to various inhibition models resulted in the best fit for the Yano and Koga equation. The well-known Haldane model, which is most often used to describe substrate inhibition by phenol, gave the poorest fit. The described method allows a precise data estimation under steady-state conditions from the maximum of the biological reaction rate up to high substrate concentrations in the inhibitory branch. Inhibition parameter estimation by controlling unstable steady states may thus be useful in avoiding discrepancies between data generated by batch runs and their application to continuous cultures which have been often described in the literature. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 567-576, 1997.

Inhibition kinetics of phenol degradation from unstable steady‐state data

Multiplicity of steady states of a continuous culture with an inhibitory substrate was used to estimate kinetic parameters under steady-state conditions. A continuous culture of Pseudomonas cepacia G4, using phenol as the sole source of carbon and energy, was overloaded by increasing the dilution rate above the critical dilution rate. The culture was then stabilized in the inhibitory branch by a proportional controller using the carbon dioxide concentration in the reactor exhaust gas as the controlled variable and the dilution rate as the manipulated variable. By variation of the set point, several unstable steady states in the inhibitory branch were investigated and the specific phenol conversion rates calculated. In addition, phenol degradation was investigated under substrate limitation (chemostat operation). The results show that the phenol degradation by P. cepacia can be described by the same set of inhibition parameters under substrate limitation and under high substrate concentrations in the inhibitory branch. Biomass yield and maintenance coefficients were identical. Fitting of the data to various inhibition models resulted in the best fit for the Yano and Koga equation. The well-known Haldane model, which is most often used to describe substrate inhibition by phenol, gave the poorest fit. The described method allows a precise data estimation under steady-state conditions from the maximum of the biological reaction rate up to high substrate concentrations in the inhibitory branch. Inhibition parameter estimation by controlling unstable steady states may thus be useful in avoiding discrepancies between data generated by batch runs and their application to continuous cultures which have been often described in the literature. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 567–576, 1997.

Symmetries of the massless Dirac equation in Minkowski space.

All symmetries of the massless Dirac equation in Minkowski space are obtained by explicitly solving the conformal versions of the Killing, Penrose-Floyd, and Yano equations. In an arbitrary curved four-space, it is also shown that the dual of a conformal Yano tensor is a conformal Killing vector and that the set of conformal Penrose-Floyd tensors is stable under the dual map.