The Structure of Trivalent Graphs with Minimal Eigenvalue Gap

Let G be a connected trivalent graph on nvertices (n10) such that among all connected trivalentgraphs on n vertices, G has the largest possiblesecond eigenvalue. We show that G must be reduced path-like, i.e. G must be of the form: where theends are one of the following:(the right-hand end block is the mirror image of one of the blocks shown)and the middle blocks are one of the following: This partially solves a conjecture implicit in a paper of Bussemaker,obelji, Cvetkovi, and Seidel [3].     

Continued fractions and fermionic representations for characters of M(p,p′) minimal models

We present fermionic sum representations of the characters _{, s} ^{(p, p)} of the minimal M(p,p) models for all relatively prime integers p>p for some allowed values of r and s. Our starting point is biomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin 1/2 chain of anisotropy –=–cos((p/p)). We use the Takahashi-Suzuki method to express the allowed values of r (and s) in terms of the continued fraction decomposition of {p/p} (and p/p), where {x} stands for the fractional part of x. These values are, in fact, the dimensions of the Hermitian irreducible representations of SU _q- (2) (and SU _q+ (2)) with q–=exp(i{p/p}) (and q+=exp(i(p/p))). We also establish the duality relation M(p,p) M(p–p,p) and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Dedicated to Prof. Vladimir Rittenberg on his 60th birthday     

Absence of ballistic motion

For large classes of Schrödinger operators and Jacobi matrices we prove that ifh has only one point spectrum then for φ₀ of compact support $$\mathop {\lim }\limits_{t \to \infty } t^{ - 2} \left\| {xe^{ - ith} \phi _0 } \right\|^2 = 0.$$      

Infrared photodissociation spectroscopy of electrosprayed ions in a Fourier transform mass spectrometer

Previous gas-phase methods for infrared photodissociation spectroscopy (IRPD) require sample volatility. Our method instead uses electrospray ionization to introduce even large nonvolatile molecules into a Fourier transform mass spectrometer, where extended (>15 s) ion storage makes possible high sensitivity spectral measurements with an OPO laser over a range of 3050-3800 cm(-1). The spectra of 22 gaseous proton-bound amino acid complexes are generally correlated with the H-stretching frequencies established for O-H and N-H functional groups in solution. For theoretical structure predictions of the Gly2H+ and N-acylated Asp2H+ dimers, IRPD spectra clearly differentiate between the predicted lowest energy conformers. In contrast to solution, in the gas phase the glycine zwitterion is approximately 20 kcal/mol less stable than the neutral; however, glycine is clearly zwitterionic in the gaseous GlyLysH+ dimer. The level of theory is inadequate for the larger Lys2H+ dimer, as all low energy predicted structures have free carboxyl O-H groups, in contrast to the IR spectrum. IRPD appears to be a promising new technique for providing unique information on a broad range of biomolecular and other gaseous ions, especially on noncovalent bonding involving O-H and N-H groups.     

Tri-alpha-naphthylbenzene as a crystalline or glassy matrix for matrix-assisted laser desorption/ionization: a model system for the study of effects of dispersion of polymer samples at a molecular level

Tri-alpha-naphthylbenzene (TalphaNB) can exist as either a crystalline or glassy solid at ambient temperatures, making it a unique matrix in matrix-assisted laser desorption/ionization (MALDI) spectroscopy. Electrosprayed TalphaNB is crystalline and has a melting point of 180 +/- 2 degrees C, as measured by differential scanning calorimetry (DSC). A glass of TalphaNB is obtained upon heating above the crystalline melting point with a glass transition temperature of 68 +/- 2 degrees C having no remaining crystallinity. MALDI samples containing mass fraction 1% polystyrene (PS) are run in both the crystalline and amorphous states. In the crystalline state, there is a strong spectrum typical of PS, but upon melting and quenching to the glassy state, the MALDI signal disappears. If the transparent, amorphous sample is treated with 1-butanol, it becomes white, and the MALDI signal returns. DSC shows that the 1-butanol treatment leads to the return of some of the crystallinity. Small angle neutron scattering (SANS) shows that the crystalline state has large aggregations of PS while the amorphous state has molecularly dispersed PS molecules. MALDI gives strong signals only when there are large aggregations of polymer molecules, with individually dispersed molecules producing no signal.     

