Synthesis and X-ray structural characterisation of the tetramethylene oxonium derivative of the hydrodecaborate anion. A versatile route for derivative chemistry of [B10H10]

The oxonium derivative P(C₆H₅)₄[2-B₁₀H₉O(CH₂)₄] (1) has been prepared from [B₁₀H₁₀]²⁻ by a solvent-addition reaction route, promoted by Et₂O · BF₃. Its structure has been confirmed by single crystal X-ray analysis. 1 is assumed to be a useful synthon for the derivative chemistry of [B₁₀H₁₀]²⁻. As an illustration, ring-opening reaction occurred in presence of the strong nucleophilic agent OH⁻, giving the monoanionic derivative [P(C₆H₅)₄]₂[2-B₁₀H₉O(CH₂)₄OH] (2).     

Real-time onboard wind and windshear determination,part 2: Detection

This paper is concerned with windshear detection in connection with real-time wind identification (Ref. 1). It presents a comparative evaluation of two techniques, one based on the shear/downdraft factor and one based on the wind difference index. The comparison is done with reference to a particular microburst, that which caused the 1985 crash of Flight Delta 191 at Dallas-Fort Worth International Airport.The shear/downdraft factor has the merit of combining the effects of the shear and the downdraft into a single entity. However, its effectiveness is hampered by the fact that, in a real situation, the windshear is accompanied by free-stream turbulence, which tends to blur the resulting signal. In turn, this results in undesirable nuisance warnings if the magnitude of the shear factor due to free-stream turbulence is temporarily larger than that due to true windshear. Therefore, proper filtering is necessary prior to using the shear/downdraft factor in detection and guidance. One effective way for achieving this goal is to average the shear/downdraft factor over a specified time interval . The effect of on the average shear/downdraft factor is studied.     

Real-time onboard wind and windshear determination,part 1: Identification

Standard wind identification techniques employed in the analysis of aircraft accidents are post-facto techniques; they are processed after the event has taken place and are based on the complete time histories of the DFDR/ATCR data along the entire trajectory. By contrast, real-time wind identification techniques are processed while the event is taking place; they are based solely on the knowledge of the preceding time histories of the DFDR/ATCR data.In this paper, a real-time wind identification technique is developed. First, a 3D-kinematic approach is employed in connection with the DFDR/ATCR data covering the time interval preceding the present time instant. The aircraft position, inertial velocity, and accelerometer bias are determined by matching the flight trajectory computed from the DFDR data with the flight trajectory available from the ATCR data. This leads to a least-square problem, which is solved analytically every seconds, with / small.With the inertial velocity and accelerometer bias known, an extrapolation process takes place so as to predict the inertial velocity profile over the subsequent -subinterval. At the end of this subinterval, the extrapolated inertial velocity and the newly identified inertial velocity are statistically reconciled and smoothed. Then, the process of identification, extrapolation, reconciliation, and smoothing is repeated. Subsequently, the wind is computed as the difference between the inertial velocity and the airspeed, which is available from the DFDR data. With the wind identified, windshear detection can take place (Ref. 1).As an example, the real-time wind identification technique is applied to Flight Delta 191, which crashed at Dallas-Fort Worth International Airport on August 2, 1985. The numerical results show that the wind obtained via real-time identification is qualitatively and quantitatively close to the wind obtained via standard identification. This being the case, it is felt that real-time wind identification can be useful in windhsear detection and guidance, above all if the shear/downdraft factor signal is replaced by the wind difference signal (Ref. 1).This paper and its companion (Ref. 1) are based on Refs. 2–4.This research was supported by the Aviation Research and Education Foundation and by Texas Advanced Technology Program, Grant No. TATP-003604020.     

Synthesis, characterization and optical properties of pi-conjugated systems incorporating closo-dodecaborate clusters: new potential candidates for two-photon absorption processes

Non-centrosymmetric pi-conjugated systems incorporating closo-dodecaborate clusters, [NC-C6H4-C(H=N(H)-B12H11]-(2), [NC-C6H4-C(H)=C(H)-C(6)H(4)-C(H)=N(H)-B12H11]-(3), and [NC-C6H4-C(H)=C(H)-C6H4-C(H)=C(H)-C6H4-C(H)=N(H)-B12H11]-(4) have been synthesized by reaction of the monoamino derivative of B12, [B12H11NH3]-(1), with various arylaldehydes, R-C6H4-CHO. These Schiff base-like compounds were fully characterized by multinuclear NMR spectroscopy and mass spectrometry. In order to evaluate these boron rich pi-systems as potential materials for two-photon absorption (TPA) processes, UV linear absorption curves were recorded for 3 and 4, and comparatively studied with those of the boron-free pi-systems NC-C6H4-C(H)=N-CH3(5) and NC-C6H4-C(H)=C(H)-C6H4-C(H)=N-CH3(6). The donor effect of the boron cluster was evidenced by a shift to the lower energy of the absorption band in the spectra of systems incorporating B12. The two photon absorption (TPA) spectrum of compound , obtained by the up-conversion method, shows a resonance at 720 nm with a cross-section sigma(TPA) of 35 x 10(-50) cm(4) s photon(-1) molecule(-1). This value suggests the potential of B12 clusters to be used as new donor groups for the synthesis of non-linear materials.     

Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

Simple Synthesis of Deuterated Pterosines

Ptaquiloside, a potent carcinogen present in bracken fern, a plant consumed by farm animals, may be detected in traces by converting it into the bromopterosine. A simple synthesis of bromopterosine d₂, to be used as standard in GC/MS or LC/MS analyses, is described.     

Optimal Trajectories and Guidance Schemes for Ship Collision Avoidance

The best strategy for collision avoidance under emergency conditions is to maximize wrt the controls the timewise minimum distance between the host ship and the intruder ship. In a restricted waterway area, two main constraints must be satisfied: the lateral deviation of the host ship from the original course is to be contained within certain limits; the longitudinal distance covered by the host ship is to be subject to a prescribed bound. At the maximin point of the encounter, the time derivative of the relative distance vanishes; this yields an inner boundary condition (orthogonality between the relative position vector and the relative velocity vector) separating the main phases of the maneuver: the avoidance and recovery phases. In this way, the optimal trajectory problem (a Chebyshev problem) can be converted into a Bolza problem with an inner boundary condition. Numerical solutions are obtained via the multiple-subarc sequential gradient-restoration algorithm (SGRA). Because the optimal trajectory is not suitable for real-time implementation, a guidance scheme approximating the optimal trajectory in real time is to be developed. For ship collision avoidance, the optimal trajectory results show that the rudder angle time history has a bang-bang form characterized by the alternation of saturated control subarcs of opposite signs joined by rapid transitions. Just as the optimal trajectory can be partitioned into three phases (avoidance phase, recovery phase, steady phase), a guidance trajectory can be constructed in the same way. For the avoidance and recovery phases, use of decomposition techniques leads to an algorithm computing the time lengths of these phases in real time. For the steady phase, a feedback control scheme is used to maneuver the ship steadily. Numerical results are presented. Portions of this paper were presented by the senior author at the 13th International Workshop on Dynamics and Control, Wiesensteig, Germany, 22-26 May 2005, in honor of George Leitmann. This research was supported by NSF Grant CMS-02-18878.     

Parallel computation of two-point boundary-value problems via particular solutions

Nonlinear two-point boundary-value problems (TPBVP) can be reduced to the iterative solution of a sequence of linear problems by means of quasilinearization techniques. Therefore, the efficient solution of linear problems is the key to the efficient solution of nonlinear problems.Among the techniques available for solving linear two-point boundary-value problems, the method of particular solutions (MPS) is particularly attractive in that it employs only one differential system, the original nonhomogeneous system, albeit with different initial conditions. This feature of MPS makes it ideally suitable for implementation on parallel computers in that the following requirements are met: the computational effort is subdivided into separate tasks (particular solutions) assigned to the different processors; the tasks have nearly the same size; there is little intercommunication between the tasks.For the TPBVP, the speedup achievable is ofO(n), wheren is the dimension of the state vector, hence relatively modest for the differential systems of interest in trajectory optimization and guidance. This being the case, we transform the TPBVP into a multi-point boundary-value problem (MPBVP) involvingm time subintervals, withm–1 continuity conditions imposed at the interface of contiguous subintervals. For the MPBVP, the speedup achievable is ofO(mn), hence substantially higher than that achievable for the TPBVP. It reduces toO(m) if the parallelism is implemented only in the time domain and not in the state domain.A drawback of the multi-point approach is that it requires the solution of a large linear algebraic system for the constants of the particular solutions. This drawback can be offset by exploiting the particular nature of the interface conditions: if the vector of constants for the first subinterval is known, the vector of constants for the subsequent subintervals can be obtained with linear transformations. Using decomposition techniques together with the discrete version of MPS, the size of the linear algebraic system for the multi-point case becomes the same as that for the two-point case.Numerical tests on the Intel iPSC/860 computer show that substantial speedup can be achieved via parallel algorithms vis-a-vis sequential algorithms. Therefore, the present technique has considerable interest for real-time trajectory optimization and guidance.Dedicated to the Memory of Professor Jan M. SkowronskiThis paper, based on Refs. 1–3, is a much condensed version of the material contained in these references.The technical assistance of the Research Center on Parallel Computation of Rice University, Houston, Texas is gratefully acknowledged.