Study of the reactione + e −→K + K − in the energy range1350 \leqq \sqrt s \leqq 2400 MeV

Thee ⁺ e ^?→K ⁺ K ^? cross section has been measured from about 750 events in the energy interval \(1350 \leqq \sqrt s \leqq 2400 MeV\) with the DM2 detector at DCI. TheK ^± form factor |F _F ^±| cannot be explained by the ρ, ω, ? and ρ′(1600). An additional resonant amplitude at 1650 MeV has to be added as suggested by a previous experiment.     

Asset pricing under ambiguous information: an empirical game-theoretic analysis

In a representative agent model, the behavior of a social system is described in terms of a single aggregate decision maker. Such models are popular in economic and finance research, largely due to their analytic tractability, but fail to account for real-world agent heterogeneity, and may ignore effects of market microstructure. Agent-based simulation models naturally incorporate agent heterogeneity, and can account for any particular market microstructure; however, such models have gained only limited acceptance by the mainstream economic research community, due to concerns over how much general insight can be gleaned from simulating a particular configuration of agent behaviors. We address such concerns by employing game-theoretic criteria in behavior selection. We present a case study investigating a recent model from the finance literature proposed by Epstein and Schneider (ES), and its ability to explain the classic equity premium puzzle in risky asset pricing. For all market configurations that we examined, ambiguity-averse pricing was played with little or no probability in equilibrium. Moreover, none of the market configurations exhibited significant equity premia. Both our use of strategic equilibrium as a market composition concept, and the actions of our simulated market microstructure contribute to removing any equity premium. These findings underscore the value of checking that results from abstract representative-agent models are supportable in a higher-fidelity model where heterogeneity and strategic interactions are taken into account.     

The Use of tert-Butyl Vinyl Ether in Stepwise Electrophilic Addition Reactions

tert-Butyl vinyl ether (1) reacts with p-TolSCl to give 2-tert-butoxy-2-chloroethyl p-tolyl sulfide (2). In the presence of SnCl₄, 2 reacts with silyl enol ethers, allyltrimethylsilane, and vinyl ethers to form a C-C bond. In the case of vinyl ethers, the reaction proceeds through the formation of the 5-membered sulfonium salt intermediate which in turn can react with H₂O, TMSCN, allyltrimethylsilane, and Grignard reagents.     

Radiative decay ofJ/ψ into γ π+ π−

The radiative decayJ/ψ → γ π⁺ π^? has been studied using the 8.6 millionJ/ψ produced in the DM2 experiment at the DCIe ⁺e^? storage rings at Orsay. The π⁺ π^? mass spectrum shows a cleanf ₂ (1270) signal, and the possible presence of two other states at thef ₂ (1720) andf ₄ (2030) masses. For thef ₂ (1270), the branching ratio BR(J/ψ →γf)xBR(f→π⁺ π^?) is measured to be (7.50±0.30±1.12)×10^?4, and the spin analysis prefers theJ=2 assignment, with helicity parametersx=0.83±0.06 andy=0.01±0.06. The existence of higher mass states is discussed.     

Non-planar smoulder propagation governed by diffusion

The steady propagation of a thin smouldering front in a half-spacehas been considered. A suitable coordinate transformation hasallowed the region near the leading edge of the front to beexamined for both a maintained planar surface and with surfacecollapse due to material shrinkage. The change in the oxidizerconcentration for a small increment in the propagation speedfor large time and surface collapse has been determined. Theinfluence of two types of nonlinear diffusion on the shape ofthe smouldering front has been found; other cases can be dealtwith in a similar manner.     

On the Spectra of Left-Definite Operators

If A is a self-adjoint operator that is bounded below in a Hilbert space H, Littlejohn and Wellman (J Diff Equ 181(2):280–339, 2002) showed that, for each r > 0, there exists a unique Hilbert space H _r and a unique self-adjoint operator A _r in H _r satisfying certain conditions dependent on H and A. The space H _r and the operator A _r are called, respectively, the rth left-definite space and rth left-definite operator associated with (H, A). In this paper, we show that the operators A, A _r , and A _s (r, s > 0) are isometrically isomorphically equivalent and that the spaces H, H _r , and H _s (r, s > 0) are isometrically isomorphic. These results are then used to reproduce the left-definite spaces and left-definite operators. Furthermore, we will see that our new results imply that the spectra of A and A _r are equal, giving us another proof of this phenomenon that was first established in Littlejohn and Wellman (J Diff Equ 181(2):280–339, 2002).     

Separation and detection of individual submicron particles by capillary electrophoresis with laser-light-scattering detection

Separation and detection of individual submicron polystyrene spheres using capillary electrophoresis with laser-light-scattering detection has been demonstrated. Electrophoretically separated particles were passed through a focused laser beam and light scattered from individual particles was collected at 90 degrees. Each diameter of polystyrene spheres injected (from 110 to 992 nm) resulted in the observation of a well-defined migration window containing multiple peaks, each arising from the light scattered by an individual particle. The migration time window for individual particles of a particular size corresponded well to the migration time of a peak from a population of particles of the same size detected using a UV absorbance detector. The electrophoretic mobility and scattered light intensity were determined for each particle detected. The average scattered light intensity for each particle size was consistent with Mie scattering theory. Particles as small as 110 nm in diameter were detected individually using this method, but particles with a diameter of 57 nm could not be individually detected. The number of single particle scattering events was counted and compared to the theoretical number of particles injected electrokinetically, and the detection efficiency determined ranged from 38 to 57% for polystyrene spheres of different sizes. The laser-light-scattering detection method was directly compared to laser-induced fluorescence detection using fluorescent polystyrene microspheres. The number of particles detected individually by each method was in agreement.     

Synthesis of organically templated nanoporous Tin(II/IV) phosphate for radionuclide and metal sequestration

Nanoporous tin(II/IV) phosphate materials, with spherical morphology, have been synthesized using cetyltrimethylammonium chloride [CH3(CH2)15N(CH3)3Cl] as the surfactant. The structure of the material is stable at 500 degrees C; however, partial oxidation of the material occurs with redox conversion of Sn2+ to Sn4+, resulting in a mixed Sn(II)/Sn(IV) material. Preliminary batch contact studies were conducted to assess the effectiveness of nanoporous tin phosphate, NP-SnPO, in sequestering redox-sensitive metals and radionuclides, technetium(VII), neptunium(V), thorium(IV), and a toxic metal, chromium(VI), from aqueous matrixes. Results indicate that tin(II) phosphate removed >95% of all contaminants investigated from solution.     

On Birman's sequence of Hardy–Rellich-type inequalities

In 1961, Birman proved a sequence of inequalities $\{I_n\}$, for $n\in \mathbb{N}$, valid for functions in $C_0^n((0,\infty ))?L^2((0,\infty ))$. In particular, $I_1$ is the classical (integral) Hardy inequality and $I_2$ is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space $H_n([0,\infty ))$ of functions defined on $[0,\infty )$. Moreover, $f\in H_n([0,\infty ))$ implies $f^{\prime }\in H_{n?1}([0,\infty ))$; as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite $b>0$, these inequalities hold on the standard Sobolev space $H_0^n((0,b))$. Furthermore, in all cases, the Birman constants ${[(2n?1)!!]}^2/2^{2n}$ in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in $L^2((0,\infty ))$ (resp., $L^2((0,b))$). We also show that these Birman constants are related to the norm of a generalized continuous Cesàro averaging operator whose spectral properties we determine in detail.