New exact solutions of the Yang-Mills equation

New exact classical solutions of the Euclidean Yang-Mills equation are constructed. The exact solutions presented here are characterized by infinite values of topological charges and therefore they are in striking contrast to the well-known instanton and meron solutions which have finite topological charges.     

Biological identification of peptides that specifically bind to poly(phenylene vinylene) surfaces: recognition of the branched or linear structure of the conjugated polymer

Peptides that bind to poly(phenylene vinylene) (PPV) were identified by the phage display method. Aromatic amino acids were enriched in these peptide sequences, suggesting that a π-π interaction is the key interaction between the peptides and PPV. The surface plasmon resonance (SPR) experiments using chemically synthesized peptides demonstrated that the Hyp01 peptide, with the sequence His-Thr-Asp-Trp-Arg-Leu-Gly-Thr-Trp-His-His-Ser, showed an affinity constant (7.7 × 10(5) M(-1)) for the target, hyperbranched PPV (hypPPV) film. This value is 15-fold greater than its affinity for linear PPV (linPPV). In contrast, the peptide screened for linPPV (Lin01) showed the reverse specificity for linPPV. These results suggested that the Hyp01 and Lin01 peptides selectively recognized the linear or branched structure of PPVs. The Ala-scanning experiment, circular dichroism (CD) spectrometry, and molecular modeling of the Hyp01 peptide indicated that adequate location of two Trp residues by forming the polyproline type II (P(II)) helical conformation allowed the peptide to specifically interact with hypPPV.     

Inverse electron demand asymmetric cycloadditions of cyclic carbonyl ylides catalyzed by chiral Lewis acids—Scope and limitations of diazo and olefinic substrates

High enantioselectivities (94-96% ee) were obtained for the inverse electron-demand 1,3-dipolar cycloadditions between cyclohexyl vinyl ether and 2-benzopyrylium-4-olate generated via Rh₂(OAc)₄-catalyzed decomposition of o-methoxycarbonyl-α-diazoacetophenone. The reactions were effectively catalyzed by Eu(OTf)₃, Ho(OTf)₃, or Gd(OTf)₃ complexes (10 mol %) of chiral 2,6-bis[(4S,5S)-4,5-diphenyl-2-oxazolinyl]pyridine. The reactions with the other electron-rich dipolarophiles such as allyl alcohol, 2,3-dihydrofuran, and butyl-tert-butyldimethylsilylketene acetal showed moderate enanantioselectivities (60-73% ee). Good to high enantioselectivities (73-97% ee) were also obtained for the cycloadditions between 3-acyl-2-benzopyrylium-4-olates, generated from methyl 2-(2-diazo-1,3-dioxoalkyl)benzoates and butyl or cyclohexyl vinyl ethers, in the presence of binaphthyldiimine (BINIM)-Ni(II) complexes (10 mol %). Under similar conditions, the reaction between methyl 2-(2-diazo-1,3-dioxohexyl)benzoate and 2,3-dihydrofuran was highly endo-selective, and moderately enantioselective (70% ee). For the BINIM-Ni(II)-catalyzed reactions of cyclohexyl vinyl ether, the use of an epoxyindanone as the 3-acyl-2-benzopyrylium-4-olate precursor revealed that the chiral Lewis acid can function as a catalyst for asymmetric induction. The scope of the cyclic carbonyl ylides was extended to those generated from 1-diazo-2,5-pentanedione derivatives, which were reacted with butyl or TBS vinyl ether and catalyzed using the (4S,5S)-Pybox-4,5-Ph₂-Lu(OTf)₃ complex to give good levels of asymmetric inductions (75-84% ee).     

Effective 2,6-substitution of piperidine nitroxyl radical by carbonyl compound

Nitroxyl radicals (nitroxides) with unpaired electron are widely used as antioxidants, contrast agents, and spin probes. Although piperidine nitroxyl radicals have many applications, these are mainly tetramethylpiperidine compounds, and only a few reports consider the substitution of N-O surround as a reaction site, such as 2,2,6,6-tetrasubstituted piperidine nitroxyl radicals. Our results revealed that the 2,6-position of the 2,2,6,6-tetramethylpiperidin-4-one compound was substituted by cyclohexyl groups to produce 2,2,6,6-tetrasubstituted piperidin-4-one derivatives under mild reaction conditions. An interesting result was obtained by using ¹⁵N-labeled NH₄Cl instead of ¹⁴NH₄Cl: it gave ¹⁵N-labeled 2,2,6,6-tetrasubstituted piperidin-4-one-1-oxyls with a high ¹⁵N content. In conclusion, the new method for the synthesis of nitroxyl radicals readily yields 2,2,6,6-tetrasubstituted piperidin-4-one under mild conditions.     

Effects of crystalline grain size and packing ratio of self-forming core/shell nanoparticles on magnetic properties at up to GHz bands

Self-forming core/shell nanoparticles of magnetic metal/oxide with crystalline grain size of less than 40 nm were synthesized. The nanoparticles were highly concentrated in an insulating matrix to fabricate a nanocomposite, whose magnetic properties were investigated. The crystalline grain size of the nanoparticles strongly influenced the magnetic anisotropy field, magnetic coercivity, relative permeability, and loss factor (tan δ=μ″/μ′) at high frequency. The packing ratio of the magnetic metallic phase in the nanocomposite also influenced those properties. High permeability with low tan δ of less than 1.5% at up to 1 GHz was obtained in the case of the nanoparticles with crystalline grain size of around 15 nm with large packing ratio of the nanoparticles.     

The N-soliton solution of a two-component modified nonlinear Schrödinger equation

The N-soliton solution is presented for a two-component modified nonlinear Schrödinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit.     

A Fast Algorithm For Finding A Maximum Free Multiflow In An Inner Eulerian Network And Some Generalizations

be a network, where is an undirected graph with nodes and edges, is a set of specified nodes of , called terminals, and each edge of has a nonnegative integer capacity . If the total capacity of edges with one end at is even for every non-terminal node , then is called inner Eulerian. A free multiflow is a collection of flows between arbitrary pairs of terminals such that the total flow through each edge does not exceed its capacity. In this paper we first generalize a method in Karzanov [11] to find a maximum integer free multiflow in an inner Eulerian network, in time, where is the complexity of finding a maximum flow between two terminals. Next we extend our algorithm to solve the so-called laminar locking problem on multiflows, also in time. We then consider analogs of the above problems in inner balanced directed networks, which means that for each non-terminal node , the sums of capacities of arcs entering and leaving are the same. We show that for such a network a maximum integer free multiflow can be constructed in time, and then extend this result to the corresponding locking problem. Received: March 24, 1997     

Implementing an efficient minimum capacity cut algorithm

In this paper, we present an efficient implementation of theO(mn + n ² logn) time algorithm originally proposed by Nagamochi and Ibaraki (1992) for computing the minimum capacity cut of an undirected network. To enhance computation, various ideas are added so that it can contract as many edges as possible in each iteration. To evaluate the performance of the resulting implementation, we conducted extensive computational experiments, and compared the results with that of Padberg and Rinaldi's algorithm (1990), which is currently known as one of the practically fastest programs for this problem. The results indicate that our program is considerably faster than Padberg and Rinaldi's program, and its running time is not significantly affected by the types of the networks being solved.Corresponding author.