Mass extrapolation of quarks and leptons to higher generations

An empirical mass formula is tested for the basic fermion sequences of charged quarks and leptons. This relation is a generalization of Barut’s mass formula for the lepton sequence (e, μ, τ......). It is found that successful mass extrapolation to the third and possibly to other higher generations (N>2) can be obtained with the first and second generation masses as inputs, which predicts the top quark massm _t to be around 20 GeV. This also leads to the mass ratios between members of two different sequences (i) and (i′) corresponding to the same higher generations (N>2).     

Control of molecular architecture by steric factors: mononuclear vs polynuclear manganese(III) compounds with tetradentate N2O2 donor Schiff bases

Three manganese(III) compounds, [Mn(III)(vanoph)(DMF)(H(2)O)]ClO(4) (1), [Mn(III)(vanoph)(N(3))(H(2)O)]·2H(2)O (2) and [Mn(III)(saloph)(μ(1,3)-N(3))](n) (3), where H(2)vanoph = N,N'-(1,2-phenylene)-bis(3-methoxysalicylideneimine), H(2)saloph = N,N'-(1,2-phenylene)-bis(salicylideneamine) are tetradentate N(2)O(2) ligands and DMF = N,N-dimethylformamide, have been prepared and characterised by elemental analysis, IR and UV-Vis spectroscopy and single-crystal X-ray diffraction studies. Compounds 1 and 2 are monomeric but compound 3 consists of a chain system with the repeating unit [Mn(III)(saloph)(N(3))] bridged by μ-1,3 azide. Compound 1 crystallises in monoclinic space group P2(1)/n with cell dimensions of a = 11.1430(2), b = 16.3594(3), c = 15.4001(3) ?, β = 108.417(1), Z = 4 whereas compounds 2 and 3 crystallise in orthorhombic space groups Pbca and Pna2(1), respectively, with cell dimensions of a = 16.069(3), b = 15.616(3), c = 18.099(4) ?, Z = 8 (for 2) and a = 18.760(9), b = 13.356(5), c = 6.616(3) ?, Z = 4 (for 3). In all the compounds, Mn(III) has a six-coordinated pseudo-octahedral geometry in which O(2), O(3), N(1) and N(2) atoms of the deprotonated di-Schiff base constitute the equatorial plane. In both compounds 1 and 2, water molecules are present in the fifth coordination sites in the apical positions. The sixth coordination sites are occupied by one O atom of a solvent DMF in compound 1 and an N atom of azide in compound 2. The coordinated water initiates hydrogen-bonded networks in both compounds 1 and 2 to form well-isolated supramolecular dimers. At room temperature the χ(M)T values for the compounds 1 and 2 remain almost constant until 30 K. Below this temperature, the χ(M)T values drastically drop to 0.72 cm(3) mol(-1) K for 1 and 0.52 cm(3) mol(-1) K for 2. The best fits were obtained with J = -0.92 cm(-1), |D| = 2.05 cm(-1), g = 2.0 and R = 8.1 × 10(-4) for 1 and J = -1.16 cm(-1), |D| = 2.05 cm(-1), g = 2.0 and R = 1.2 × 10(-3) for 2. However, in compound 3, two axial positions are occupied by the azide ions. The Mn···Mn repeating distance is 6.616 ? along the chain. Magnetic characterisation shows that the μ(1,3)-bridging azide ion mainly transmits an antiferromagnetic interaction (J = -6.36 cm(-1)) between Mn(III) ions. The presence of two methoxy groups increases the steric crowding in the H(2)vanoph moiety and thereby inhibits the formation of a polynuclear compound with this ligand.     

On Hadamard diagonalizable graphs

Of interest here is a characterization of the undirected graphs G such that the Laplacian matrix associated with G can be diagonalized by some Hadamard matrix. Many interesting and fundamental properties are presented for such graphs along with a partial characterization of the cographs that have this property.     

