Study of the K(0)(L) --> pi(+)pi(-)gamma Direct Emission Vertex

We have performed studies of the K(0)(L)-->pi(+)pi(-)gamma direct emission ( DE) and inner Bremsstrahlung ( IB) vertices, based on data collected by KTeV during the 1996 Fermilab fixed target run. We find a(1)/a(2) = -0.737+/-0.034 GeV2 for the DE form-factor parameter in the rho-propagator parametrization, and report on fits of the form factor to linear and quadratic functions as well. We concurrently measure gamma(K(0)(L)-->pi(+)pi(-)gamma,E(*)(gamma)>20 MeV)/gamma(K(0)(L)-->pi(+)pi(-)) = (20.8+/-0.3)x10(-3), and a K(0)(L)-->pi(+)pi(-)gamma DE/(DE+IB) branching ratio of 0.683+/-0.011.     

Measurement of the K(L) charge asymmetry

We present a measurement of the charge asymmetry delta(L) in the mode K(L)-->pi(+/-)e(-/+)nu based on 298 x 10(6) analyzed decays. We measure a value of delta(L) = [3322+/-58(stat)+/-47(syst)]x10(-6), in good agreement with previous measurements and 2.4 times more precise than the current best published result. The result is used to place more stringent limits on CPT and DeltaS = DeltaQ violation in the neutral kaon system.     

Shaping quantum pulses of light via coherent atomic memory

We describe proof-of-principle experiments demonstrating a novel approach for generating pulses of light with controllable photon numbers, propagation direction, timing, and pulse shapes. The approach is based on preparation of an atomic ensemble in a state with a desired number of atomic spin excitations, which is later converted into a photon pulse. Spatiotemporal control over the pulses is obtained by exploiting long-lived coherent memory for photon states and Electromagnetically Induced Transparency in an optically dense atomic medium. Using photon counting experiments, we observe Electromagnetically Induced Transparency based generation and shaping of few-photon sub-Poissonian light pulses.     

Synthesis of amino-5-arylsulfonylpyrimidines

Several new 4-amino-5-arylsulfonylpyrimidines were prepared via the reaction of various α-(ethoxymethylene)arylsulfonylacetonitriles with guanidine or variously substituted amidines (Table II). 2,4-Diamino-5-(p-chlorophenylsulfonyl)pyrimidine (IIIg), a typical example, was prepared from the reaction of 2-(p-chlorophenylsulfonyl)-3-ethoxyacrylonitrile (IId) with guanidine in refluxing ethanol containing sodium ethoxide. With proper substitution of the ethoxymethylene intermediate, the method was found suitable for the preparation of other compounds having either a hydroxy or methyl group at the 4-position of the 5-arylsulfonylpyrimidine. The fluoro group in 2,4-diamino-5-(p-fluorophenylsulfonyl)pyrimidine (IIIx) was successfully replaced by nucleophilic reagents such as sodium ethoxide, N-methylpiperazine and N,N-diethylethylene-diamine. Attempts at direct displacement of fluorine by ammonia at 190° were unsuccessful.     

A pericyclic cascade to the stereocontrolled synthesis of 9-cis-retinoids

A domino reaction that is pericyclic in nature is thought to be triggered upon treatment of alkenynol 10 with arylsulfenyl chlorides. The process comprises an ordered sequence of sigmatropic rearrangements: a reversible [2,3]-allyl sulfenate to allyl sulfoxide shift, followed by a [2,3]-propargyl sulfenate to allenyl sulfoxide rearrangement, and last a stereodifferentiating [1,5]-sigmatropic hydrogen migration leading to polyene 13. The occurrence of the C7 to C11 hydrogen migration has been demonstrated by labeling experiments. The double diastereoselection of the [1,5]-sigmatropic hydrogen shift to afford a single isomer of the final polyene 13 is thought to arise from a combination of the electronic effect of the sulfoxide at one terminus, and the steric effect imparted by the bulky trimethylcyclohexenyl substituent at the other terminus. The overall process thus constitutes a stereoselective synthesis of an E,Z,Z-triene fragment from an alkenynol and, in particular, a retinoid with the 7E,9Z,11Z,13E configuration on the conjugated polyenic side chain. Application of this method to the synthesis of retinoids, including labeled analogues, is straightforward.     

Thallophilic interactions in aryloxide compounds: the [Tl2(mu2-OAr)4] structural motif in (TlOAr)4 and Tl2Cu(OAr)4 compounds

Two thallium aryloxide compounds TlOC6F5 (TlOAr(F)) and bis-3,5-TlOC6H3(CF3)2 (TlOAr') have been recrystallized from THF and crystallographically characterized in different isomeric forms. The latter compound forms a solvated tetrameric cubane, [TlOAr']4.THF, 1. The TlOAr(F) compound crystallized with a similar stoichiometry, [TlOAr(F)]4.2 THF, 2, but contains a [Tl2(mu2-OAr(F))4] unit that includes a thallophilic interaction at a distance of 3.5943(15) angstroms. Solution 205Tl and 203Tl NMR studies of 1 and 2 support the retention of a cubane structure for 1 in solution and suggest a similar structure for 2 with coupled thallium centers down to -90 degrees C. Fluorescence spectroscopy data for both compounds 1 and 2 in THF are consistent with LMCT. DFT calculations of 1, 2, and three models of the [Tl2(mu2-OAr(F))4] unit show a bonding overlap of the bridged thallium atoms in 2 and are also used to describe the bonding in 1. The structures of two heterobimetallic compounds, Tl2Cu(OAr(F))4, 4, and Tl2Cu(OAr')4, 5, with the [Tl2(mu2-OAr(F))4] structural motif and thallophilic contacts of 3.86(6) and 3.564(1) angstroms, respectively, are described. The crystal structures of the unsolvated of TlOAr(F), 2b, solvated heterobimetallic derivative Tl2Cu(OAr')4.2THF, 5b, and the monomeric (18-crown-6)TlOAr(F), 3, and 205Tl NMR spectra of TlOC6H5, 6, are also reported for comparison purposes.     

Probabilistic Inductive Classes of Graphs

A unifying framework—probabilistic inductive classes of graphs (PICGs)—is defined by imposing a probability space on the rules and their left elements from the standard notion of inductive class of graphs. The rules can model the processes creating real-world social networks, such as spread of knowledge, dynamics of acquaintanceships or sexual contacts, and emergence of clusters. We demonstrate the characteristics of PICGs by casting some well-known models of growing networks in this framework. Results regarding expected size and order are derived. For PICG models of connected and 2-connected graphs order, size and asymptotic degree distribution are presented. The approaches used represent analytic alternative to computer simulation, which is mostly used to obtain the properties of evolving graphs.     

Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

碳税机制下考虑不同低碳策略的动态博弈模型及复杂性研究

考虑碳排放税,建立双寡头制造商分别实施废品回收和绿色低碳广告投入策略的动态博弈模型。通过系统稳定域,分岔图,功率谱等分析了博弈模型纳什均衡解处的稳定性及参数对系统稳定域的影响,同时对系统的复杂性特征进行了研究。结果表明,消费者回收价格敏感性增加会使整个系统稳定域缩小,而绿色低碳广告投入水平增加只会使实施该策略的企业自身稳定域扩大;当制造商价格调整速度过快时,系统会进入混沌状态;混沌状态下,对比实施广告策略的制造商,实施废品回收策略的制造商价格调整行为对市场造成的震荡更大。最后使用反馈控制策略对系统混沌状态进行了有效的控制,研究结果对制造商低碳策略选择及价格决策有着较好的借鉴意义。