Gravitational couplings and Z2 orientifolds

The interplay between gravitational couplings on branes and the occurrence of fractional flux in low-dimensional orientifolds is examined. It is argued that gravitational couplings need to be assigned not only to D-branes but also to orientifold planes. The fractional charges of the orientifold d-planes can be understood in terms of flux quantization of the d − 3 form potential and modified Bianchi identities. Detailed results are presented for the case of the type IIB orientifold on T⁶/Z₂, which is dual to F-theory on a complex 4-fold with terminal singularities.     

Singularities in Weyl gravitational fields

The peculiarities of the scalarS ≡R _ijkl R ^ijkl are exhibited for two axially-symmetric static (Weyl) gravitational fields. By examiningS along curved families of trajectories to the Weyl singularities, examples are found which contradict previous claims by Gautreau and Anderson regarding ‘directional singularities’. Proper circumferences about the Bach and Weyl line-mass singularity are also examined. There is no apparent correlation between the source structure and the behaviour ofS from this analysis.     

Charged axially symmetric solution and energy in teleparallel theory equivalent to general relativity

An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity. The associated metric has the structure function G(ξ)=1-ξ²-2mAξ³-q²A²ξ⁴. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorizable form (1-ξ²)(1+r₊Aξ)(1+r_-Aξ) with r_± as the horizons of Reissner–Nordström space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner–Nordström black hole. In calculating the energy content of this tetrad field using the gravitational energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the gravitational energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the energy.     

Solutions of the Einstein-Maxwell equations with many black holes

In Newtonian gravitational theory a system of point charged particles can be arranged in static equilibrium under their mutual gravitational and electrostatic forces provided that for each particle the charge,e, is related to the mass,m, bye=G ^1/2 m. Corresponding static solutions of the coupled source free Einstein-Maxwell equations have been given by Majumdar and Papapetrou. We show that these solutions can be analytically extended and interpreted as a system of charged black holes in equilibrium under their gravitational and electrical forces.We also analyse some of stationary solutions of the Einstein-Maxwell equations discovered by Israel and Wilson. If space is asymptotically Euclidean we find that all of these solutions have naked singularities.Alfred P. Sloan Research Fellow, supported in part by the National Science Foundation.     

On the genericity of spacetime singularities

We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event horizon of gravity. It is shown that the visible singularities that develop as final states of spherical collapse are generic. Some consequences of this fact are discussed.      

The nature of singularities

Conclusions We have established, under reasonable conditions, that singularities must be either curvature singularities or primordial singularities. There is still the possibility that the Cauchy data for, say, a gravitational collapse might be compatible with or might necessitate a quasi-regular singularity that, though technically primordial, lies entirely to the future of the data-surface. Until this is ruled out, we cannot be sure that classical relativity does give curvature singularities in physically reasonable situations.The methods examined here are concerned only with whether the Riemann tensor is bounded, and so they can say nothing on the crucial question ofhow badly the Riemann tensor may be unbounded. Upper limits on the behavior on some geodesies have been set by Tipler [6], but more work needs to be done here. One would like to know whether the curvature could fail to be, say,L ¹; but to answer this we should have to use quite different methods based on integration overM rather than the behavior along curves.A revised version of material presented at the Singularities Symposium of the 8th International Conference on General Relativity and Gravitation, August 1977.     

Foliation analysis of gravitation singularities

Gravitation singularities are examined as singularities of space-time foliations which represent critical points of real functions on a space-time.     

Measurements of the isotopic composition of UF<Subscript>6</Subscript> according to the fine structure of the IR absorption spectrum in the ν<Subscript>1</Subscript> + ν<Subscript>3</Subscript> band

Absorption spectra of the Q-branch of the ν₁ + ν₃ vibrational–rotational band of uranium hexafluoride (UF₆) recorded in a range of 1290.0–1292.5 cm^–1 using a laser spectrometer based on a quantum cascade laser have been studied. The spectra of samples with a natural isotopic composition (0.7% U²³⁵), an enriched sample (90% U²³⁵), and their gas mixtures (2, 5, and 20% U²³⁵) in a pressure range of 10–70 Torr at a temperature of T = 296 K have been analyzed. The experiments have revealed a highly reproducible fine structure of the recorded spectra. Periodic singularities in the fine-structure spectra have been interpreted as a manifestation of hot band transitions near the Q-branch. Anharmonicity constants X ₂₁, X ₃₁, and X ₃₂ and their combinations X _i1 + X _i3 (i = 4, 5, 6) have been determined. The characteristic features in the fine-structure spectra and the initial spectrum have been used to determine the isotopic composition of enriched UF₆ samples.     

