The index problem for eigenvalues for coupled boundary conditions and Fulton’s conjecture

This paper deals with regular self-adjoint Sturm–Liouville problems with coupled boundary conditions. The spectrum of the problems can be either bounded from below, or unbounded from both below and above. We consider the following question: given an eigenvalue, how to determine its index or indices efficiently? Using results on the level surfaces of the nth eigenvalue and certain inequalities among eigenvalues, the determination is converted into that of the index of the same eigenvalue for an appropriate separated boundary condition and hence can be achieved in terms of the Prüfer angle. As an application of this complete solution of the index problem, we show that Fulton’s conjecture about such an index is true.     

On the decidability of the word problem for amalgamated free products of inverse semigroups

We study inverse semigroup amalgams [S ₁,S ₂;U], where S ₁ and S ₂ are finitely presented inverse semigroups with decidable word problem and U is an inverse semigroup with decidable membership problem in S ₁ and S ₂. We use a modified version of Bennett’s work on the structure of Schützenberger graphs of the ℛ-classes of S ₁* _U S ₂ to state sufficient conditions for the amalgamated free products S ₁* _U S ₂ having decidable word problem.     

Energy levels and spectral lines of Ne VII

All experimental data on Ne VII, including previously unpublished beam-foil spectroscopy data, have been compiled and critically evaluated. More than a hundred spectral lines have been newly identified. For 40 transitions, the previous identifications have been revised. These revisions resolved all existing contradictions between previously published interpretations of the spectrum. An optimized level scheme has been derived from the total list of observed lines. About a hundred new energy levels have been found, including several highly excited hydrogenic levels. Based on these newly determined levels, as well as on the analysis of theoretical data, the ionization potential has been newly determined with improved confidence. Electronic supplementary material Online Material     

Assembly of a Benzo-Fused Bridged Ketone Scaffold from 1,5,10-Enediynes through One-Pot Ruthenium-Catalyzed Cyclization/Iodine-Mediated Oxidative Ring Expansion

In the presence of a cationic Ru catalyst, 1,6-diynes bearing a terminal styryl moiety underwent [2+2+2] cyclization to produce dehydrobiphenylenes fused with a five-membered ring. Although the cycloadducts were unstable toward purification, their one-pot iodine-mediated ring expansion successfully afforded unprecedented bridged ketone products containing a benzo-fused bicyclo[3.2.1] framework.     

Application of thiophilic chromatography to deplete serum immunoglobulins in sample preparation for bidimensional electrophoresis

Serum is a typical sample for non-invasive studies in clinical research. Its proteome characterization is challenging, since requires extensive protein depletion. Methods used nowadays for removal of high-abundance proteins are expensive or show quite often a low loading capacity, which has strong repercussions on the number of samples and replicates per analysis.In order to deplete immunoglobulins (Igs) and albumin (HSA) from 1 mL serum samples, we have developed a protocol based on a combination of thiophilic chromatography, not previously used in clinical proteomics, and a HSA-specific resin. Ig/HSA-depleted samples, immunoglobulinome and albuminone were analyzed by 2-DE. Thiophilic chromatography, coupled with HSA-depletion, allows a good 2-DE resolution as well as the visualization of new spots. Moreover, it yields enough protein to evaluate technical variability and facilitate subsequent protein identification. To validate the protocol, we carried out a preliminary comparative study between triplicate Igs/HSA-depleted serum samples from healthy control individuals and recently diagnosed/untreated rheumatoid arthritis (RA) patients. RA patients showed several acute phase proteins, as well as additional serum proteins, differentially and significantly regulated.Therefore, thiophilic chromatography can be used as an efficient and economical method in 2-DE to deplete immunoglobulins from large human serum samples before a more extensive fractioning.     

Isomorphisms of fiber spaces over Teichmüller spaces

We will be mainly concerned with some important fiber spaces over Teichmüller spaces, including the Bers fiber space and Teichmüller curve, establishing an isomorphism theorem between “punctured” Teichmüller curves and determining the biholomorphic isomorphisms of these fiber spaces.     

Families of Dot-Product Snarks on Orientable Surfaces of Low Genus

We introduce a generalized dot product and provide some embedding conditions under which the genus of a graph does not rise under a dot product with the Petersen graph. Using these conditions, we disprove a conjecture of Tinsley and Watkins on the genus of dot products of the Petersen graph and show that both Grünbaum’s Conjecture and the Berge-Fulkerson Conjecture hold for certain infinite families of snarks. Additionally, we determine the orientable genus of four known snarks and two known snark families, construct a new example of an infinite family of snarks on the torus, and construct ten new examples of infinite families of snarks on the 2-holed torus; these last constructions allow us to show that there are genus-2 snarks of every even order n ≥ 18.     

TN-LCD的视角特性

研究TN-LCD显示器的视角特性,分析视角问题产生的原因。最后定性地分析TN-LCD视角特性的优化和应用。