Oscillation of higher order neutral functional difference equations with positive and negative coefficients

Sufficient conditions are obtained so that every solution of the neutral functional difference equation

Unified reciprocity of dithiophosphate by dichalcogenophosph(in)ate ligands on copper hydride nanoclusters via ligand exchange reaction

A structural study of ligand exchange on chalcogen‐passivated copper nanoclusters is far less developed. Herein, we report the synthesis of polyhydrido copper nanoclusters [Cu₂₀H₁₁{Se₂P(O ⁱBu)₂}₉] ( 2 ) passivated by Se‐donor ligands via ligand replacement reaction on [Cu₂₀H₁₁{S₂P(O ⁱPr)₂}₉] ( 1 ) with NH₄[Se₂P(O ⁱBu)₂]. In parallel to the synthesis of 2 , cluster [Cu₂₀H₁₁{S₂P(CH₂CH₂Ph)₂}₉] ( 4 ) was produced by the ligand exchange reaction on a new derivative of 1 , that is [Cu₂₀H₁₁{S₂P(O ⁿPr)₂}₉] ( 3 ). Solid state structures of both clusters 2 and 4 were unequivocally established by single‐crystal X‐ray diffraction studies and cluster 4 epitomizes exceptional case to preserve both the shape and size of the nanocluster during the course of ligand exchange. Structurally precise cluster 2 is the second example where the copper hydride nanocluster is stabilized by Se‐donor ligands. The anatomy of 2 can be visualized as a twisted cuboctahedral Cu₁₃ core, two triangular faces of which are capped by a Cu₆ cupola and a single Cu atom along the C₃ rotational axis.     

A pyrazole-based orthogonal ferromagnetically coupled [2 × 2] homoleptic square Cu4 grid: Magnetostructural correlations

The synthesis and structure of a pyrazole-based orthogonal ferromagnetically coupled tetracopper(II) 2 × 2 homoleptic grid complex [Cu₄(PzOAPyz)₄(ClO₄)₂](ClO₄)₂ · 6H₂O (1), formed by the reaction between the ditopic ligand PzOAPyz and Cu(ClO₄)₂ · 6H₂O, are described. The ligand contains terminal pyrazole and pyrazine residues bound to a central flexible diazine subunit (N–N) as well as one potentially bridging alkoxo group. The two adjacent metal centers are linked by an alkoxo oxygen forming essentially a square Cu₄(μ-O₄) cluster. In the Cu₄(μ-O₄) core, out of the four copper centers, two copper centers are penta-coordinated and the remaining two are hexa-coordinated. In each case of hexa-coordination, the sixth position is occupied by one of the oxygen atoms of a coordinated perchlorate ion. Complex 1 has been characterized structurally and magnetically. Although the large Cu–O–Cu bridge angles (137–138°) and short Cu–Cu distances (3.964–3.970 Å) are suitable for the transmission of the expected antiferromagnetic coupling, the square-based Cu₄(μ-O₄) cluster exhibits an intramolecular ferromagnetic exchange (J = 7.47 cm⁻¹) between the metal centers with an S = 2 magnetic ground state associated with the quasi orthogonal arrangement of the magnetic orbitals (d_x2-y2${\text{d}}_{x^2-y^2}$). The exchange pathway parameters have been evaluated from density functional calculations.     

Structural Transformation of Three‐Dimensional Bimetallic Phosphites Containing Corner‐Sharing 4‐Ring Chains

Two open‐framework bimetallic phosphites, [C₆H₁₈N₂][Co_0.3Zn_2.7 (HPO₃)₄] ( 1 ) and [C₂H₈N]₂[Co_0.3Zn_2.7(HPO₃)₄] ( 2 ) were synthesized and characterized. The inorganic frameworks of the two compounds are constructed from strictly alternating MO₄ (M = Zn, Co)tetrahedra and HPO₃ pseudo pyramids, forming three‐dimensional networks with 8‐ring and 12‐ring channels for 1 and 16‐ring channels for 2 . The anionic frameworks of the two compounds can be easily transformed to a neutral framework structure with 16‐ring channels at room temperature.     

Palladium-mediated intramolecular aryl amination on furanose derivatives: an expedient approach to the synthesis of chiral benzoxazocine derivatives and tricyclic nucleosides

Pd-catalyzed intramolecular arylamination on sugar derivatives has been accomplished by using bulky biaryl phosphine ligands. An application of this methodology on a variety of D-glucose-derived substrates, 2a-f, led to the synthesis of highly functionalized cis-fused tricyclic oxazocines, 3a-e. The products could subsequently be transformed to the optically active benzoxazocine derivative 4 and tricyclic nucleoside 6. This is the first example of the synthesis of eight-membered rings via intramolecular cycloamination of furanose derivatives, which provides a very useful method for the catalytic synthesis of medium-ring heterocycles.