On the Symmetry of a Zig-Zag and an Armchair Polyhex Carbon Nanotorus
Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, I. R. Iran * Author to whom correspondence should be addressed: E-mail: Ashrafi@kashanu.ac.ir Received: 17 July 2009; in revised form: 13 September 2009 / Accepted: 14 September 2009 / Published: 8 October 2009 Abstract: A Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [d
Group Theoretical Analysis of Vibrational Modes, Rovibronic Levels and Nuclear Spin Statistics of extended aromatic C48N12 Azafullerene
We have presented a group theoretical analysis of the vibrational modes and rovibronic levels of a novel extended aromatic C{sub 48}N{sub 12} azafullerene. The nuclear spin multiplets and statistical weights of {sup 14}N spin-1 bosons, vibrational and rotational analysis and computed vibrational spectra are provided. We have also predicted the properties of the {sup 3}A{sub u}, {sup 3}E{sub g}, and {sup 3}E{sub u} excited states of C{sub 48}N{sub 12} that lie 1.9 eV above the {sup 1}A{sub g} ground state, and that the {sup 3}E{sub g} and {sup 3}E{sub u} states would undergo Jahn-Teller distortion into chiral structures with no symmetry and an achiral structure with C{sub i} symmetry.
On a New Subclass of p-Valent Close-to-Convex Mappings Defined by Two-Sided Inequality
<jats:p>A new subclass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>β</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-valent close-to-convex mappings defined by two-sided inequality is introduced. Some sufficient conditions for functions to be in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>β</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> are given.</jats:p>