Bis-β,β′-conjugate addition

Addition of organocuprates to α,β-enones which possess on the β′-carbon a heteroatom substituent leads in good to excellent yield to β,β′-dialkylated ketones. This process is termed bis-β,β′-conjugate addition.     

Complexes with metal-carbon bonds,part IV(1). Binuclear diarylplatinum(III) complexes. Long-rangetrans-effect in platinum-platinum bonded compounds containing methyl and aryl groups

Summary The platinum-platinum bonded [PtR₂(OAc)L¹]₂ complexes (R = Ph, L¹ = Et₂S, n-Pr₂S; R =p-tolyl, L¹ = Et₂S), have been prepared by oxidising [PrR₂L¹ ]₂ with AgOAc or Tl(OAc)₃. The sulphide ligand is replaced by weak ligands to give [PtR₂(OAc)L²]₂ (L² = PhNH₂, 4-picoline, CI^–) whereas PEt₃ or P(OMe)₃ react to give Pt₂R₄(OAc)₂(PR₃)(R = Et, OMe). The methyl platinum analogues could also be prepared. Similar complexes Pt₂Me₄(O₂CCF₃)₂L³ (L³ = Et₂S₁ 4-picoline) were obtained by the reaction of Hg(O₂CCF₃)₂ with [PtMe₂(O₂CCF₃)L³]₂.³¹p,¹H and¹³C n.m.r. of the complexes are reported.     

Structural and functional alterations in major peanut allergens caused by thermal processing

The majority of foods that we eat are subjected to some type of processing either at home or by the manufacturer. The biochemical reactions that occur in foods as a result of thermal processing can be both beneficial and harmful. Here, we briefly review the effects of thermal processing and some of the effects of the Maillard reaction on the allergenicity of food proteins. Specifically, we focus on the known effects of roasting on the allergenic properties of peanut proteins and the contribution of Maillard reaction products or advanced glycation end products to these observed effects. The most thorough understanding of the effects of thermal processing on allergenicity involves the peanut proteins. Thermal processing alters specific biophysical and immunological properties of peanut proteins, such as structure, function, solubility, digestibility, immunoglobulin E (IgE) binding, and T-cell responses. A better understanding of the effects of thermal processing-induced biochemical and immunological alterations is of utmost importance for proper risk assessment of existing and newly introduced proteins in the food source, as well as development of effective diagnostic tools and therapeutic treatments for food allergy.     

A unitary group formulation of many-body theory: Diagram systematics and use of the spin shifts

This paper shows that the spin-shift formalism developed in B. T. Pickup and A. Mukhopadhyay [Int. J. Quantum Chem. 26 , 101 (1984)] supports a one-component diagrammatics which has a systematics akin to that in the spin-orbital many-body theory. The diagrams are neither Goldstone nor Yutsis type, and characterize the chain U(2R) ? U(R)?SU(2) on which the spin-shift formalism is based. Accordingly, while the lines in such diagrams are labeled by the orbital indices, the diagram structure adequately reflects the irreducible representation of the group U(R). In this sense the paper presents a unitary group approach to the natural generalization of the usual many-body theory for the spin-adapted cases. A set of very simple rules is derived; their similarity with the corresponding rules in the ordinary many-body theory and practical utility are discussed in connection with (a) matrix elements over many-electron spin states and (b) closed- and open-shell many-body perturbation theory. A possibility of integral-driven many-body perturbation theory for open-shells is indicated. Connections of this formalism with others are also discussed.