Conifold transitions and mirror symmetry for Calabi-Yau complete intersections in Grassmannians

In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for the construction of mirror manifolds and for the computation of the instanton numbers of rational curves on complete intersection Calabi-Yau 3-folds in Grassmannians. Using a natural degeneration of Grassmannians G(k, n) to some Gorenstein toric Fano varieties P(k, n) with conifolds singularities which was recently described by Sturmfels, we suggest an explicit mirror construction for Calabi-Yau complete intersections X ⊂ G(k, n) of arbitrary dimension. Our mirror construction is consistent with the formula for the Lax operator conjectured by Eguchi, Hori and Xiong for gravitational quantum cohomology of Grassmannians.     

Resolving the on- and off-shell ambiguity of perturbative QCD using sum rules

The orderg ^?2 coefficient functions for hard processese ⁺ e ^?→hX andlh→l′ h′ X are calculated in perturbative QCD. On- and off-shell regularization of the mass singularities leads to different results. Sum rules of energy and quantum number conservation are satisfied when using the on-shell regularization and force us to reject the result of the conventional off-shell regularization.     

Gravitational singularities and disruption of causality

Basic aspects of describing gravitational singularities as singularities of causal space-time layering are considering. The relationship between disruption of causality and the existence of singularities is studied. It is shown that under certain conditions disruption of causality may prevent the development of a gravitational singularity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 41–45, April, 1985.     

The Numerical Methods for Oscillating Singularities in Elliptic Boundary Value Problems

The singularities near the crack tips of homogeneous materials are monotone of type r^α and r^α log^δr (depending on the boundary conditions along nonsmooth domains). However, the singularities around the interfacial cracks of the heterogeneous bimaterials are oscillatory of type r^α sin( log r). The method of auxiliary mapping (MAM), introduced by Babu ka and Oh, was proven to be successful in dealing with r^α type singularities. However, the effectiveness of MAM is reduced in handling oscillating singularities. This paper deals with oscillating singularities as well as the monotone singularities by extending MAM through introducing the power auxiliary mapping and the exponential auxiliary mapping.     

A slice theorem for the space of solutions of Einstein's equations

A slice for the action of a group G on a manifold X at a point x ? X is, roughly speaking, a submanifold S_x which is transverse to the orbits of G near x. Ebin and Palais proved the existence of a slice for the diffeomorphism group of a compact manifold acting on the space of all Riemannian metrics. We prove a slice theorem for the group $\text{D}$ of diffeomorphisms of spacetime acting on the space $\text{E}$ of spatially compact, globally hyperbolic solutions of Einstein's equations. New difficulties beyond those encountered by Ebin and Palais arise because of the Lorentz signature of the spacetime metrics in $\text{E}$ and because $\text{E}$ is not a smooth manifold- it is known to have conical singularities at each spacetime metric with symmetries. These difficulties are overcome through the use of the dynamic formulation of general relativity as an infinite dimensional Hamiltonian system (ADM formalism) and through the use of constant mean curvature foliations of the spacetimes in $\text{E}$. (We devote considerable space to a review and extension of some special properties of constant mean curvature surfaces and foliations that we need.) The conical singularity structure of $\text{E}$, the sympletic aspects of the ADM formalism, and the uniqueness of constant mean curvature foliations play key roles in the proof of the slice theorem for the action of $\text{D}$ on $\text{E}$. As a consequence of this slice theorem, we find that the space $\text{D}$ = $\text{E}$/$\text{D}$ of gravitational degrees of freedom is a stratified manifold with each stratum being a sympletic manifold. The spaces for homogeneous cosmologies of particular Bianchi types give rise to special finite dimensional symplectic strata in this space $\text{G}$. Our results should extend to such coupled field theories as the Einstein-Yang-Mills equations, since the Yang-Mills system in a given background spacetime admits a slice theorem for the action of the gauge transformation group on the space of Yang-Mills solutions, since there is a satisfactory Hamiltonian treatment of the Einstein-Yang-Mills system, and since the singularity structure of the solution set is known.     

