Restriction of Odd Degree Characters of Sn\mathfrak{S}_n

Let $n$ and $k$ be natural numbers such that $2^k < n$. We study the restriction to $\mathfrak{S}_{n-2^k}$ of odd-degree irreducible characters of the symmetric group $\mathfrak{S}_n$. This analysis completes the study begun in [Ayyer A., Prasad A., Spallone S., Sem. Lothar. Combin. 75 (2015), Art. B75g, 13 pages] and recently developed in [Isaacs I.M., Navarro G., Olsson J.B., Tiep P.H., J. Algebra 478 (2017), 271-282]

“Tax Simplification”—Grave Threat to the Charitable Contribution Deduction: The Problem and a Proposed Solution

The present National Administration has continued to support proposed legislative changes aimed at substantially reducing the number of income tax returns in which deductions are itemized. The author contends that these tax simplification proposals are incompatible with the preservation of the charitable contribution deduction and would undermine the position of voluntary charitable organizations by reducing the incentives for giving. He proposes a solution to this dilemma by promoting the charitable contribution deduction, with certain limitations, to the position of a deduction from gross income, rather than a deduction from adjusted gross income

Volume Analysis of the Proximal Tibial Metaphysis

Purpose The Vitrea 2 imaging software (Vital Images Inc, Minnetonka, MN) was used for the volume analysis of the proximal tibial metaphysis. Materials and Methods Eighteen computed tomography scans of the proximal tibia were processed through the software, and 3-dimensional imaging of the proximal tibia was reconstructed. Results The volume and area of the proximal tibia that were generated resulted in a mean area of 127 cm2 and a mean volume of 77.2 cm2. Conclusion This study supports the use of the proximal tibial metaphysis as a source of low to moderate volume of autologous bone. When compared with the accepted average volume of 25 cm2, the computed results showed that there could be up to 3 times the amount of bone available in the proximal tibial metaphysis. The reported volume of bone harvested from previous studies was based on need and not the total amount available; subsequently, the results showed the possibility of a larger resource of bone, which provides the surgeon with the volumetrical limits of the proximal tibia metaphysis

Complex group algebras of the double covers of the symmetric and alternating groups

We prove that the double covers of the alternating and symmetric groups are determined by their complex group algebras. To be more precise, let $n\geq 5$ be an integer, $G$ a finite group, and let \AAA and \SSS^\pm denote the double covers of \Al_n and \Sy_n, respectively. We prove that \CC G\cong \CC \AAA if and only if G\cong \AAA, and \CC G\cong \CC \SSS^+\cong\CC\SSS^- if and only if G\cong \SSS^+ or \SSS^-. This in particular completes the proof of a conjecture proposed by the second and fourth authors that every finite quasi-simple group is determined uniquely up to isomorphism by the structure of its complex group algebra. The known results on prime power degrees and relatively small degrees of irreducible (linear and projective) representations of the symmetric and alternating groups together with the classification of finite simple groups play an essential role in the proofs.Comment: 27 pages, the previous version is revised slightly, to appear in Algebra & Number Theor

The Pion-Nucleon coupling constant from np charge exchange scattering

A novel extrapolation method has been used to deduce the charged Pion-Nucleon coupling constant from backward $np$ differential scattering cross sections. We applied it to new measurements performed at 162 MeV at the The Svedberg Laboratory in Uppsala. In the angular range $150^\circ-180^\circ$, the carefully normalized data are steeper than those of most previous measurements. The extracted value, $g^2_{\pi^\pm} = 14.52 \pm 0.26$, in good agreement with the classical value, is higher than those determined in recent nucleon-nucleon partial-wave analyses.Comment: 6 pages, 3 encapsulated figures, epsfig, menu97.cls (included

Semi-leptonic B decays into higher charmed resonances

We apply HQET to semi-leptonic $B$ meson decays into a variety of excited charm states. Using three realistic meson models with fermionic light degrees of freedom, we examine the extent that the sum of exclusive single charmed states account for the inclusive semi-leptonic $B$ decay rate. The consistency of form factors with the Bjorken and Voloshin sum rules is also investigated.Comment: Latex, 27 pages. A few references and errors corrected, to appear in Phys. Rev.