Forged Checks the Duty of the Depositor to His Bank

During the last twenty-five years the courts with increasing frequencyhave been called upon to decide where the law ought to placethe loss when a bank pays a forged check and charges it to the accountof a depositor, believing that he drew the check as presented. Thebroad statement that a bank pays a check at its peril is so frequently metwith that it is likely to make the impression that a depositor enjoys animmunity from change in his legal relations to the bank, save as thebank pays checks that are in fact his orders. It is well settled, however,that the failure of a depositor to notify his bank after he knows,or ought to know, that it has paid a forged check and charged it to hisaccount, will, under some circumstances, result in undesirable financialconsequence to him, though its extent, as well as the basis upon whichit is imposed, are matters about which there is a variety of judicialopinion. It is proposed to examine herein the broad principle referredto above and seek to ascertain when and to what extent the depositor\u27sconduct subsequent to payment affects his legal relations to the bank

Yielding and flow in adhesive and non-adhesive concentrated emulsions

The nonlinear rheological response of soft glassy materials is addressed experimentally by focusing on concentrated emulsions where interdroplet attraction is tuned through varying the surfactant content. Velocity profiles are recorded using ultrasonic velocimetry simultaneously to global rheological data in the Couette geometry. Our data show that non-adhesive and adhesive emulsions have radically different flow behaviors in the vicinity of yielding: while the flow remains homogeneous in the non-adhesive emulsion and the Herschel-Bulkley model for a yield stress fluid describes the data very accurately, the adhesive system displays shear localization and does not follow a simple constitutive equation, suggesting that the mechanisms involved in yielding transitions are not universal.Comment: 4 pages, 5 figures, to appear in Physical Review Letter

Exploring constrained quantum control landscapes

The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls. The control landscape can be shown to contain no suboptimal trapping extrema upon satisfaction of reasonable physical assumptions, but this topological analysis does not hold when significant constraints are placed on the control resources. This work employs simulations to explore the topology and features of the control landscape for pure-state population transfer with a constrained class of control fields. The fields are parameterized in terms of a set of uniformly spaced spectral frequencies, with the associated phases acting as the controls. Optimization results reveal that the minimum number of phase controls necessary to assure a high yield in the target state has a special dependence on the number of accessible energy levels in the quantum system, revealed from an analysis of the first- and second-order variation of the yield with respect to the controls. When an insufficient number of controls and/or a weak control fluence are employed, trapping extrema and saddle points are observed on the landscape. When the control resources are sufficiently flexible, solutions producing the globally maximal yield are found to form connected `level sets' of continuously variable control fields that preserve the yield. These optimal yield level sets are found to shrink to isolated points on the top of the landscape as the control field fluence is decreased, and further reduction of the fluence turns these points into suboptimal trapping extrema on the landscape. Although constrained control fields can come in many forms beyond the cases explored here, the behavior found in this paper is illustrative of the impacts that constraints can introduce.Comment: 10 figure

Description of a lunar rainbow

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Letters to the Editor

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65147/1/j.1752-7325.1989.tb02065.x.pd

Direct Observation of the Fourth Star in the Zeta Cancri System

Direct imaging of the zeta Cnc system has resolved the fourth star in the system, which is in orbit around zeta Cnc C. The presence of the fourth star has been inferred for many years from irregularities in the motion of star C, and recently from C's spectroscopic orbit. However, its mass is close to that of C, making its non-detection puzzling. Observing at wavelengths of 1.2, 1.7, and 2.2 microns with the adaptive-optics system of the CFHT, we have obtained images which very clearly reveal star D and show it to have the color of an M2 star. Its brightness is consonant with its being two M stars, which are not resolved in our observations but are likely to be in a short-period orbit, thereby accounting for the large mass and the difficulty of detection at optical wavelengths, where the magnitude difference is much larger. The positions and colors of all four stars in the system are reported and are consistent with the most recent astrometric observations.Comment: 7 pages including 3 tables, 1 figure; To appear in PAS

A Simplified Approach to Optimally Controlled Quantum Dynamics

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol. 102, pag. 226 (1995)]. Quantum Lagrange multiplier functions are used to preserve a chosen subset of the observable dynamics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of time. This is a considerable simplification over traditional quantum optimal control theory[S. shi and H. Rabitz, comp. Phys. Comm. Vol. 63, pag. 71 (1991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum control to meet a physical objective. A family of such simplified formulations is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model problem for selective unimolecular reaction induced by an external optical electric field.Comment: Revtex, 29 pages (incl. figures