A Convergence Analysis of Newton-Like Method for Singular Equations Using Recurrent Functions

We provide new semilocal convergence results for Newton-like method involving outer or generalized inverses in a Banach space setting. Using our new idea of recurrent functions and the same or weaker conditions than before [5-19 A. Ben-Israel and N.E. Greville ( 1974 ). Generalized Inverses: Theory and Applications, Pure and Applied Mathematics . Wiley-Interscience , New York . X. Chen and T. Yamamoto ( 1989 ). Convergence domains of certain iterative methods for solving nonlinear equations . Numer. Funct. Anal. Optimiz. 10 : 37 – 48 . J.E. Dennis , Jr. ( 1968 ). On Newton-like methods . Numer. Math. 11 : 324 – 330 . P. Deuflhard and C. Heindl ( 1979 ). Convergence theorems for Newton's method and extensions to related methods . SIAM J. Numer. Anal. 16 : 1 – 10 . J.M. Gutiérrez ( 1997 ). A new semilocal convergence theorem for Newton's method . J. Comp. Appl. Math. 79 : 131 – 145 . J.M. Gutiérrez , M.A. Hernández , and M.A. Salanova ( 1995 ). Accessibility of solutions by Newton's method . Internat. J. Comput. Math. 57 : 239 – 247 . W.M. Häubler ( 1986 ). A Kantorovich-type convergence analysis for the Gauss–Newton methods . Numer. Math. 48 : 119 – 125 . L.V. Kantorovich and G.P. Akilov ( 1964 ). Functional Analysis . Pergamon Press , Oxford . M.Z. Nashed and X. Chen ( 1993 ). Convergence of Newton-like methods for singular operator equations using outer inverses . Numer. Math. 66 : 235 – 257 . F.A. Potra and V. Ptàk ( 1980 ). Sharp error bounds for Newton's process . Numer. Math. 34 : 67 – 72 . W.C. Rheinboldt ( 1968 ). A unified convergence theory for a class of iterative processes . SIAM J. Numer. Anal. 5 : 42 – 63 . W.C. Rheinboldt ( 1977 ). An adaptive continuation process for solving systems of nonlinear equations . Polish Academy of Sciences, Banach Ctr. Publ. 3 : 129 – 142 . T. Yamamoto ( 1987 ). A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions . Numer. Math. 49 : 203 – 230 . T. Yamamoto ( 1987 ). A convergence theorem for Newton-like methods in Banach spaces . Numer. Math. 51 : 545 – 557 . T. Yamamoto ( 1989 ). Uniqueness of the solution in a Kantorovich-type theorem of Haubler for the Gauss–Newton method . Japan J. Appl. Math. 6 : 77 – 81 . ], we provide more precise information on the location of the solution and finer bounds on the distances involved. Moreover, since our Newton–Kantorovich-type hypothesis is weaker than before, we can now cover cases not previously possible.

Applications and numerical examples involving a nonlinear integral equation of Chandrasekhar-type and a differential equation with Green's function are also provided in this study.     

Antisense-mediated isoform switching of steroid receptor coactivator-1 in the central nucleus of the amygdala of the mouse brain

Background

Antisense oligonucleotide (AON)-mediated exon skipping is a powerful tool to manipulate gene expression. In the present study we investigated the potential of exon skipping by local injection in the central nucleus of the amygdala (CeA) of the mouse brain. As proof of principle we targeted the splicing of steroid receptor coactivator-1 (SRC-1), a protein involved in nuclear receptor function. This nuclear receptor coregulator exists in two splice variants (SRC-1a and SRC-1e) which display differential distribution and opposing activities in the brain, and whose mRNAs differ in a single SRC-1e specific exon.

