On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N`Guerekata (2009) [6,7], Mophou (2010) [8,9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations. (C) 2010 Elsevier Ltd. All rights reserved.

Existence results for a damped second order abstract functional differential equation with impulses

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions. (C) 2009 Elsevier Ltd. All rights reserved.

Existence results for abstract impulsive second-order neutral functional differential equations

We establish the existence of mild solutions for a class of impulsive second-order partial neutral functional differential equations with infinite delay in a Banach space. (C) 2009 Published by Elsevier Ltd

Existence Results for Second Order Differential Equations with Nonlocal Conditions in Banach Spaces

This work is concerned with implicit second order abstract differential equations with nonlocal conditions. Assuming that the involved operators satisfy sonic compactness properties, we establish the existence of local mild solutions, the existence of global mild solutions and the existence of asymptotically almost periodic solutions.

Approximate controllability of second-order distributed implicit functional systems

In this paper we study the approximate controllability of control systems with states and controls in Hilbert spaces, and described by a second-order semilinear abstract functional differential equation with infinite delay. Initially we establish a characterization for the approximate controllability of a second-order abstract linear system and, in the last section, we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system. (C) 2008 Elsevier Ltd. All rights reserved.

Existence of solutions for second order partial neutral functional differential equations

We establish existence of mild solutions for a class of abstract second-order partial neutral functional differential equations with unbounded delay in a Banach space.

The kinetics of baculovirus adsorption to insect cells in suspension culture

The influence of various culture parameters on the attachment of a recombinant baculovirus to suspended insect cells was examined under normal culture conditions. These parameters included cell density, multiplicity of infection, and composition of the cell growth medium. It was found that the fractional rate of virus attachment was independent of the multiplicity of infection but dependent on the cell density. A first order mathematical model was used to simulate the adsorption kinetics and predict the efficiency of virus attachment under the various culture conditions. This calculated efficiency of virus attachment was observed to decrease at high cell densities, which was attributed to cell clumping. It was also observed that virus attachment was more efficient in Sf900II serum free medium than it was in IPL-41 serum-supplemented medium. This effect was attributed to the protein in serum which may coat the cells and so inhibit adsorption. A general discussion relating the observations made in-these experiments to the kinetics of recombinant baculovirus adsorption to suspended insect cells is presented.

State-dependent microstructural white matter changes in bipolar I depression

Abnormalities in fronto-limbic-striatal white matter (WM) have been reported in bipolar disorder (BD), but results have been inconsistent across studies. Furthermore, there have been no detailed investigations as to whether acute mood states contribute to microstructural changes in WM tracts. In order to compare fiber density and structural integrity within WM tracts between BD depression and remission, whole-brain fractional anisotropy (FA) and mean diffusivity (MD) were assessed in 37 bipolar I disorder (BD-I) patients (16 depressed and 21 remitted), and 26 healthy individuals with diffusion tensor imaging. Significantly decreased FA and increased MD in bilateral prefronto-limbic-striatal white matter and right inferior fronto-occipital, superior and inferior longitudinal fasciculi were shown in all BD-I patients versus controls, as well as in depressed BD-I patients compared to both controls and remitted BD-I patients. Depressed BD-I patients also exhibited increased FA in the ventromedial prefrontal cortex. Remitted BD-I patients did not differ from controls in FA or MD. These findings suggest that BD-I depression may be associated with acute microstructural WM changes.

Anisotropic Reversible Aggregation of Latex Nanoparticles Suspended in a Lyotropic Nematic Liquid Crystal: Effect of Gradients of Biaxial Order

We studied the anisotropic aggregation of spherical latex particles dispersed in a lyotropic liquid crystal presenting three nematic phases; calamitic, biaxial, and discotic. We observed that in the nematic calamitic phase aggregates of latex particles are formed, which become larger and anisotropic in the vicinity of the transition to the discotic phase, due to a coalescence process. Such aggregates are weakly anisotropic and up to 50 mu m long and tend to align parallel to the director field. At the transition to the discotic phase, the aggregates dissociated and re-formed when the system was brought back to the calamitic phase. This shows that the aggregation is due to attractive and repulsive forces generated by the particular structure of the nematic phase. The surface-induced positional order was investigated by surface force apparatus experiments with the lyotropic system confined between mica surfaces, revealing the existence of a presmectic wetting layer around the surfaces and oscillating forces of increasing amplitude as the confinement thickness was decreased. We discuss the possible mechanisms responsible for the reversible aggregation of latex particles, and we propose that capillary condensation of the N(C) phase, induced by the confinement between the particles, could reduce or remove the gradient of order parameter, driving the transition of aggregates from solidlike to liquidlike and gaslike.

