Half-integral packing of odd cycles through prescribed vertices

The well-known theorem of Erd?s-Pósa says that a graph G has either k disjoint cycles or a vertex set X of order at most f(k) for some function f such that G\X is a forest. Starting with this result, there are many results concerning packing and covering cycles in graph theory and combinatorial optimization. In this paper, we discuss packing disjoint S-cycles, i.e., cycles that are required to go through a set S of vertices. For this problem, Kakimura-Kawarabayashi-Marx (2011) and Pontecorvi-Wollan (2010) recently showed the Erd?s-Pósa-type result holds. We further try to generalize this result to packing S-cycles of odd length. In contrast to packing S-cycles, the Erd?s-Pósa-type result does not hold for packing odd S-cycles. We then relax packing odd S-cycles to half-integral packing, and show the Erd?s-Pósa-type result for the half-integral packing of odd S-cycles, which is a generalization of Reed (1999) when S=V. That is, we show that given an integer k and a vertex set S, a graph G has either 2k odd S-cycles so that each vertex is in at most two of these cycles, or a vertex set X of order at most f(k) (for some function f) such that G\X has no odd S-cycle.     

Dynamic transition in the structure of an energetic crystal during chemical reactions at shock front prior to detonation

Mechanical stimuli in energetic materials initiate chemical reactions at shock fronts prior to detonation. Shock sensitivity measurements provide widely varying results, and quantum-mechanical calculations are unable to handle systems large enough to describe shock structure. Recent developments in reactive force-field molecular dynamics (ReaxFF-MD) combined with advances in parallel computing have paved the way to accurately simulate reaction pathways along with the structure of shock fronts. Our multimillion-atom ReaxFF-MD simulations of l,3,5-trinitro-l,3,5-triazine (RDX) reveal that detonation is preceded by a transition from a diffuse shock front with well-ordered molecular dipoles behind it to a disordered dipole distribution behind a sharp front.     

Efficient passively Q-switched Yb:LuAG microchip laser

An efficient passively Q-switched Yb:LuAG microchip laser with Cr4+:YAG as saturable absorber was demonstrated for the first time to our knowledge. Slope efficiencies of 40% and 28% were measured for the initial transmission of Cr4+:YAG, T(0)=95% and 90%, respectively. Laser pulses with a pulse energy of 19 microJ and a pulse width of 610 ps at the repetition rate of 12.8 kHz were achieved for T(0)=90%; the corresponding peak power of over 31 kW was obtained. The lasers oscillated at two or three longitudinal modes owing to the broad emission spectra of Yb:LuAG and mode selection by Cr4+:YAG thin plate acting as an intracavity etalon.     

Entrapment of [Ru(bpy)3]2+ in the anionic metal-organic framework: novel photoluminescence behavior exhibiting dual emission at room temperature

[Ru(bpy)(3)](2+) (bpy = 2,2'-bipyridine) ions were entrapped into the cavities of two-dimensional anionic sheet-like coordination polymeric networks of [M(dca)(3)](-) (dca = dicyanamide; M = Mn(II) and Fe(II)). The prepared compounds, {[Ru(bpy)(3)][Mn(dca)(3)](2)}(n) (1) and {[Ru(bpy)(3)][Fe(dca)(3)](2)}(n) (2), were structurally characterized by X-ray single crystal analysis. The spectroscopic properties of the [Ru(bpy)(3)](2+) ion dramatically changed on its entrapment in [M(dca)(3)](-). The [Ru(bpy)(3)](2+) moiety present in 1 and 2 exhibits novel dual photo-emission at room temperature.     

Characterization of intermediate values of the triangle inequality II

In [Mineno K., Nakamura Y., Ohwada T., Characterization of the intermediate values of the triangle inequality, Math. Inequal. Appl., 2012, 15(4), 1019–1035] there was established a norm inequality which characterizes all intermediate values of the triangle inequality, i.e. C _n that satisfy 0 ≤ C _n ≤ Σ _j=1 ⁿ ‖x _j ‖ ? ‖Σ _j=1 ⁿ x _j ‖, x ₁,...,x _n ∈ X. Here we study when this norm inequality attains equality in strictly convex Banach spaces.     

General entry to asymmetric one-pot [N + 2 + N] cyclization for the synthesis of three- to seven-membered azacycloalkanes

Enantio- and diastereoselective one-pot synthesis of three- to seven-membered cis-azaheterocycles was achieved using a triggered asymmetric conjugate addition reaction of lithium amide with an enoate, followed by alkylation of the resulting lithium enolate with α,ω-dihaloalkane and N-alkylation. Isomerization of cis-azaheterocycles with a base yielded the trans-product, constituting a one-pot synthesis of cis-azacycles and a two-step synthesis of trans-azacycles. The four-step asymmetric synthesis of nemonapride highlights the general utility of the method.     

Determination of the absolute structure of (+)-akaterpin

We describe the total synthesis and structural determination of (+)-akaterpin (1), an inhibitor of phosphatidylinositol-specific phospholipase C (PI-PLC). The key features of the synthetic strategy include the resolution of β,γ-unsaturated ketone (±)-2a with chiral sulfoximine 6. The absolute stereochemistry was determined by comparison of the specific optical rotation data of (+)-1 and (-)-1 with that of natural akaterpin.     

Dual of two dimensional Lorentz sequence spaces

In [M. Kato and L. Maligranda, On James and Jordan–von Neumann constants of Lorentz sequence spaces, J. Math. Anal. Appl. 258 (2001) 457–465], it is an open problem to compute the James constant of the dual space of two dimensional Lorentz sequence space d⁽²⁾(w,q). In this paper, we shall determine the dual norm of d⁽²⁾(w,q) and completely compute the James constant of d⁽²⁾(w,q).     

Molecular Structure and Mutual Recognition Between Host and Guest Molecules Found in the Crystal Structures of Oxacalix[4]arenes Complexed with Xylene Isomers

The crystal structures of two complexes of oxacalix[4]arene derivatives {p-isopropyl-dihomooxacalix[4]arene (IOC-4)and p-tert-butyldihomooxacalix[4]arene(BOC-4)} with xylene isomers have been determined byX-ray diffraction method. Furthermore, in order toestimate the strength of the mutual interactionsbetween host (IOC-4 and BOC-4) and guest (o-, m-and p-xylene), the heat of complex formation forthe IOC-4 : xylene complexes was calculated using a molecularorbital method, and a differential scanningcalorimetric investigation was performed forthe BOC-4 : xylene complexes.