Methods

For proof of principle of feasibility, we used immunofluorescent stainings to study uptake by different cell types, translocation to the nucleus and potential immunostimulatory effects at different time points after a local injection in the CeA of the mouse brain of a control AON targeting human dystrophin with no targets in the murine brain. To evaluate efficacy we designed an AON targeting the SRC-1e-specific exon and with qPCR analysis we measured the expression ratio of the two splice variants.

Results

We found that AONs were taken up by corticotropin releasing hormone expressing neurons and other cells in the CeA, and translocated into the cell nucleus. Immune responses after AON injection were comparable to those after sterile saline injection. A successful shift of the naturally occurring SRC-1a:SRC-1e expression ratio in favor of SRC-1a was observed, without changes in total SRC-1 expression.

Conclusions

We provide a proof of concept for local neuropharmacological use of exon skipping by manipulating the expression ratio of the two splice variants of SRC-1, which may be used to study nuclear receptor function in specific brain circuits. We established that exon skipping after local injection in the brain is a versatile and useful tool for the manipulation of splice variants for numerous genes that are relevant for brain function.     

An inventory control model with stochastic review interval and special sale offer

Periodic review inventory models are widely used in practice, especially for inventory systems in which many different items are purchased from the same supplier. However, most of periodic review models have assumed a fixed length of the review periods. In practice, it is possible that the review periods are of a random (stochastic) length. This paper presents an inventory control model in the case of random review intervals and special sale offer from the supplier. The replenishment interval is assumed to obey from two different distributions, namely, exponential and uniform distributions. Also, shortages are allowed in the term of partial backordering. For this model, its convexity condition is discussed and closed form solutions are proposed.     

Elucidating a normal function of huntingtin by functional and microarray analysis of huntingtin-null mouse embryonic fibroblasts

Background

Multi-sensory integration is necessary for organisms to discriminate different environmental stimuli and thus determine behavior. Caenorhabditis elegans has 12 pairs of amphid sensory neurons, which are involved in generating behaviors such as thermotaxis toward cultivation temperature, and chemotaxis toward chemical stimuli. This arrangement of known sensory neurons and measurable behavioral output makes C. elegans suitable for addressing questions of multi-sensory integration in the nervous system. Previous studies have suggested that C. elegans can process different chemoattractants simultaneously. However, little is known about how these organisms can integrate information from stimuli of different modality, such as thermal and chemical stimuli.

Results

We studied the behavior of a population of C. elegans during simultaneous presentation of thermal and chemical stimuli. First, we examined thermotaxis within the radial temperature gradient produced by a feedback-controlled thermoregulator. Separately, we examined chemotaxis toward sodium chloride or isoamyl alcohol. Then, assays for simultaneous presentations of 15°C (colder temperature than 20°C room temperature) and chemoattractant were performed with 15°C-cultivated wild-type worms. Unlike the sum of behavioral indices for each separate behavior, simultaneous presentation resulted in a biased migration to cold regions in the first 10 min of the assay, and sodium chloride-regions in the last 40 min. However, when sodium chloride was replaced with isoamyl alcohol in the simultaneous presentation, the behavioral index was very similar to the sum of separate single presentation indices. We then recorded tracks of single worms and analyzed their behavior. For behavior toward sodium chloride, frequencies of forward and backward movements in simultaneous presentation were significantly different from those in single presentation. Also, migration toward 15°C in simultaneous presentation was faster than that in 15°C-single presentation.

Conclusion

We conclude that worms preferred temperature to chemoattractant at first, but preferred the chemoattractant sodium chloride thereafter. This preference was not seen for isoamyl alcohol presentation. We attribute this phase-dependent preference to the result of integration of thermosensory and chemosensory signals received by distinct sensory neurons.     

