The Selberg integral and Young books

The Selberg integral is an important integral first evaluated by Selberg in 1944. Stanley found a combinatorial interpretation of the Selberg integral in terms of permutations. In this paper, new combinatorial objects "Young books" are introduced and shown to have a connection with the Selberg integral. This connection gives an enumeration formula for Young books. It is shown that special cases of Young books become standard Young tableaux of various shapes: shifted staircases, squares, certain skew shapes, and certain truncated shapes. As a consequence, product formulas for the number of standard Young tableaux of these shapes are obtained.Comment: 13 pages, 11 figure

The Selberg integral and Young books

The Selberg integral is an important integral first evaluated by Selberg in 1944. Stanley found a combinatorial interpretation of the Selberg integral in terms of permutations. In this paper, new combinatorial objects "Young books'' are introduced and shown to have a connection with the Selberg integral. This connection gives an enumeration formula for Young books. It is shown that special cases of Young books become standard Young tableaux of various shapes: shifted staircases, squares, certain skew shapes, and certain truncated shapes. As a consequence, enumeration formulas for standard Young tableaux of these shapes are obtained

Modeling of asymmetric giant magnetoimpedance in amorphous ribbons with a surface crystalline layer

A model describing the asymmetric giant magnetoimpedance (GMI) in field-annealed amorphous ribbons is proposed. It is assumed that the ribbon consists of an inner amorphous core and surface hard magnetic crystalline layers. The model is based on a simultaneous solution of linearizied Maxwell equations and Landau-Lifshitz equation. The coupling between the surface layers and the amorphous core is described in terms of an effective bias field. Analytical expressions for the frequency and field dependences of the ribbon impedance are found. The calculated dependences are in a qualitative agreement with results of experimental studies of the high-frequency asymmetric giant GMI in field-annealed amorphous ribbons.Comment: 13 pages, 3 figure

Injection scheme with deflecting cavity for a fourth-generation storage ring

We suggest a new on-axis injection scheme that uses a transverse deflecting rf cavity to kick the incoming beam into an already populated bucket but with a timing offset from the synchronous phase. In a new on-axis injection scheme, two deflecting rf cavities are required: one upstream of the injection point that crabs the stored beam and the other downstream of the injection point that both uncrabs the stored beam and kicks the incoming beam onto the axis of the orbital plane. We present a theoretical analysis and numerical simulations of the stored beam and injected beam with the new injection scheme.11Ysciescopu

Application of Virtual and Augmented Reality to the Field of Adult Education

This research reviews the extant literature and web resources on Virtual Reality (VR) and Augmented Reality (AR) to provide new insights and future direction of adult learning. Based on the review, we discuss implications for research and practice on the use of VR and AR in the field of Adult Education

Percutaneous Full Endoscopic Ligamentum Flavum Splitting Interlaminar Approach for Removal of Dorsally Migrated Lumbar Disc Herniation: A case Report with Technical Note

Treatment of dorsally migrated lumbar disc described so far commonly in present literature is removal by open technique through hemi or complete laminectomy or by use of microsurgical technique or by partial use of endoscope without use of irrigation system. We present a case of dorsally migrated disc herniation treated safely with good outcome by Percutaneous Full Endoscopic Ligamentum Flavum Splitting Interlaminar Approach. A 60 years old man presented with subacute onset of back pain and right leg radiating pain with weakness of right great toe dorsiflexion and diagnosed as a case of dorsally migrated L4-5 disc herniation was treated with this technique. He had also subtle instability at that level.His pain resolved immediately after surgery. Weakness of right great toe also resolved gradually in 2 months. Postoperative X-ray showed no further instability. Postoperative MRI revealed complete removal of disc with resolution of cauda equina compression. No complication was noted related to this technique. This new technique ultimately preserves motion segment while simultaneously addressing symptomatic pathology of dorsally migrated HNP with added benefits of minimally invasive spine surgery

RECYCLING PROCESS OF U3O8 POWDER IN MnO-Al2O3 DOPED LARGE GRAIN UO2 PELLETS

The effect of various process variables on the powder properties of recycled U3O8 from MnO-Al2O3 doped large grain UO2 pellets and the effect of those recycled U3O8 powders on the sintered density and grain size of MnO-Al2O3 doped large grain UO2 pellets have been investigated. The evolution of morphology, size, and BET surface area of the recycled U3O8 powders according to the respective variation of the thermo-mechanical treatment variables of oxidation temperature, powder milling, and sequential cyclic heat treatment of oxidation and then reduction was examined. The correlation between the BET surface area of recycled U3O8 powder and the sintered pellet properties of MnO-Al2O3 doped pellets showed that the pellet density and grain size of doped pellets were increased and then saturated by increasing the BET surface area of the recycled U3O8 powder. The density and grain size of the pellets were maximized when the BET surface area of the recycled U3O8 powder was in the vicinity of 3m2/g. Among the process variables applied in this study, the cyclic heat treatment followed by low temperature oxidation was a potential process combination to obtain the sinter-active U3O8 powder