Dunkl operators and a family of realizations of osp(1|2)

In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects of this operator are studied, such as the associated measure, the related Laguerre polynomials and the related Fourier transform. For special values of the parameters, it is possible to construct the kernel of the Fourier transform explicitly, as well as the related intertwining operator.Comment: 28 pages, some small changes, accepted in Trans. Amer. Math. So

Spherical harmonics and integration in superspace

In this paper the classical theory of spherical harmonics in R^m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of this operator, a new type of integration over the supersphere is introduced by exploiting the formal equivalence with an old result of Pizzetti. This integral is then used to prove orthogonality of spherical harmonics of different degree, Green-like theorems and also an extension of the important Funk-Hecke theorem to superspace. Finally, this integration over the supersphere is used to define an integral over the whole superspace and it is proven that this is equivalent with the Berezin integral, thus providing a more sound definition of the Berezin integral.Comment: 22 pages, accepted for publication in J. Phys.

Superspace realizations of the Bannai-Ito algebra

A model of the Bannai-Ito algebra in a superspace is introduced. It is obtained from the three-fold tensor product of the basic realization of the Lie superalgebra $osp(1|2)$ in terms of operators in one continuous and one Grassmanian variable. The basis vectors of the resulting Bannai-Ito algebra module involve Jacobi polynomials

Cloning and expression analysis of a blue copperbinding protein gene from Dasypyrum Villosum

Adifferentially expressed fragment EST145 was isolated by suppression subtractive hybridization (SSH) method. Using EST145 as the probe, a blue copper-binding protein gene designated as DvBCB was screened from Dasypyrum villosum cDNA Library. The DvBCB gene was 845 bp in length with an open reading frame (ORF) which encoded a 178-amino acid polypeptide and contained the deduced functional sites: H66, C107, H112 and M121. Northern blot analysis showed that, the expression of DvBCB gene was enhanced in leaves after inoculation with Erysiphe graminis; reached a peak level at 24 h and decreased to constitutive level at 72 h after inoculation in resistant Gh21 line. The expression level in susceptible mutant M14S line was slightly lower than that in the resistant Gh21 line at all stages after inoculation, and the peak could not appear in M14S line. The function of DvBCB gene might include lignification of cell wall or scavenging of reactive oxygen species (ROS) during powdery mildew attack.Key words: Dasypyrum villosum, powdery mildew, suppression subtractive hybridization, blue copper-binding protein gene

Perancangan Buku Visual Grafis Tentang Pola Makan Food Combining

Perancangan Buku Visual Grafis tentang Pola Makan Food Combining ini bertujuan untuk membuat sebuah buku visual yang mengangkat tema pola makan yang sehat. Buku ini menggunakan pendekatan visual yang bertujuan untuk memberikan arahan atau sekedar menjadi pendukung visual sehingga lebih menarik. Perancangan Buku Visual Grafis tentang Pola Makan Food Combining ini mencakup desain cover buku dan isi buku yang dirancang secara komunikatif. Dengan pendekatan komunikasi visual dalam sebuah buku tentang pola makan diharapkan dapat mempermudah pembaca untuk memahami dan menerima informasi dari buku tersebut

Tuberculosis of pancreas and peripancreatic lymph nodes in immunocompetent patients: Experience from China

Aim: To determine the clinical, radiographic and laboratory characteristics, diagnostic methods, and therapeutic variables in immunocompetent patients with tuberculosis (TB) of the pancreas and peripancreatic lymph nodes. Methods: The records of 16 patients (6 male, 10 female; mean age 37 years, range 18-56years) with tuberculosis of the pancreas and peripancreatic lymph nodes from 1983 to 2001 in the Southwest Hospital were analyzed retrospectively. In addition, 58 similar cases published in Chinese literature were reviewed and summarized. We reviewed the clinical, radiographic and laboratory findings, diagnostic methods, therapeutic approaches, and outcome in the patients. Criteria for the diagnosis of pancreatic tuberculosis were the presence of granuloma in histological sections or the presence of Mycobacterium tuberculosis DNA by polymerase chain reaction (PCR). Results: Predominant symptoms consisted of abdominal nodule and pain (75 %), anorexia/weight loss (69 %), malaise/weakness (64 %), fever and night sweats (50 %), back pain (38 %) and jaundice (31 %). Swelling of the head of the pancreas with heterogeneous attenuation echo was detected with ultrasound in 75 % (12/16). CT scan showed pancreatic mass with heterogeneous hypodensity focus in all patients, with calcification in 56 % (9/16) patients, and peripancreatic nodules in 38 % (6/16) patients. Anemia and lymphocytopenia were seen in 50 % (8/16) patients, and pancytopenia occurred in 13 % (2/ 16) patients. Hypertransaminasemia, elevated alkaline phosphatase (AP) and GGT were seen in 56 % (9/16) patients. The erythrocyte sedimentation rate (ESR) was elevated in 69 % (11/16) cases. Granulomas were found in 75 % (12/16) cases, and in 38 % (6/16) cases caseous necrosis tissue was found. Laparotomy was performed in 75 % (12/16) cases, and ultrasound-guided fine needle aspiration (FNA) was done in 63 % (10 of 16). The most commonly used combinations of medications were isoniazid/rifampin/streptomycin (63 %, n=10) and isoniazid/rifampin pyrazinamide/streptomycin or ethambutol (38 %, n=6). The duration of treatment lasted for half or one year and treatment was successful in all cases. The characteristics of 58 cases from Chinese literature were also summarized. Conclusion: Tuberculosis of the pancreas and peripancreatic lymph nodes should be considered as a diagnostic possibility in patients presenting with a pancreatic mass, and diagnosis without laparotomy is possible if only doctors are aware of its clinical features and investigate it with appropriate modalities. Pancreatic tuberculosis can be effectively cured by antituberculous drugs.published_or_final_versio