A Uniqueness Criterion for Unbounded Solutions to the Vlasov–Poisson System

We prove uniqueness for the Vlasov–Poisson system in two and three dimensions under the condition that the L^p norms of the macroscopic density grow at most linearly with respect to p. This allows for solutions with logarithmic singularities. We provide explicit examples of initial data that fulfill the uniqueness condition and that exhibit a logarithmic blow-up. In the gravitational two-dimensional case, such states are intimately related to radially symmetric steady solutions of the system. Our method relies on the Lagrangian formulation for the solutions, exploiting the second-order structure of the corresponding ODE.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

Interaction between two hydrogen atoms approaching a metal surface

Two regimes of HH interaction outside a metal surface are considered: (i) Beyond the spill-out region of the metal electrons (physisorption) (ii) Embedded protons in the electron spill-out. Using an extension of the Heitier-London model to treat (i), the H₂ binding energy for the molecule parallel to the surface is reduced, whereas for the perpendicular configuration stronger binding obtains. In (ii), the asymptotic form of the screening charge round a single proton is considered, in a linear response framework, and for an infinite barrier model of the surface. If the screened potential has no singularities in k space, then the interaction energy ΔE(X), X being the distance between the protons, falls off as X^?5 times an oscillatory function, for H₂ parallel to the planar metal surface. The effect of self-consistency on this result is then examined and it is concluded that the asymptotic interaction energy is unchanged in form, though the amplitude is altered.     

Luminescent properties of nanoparticles YPXV1−XO4:Dy phosphors

Phosphors of nanoparticles YP_XV_1−XO₄:Dy³⁺ (0?X?1) have been prepared by a citrate sol-gel method. X-ray diffraction, transmission electron microscope (TEM), scanning electron microscope (SEM) and photoluminescence excitation and emission spectra were utilized to characterize the phosphors. The results of XRD showed that a solid solution formed in YP_XV_1−XO₄:Dy³⁺ phosphor series from X=0 to X=1 with zircon structure. TEM and SEM studies revealed that the obtained YP_XV_1−XO₄:Dy³⁺ nanocrystals appeared to be spherical with some agglomeration and their sizes ranged from 30 to 80 nm. Upon short ultraviolet excitation, the optical properties of all the powder presented that the characteristic transitions of Dy³⁺ due to ⁴F_9/2-⁶H_15/2 (blue) and ⁴F_9/2-⁶H_13/2 (yellow) were detected. Besides this, in the system of YP_XV_1−XO₄:Dy³⁺, the yellow-to-blue intensity ratio (Y/B) depended on the value of P/V greatly, with the increasing of X value and the decreased Y/B value. The phosphor found to yield white light when the value of X in the range of X=0.775-0.85, the optimum concentration for Dy³⁺ is 1 mol% of Y in the host, and the emission intensity increased with the annealing temperature.     

A Model Independent Method of the X° (960) Meson Spin Parity Determination

To establish the X→ (960) meson spin parity it is suggested to study the correlation between the production process K^?He⁴ → X⁰ ΔH⁴ and the decay process X⁰ → η²π.     

Motion of charges and singularities in the vacancy spectrum in crystalline helium

The Van Hove singularities in the vacancy spectrum of ⁴He crystals are manifested as singularities in the field dependence of the drift velocity of charges. In ³He, the field dependence of the drift velocity is determined by the vacancy spectrum in the completely spin-polarized state of the crystal.     

Variation of fundamental constants in space and time: Theory and observations

Review of recent works devoted to the temporal and spatialvariation of the fundamental constants and dependence of the fundamentalconstants on the gravitational potential (violation of local position invariance) is presented. We discuss the variation of the fine structure constant α=e²/ħc, strong interaction andfundamental masses (Higgs vacuum), e.g. the electron-to-proton mass ratioμ=m_e/M_p or X_e=m_e/Λ_QCD and X_q=m_q/Λ_QCD.We also present new results from Big Bang nucleosynthesisand Oklo natural nuclear reactor data and propose new measurements of enhanced effects in atoms, nuclei and molecules, both in quasar and laboratory spectra.