Hodge rank of ACM bundles and Franchetta's conjecture

We prove that on a general hypersurface in $\mathbb{P}^N$ of degree $d$ and dimension at least $2$, if an arithmetically Cohen-Macaulay (ACM) bundle $E$ and its dual have small regularity, then any non-trivial Hodge class in $H^{n}(X, E\otimes\Omega^n_X)$, $n = \lfloor\frac{N-1}{2}\rfloor$, produces a trivial direct summand of $E$. As a consequence, we prove that there is no universal Ulrich bundle on the family of smooth hypersurfaces of degree $d\geq 3$ and dimension at least $4$. This last statement may be viewed as a Franchetta-type conjecture for Ulrich bundles on smooth hypersurfaces.Comment: 16 pages, final version, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (to appear

A Budget Planning Model for Health Care Hospitals

This paper is devoted to the application of goal programming to Health care planning. More specifically, the paper presents the goal programming approach to the budget planning of health care Hospitals and drawing valid decisions for further improvement in future not only for healthcare but also for quality healthcare administration and resources. Key Words: Financial Catastrophe, Business Manager, Optimization Techniques, Health Servic

Image Processing Technique for Authentication of Indian Paper Currency

As we all know day by day the technology is getting better and better, the production of counterfeit currency has been rapidly increasing. The counterfeit currency problem is faced by almost all countries. Since the real economy is affected, it has affected the economy of the country. Even when the drastic step of demonetization was taken in 2016 to overcome counterfeit currency, this problem did not end.  The only one solution for this problem for a common man is to detect the fake currency, by using the fake currency detector machine. These machines are used in banks and large scale business, but for small scale businesses or for a common man  these machines are not affordable. There are lot of  researches taking place on this matter by using deep learning, image processing and machine learning techniques. This paper  gives  the complete methodology of fake note detector machine,  which is affordable even for a common man.  By  implementing the applications of image processing  techniques  we  can  find  out whether  the  currency  notes  are  fake  or not.  Image  processing  technique  consists  of  a  number  of operations  that  can  be  performed  on  an  image,  some  of  which  include  image  segmentation,  edge detection,  gray  scale  conversion,  pre-processing etc.  The  proposed  system  will detect the  counterfeit currency of new denominations by distinguishing each denomination based on its size and depending on the features of each currency the comparison takes place. Based on the features matched, it detects whether the currency is counterfeit or not. The system have advantages like simplicity, reliability and cost effective. Which is affordable by a common man since the common man is the one who will be effected most, when the counterfeit currency are circulated in the market because he has to pay the real value of that currency

Generators for vector bundles on generic hypersurfaces

We prove that on a generic hypersurface in Pm+1 of dimension at least 3, a vector bundle with r ≤ m generators must be split if m is odd. If m is even, then the same is true if the degree of X is at least 3

Remarks on higher-rank ACM bundles on hypersurfaces

In terms of the number of generators, one of the simplest non-split rank-3 arithmetically Cohen–Macaulay bundles on a smooth hypersurface in P5 is 6-generated. We prove that a general hypersurface in P5 of degree d≥3 does not support such a bundle. We also prove that a smooth positive dimensional hypersurface in projective space of even degree does not support an Ulrich bundle of odd rank and determinant of the form OX(c) for some integer c. This verifies some cases of conjectures we discuss here