Hawking Radiation as Tunneling

We present a short and direct derivation of Hawking radiation as a tunneling process, based on particles in a dynamical geometry. The imaginary part of the action for the classically forbidden process is related to the Boltzmann factor for emission at the Hawking temperature. Because the derivation respects conservation laws, the exact spectrum is not precisely thermal. We compare and contrast the problem of spontaneous emission of charged particles from a charged conductor.Comment: LaTeX, 10 pages; v2. journal version, added section on relation of black hole radiation to electric charge emission from a charged conducting sphere; v3. restored cut referenc

Beneficiation studies on Bolani iron ore

The iron ore washing plants generate slime on an average of 10 - 20% by weight of the ore and is wasted. Apart from loss of resource, these slimes pose problem of disposal and consequent damage to environment. To reduce problems of slime, it should be treated, as a part of beneficiation, to minimise waste generation. Out of five number of different varieties of Bolani iron ore bulk samples, two bulk composite samples were prepared in the proportions as decided by the sponsor. The first sample was found to be of very good quality assaying 66.69% Fe, 1.27% SiO, and 1.8% Al,O and only crushing and sizing (dry) were done for physical characterisation. The second sample (assaying 63.68% Fe, 2.05% SiO, and 2.6% AI,O,) was beneficiated to produce washed lump weighing 49.9% and with assay of 65.0% Fe. 1.8% SiO, and 2.1% Al,Or Combined fines weighed 42.7% assaying 63.95% Fe, 1.81% Si02 and 2.54% A1,03 leaving slime reject 7.4% by weight and assaying 51.27 % Fe, 5.6 % SiO, and 8.82% Al,O3 which not only reduced waste generation but improved recovery also

Reduction of Environment Pollution in Processing of Barite

One of the largest indigenous manufacturing plants of barium chemicals is located at Cuddapah in Andhra Pradesh. During production of barium carbonate, two types of rejects (flue ash and sludge) have been generated and accumulate for last few decades at the Cuddapah plant. Earlier, briquetting of charge was suggested to restrict physical losses of material as flue ash. Afterwards, to generate product having > 90% barium sulphate which could be reused, studies have been carried out with the rejects currently produced. Detailed investigations suggested seperate treatment of sludge because the flue ash sample was found to be suitable as feed to the reduction circuit. Both gravity and flotation processes were found to generate product meeting specification. It was also found that more than 55% of the combined rejects currently generated at Cuddapah plant could be used again for the production of barium carbonate. In the process, recovey of barite value could be more than 64

Extremes of multitype branching random walks: Heaviest tail wins

We consider a branching random walk on a multi(Q)-type, supercritical Galton-Watson tree which satisfies Kesten-Stigum condition. We assume that the displacements associated with the particles of type Q have regularly varying tails of index α, while the other types of particles have lighter tails than that of particles of type Q. In this article, we derive the weak limit of the sequence of point processes associated with the positions of the particles in the nth generation. We verify that the limiting point process is a randomly scaled scale-decorated Poisson point process (SScDPPP) using the tools developed in \cite{bhattacharya:hazra:roy:2016}. As a consequence, we shall obtain the asymptotic distribution of the position of the rightmost particle in the nth generation

Extremes of multitype branching random walks: Heaviest tail wins

We consider a branching random walk on a multitype (with Q types of particles), supercritical Galton-Watson tree which satisfies the Kesten-Stigum condition. We assume that the displacements associated with the particles of type Q have regularly varying tails of index α, while the other types of particles have lighter tails than the particles of type Q. In this paper we derive the weak limit of the sequence of point processes associated with the positions of the particles in the nth generation. We verify that the limiting point process is a randomly scaled scale-decorated Poisson point process using the tools developed by Bhattacharya, Hazra, and Roy (2018). As a consequence, we obtain the asymptotic distribution of the position of the rightmost particle in the nth generation

Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms

Given any smooth toric surface S, we prove a SYM-HILB correspondence which relates the 3-point, degree zero, extended Gromov-Witten invariants of the n-fold symmetric product stack [Sym^n(S)] of S to the 3-point extremal Gromov-Witten invariants of the Hilbert scheme Hilb^n(S) of n points on S. As we do not specialize the values of the quantum parameters involved, this result proves a strengthening of Ruan's Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphism from Hilb^n(S) to Sym^n(S) and yields a method of reconstructing the cup product for Hilb^n(S) from the orbifold invariants of [Sym^n(S)].Comment: Revised versio

