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This paper presents a general formula for (2m + 2)-point n-ary interpolating subdivision scheme for curves for any integer m ≥ 0 and n ≥ 2 by using Newton interpolating polynomial. As a consequence, the proposed work is extended for surface case, which is equivalent to the tensor product of above proposed curve case. These formulas merge several notorious curve/surface schemes. Furthermore, visual performance of the subdivision schemes is also presented.
This paper offers a
general formula for surface subdivision rules for quad meshes by using 2-D Lagrange interpolating polynomial .
We also see that the result
obtained is equivalent to the tensor product of (2N + 4)-point n-ary interpolating curve scheme for N ≥ 0 and n ≥ 2. The
simple interpolatory subdivision scheme for quadrilateral nets with arbitrary
topology is presented by L. Kobbelt , which can be directly calculated from
the proposed formula. Furthermore, some characteristics and applications of the
proposed work are also discussed.
Background: A cross
sectional comparative study was conducted in a well populated city named
Rawalpindi, which is located in the Northern part of Pakistan. Objectives: This
study was aimed to document the comparison of menopausal-related symptoms among
educated and non educated women of Rawalpindi, Pakistan. Methods: MRS was used
to measure the intensity of menopausal symptoms. 100 educated and 100 uneducated
women were selected for study purpose. Pakistan Institute of Medical Sciences,
Military Hospital and Combined Military Hospital were selected as a study
setting. Findings: Correlation & Fisher exact test was applied for
statistical analysis. The intensity of symptoms reported by Educated women as:
sleeping problems (93.0%); heart discomfort (80.0%); hot flushes and sweating
(70.0%); joint and muscular pain (52.0); depressive mood (63.0%); irritability
(42%); anxiety (60.0%). physical and mental exhaustion; (48.0%); sexual problem
(61.0%); dryness of vagina (57.0%); and bladder problem (65.0%). The severity
of symptoms in uneducated women; sleeping problems (77.0%); heart discomfort
(73.0%); hot flushes (69.0%); joint and muscular pain (66.0); depressive mood
(71.0%); irritability (58%); anxiety (80.0%). physical and mental exhaustion
(70.0%); sexual problem (66.0%); dryness of vagina (70.0%); and bladder problem
(83.0%). Conclusions: Somatic symptoms were high in educated women as compare
to uneducated women while the prevalence of psychological and Urogenital
symptoms were high in uneducated women as compare to educated women.