Optimal Synthesis of the Asymmetric Sinistral/Dextral Markov–Dubins Problem

We consider a variation of the classical Markov–Dubins problem dealing with curvature-constrained, shortest paths in the plane with prescribed initial and terminal positions and tangents, when the lower and upper bounds of the curvature of the path are not necessarily equal. The motivation for this problem stems from vehicle navigation applications, when a vehicle may be biased in taking turns at a particular direction due to hardware failures or environmental conditions. After formulating the shortest path problem as a minimum-time problem, a family of extremals, which is sufficient for optimality, is characterized, and subsequently the complete analytic solution of the optimal synthesis problem is presented. In addition, the synthesis problem, when the terminal tangent is free, is also considered, leading to the characterization of the set of points that can be reached in the plane by curves satisfying asymmetric curvature constraints.     

A new mathematical construction of the general nonlinear ODEs of motion in rigid body dynamics (Euler’s equations)

It is shown that the three nonlinear dynamic Euler ordinary differential equations (ODEs), concerning the motion of a rigid body free to rotate about a fixed point, are reduced, by means of a subsidiary function which is to be determined, to three Abel equations of the second kind of the normal form. Based on a recently developed mathematical construction concerning exact analytic solutions of the Abel nonlinear ODEs of the second kind, we perform a new mathematical solution for the classical dynamic Euler nonlinear ODEs.     

Contact Transcleral Ciliary Body Photodynamic Therapy with Verteporfin in Pigmented Rabbits: Effect of Repeated Treatments

We studied the effect on the intraocular pressure (IOP) and the ciliary body (CB) morphology after four consecutive contact transcleral photodynamic treatments of the ciliary body (CB-PDT) with verteporfin in pigmented rabbits. Twenty-two pigmented rabbits underwent CB-PDT (study group), performed once (six rabbits) or repeated for up to four times (16 rabbits). Six additional rabbits received only laser treatment without photosensitizer administration (control group). CB-PDT was performed in one eye in rabbits of the study group, with the fellow eye serving as internal control. Verteporfin dosage was 1 mg kg ⁻¹ as bolus injection and laser settings were 40 mW (600 μm core optical fiber) for 1.5 min per spot, for 10 spots. In repeated CB-PDT, treatments were performed in 4-day intervals. Daily IOP measurements were recorded. Histological studies were performed at selected time points. An IOP reduction, more sustained following repeated treatments, was detected in all treated eyes but not in fellow eyes or in the control group. On the average, the IOP was restored to pretreatment levels 4 days after the last treatment. No serious adverse events were observed and the CB architecture was intact at the end of the experiment. Repeated CB-PDT is safe and results in a short-term reduction of IOP. Induced CB alterations are reversible.     

Local block bootstrapBloc re-échantillonnage local

For time series that are not stationary, the block bootstrap method is not directly applicable. However, if the underlying stochastic structure is slowly changing with time, one may employ a local block-resampling procedure. We define such a procedure, and give an example of its applicability. To cite this article: E. Paparoditis, D.N. Politis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 959–962.     

Optimal Guidance of the Isotropic Rocket in the Presence of Wind

We address the minimum-time guidance problem for the so-called isotropic rocket in the presence of wind under an explicit constraint on the acceleration norm. We consider the guidance problem to a prescribed terminal position and a circular target set with a free terminal velocity in both cases. We employ standard techniques from optimal control theory to characterize the structure of the optimal guidance law as well as the corresponding minimum time-to-go function. It turns out that the complete characterization of the solution to the optimal control problem reduces to the solution of a system of nonlinear equations in triangular form. Numerical simulations, that illustrate the theoretical developments, are presented.     

