20 research outputs found
A Study Of The Metric Induced By The Robin Function
No full textLet D be a smoothly bounded domain in Cn , n> 1. For each point p _ D, we have the Green function G(z, p) associated to the standard sum-of-squares Laplacian Δ with pole at p and the Robin constant __
Λ(p) = lim G(z, p) −|z − p−2n+2
z→p |
at p. The function p _→ Λ(p) is called the Robin function for D.
Levenberg and Yamaguchi had proved that if D is a C∞-smoothly bounded pseudoconvex domain, then the function log(−Λ) is a real analytic, strictly plurisubharmonic exhaustion function for D and thus induces a metric
ds2 = n∂2 log(−Λ)(z) dzα ⊗ dzβ
z
∂zα∂zβ
α,β=1
on D, called the Λ-metric. For an arbitrary C∞-smoothly bounded domain, they computed the boundary asymptotics of Λ and its derivatives up to order 3, in terms of a defining function for the domain. As a consequence it was shown that the Λ-metric is complete on a C∞-smoothly bounded strongly pseudoconvex domain or a C∞-smoothly bounded convex domain.
In this thesis, we study the boundary behaviour of the function Λ and its derivatives of all orders near a C2-smooth boundary point of an arbitrary domain. We compute the boundary asymptotics of the Λ-metric on a C∞-smoothly bounded pseudoconvex domain and as a consequence obtain that on a C∞-smoothly bounded strongly pseudoconvex domain, the Λ-metric is comparable to the Kobayashi metric (and hence to the Carath´eodory and the Bergman metrics). Using the boundary asymptotics of Λ and its derivatives, we calculate the holomorphic sectional curvature of the Λ-metric on a C∞-smoothly bounded strongly pseudoconvex domain at points on the inner normals and along the normal directions. The unit ball in Cn is also characterised among all C∞-smoothly bounded strongly convex domains on which the Λ-metric has constant negative holomorphic sectional curvature. Finally we study the stability of the Λ-metric under a C2 perturbation of a C∞-smoothly bounded pseudoconvex domain.
(For equation pl refer the abstract pdf file
Comments on the Green's function of a planar domain
No full textWe study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and -cohomology of the capacity metric and critical points of the Green's function. The principal idea used is an affine scaling of the domain that furnishes quantitative boundary behaviour of the Green's function and related objects
The squeezing function: exact computations, optimal estimates, and a new application
No full textWe present a new application of the squeezing function , using which one
may detect when a given bounded pseudoconvex domain , , is not biholomorphic to any product domain. One of
the ingredients used in establishing this result is also used to give an exact
computation of the squeezing function (which is a constant) of any bounded
symmetric domain. This extends a computation by Kubota to any Cartesian product
of Cartan domains at least one of which is an exceptional domain. Our method
circumvents any case-by-case analysis by rank and also provides optimal
estimates for the squeezing functions of certain domains. Lastly, we identify a
family of bounded domains that are holomorphic homogeneous regular.Comment: 18 pages, 1 figure. Several expository observations in Sections 1-3
and references added; typos in Section 7 corrected. This is not the final
accepted version; the publishers of J. Geom. Anal. -- in which the article
has appeared -- do not want the final accepted version to appear publicly
during a certain period. The version of record is available online: DOI given
somewhere on this page>
Synthesis and characterization of new complexes formed by insertion of carbon disulphide in RuL₃Cl3 (L=PPh₃ and AsPh₃)
No full text1113-1115Reaction of RuL₃Cl₃ (L=PPh₃ and AsPh₃) with stoichiometric amount of CS₂ in ethanol-dichloromethane mixed solvent systems at room temperature yields paramagnetic complexes of the type [RuL₂Cl₂(S₂COEt)].The complexes have been characterized by conductance, IR, electronic, ESR spectral, magnetic moment measurement and thermal data as well as by elemental analysis. The appearance of three g-values in the ESR spectra reveal a highly distorted octahedral environment around ruthenium(III) ion with one bidented EtOCS₂⁻ ligand
Lignocellulosic-Based Activated Carbon Prepared by a Chemical Impregnation Method as Electrode Materials for Double Layer Capacitor
No full textDemographic and Clinical Profile of Post-polio Residual Paralysis Patients in a Tertiary Care Hospital in India: A Retrospective Study
No full textObjectives:
To study demographic and clinical characteristics of post-polio residual survivors presenting in a polio clinic at a tertiary care hospital in the capital city of India.
Materials and Methods:
A retrospective observational study was conducted in the department of physical medicine and rehabilitation by reviewing case records of post-polio residual paralysis patients attending the polio clinic for 3 years, i.e. June 2011–May 2014. Basic demographic details and socioeconomic status of the patient were collected. Clinical details relating to residual paralysis, limb length discrepancy, deformities, ambulatory status and devised customised plan for each patient were analysed.
Results:
Forty-five patients with a mean age of 26.5 ± 12.92 years with male: female of 1.36:1 presented mainly with involvement of lower limbs. The right lower limb was most commonly involved and seen in 22 patients (48.8%) with knee flexion deformity as most frequently observed in 24 patients (53.33%). Almost two-third of patients were ambulating without assistance. Nineteen patients (42.22%) required surgical method for correction of deformity.
Conclusion:
Post-polio survivors experience varied musculoskeletal complications affecting their activities of daily living. Optimal holistic rehabilitation including surgical correction is needed for prevention and reduction of negative health outcomes
Dimension reduction of hyperion data for improving classification performance — An assessment
No full textOptimization of Square Microneedle Arrays for increasing Drug Permeability in Skin
No full textmicroneedle arrays for increasing drug permeability in skin This item was submitted to Loughborough University’s Institutional Repository by the/an author
On the contribution of demographic change to aggregate poverty measures for the developing world
No full textRecent literature and new data help determine plausible bounds to some key demographic differences between the poor and non-poor in the developing world. The author estimates that selective mortality-whereby poorer people tend to have higher death rates-accounts for 10-30 percent of the developing world's trend rate of"$1 a day"poverty reduction in the 1990s. However, in a neighborhood of plausible estimates, differential fertility-whereby poorer people tend also to have higher birth rates-has had a more than offsetting poverty-increasing effect. The net impact of differential natural population growth represents 10-50 percent of the trend rate of poverty reduction.Health Monitoring&Evaluation,Services&Transfers to Poor,Safety Nets and Transfers,Rural Poverty Reduction,Health Indicators
