Multiplicity one theorems: the Archimedean case

Let $G$ be one of the classical Lie groups \GL_{n+1}(\R), \GL_{n+1}(\C), \oU(p,q+1), \oO(p,q+1), \oO_{n+1}(\C), \SO(p,q+1), \SO_{n+1}(\C), and let $G'$ be respectively the subgroup \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \oO(p,q), \oO_n(\C), \SO(p,q), \SO_n(\C), embedded in $G$ in the standard way. We show that every irreducible Casselman-Wallach representation of $G'$ occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of $G$. Similar results are proved for the Jacobi groups \GL_{n}(\R)\ltimes \oH_{2n+1}(\R), \GL_{n}(\C)\ltimes \oH_{2n+1}(\C), \oU(p,q)\ltimes \oH_{2p+2q+1}(\R), \Sp_{2n}(\R)\ltimes \oH_{2n+1}(\R), \Sp_{2n}(\C)\ltimes \oH_{2n+1}(\C), with their respective subgroups \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \Sp_{2n}(\R), \Sp_{2n}(\C).Comment: To appear in Annals of Mathematic

The sectional curvature remains positive when taking quotients by certain nonfree actions

We study some cases when the sectional curvature remains positive under the taking of quotients by certain nonfree isometric actions of Lie groups. We consider the actions of the groups $S^1$ and $S^3$ such that the quotient space can be endowed with a smooth structure using the fibrations $S^3/S^1{\simeq}S^2$ and $S^7/S^3\simeq S^4$. We prove that the quotient space carries a metric of positive sectional curvature, provided that the original metric has positive sectional curvature on all 2-planes orthogonal to the orbits of the action.Comment: 26 pages, 1 figure. Changed the spelling of the author's nam

Design Criteria for Zero Leakage Connectors for Launch Vehicles. Mathematical Model of Interface Sealing Phenomenon, Volume 2 Final Report

Mathematical model of interface sealing phenomenon in determining design criteria for zero leakage connectors for launch vehicle

Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions

We consider invariant Riemannian metrics on compact homogeneous spaces G/H where an intermediate subgroup K between G and H exists, so that the homogeneous space G/H is the total space of a Riemannian submersion. We study the question as to whether enlarging the fibers of the submersion by a constant scaling factor retains the nonnegative curvature in the case that the deformation starts at a normal homogeneous metric. We classify triples of groups (H,K,G) where nonnegative curvature is maintained for small deformations, using a criterion proved by Schwachh\"ofer and Tapp. We obtain a complete classification in case the subgroup H has full rank and an almost complete classification in the case of regular subgroups.Comment: 23 pages; minor revisions, to appear in Geometriae Dedicat

The Boss-Employee Relationship: Influence on Job Retention

This research paper explores and reveals the dynamic relationship between employees and their bosses as this relationship influences retention. Employee unhappiness has been cited as a common reason that an employee may leave his or her job; but unfortunately, a boss does not often realize that it is his or her own management style which may cause a valued employee to quit. Bosses who fail to retain their staff, end up costing the company anywhere from 90% to 200% of that employee’s annual salary. A primary conclusion of this research is that managers need to be educated; they are the link between a high potential employee staying or leaving the job. Managers have a large impact on their employees’ attitude toward their jobs, and their relationship with the employees remains the single greatest reason why employees leave organizations

Four-qubit entanglement from string theory

We invoke the black hole/qubit correspondence to derive the classification of four-qubit entanglement. The U-duality orbits resulting from timelike reduction of string theory from D=4 to D=3 yield 31 entanglement families, which reduce to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references adde

Constructing patch-based ligand-binding pocket database for predicting function of proteins

Background Many of solved tertiary structures of unknown functions do not have global sequence and structural similarities to proteins of known function. Often functional clues of unknown proteins can be obtained by predicting small ligand molecules that bind to the proteins. Methods In our previous work, we have developed an alignment free local surface-based pocket comparison method, named Patch-Surfer, which predicts ligand molecules that are likely to bind to a protein of interest. Given a query pocket in a protein, Patch-Surfer searches a database of known pockets and finds similar ones to the query. Here, we have extended the database of ligand binding pockets for Patch-Surfer to cover diverse types of binding ligands. Results and conclusion We selected 9393 representative pockets with 2707 different ligand types from the Protein Data Bank. We tested Patch-Surfer on the extended pocket database to predict binding ligand of 75 non-homologous proteins that bind one of seven different ligands. Patch-Surfer achieved the average enrichment factor at 0.1 percent of over 20.0. The results did not depend on the sequence similarity of the query protein to proteins in the database, indicating that Patch-Surfer can identify correct pockets even in the absence of known homologous structures in the database