Existence and Stability of Periodic Solutions of a Duffing Equation by Using a New Maximum Principle

The purpose of this paper is to obtain new criteria for existence and asymptotic stability of periodic solutions of a Duffing equation x + cx + g(t, x) = 0, taking advantage of a new maximum principle with L^p-conditions combined with known relations between upper and lower solutions, topological degree and stability.Partially supported by D.G.I. BFM2002-01308, Ministerio Ciencia y Tecnología, Spain.     

Taming chaotic solitons in Frenkel-Kontorova chains by weak periodic excitations

We have proposed theoretically and confirmed numerically the possibility of controlling chaotic solitons in damped, driven Frenkel-Kontorova chains subjected to additive bounded noise by weak periodic excitations. Theoretically, we obtained an effective equation of motion governing the dynamics of the soliton center of mass for which we deduced Melnikov's method-based predictions concerning the regions in the control parameter space where homoclinic bifurcations are frustrated. Numerically, we found that such theoretical predictions can be reliably applied to the original Frenkel-Kontorova chains, even for the case of localized application of the soliton-taming excitations, and there is strikingly good agreement between analytical estimates and numerical results.     

Deterministic primality test for numbers of the form odd

We use a result of E. Lehmer in cubic residuacity to find an algorithm to determine primality of numbers of the form , odd, . The algorithm represents an improvement over the more general algorithm that determines primality of numbers of the form , , presented by Berrizbeitia and Berry (1999).

     

The measurement of the spatial average temporal average intensity I(sata) and ultrasonic power W in composite ultrasonic transducers for medical application

Two possible methods to determine the spatial average temporal average intensity I(sata) and ultrasonic power W in composite ltrasonic transducers for medical application are described. Results showed that integrals using one method will yield accurate results but a vast amount of computational effort is required. On the other hand, using an alternative method these integrals may readily be solved at the expense of the accuracy of the results deduced.     

Retrieval of the zero-dispersion wavelength map of an optical fiber from measurement of its continuous-wave four-wave mixing efficiency

We present a novel algorithm for reconstruction of the longitudinal distribution of zero-dispersion wavelength in an optical fiber from low power, end-to-end measurements of four-wave mixing efficiency. It is based on a modified version of the error-reduction approach used in classic phase-retrieval problems. Experimental results demonstrate the validity of this algorithm.     

Separate urinary bladder and prostate neurons in the central nervous system of the rat: simultaneous labeling with two immunohistochemically distinguishable pseudorabies viruses

Background

This work examines the central nervous system distribution of virus-labeled neurons from the rat urinary bladder and the prostate simultaneously within the same tissue sections. Two immunohistochemically distinct pseudorabies virus strains were simultaneously injected into male Sprague Dawley rats (~280 gm). One virus was injected into the bladder and the other into the prostate. After incubation intervals of 2.25, 2.5, 2.75, 3 and 4 days, sections from the spinal cord and brain were processed immunohistochemically to detect cells, within a single section, which were labeled separately by each virus or were labeled by both viruses.

Results

Each strain of virus labeled a separate population of neurons and some neurons were labeled by both strains. The majority of neurons labeled by virus from the urinary bladder were found in the L6-S1 spinal cord segments within the dorsal gray commissure, the intermediolateral area and the superficial dorsal horn. Neurons labeled by virus from the prostate were mainly found in the L1-L2 spinal cord segments in the dorsal gray commissure and the intermediolateral areas. Double-labeled interneurons in L1-L2 were mainly located in the intermediolateral area. In L6-S1 they were divided between the dorsal gray commissure and the intermediolateral area.

Conclusions

Spinal neurons innervating the bladder are clearly separate and different from those innervating the prostate. This difference also persists in the brain. In disagreement with previous reports, no direct anatomical evidence of parasympathetic innervation of the prostate was observed.     

An unexpected chelation-controlled Yb(OTf)(3)-catalyzed aminolysis and azidolysis of cyclitol epoxides

A chelation-controlled aminolysis and azidolysis of cyclitol epoxides with Yb(OTf)(3) has been disclosed. The presence of a free OH group able to direct the coordination with the lanthanide seems essential for an efficient regiocontrol of the process.     

C-C bond-forming reactions of Ir(III)-alkenyls and nitriles or aldehydes: generation of reactive hydride- and alkyl-alkylidene compounds and observation of a reversible 1, 2-H shift in stable hydride-Ir(III) alkylidene complexes

Nucleophilic attack of the beta-carbon of an Ir(III)-alkenyl functionality onto the alpha-carbon of a coordinated nitrile- or aldehyde occurs intramoleculary to yield initially iridacyclic structures. Nitriles give rise to isolable complexes that contain delocalized five-membered rings (iridapyrroles, e.g. 3'-8') in a reaction catalyzed by H2O (for some of these syntheses, Ir(III)-eta 3-allyl derivatives may be used as the source of the Ir(III)-alkenyl moiety). In contrast, the alkenyl-to-aldehyde C-C coupling gives transient iridacycles that evolve by a fast alkyl-to-alkylidene migration and beta-H elimination. The end products (13* and 14*) contain an elaborated chelating alkoxide-olefin ligand. Addition of [H(OEt2)2][BAr'4] to the iridapyrroles effects stereospecific protonation of the beta-ring carbon. Those iridapyrroles which contain an additional metal-alkyl functionality (e.g. 3a*, alkyl = C2H5) afford highly reactive cationic alkyl-alkylidene intermediates that evolve instantaneously by migratory insertion/beta-H elimination. The end products also contain an elaborated, chelating ligand, although this time with an olefin and imine terminus compared with the previous ligand. Contrary to this result, protonation of the hydride-iridapyrrole complex 8a* in weakly coordinating solvents permits isolation of two unusual cationic cis-hydride-alkylidene compounds 11*, which undergo reversible 1,2-H shifts.     

Unprecedented highly stereoselective alpha- and beta-C-glycosidation with chiral titanium enolates

[reaction: see text] Lewis acid mediated addition of chiral titanium enolates to glycals provides either alpha- or beta-1'-methyl-substituted C-glycosides. This highly stereoselective methodology permits the modular preparation of three of the four possible diastereomers.     

A Canonical Directly Infinite Ring

Let be the set of nonnegative integers and the ring of integers. Let be the ring of N × N matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of yields that the subrings generated by them coincide. This subring is the sum of the ideal consisting of all matrices in with only a finite number of nonzero entries and the subring of generated by the identity matrix. Regular elements are also described. We characterize all ideals of , show that all ideals are finitely generated and that not all ideals of are principal. Some general ring theoretic properties of are also established.