Minerological aspects of lead sintering

A brief overview on lead sinter microstructure is presented. Characteristic micro-structural features of a good and bad sinter are highlighted and these are used in a case study involving use of a low grade and complex concentrate of lead (-40% Pb) in the sintering operation. The plant sinter produced exhibited low strength and its nticrostructural examination revealed non-uniform distribution of porosity along with unsintered galena and low melting lead silicate phase. Part replacement of limestone by lime helped in producing sinter with good physical properties and desirable microstructure. The sinter with modified feed chemistry had more uniform distribution of porosity and presence of primarily a Pb-Fe silicate phase characterised by a (Pb+Fe):Si mole ratio of 3:1. Ca-Pb-Zn-Fe-Al-silicate phase identified as hardysonite and a spine! phase of the type (Fe,Zn)O.(Fe,Al),OJ. Lead nietal/oxide/sulphide occurred in the sinter only rarely. The likely implications of lime addition to the sinter charge mix are discussed Key Words: Lead. Complex and low grade concentrate. Sintering. Process Mineralog

Curve counting via stable pairs in the derived category

For a nonsingular projective 3-fold $X$, we define integer invariants virtually enumerating pairs $(C,D)$ where $C\subset X$ is an embedded curve and $D\subset C$ is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of $X$. The resulting invariants are conjecturally equivalent, after universal transformations, to both the Gromov-Witten and DT theories of $X$. For Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing formula in the derived category. Several calculations of the new invariants are carried out. In the Fano case, the local contributions of nonsingular embedded curves are found. In the local toric Calabi-Yau case, a completely new form of the topological vertex is described. The virtual enumeration of pairs is closely related to the geometry underlying the BPS state counts of Gopakumar and Vafa. We prove that our integrality predictions for Gromov-Witten invariants agree with the BPS integrality. Conversely, the BPS geometry imposes strong conditions on the enumeration of pairs.Comment: Corrected typos and duality error in Proposition 4.6. 47 page

Designing Flotation Process for Lead-Zinc ore from Nepal

The paper deals with the development of a process based on froth flotation for the concentration of a lead-zinc ore from Ganesh-Himal region of Nepal. A detailed chara-cterisation and flotation studies were carried out under the varying process conditions. The ore was predomionantly made up of sphalerite and pyrite in association with sub-ordinate amount of galena, minor amount of pyrrhotite and chalcopyrite with dolomite as the major gangue. Under the optimum process conditions the rougher lead and zinc recovery were 96.3% and 90.8% respectively. Regrinding followed by three stage cleaning of the lead rougher conc-entrate resulted in cleaner concentrate assaying 79.11 % Pb with 83.4% recovery. Similarly two stage cleaning of the zinc rougher concentrate produced cleaner concentrate analysing 60.08% Zn with 80.4% recovery. Based on the studies undertaken a process flow-sheet for the conc-entration of the ore to individual lead and zinc concen-trates has been recommended

Multi-Class Clustering of Cancer Subtypes through SVM Based Ensemble of Pareto-Optimal Solutions for Gene Marker Identification

With the advancement of microarray technology, it is now possible to study the expression profiles of thousands of genes across different experimental conditions or tissue samples simultaneously. Microarray cancer datasets, organized as samples versus genes fashion, are being used for classification of tissue samples into benign and malignant or their subtypes. They are also useful for identifying potential gene markers for each cancer subtype, which helps in successful diagnosis of particular cancer types. In this article, we have presented an unsupervised cancer classification technique based on multiobjective genetic clustering of the tissue samples. In this regard, a real-coded encoding of the cluster centers is used and cluster compactness and separation are simultaneously optimized. The resultant set of near-Pareto-optimal solutions contains a number of non-dominated solutions. A novel approach to combine the clustering information possessed by the non-dominated solutions through Support Vector Machine (SVM) classifier has been proposed. Final clustering is obtained by consensus among the clusterings yielded by different kernel functions. The performance of the proposed multiobjective clustering method has been compared with that of several other microarray clustering algorithms for three publicly available benchmark cancer datasets. Moreover, statistical significance tests have been conducted to establish the statistical superiority of the proposed clustering method. Furthermore, relevant gene markers have been identified using the clustering result produced by the proposed clustering method and demonstrated visually. Biological relationships among the gene markers are also studied based on gene ontology. The results obtained are found to be promising and can possibly have important impact in the area of unsupervised cancer classification as well as gene marker identification for multiple cancer subtypes