The Lax conjecture is true

In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recent observation of Helton and Vinnikov.Comment: 7 pages, Proceedings to the AMS, to appear. Added background materia

Study of histopathological pattern of endometrium in abnormal uterine bleeding and its management

Background: Abnormal uterine bleeding is one of the most common and challenging problems presenting as an enigma to the gynecologist regardless of the age of the women.  Histopathological evaluation of endometrium plays a significant and pivotal role in the diagnosis and management of endometrial causes of Abnormal Uterine Bleeding. The main aim was to study the frequency of different histopathological patterns of endometrium in patients with abnormal uterine bleeding across different age groups, know the endometrial causes of abnormal uterine bleeding and its managements.Methods: This study was conducted on 300 patients from March 2014 to February 2015 in the department of Obstetrics and Gynaecology in a reputed teaching hospital and research centre in South India. Demographic indices were collected and recorded. Endometrial samples were sent for histopathological examinations and different endometrial patterns were noted.Results: Abnormal Uterine Bleeding (AUB) presented mostly in the 41-50 years age spectrum (48.6%) and most of the patients were multipara. The main presenting complaint among our patients was menorrhagia (42%) followed by polymenorrhagia (15%), menometrorrhagia (10.6%) ,continuous vaginal bleeding (9.6%), Polymenorrhea (9.3%), postmenopausal bleeding (8.6%) and metrorrhagia (4.6%).The commonest histopathological  pattern in abnormal uterine bleeding was  normal physiological phases of menstrual cycle - proliferative and secretary endometrium (37% and 30%  respectively). Endometrial hyperplasia was the most common endometrial pathology observed (22.6%).Conclusions: Endometrial evaluation in abnormal uterine bleeding in different age groups helps in the management, especially in the perimenopausal and postmenopausal age groups to rule out premalignant conditions and malignancy

Comparison between experimental and analytical behaviour of the steel – concrete composite pushout specimen with stud and channel shear connector

To investigate the behaviour of composite action with various shear connectors, push-out tests were performed for eight specimens. Test parameters includes are type of shear connector (headed stud connector and channel connector), number of connectors (one and two) and specimen with or without decking sheet. Test results showed that performance of the push-out specimens depends greatly on type of connector and decking sheet. From the experimental study it was observed that the performance and shear capacity of channel connector was 60 % more than the stud connector. The shear resistance between the steel and concrete was enhanced up to 50 % for the push out specimen without decking. The specimen with two numbers of stud and channel connector increases the strength by 58% and 23% respectively as compared to specimen with single connector. The behaviour of the push out specimen was stimulated by three-dimensional finite element model using software ANSYS workbench. The analytical behaviour was well agreement with the real push out specimen studied experimentally

Comparison between experimental and analytical behaviour of the steel – concrete composite pushout specimen with stud and channel shear connector

To investigate the behaviour of composite action with various shear connectors, push-out tests were performed for eight specimens. Test parameters includes are type of shear connector (headed stud connector and channel connector), number of connectors (one and two) and specimen with or without decking sheet. Test results showed that performance of the push-out specimens depends greatly on type of connector and decking sheet. From the experimental study it was observed that the performance and shear capacity of channel connector was 60 % more than the stud connector. The shear resistance between the steel and concrete was enhanced up to 50 % for the push out specimen without decking. The specimen with two numbers of stud and channel connector increases the strength by 58% and 23% respectively as compared to specimen with single connector. The behaviour of the push out specimen was stimulated by three-dimensional finite element model using software ANSYS workbench. The analytical behaviour was well agreement with the real push out specimen studied experimentally

Mutation induced enhanced biosynthesis of lipase

The purpose of the present investigation is to enhance production of biomedically important enzyme lipase by subjecting the indigenous lipase producing strain Rhizopus sp. BTS-24 to improvement by natural selection and random mutagenesis (UV and N-methyl-N'-nitro-N-nitroso guanidine, NTG). The isolation of mutants and the lipolytic activity of selected mutants were described. The best natural selectant BTNS12 showed 110% higher lipase activity than the wild strain (BTS-24). The lipase yield of the best UV mutant BTUV3 was 164% higher than the parent strain (BTNS12) and 180% times higher than the wild strain (BTS-24). Also, the lipase yield of the best NTG mutant BTNT2 was 133 % higher than the parent strain (BTUV3) and 232% higher than the wild strain (BTS-24). The results indicated that UV and NTG were effective mutagenic agents for strain improvement of Rhizopus sp. BTS-24 for enhanced lipase productivity. Key Words: Lipase, Rhizopus, UV, NTG. African Journal of Biotechnology Vol.3(11) 2004: 618-62

Dimension Reduction via Colour Refinement

Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into "colour classes" in such a way that all vertices in the same colour class have the same number of neighbours in every colour class. Tinhofer (Disc. App. Math., 1991), Ramana, Scheinerman, and Ullman (Disc. Math., 1994) and Godsil (Lin. Alg. and its App., 1997) established a tight correspondence between colour refinement and fractional isomorphisms of graphs, which are solutions to the LP relaxation of a natural ILP formulation of graph isomorphism. We introduce a version of colour refinement for matrices and extend existing quasilinear algorithms for computing the colour classes. Then we generalise the correspondence between colour refinement and fractional automorphisms and develop a theory of fractional automorphisms and isomorphisms of matrices. We apply our results to reduce the dimensions of systems of linear equations and linear programs. Specifically, we show that any given LP L can efficiently be transformed into a (potentially) smaller LP L' whose number of variables and constraints is the number of colour classes of the colour refinement algorithm, applied to a matrix associated with the LP. The transformation is such that we can easily (by a linear mapping) map both feasible and optimal solutions back and forth between the two LPs. We demonstrate empirically that colour refinement can indeed greatly reduce the cost of solving linear programs

An Improved Face Recognition Using Neighborhood Defined Modular Phase Congruency Based Kernel PCA

A face recognition algorithm based on NMPKPCA algorithm presented in this paper. The proposed algorithm when compared with conventional Principal component analysis (PCA) algorithms has an improved recognition Rate for face images with large variations in illumination, facial expressions. In this technique, first phase congruency features are extracted from the face image so that effects due to illumination variations are avoided by considering phase component of image. Then, face images are divided into small sub images and the kernel PCA approach is applied to each of these sub images. but, dividing into small or large modules creates some problems in recognition. So a special modulation called neighborhood defined modularization approach presented in this paper, so that effects due to facial variations are avoided. Then, kernel PCA has been applied to each module to extract features. So a feature extraction technique for improving recognition accuracy of a visual image based facial recognition system presented in this paper

Lossless Linear Integer signal Resampling

This paper describes about signal resampling based on polynomial interpolation is reversible for all types of signals, i.e., the original signal can be reconstructed losslessly from the resampled data. This paper also discusses Matrix factorization method for reversible uniform shifted resampling and uniform scaled and shifted resampling. Generally, signal resampling is considered to be irreversible process except in some special cases because of strong attenuation of high frequency components. The matrix factorization method is actually a new way to compute linear transform. The factorization yields three elementary integer-reversible matrices. This method is actually a lossless integer-reversible implementation of linear transform. Some examples of lower order resampling solutions are also presented in this paper