Studies in Ultrafine Particle Production

Ultra fine grinding has attracted many industries for the better product quality. It has been seen that new developments in electronic industries have demand for the desired size distribution (narrow distribution) offine sizes. Attrition mill has specific advantage over other conventional milling equipment such as Ball Mill and fluid energy mill due to the energy saving in the combination process. An attempt has been made to study the performance of grinding in a laboratory Attrition millfor the control of the product size distribution.The experiments were carried in the laboratory Attrition mill and the effect of ball size distribution on product size distribution was studied. The study was concentrated in the estimation of the comm inution functions such as specific rate grinding by experimental techniques. The experimentally estimated breakage distribution functions were used to predict the rate of grinding, and the product size distribution

Supersolid and solitonic phases in one-dimensional Extended Bose-Hubbard model

We report our findings on quantum phase transitions in cold bosonic atoms in a one dimensional optical lattice using the finite size density matrix renormalization group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest neighbor interactions. At commensurate fillings, we obtain two different types of charge density wave phases and a Mott insulator phase. However, departure from commensurate fillings yield the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain signatures for solitary waves and also superfluidity.Comment: 7 pages, 11 figure

On Nori's Fundamental Group Scheme

We determine the quotient category which is the representation category of the kernel of the homomorphism from Nori's fundamental group scheme to its \'etale and local parts. Pierre Deligne pointed out an error in the first version of this article. We profoundly thank him, in particular for sending us his enlightning example reproduced in Remark 2.4 2).Comment: 29 page

Predicting Short-term MCI-to-AD Progression Using Imaging, CSF, Genetic Factors, Cognitive Resilience, and Demographics.

In the Alzheimer’s disease (AD) continuum, the prodromal state of mild cognitive impairment (MCI) precedes AD dementia and identifying MCI individuals at risk of progression is important for clinical management. Our goal was to develop generalizable multivariate models that integrate highdimensional data (multimodal neuroimaging and cerebrospinal fuid biomarkers, genetic factors, and measures of cognitive resilience) for identifcation of MCI individuals who progress to AD within 3 years. Our main fndings were i) we were able to build generalizable models with clinically relevant accuracy (~93%) for identifying MCI individuals who progress to AD within 3 years; ii) markers of AD pathophysiology (amyloid, tau, neuronal injury) accounted for large shares of the variance in predicting progression; iii) our methodology allowed us to discover that expression of CR1 (complement receptor 1), an AD susceptibility gene involved in immune pathways, uniquely added independent predictive value. This work highlights the value of optimized machine learning approaches for analyzing multimodal patient information for making predictive assessments

On semistable principal bundles over a complex projective manifold, II

Let (X, \omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.Comment: 15 page