Degree-regular triangulations of torus and Klein bottle

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In [8], Lutz has classified all the weakly regular triangulations on at most 15 vertices. In [5], Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices. In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there exists ann-vertex degree-regular triangulation of the Klein bottle if and only if n is a composite number ≥ 9. We have constructed two distinctn-vertex weakly regular triangulations of the torus for eachn ≥ 12 and a (4m + 2)-vertex weakly regular triangulation of the Klein bottle for eachm ≥ 2. For 12 ≤n ≤ 15, we have classified all then-vertex degree-regular triangulations of the torus and the Klein bottle. There are exactly 19 such triangulations, 12 of which are triangulations of the torus and remaining 7 are triangulations of the Klein bottle. Among the last 7, only one is weakly regular.     

Re-hardening of hadron transverse mass spectra in relativistic heavy-ion collisions

We analyze the spectra of pions and protons in heavy-ion collisions at relativistic energies from 2 A GeV to 65+65 A GeV by using a jet-implemented hadron-string cascade model. In this energy region, hadron transverse mass spectra first show softening until SPS energies, and re-hardening may emerge at RHIC energies. Since hadronic matter is expected to show only softening at higher energy densities, this re-hardening of spectra can be interpreted as a good signature of the quark-gluon plasma formation     

Combinatorial manifolds with complementarity

A simplicial complex is said to satisfy complementarity if exactly one of each complementary pair of nonempty vertex-sets constitutes a face of the complex. We show that if a d-dimensional combinatorial manifold M with n vertices satisfies complementarity then d=0, 2, 4, 8, or 16 with n=3d/2+3 and |M| is a “manifold like a projective plane”. Arnoux and Marin had earlier proved the converse statement.     

Engel type identities with derivations for right ideals in prime rings

Let R be a prime ring of char R≠2, d a non-zero derivation of R and ρ a non-zero right ideal of R such that [[d(x),d(y)]_n [y,x]_m] = 0 for all x,y ∈ ρ or [[d(x),d(y)]_n d[y,x]_m] = 0 for all x,y ∈ ρ, n, m ≥ 0 are fixed integers. If [ρ,ρ]ρ ≠ 0, then d(ρ)ρ = 0.     

Skew-commuting and Commuting Mappings in Rings with Left Identity

Our main object in this paper is to discuss some results on rings with left identity in which certain subsets satisfy some functional identities.     

Invariants for normal completely positive maps on the hyperfinite II1 factor

We investigate certain classes of normal completely positive (CP) maps on the hyperfinite II₁ factorA. Using the representation theory of a suitable irrational rotation algebra, we propose some computable invariants for such CP maps. Dedicated to Professor K B Sinha     

Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

Electron transfer reactions of nickel(III) and nickel(IV) complexes

This review narrates the electron transfer reactions of various nickel(III) and nickel(IV) complexes reported during the period 1981 until today. The reactions have been categorized mainly with respect to the type of nickel complexes. The reactivity of nickel(III) complexes of macrocycles, 2,2′-bipyridyl and 1,10-phenanthroline, peptides and oxime–imine, and of nickel(IV) complexes derived from oxime–imine, oxime and miscellaneous ligands with various organic and inorganic electron donors have been included. Kinetic and mechanistic features associated with such interactions have been duly analyzed. The relevance of Marcus cross-relation equations in the delineation of the electron transfer paths has also been critically discussed.     

Synthesis of arenediynes via the vinylidenecarbene-acetylene rearrangement

A convenient method for the two-step synthesis of arenediynes from 1,2-arenedialdehydes is reported. Dibromomethylenation of dialdehydes under Corey-Fuchs conditions (CBr₄, Ph₃P, Zn) provides the tetrabromides in excellent yields. Treatment of the tetrabromides with n-BuLi or LDA affords 3,4-unsaturated 1,5-diynes, the key structural moiety present in several naturally occurring antitumour antibiotics, in varying yields. The key intermediates in these transformations appear to be vinylidenecarbenes or carbenoids, generated in situ via metal-halogen exchange and elimination.     

Vinyl polymerization of acrylamide initiated by Thallium(III) ions in solution

Kinetics of polymerization of acrylamide initiated by Thallium(III) perchlorate was investigated in aqueous perchloric acid medium in the temperature range of 55–70°C. The rates of polymerization were measured varying the concentration of the monomer, initiator, and perchloric acid. The rate of polymerization was found to increase with increase of temperature, monomer concentration, initiator concentration, and perchloric acid concentration. The effect of additives like different solvents, surfactants, and retarders on the rate of polymerization was studied. Molecular weights of the polymer were determined by viscometry. The chain transfer constants for the monomer (C_M) and that for the solvent dioxan (C_s) were calculated to be 7.33 × 10^?3 and 6.66 × 10^?3, respectively. From the Arrhenius plot, the overall activation energy (E_a) was calculated to be 10.68 kcal/mol. The energy of initiation was calculated to be 12.36 kcal/mol. Depending on the results obtained, a suitable reaction mechanism has been suggested and a rate equation has been derived.