On Real Solutions of the Equation Φ\u3csup\u3e\u3cem\u3et\u3c/em\u3e\u3c/sup\u3e (\u3cem\u3eA\u3c/em\u3e) = 1/\u3cem\u3en\u3c/em\u3e J\u3csub\u3e\u3cem\u3en\u3c/em\u3e\u3c/sub\u3e

For a class of n × n-matrices, we get related real solutions to the matrix equation Φt (A) = 1/n Jn by generalizing the approach of and applying the results of Zhang, Yang, and Cao [SIAM J. Matrix Anal. Appl., 21 (1999), pp. 642–645]. These solutions contain not only those obtained by Zhang, Yang, and Cao but also some which are neither diagonally nor permutation equivalent to those obtained by Zhang, Yang, and Cao. Therefore, the open problem proposed by Zhang, Yang, and Cao in the cited paper is solved

On discreteness of subgroups of quaternionic hyperbolic isometries

Let ${{\bf H}_{\mathbb H}}^n$ denote the $n$-dimensional quaternionic hyperbolic space. The linear group ${\rm{Sp}}(n,1)$ acts by the isometries of ${{\bf H}_{\mathbb H}}^n$. A subgroup $G$ of ${\rm {Sp}}(n,1)$ is called \emph{Zariski dense} if it does not fix a point on ${{\bf H}_{\mathbb H}}^n \cup \partial {{\bf H}_{\mathbb H}}^n$ and neither it preserves a totally geodesic subspace of ${{{\bf H}}_{\mathbb H}}^n$. We prove that a Zariski dense subgroup $G$ of ${\rm{ Sp}}(n,1)$ is discrete if for every loxodromic element $g \in G$ the two generator subgroup $\langle f, g f g^{-1} \rangle$ is discrete, where the generator $f \in {\rm{Sp}}(n,1)$ is certain fixed element not necessarily from $G$.Comment: Reformatted, adding new result, and removing some. Removed parts will be subsumed elsewher

The Shadow Side of Teaching Classroom as Organization

Classroom as organization (CAO) is an approach at the extreme end of an experiential learning intensity continuum (Sleeth & Brown, 1984). While proponents suggest they would never go back to a teacher-centered classroom, CAO has not become widely adopted since its initial description by Cohen (1976). We argue this is, in part, because of shadow elements that may discourage faculty in both initial adoption and persistence in the journey from novice to master. This article reports the authors reflexive process related to the shadow elements they encountered as early adopters of the CAO methodology. The paper begins with a brief background on CAO, followed by a discussion of shadow elements that manifest at the student and faculty levels. We include our recommendations for practice

Observing the Dark Scalar Doublet and its Impact on the Standard-Model Higgs Boson at Colliders

If the Standard Model of particle interactions is extended to include a second scalar doublet $[H^{+},(H^{0}+iA^{0})/\sqrt{2}]$, which is odd under an unbroken Z_{2} discrete symmetry, it may be called the $dark$ scalar doublet, because its lightest neutral member, say H^{0}, is one posssible component for the dark matter of the Universe. We discuss the general phenomenology of the four particles of this doublet, without assuming that H^{0} is the dominant source of dark matter. We also consider the impact of this $dark$ scalar doublet on the phenomenology of the SM Higgs boson h.Comment: PRD versio

CaO impregnated highly porous honeycomb activated carbon from agriculture waste: symmetrical supercapacitor study

This study presents the electrochemical studies of activated carbon prepared from palm kernel shell (ACPKS), with CaO impregnation. The CaO is obtained from chicken eggshell waste to produce CaO/ACPKS, which shows highly porous honeycomb structure with homogeneous distribution of CaO nanoparticles (30–50 nm in size). The prepared materials are evaluated as supercapacitor electrodes by testing their electrochemical characteristics. A high specific capacitance value of 222 F g−1 at 0.025 A g−1 is obtained for CaO/ACPKS, which is around three times higher than that for ACPKS (76 F g−1). In addition, electrochemical impedance data show lower impedance for CaO/ACPKS. Lastly, a practical symmetrical supercapacitor is fabricated by CaO/ACPKS and its performance is discussed

Fabrication of 45 degrees template grain boundary junctions using a CaO lift-off technique

45 degrees grain boundary junctions have been made using (100) MgO substrates, a CeO2 template layer and an YBa2Cu3O7 top layer. To minimize the damage to the MgO surface, which will occur if the CeO2 is structured using ion milling, the CeO2 layer has been structured using the CaO lift-off technique. Electrical measurements of these junctions as a function of temperature, microwave irradiation and magnetic field will be discussed in this paper

Scanning Tunneling Microscopy and Spectroscopy of Wet-Chemically Prepared Chlorinated Si(111) Surfaces

Chlorine-terminated Si(111) surfaces prepared through the wet-chemical treatment of H-terminated Si(111) surfaces with PCl_5 (in chlorobenzene) were investigated using ultrahigh vacuum scanning tunneling microscopy (UHV cryo-STM) and tunneling spectroscopy. STM images, collected at 77 K, revealed an unreconstructed 1 × 1 structure for the chlorination layer, consistent with what has been observed for the gas phase chlorination of H-terminated Si(111). However, the wet-chemical chlorination is shown to generate etch pits in the Si(111) surface, with an increase in etch pit density correlating with increasing PCl_5 exposure temperatures. These etch pits were assumed to stabilize the edge structure through the partial removal of the 〈112̄〉 step edges. Tunneling spectroscopy revealed a nonzero density of states at zero bias. This is in contrast to the cases of H-, methyl-, or ethyl-terminated Si(111), in which similar measurements have revealed the presence of a large conductance gap