Light-ray moments as endpoint contributions to modular Hamiltonians

We consider excited states in a CFT, obtained by applying a weak unitary perturbation to the vacuum. The perturbation is generated by the integral of a local operator J(n) of modular weight n over a spacelike surface passing through x = 0. For |n| ≥ 2 the modular Hamiltonian associated with a division of space at x = 0 picks up an endpoint contribution, sensitive to the details of the perturbation (including the shape of the spacelike surface) at x = 0. The endpoint contribution is a sum of light-ray moments of the perturbing operator J(n) and its descendants. For perturbations on null planes only moments of J(n) itself contribute.

Shear-Relative Asymmetries in Tropical Cyclone Eyewall Slope

Recent studies have analyzed the azimuthal mean slope of the tropical cyclone (TC) eyewall. This study looks at the shear-relative azimuthal variability of different metrics of eyewall slope: the 20-dBZ surface, the radius of maximum wind (RMW), and an angular momentum (M) surface passing through the RMW. The data used are Doppler radar composites from the NOAA Hurricane Research Division (HRD). This study examines 34 TCs, with intensities ranging from 3 to 75 m s−1 and shear magnitudes ranging from 0 to 10 m s−1. Calculation of the mean slope in each quadrant for all cases shows that RMW slope has the strongest asymmetry, with downshear slope larger than upshear in 62% of cases. Slopes of momentum surfaces and dBZ surfaces are also greater downshear in some cases (65% for M and 47% for dBZ), but there is more variance than in the RMW slope. The azimuthal phase of maximum slope occurs most often downshear, particularly downshear left, consistent with the depiction of a mean vortex tilt approximately 10° left of shear. Filtering the cases into high and low shear illustrates that the tendency for greater slope downshear is magnified for high-shear cases. In addition, although the dBZ slope shows less shear-relative signal overall, the difference between the dBZ slope and momentum slope is an important factor in distinguishing between strengthening and weakening or steady TCs. Intensifying TCs tend to have dBZ surfaces that are more upright than M surfaces. Further investigation of these results will help to illustrate the ways in which vertical shear can play a role in altering the structure of the TC core region.

Menggali Kreativitas Seni pada Anak Berkebutuhan Khusus

Some people see children who have behaviors and habits are unusual or out of the general habit. They are ostracized, even sometimes are considered strange, cannot socialize, have lives and have fun for theirselves, even worse they are considered abnormal. People sometimes see from the surface, passing judgment of the physical without investigating the cause of why it happened. Child with special needs, or autism, is one of them. Despite of its uniqueness, it turns out that children who have special needs have extraordinary ability, especially in terms of artistic creativity. Unique paintings and the ability to express feeling should be enhanced to take advantage of the ability of the child maximally, of course with the consistent help to find the child’s ability actually.

Preliminaries to Main Results

This chapter presents a number of results and notions that will be used in subsequent chapters. In particular, it considers the concept of regular differentiability and the lemma on deformation of n-dimensional surfaces. The idea is to deform a flat surface passing through a point x (along which we imagine that a certain function f is almost affine) to a surface passing through a point witnessing that f is not Fréchet differentiable at x. This is done in such a way that certain “energy” associated to surfaces increases less than the “energy” of the functionf along the surface. The chapter also discusses linear operators and tensor products, various notions and notation related to Fréchet differentiability, and deformation of surfaces controlled by ω‎ⁿ. Finally, it proves some integral estimates of derivatives of Lipschitz maps between Euclidean spaces (not necessarily of the same dimension).

Backprojection versus backpropagation in multidimensional linearized inversion

Seismic migration can be viewed as either backprojection (diffraction‐stack) or backpropagation (wave‐field extrapolation) (e.g., Gazdag and Sguazzero, 1984). Migration by backprojection was the view supporting the first digital methods—the diffraction and common tangent stacks of what is now called classical or statistical migration (Lindsey and Hermann, 1970; Rockwell, 1971; Schneider, 1971; Johnson and French, 1982). In this approach, each data point is associated with an isochron surface passing through the scattering object. Data values are then interpreted as projections of reflectivity over the associated isochrons. Dually, each image point is associated with a reflection‐time surface passing through the data traces. The migrated image at that point is obtained as a weighted stack of data lying on the reflection‐time surface (Rockwell, 1971; Schneider, 1971). This amounts to a weighted backprojection in which each data point contributes to image points lying on its associated isochron.

Tectonic strain determined from pillow selvages: accuracy and the cut effect

Tectonic strain ratios on a surface passing through the centre of a deformed, pod-shaped lava pillow are close to the ratio of the maximum/minimum selvage thicknesses. This approximation is valid for a variety of cases with an accuracy of 20% even where the section does not pass through the centre of the pillow but as long as the section passes through the central third of the pillow. Variation in selvage thickness is unlikely to provide a meaningful estimate of strain where the pillow shape was originally tubular.

Applications of bidimensional spline functions to geophysics

Two bidimensional spline functions are applied to the interpolation and automatic contouring of data from a ground magnetic survey of the Rhinegraben, between Karlsruhe and Strasbourg. These bidimensional spline functions can be applied in the general case, i.e., where a set of nonequispaced data is given. These splines define a surface passing through the original points. The most promising spline functions are the thin plate (“plaque mince”) and the pseudocubic spline, studied by Atteia (1966), Thomann (1970), and Duchon (1975, 1976). A contouring method based on them has been implemented.

Numerical Solutions of the Viscous Flow Equations for a Class of Closed Flows

The Navier-Stokes equations are solved iteratively on a small digital computer for the class of flows generated within a rectangular “cavity” by a surface passing over its open end. Solutions are presented for depth/breadth ratios ƛ=0.5 (shallow), 10 (square), 20 (deep) and Reynolds number 100. Flow photographs ore obtained which largely confirm the predicted flows. The theoretical velocity profiles and pressure distributions through the centre of the vortex in the square cavity are calculated.In an appendix an improved finite difference formula is given for the vorticity generated at a moving boundary.Since Thorn began his pioneering work some thirty-five years ago the number of numerical solutions which have been obtained for the equations of incompressible viscous fluid motion remains small (see bibliographies of Thom and Apelt, Fromm). The known solutions are principally for steady streaming flows, although two methods have now been used with success for non-steady flows (Payne jets and Fromm flow past obstacles). By contrast this paper is concerned with the class of closed flows generated in a rectangular region of varying depth/breadth ratio by a surface passing over an open end. This problem has been considered for a number of reasons.

Note in regard to surfaces in space of four dimensions, in particular rational surfaces

To a non-singular algebraic surface in space of five dimensions there can generally (the Veronese surface, of order 4, and cones are exceptional) be drawn, from an arbitrary point, a finite number of chords. If such a surface be projected from a point into space of four dimensions, there will, therefore, in general, be a certain number of points upon the resulting surface, at which two sheets of this surface, with distinct tangent planes, have an isolated common point. Such points have been called improper double points. We consider an algebraic surface ψ, in space of four dimensions [4], with no other multiple points than such double points, which we shall call accidental double points. The chords of the surface ψ, drawn from an arbitrary point O of the space [4], form a surface, or conical sheet, of which a general generator meets the surface in two points. The locus of these points is a curve which we shall call the chord curve. This curve has an actual double point at each of the accidental double points of ψ There will also, generally, be a certain number of points of the surface which are points of contact of tangent planes of the surface passing through O (and therefore also points of contact of tangent lines through O, these tangent lines being generally tangent lines of the chord curve).