Theoretical study of the photophysical processes of a styryl-bodipy derivative eliciting an AND molecular logic gate response

We study, via density functional theory and time dependent DFT calculations, the photophysical processes of a styryl-bodipy derivative, which acts as a three metal-cation-receptor fluorophore in order to (a) gain information on the appropriate computational approach for successful prediction of molecular logic gate candidates, (b) rationalize the available experimental data and (c) understand how the given combination of three different receptors with the BODIPY fluorophore presents such interesting optoelectronic responses. The fluorophore ( 1 ), its monometallic complexes ( 1-Ca ²⁺ , 1-Zn ²⁺ , and 1-Hg ²⁺ ), and its trimetallic complex ( 2 ) are studied. The calculated λ_max values for absorption and emission are in excellent agreement with experimental data. It was found that the observed quenching of emission of 1 and of the monometallic complexes is attributed to the fact that their first excited state is a charge-transfer state whereas this does not happen for the complex 2 . It should be noted that for the correct ordering of the excited states, the inclusion of corrections to the excitation energies for nonequilibrium solvent effects is required; while in the case of 1-Ca ²⁺ , the additional explicit inclusion of the solvent is necessary for the quenching of the emission spectra.     

Approaches to primary tert-alkyl amines as building blocks

Primary tert-alkyl amines include analogues of amantadine, a fragment commonly linked to pharmacophoric groups to enhance biological activity. The preparation of primary tert-alkyl amines is considered to be a difficult problem. Four synthetic procedures, some of which have been previously reported for the synthesis of amines with primary (RCH₂NH₂) or secondary (RR'CHNH₂) alkyl and/or aryl groups, were tested for the synthesis of primary tert-alkyl amines (RR′R″CNH₂) in aliphatic series including adamantane adducts. These procedures included the formation and reduction of tert-alkyl azides, the Ritter reaction in standard and modified conditions, the addition of organometallic reagents to N-tert-butyl sulfinyl ketimines and one-pot reactions between nitriles and organometallic reagents in the presence of a Lewis acid, Τi(iPrO)₄ or CeCl_3. These synthetic routes are unexplored for primary tert-alkyl amines. Studies on the synthetic routes for primary tert-alkyl amines are currently lacking. The reaction conditions and substrate limitations were studied for each procedure, with the first procedure being the most general and applicable also for compounds bearing bulky adducts.     

Finite element modeling of the mechanical effects of the UV laser ablation of polymer coatings

Laser ablation constitutes the basis of a number of techniques aiming at the processing and diagnosis of polymeric coatings on a variety of substrates. In all these applications, however, the issue is raised about the mechanical effects of the procedure on the substrate integrity. To this end, we employ finite element modeling for simulating the mechanical effects of UV laser ablation on a polymer specimen, with particular emphasis on the structural modifications that may be induced at areas away from the ablation spot. The cylindrical specimen consists of a poly(methylmethacrylate) (PMMA) film on a silica substrate. The analysis shows that stresses of high enough amplitude may propagate to distances far away from the irradiated spot and may induce deleterious mechanical deformations (e.g., cracks or delaminations). The dependence of the distribution of the tensile stresses on the thickness of the two components, as well as on size of the ablation spot area, is examined. Finally, the possibility of growth of pre-existing defects is shown. The results are overall in very good agreement with experimental observations.     

Dispersion Characteristics of Arbitrary Periodic Structures with Rectangular Grooves

The dispersion characteristics of a circular cylindrical waveguide with periodic surface corrugations consisting of rectangular grooves with smoothing are examined using the Space Harmonic Method (SHM). The whole structure is divided into two regions, one describing the propagation volume and one inside the grooves. In the first region, the Floquet theorem is applicable and the field distribution is expressed as a summation of spatial Bloch components, whereas in the second one an appropriate Fourier expansion of standing waves is used. Applying the boundary conditions an infinite system of equations is obtained, which is solved numerically by truncation. Several cases are considered, including the limiting cases of a sinusoidal and a rectangular corrugation profile, to check the accuracy of the method proposed as well as its dependence on the corrugation profile. Numerical results are presented only for transverse magnetic modes, although the formalism can be easily extended to include all kinds of waves that can in principle propagate in such a structure.