The Local Bootstrap for Kernel Estimators under General Dependence Conditions

We consider the problem of estimating the distribution of a nonparametric (kernel) estimator of the conditional expectation g(x; ) = E((X _t+1) | Y _t,m = x) of a strictly stationary stochastic process {X _t , t 1}. In this notation (·) is a real-valued Borel function and Y _t,m a segment of lagged values, i.e., Y_t,m=(X_{t-i 1},X_{t-i 2},...,X_{t-i m}), where the integers i _i , satisfy 0 i₁2...m>. We show that under a fairly weak set of conditions on {X _t , t 1}, an appropriately designed and simple bootstrap procedure that correctly imitates the conditional distribution of X _t+1 given the selective past Y _t,m , approximates correctly the distribution of the class of nonparametric estimators considered. The procedure proposed is entirely nonparametric, its main dependence assumption refers to a strongly mixing process with a polynomial decrease of the mixing rate and it is not based on any particular assumptions on the model structure generating the observations.     

Synthesis and spectroscopic studies of 5‐arylidene‐3‐substituted tetramic acids as possible substrates for catalytic asymmetric hydrogenation

A new series of 5‐arylidene‐3‐substituted tetramic acids 6–19 have been synthesized by a condensation reaction of 3‐butanoyl tetramic acid 3 , 3‐ethoxycarbonyl tetramic acid 4 and 3 ‐acetyl tetramic acid 5 with a variety of substituted benzaldehydes. The structures of the isolated compounds 6–19 have been elucidated using FT‐IR, ¹H and ¹³C‐NMR spectroscopy, FAB‐MS spectroscopy as well as elemental analyses.     

Diagnosis of magnetoresponsive aromatic and antiaromatic zones in three‐membered rings of d‐ and f‐block elements

Magnetoresponsive three‐membered rings of d‐ and f‐block elements have been thoroughly investigated with the help of electronic structure calculation methods. The magnetic response of the clusters was evaluated by the Nucleus Independent Chemical Shifts (NICS)_zz‐scan curves, which in conjunction with symmetry‐based selection rules for the most significant translationally and rotationally allowed transitions helped rationalize and predict the orbital‐type of aromaticity/antiaromaticity of the clusters. The magnetoresponsive early (Groups 3, 4, and 5) transition metal M₃ rings exhibit successive aromatic and antiaromatic zones separated by a nodal plane. The magnetoresponsive late (Groups 11 and 12) transition metal M₃ rings exhibit long‐range aromatic zone with the NICS_zz(R) values decaying rapidly and monotonically with respect to R. The magnetic response of Group 10 transition metal M₃ rings is similar to that of the early transition metal M₃ rings, but it is long‐range antiaromatic only for the [c‐Ni₃] cluster. The NICS_zz‐scan curve of the [(H_tLa)₃(μ₂‐H)₆] cluster is indicative of weak pure σ‐aromaticity due to the induced diatropic ring current from the translationally allowed a → e′ and e′ → a transitions. The aromatic–antiaromatic behavior of the [(H_tCe)₃(μ₂‐H)₆]⁺ and [(H_tTm)₃(μ₂‐H)₆]²⁻ clusters is similar to that of the early d‐block elements. The magnetic response of [(H_tYb)₃(μ₂‐H)₆]³⁻ is similar to that of [c‐Hg₃]²⁻. The [(H_tLu)₃(μ₂‐H)₆] cluster can be considered as a doubly (σ + π) aromatic system, with the σ‐aromatic component being much stronger than the π‐aromatic one. Finally, the [(X_tRe)₃(μ₂‐X)₆] and [(X_tRu)₃(μ₂‐X)₆]⁺ (X = Cl, Br, I) clusters exhibit significant aromatic character with the greatest contribution to the induced diatropic ring currents coming from π‐type transitions. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Synthesis and spectroscopic studies of optically active n‐acetyl butenoates and n‐acetyl‐2‐alkyl‐pyrrolin‐4‐ones

The synthesis of a series of optically active N‐acetyl butenoates 3–5 is described using a facile methodology. These butenoates undergo cyclization to the corresponding N‐acetyl‐2‐alkyl‐pyrrolin‐4‐ones 6,7 retaining their stereochemical integrity. The structure of the newly synthesized compounds has been elucidated through ¹H‐¹³C NMR, IR spectroscopy and their enantiomeric excesses have been measured by chiral HPLC analysis.