A Polymatroid Approach to Generalized Weights of Rank Metric Codes

We consider the notion of a $(q,m)$-polymatroid, due to Shiromoto, and the more general notion of $(q,m)$-demi-polymatroid, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality for generalized Hamming weights of linear codes. The corresponding results of Ravagnani for Delsarte rank metric codes, and Martinez-Penas and Matsumoto for relative generalized rank weights are derived as a consequence.Comment: 22 pages; with minor revisions in the previous versio

Arithmetic Progressions in a Unique Factorization Domain

Pillai showed that any sequence of consecutive integers with at most 16 terms possesses one term that is relatively prime to all the others. We give a new proof of a slight generalization of this result to arithmetic progressions of integers and further extend it to arithmetic progressions in unique factorization domains of characteristic zero.Comment: Version 2 (to appear in Acta Arithmetica) with minor typos correcte

Computation of the aa-invariant of ladder determinantal rings

We solve the problem of effectively computing the $a$-invariant of ladder determinantal rings. In the case of a one-sided ladder, we provide a compact formula, while, for a large family of two-sided ladders, we provide an algorithmic solution.Comment: AmS-LaTeX, 20 pages; minor improvements of presentatio

Culture Positive Brucella Endocarditis in a Case of Baloon Mitral Valvotomy

Brucella endocarditis is a rare condition which occurs as a focal complication in chronic brucellosis cases. We report a rare brucella endocarditis case in a RVHD patient. A 26 years old male was admitted with fever on off for almost one year. The blood culture yielded growth of Brucella melitensis after ten days of incubation. Isolated colonies were reconfirmed as Brucella species by PCR study. Patient’s serum tested positive for brucella slide agglutination test and STAT titer was 640IU. Echocardiography showed vegetation on mitral valve. Patient was treated with both medical and surgical intervention. After chemotherapy, patient’s blood culture was sterile, slide agglutination & STAT (40IU) were negative. Repeat echocardiography showed no fresh vegetation. Considering high mortality rate (80%) in Brucella endocarditis, it is very important for clinicians to suspect it. Prompt antibiotic therapy and surgical intervention is life saving in fatal cases

Automorphism groups of Grassmann codes

We use a theorem of Chow (1949) on line-preserving bijections of Grassmannians to determine the automorphism group of Grassmann codes. Further, we analyze the automorphisms of the big cell of a Grassmannian and then use it to settle an open question of Beelen et al. (2010) concerning the permutation automorphism groups of affine Grassmann codes. Finally, we prove an analogue of Chow's theorem for the case of Schubert divisors in Grassmannians and then use it to determine the automorphism group of linear codes associated to such Schubert divisors. In the course of this work, we also give an alternative short proof of MacWilliams theorem concerning the equivalence of linear codes and a characterization of maximal linear subspaces of Schubert divisors in Grassmannians.Comment: revised versio

Cellulitis Due to Salmonella infantis.

Bacteria of the genus Salmonella are highly adapted for the growth in both humans and animals and cause a wide spectrum of disease. The growth of Serotypes S. typhi and S. paratyphi is restricted to human hosts, in whom these organisms cause enteric (typhoid) fever. The remaining Serotypes (non typhoidal Salmonella or NTS) can colonize the gastrointestinal tracts of the broad range of animals, including mammals, reptiles, birds and insects. The usual clinical presentation of non-typhoidal salmonellae (NTS) infection is self limited gastroenteritis; however bacteremia and focal extra intestinal infection may occur. However salmonella localization to the skin presenting as cutaneous ulceration is regarded as a rare event. Rates of morbidity and mortality associated with NTS are highest among the elderly, infants, and immunocompromised individuals, including those with hemoglobinopathies, HIV infection, or infections that cause blockade of the reticuloendothelial system. We isolated S.infantis in 50 years old man with left leg cellulitis. The serotype was confirmed at Central Research Institute, Kasauli