Fractional Photothermolysis for the Treatment of Hypertrophic Scars: Clinical Experience of Eight Cases

Hypertrophic scars are common problems and represent a challenging condition to treat. Fractional photothermolysis has been effective at resurfacing photodamaged skin, acne scars, and atrophic scars, but there are few reports on its use for hypertrophic scars. To evaluate the safety and efficacy of 1,550-nm erbium-doped fiber laser treatment of hypertrophic scars in eight patients. Eight patients (skin phototypes II-IV) with hypertrophic scars received monthly treatments with a 1,550-nm erbium-doped fiber laser. Energy settings ranged from 35 to 50 mJ, and eight to 10 passes were applied with treatment levels 6 to 8. An independent physician evaluator assessed the treatment response by comparing pre- and posttreatment clinical photographs using a quartile grading scale (grade 1, <= 25%=minimal to no improvement; grade 2, 26-50%=moderate improvement; grade 3, 51-75%=marked improvement; grade 4, > 75%=near total improvement. At four weeks after the last treatment session, a mean grade of 2.4 was achieved based on an independent physician`s clinical assessment. Improvement in pigmentation occurred in all hyperpigmented scars. Hypertrophic scars can be effectively and safely improved with 1,550-nm erbium-doped fiber laser treatment. The authors have indicated no significant interest with commercial supporters.

Elevated left and reduced right orbitomedial prefrontal fractional anisotropy in adults with bipolar disorder revealed by tract-based spatial statistics

Context Diffusion tensor imaging (DTI) studies in adults with bipolar disorder (BD) indicate altered white matter (WM) in the orbitomedial prefrontal cortex (OMPFC), potentially underlying abnormal prefrontal corticolimbic connectivity and mood dysregulatioin in BD. Objective: To use tract-based spatial statistics (TBSS) to examine VVM skeleton (ie, the most compact whole-brain WM) in subjects with BD vs healthy control subjects. Design: Cross-sectional, case-control, whole-brain DTI using TBSS. Setting: University research institute. Participants: Fifty-six individuals, 31 having a DSM-IV diagnosis of BD type 1 (mean age, 35.9 years [age range, 24-52 years]) and 25 controls (mean age, 29.5 years [age range, 19-52 years]). Main Outcome Measures: Fractional anisotropy (FA) longitudinal and radial diffusivities in subjects with BD vs controls (covarying for age) and their relationships with clinical and demographic variables. Results: Subjects with BD vs controls had significantly greater FA (t > 3.0, P <=.05 corrected) in the left uncinate fasciculus (reduced radial diffusivity distally and increased longitudinal diffusivity centrally), left optic radiation (increased longitudinal diffusivity), and right anterothalamic radiation (no significant diffusivity change). Subjects with BD vs controls had significantly reduced FA (t > 3.0, P <=.05 corrected) in the right uncinate fasciculus (greater radial diffusivity). Among subjects with BD, significant negative correlations (P <.01) were found between age and FA in bilateral uncinate fasciculi and in the right anterothalamic radiation, as well as between medication load and FA in the left optic radiation. Decreased FA (P <.01) was observed in the left optic radiation and in the right anterothalamic radiation among subjects with BD taking vs those not taking mood stabilizers, as well as in the left optic radiation among depressed vs remitted subjects with BD. Subjects having BD with vs without lifetime alcohol or other drug abuse had significantly decreased FA in the left uncinate fasciculus. Conclusions: To our knowledge, this is the first study to use TBSS to examine WM in subjects with BD. Subjects with BD vs controls showed greater WM FA in the left OMPFC that diminished with age and with alcohol or other drug abuse, as well as reduced WM FA in the right OMPFC. Mood stabilizers and depressed episode reduced WM FA in left-sided sensory visual processing regions among subjects with BD. Abnormal right vs left asymmetry in FA in OMPFC WM among subjects with BD, likely reflecting increased proportions of left-sided longitudinally aligned and right-sided obliquely aligned myelinated fibers, may represent a biologic mechanism for mood dysregulation in BD.

Developing logic programs from specifications using stepwise refinement

In this paper we demonstrate a refinement calculus for logic programs, which is a framework for developing logic programs from specifications. The paper is written in a tutorial-style, using a running example to illustrate how the refinement calculus is used to develop logic programs. The paper also presents an overview of some of the advanced features of the calculus, including the introduction of higher-order procedures and the refinement of abstract data types.