We study a deterministic parallel feed-forward neural network. Exact results for the response of the network are presented; given an initial state that has finite overlap with one stored random key pattern, we calculate the overlap on all subsequent layers (time steps). A region of good recall is separated by a first-order line from one of vanishing asymptotic overlap. Relaxation time to the limiting state is shown to diverge at the overloading transition.

We derive a differential equation for the time evolution of the cluster mean size in a system of particles in which both coagulation and fragmentation are occurring. Both stable and unstable solutions exist. For the stable case the equilibrium mean size, number density, and characteristic relaxation time scale with the magnitude of the coagulation and fragmentation kernels and the total primary particle concentration, with exponents related to the homogeneities of the two kernels. For large displacements from equilibrium the size varies with a power law in time, whereas for small displacements the system relaxes exponentially.

It is shown that the neutrino events associated with SN1987A are characterized by the first energetic ($E_{\nu }$∼25 MeV) electron-capture ${\nu }_e$ pulse with quite a high source neutrino flux [$L_{\nu }$,e≃(1–2)×${10}^{53}$ erg], and by the subsequent thermal-pair neutrinos with a modest average energy 〈$E_{\nu }$〉≃7 MeV and also with a reasonable source neutrino flux $L_{\nu }$≃3×${10}^{53}$ erg. Some significant constraints are also derived on particle physics.

We present a high-precision experimental verification of the universality of f(α), the fractal dimension of the subset of the attractor with scaling index α, at the transition from quasiperiodicity to chaos with the golden-mean winding number. The experimental system is cooled extrinsic p-type Ge, which is voltage biased to produce a spatially dependent active oscillation.

For a molecular system with an odd number of electrons, the electronic Hamiltonian possesses a twofold Kramers degeneracy for all nuclear configurations. It is shown that this leads to a non-Abelian gauge-field term in the effective nuclear Hamiltonian, with permissible gauge transformations belonging to SU(2). This should lead to observable effects analogous to the Berry phase for the nondegenerate case. In particular, an atom in a slowly rotating electric field exhibits changes in its component of angular momentum along the field because of the non-Abelian phase factor.

It is shown that the energy of the vacuum obtained by functional methods as the one-loop quantum effective potential may be interpreted as the sum over zero-point energies of the quantum modes of the fields provided that ζ(0), the scale dependence of the quadratic variation of the action, vanishes. This scale dependence does not vanish when one-loop renormalization counterterms are induced in the action by a scale transformation, in which case one has to add to the sum over zero-point energies a term proportional to ζ(0) to get the correct energy of the vacuum.

A Lorentzian algebra is constructed that underlies the covariant formulation of the spinning string. It is a simply laced hyperbolic Kac-Moody algebra having a realization on the ghost-extended spectrum of string states. From the weight space of this algebra, we obtain a unique indefinite superalgebra that has a realization on the superstring spectrum and that automatically implements the Gliozzi-Scherk-Olive projection.

The cubic-action formulation of bosonic string field theory is examined with regard to surface terms. Solutions of the form A=${\mathrm{g}}^{\mathrm{-}1}$${\mathrm{Q}}_{\mathrm{L}}^{\mathrm{full}\mathrm{I}}$ are seen to obey the equation -2gA*A=${\mathrm{J}}_0$+${\mathrm{J}}_{\mathrm{\infty }}$≠0, where ${\mathrm{J}}_0$ and ${\mathrm{J}}_{\mathrm{\infty }}$ are surface currents. Because ${\mathrm{J}}_0$ does not vanish at spatial infinity, the fundamental action must contain a linear term which depends upon the asymptotic background. The effect of ${\mathrm{J}}_{\mathrm{\infty }}$ is to allow scattering solutions with nonzero action.

By use of a superspace generalization of the involution technique (method of image), it is shown that dilaton tadpole amplitudes for the world sheets with the topologies of disk and projective plane cancel for the SO(32) type-I superstring. The same method also shows that the amplitudes at the one-loop level, i.e., on the torus, cylinder, Möbius strip, and Klein bottle, vanish after summation over spin structures. The results suggest that the theory is finite up to two loops.

We study the b→sγ decay. We show that the QCD corrections enhance by more than an order of magnitude the prediction for B(b→sγ), for $m_t$<$m_W$. The implications for the standard model with three generations and the possible experimental signatures in the inclusive and exclusive modes are discussed.

The branching ratio for B→$K^{\mathrm{*}}$γ is calculated as a function of the top-quark mass. We include QCD enhancement effects in the short-distance operators and the hadronic matrix elements are determined by use of the constituent-quark model. The branching ratio is in the accessible range of ∼${10}^{\mathrm{-}4}$.

The reactions J/ψ→ωKK¯π and J/ψ→φKK¯π have been studied in a sample of 5.8×${10}^6$ produced J/ψ decays. The systems $K^{\pm }$$K_S^0$${\pi }^{\mp }$ and $K^{+}$$K^{\mathrm{-}}$${\pi }^0$ produced in association with an ω have enhancements in the mass distribution near 1.44 GeV/$c^2$. The observed angular distributions are consistent with $J^P$${=1\mathrm{}}^{+}$ and do not favor a $J^P$${=0\mathrm{}}^{\mathrm{-}}$ assignment. No signal is seen at the nominal $f_1$(1285) mass. The reverse pattern is observed in the KK¯π system produced in association with a φ, which shows an enhancement near 1.280 GeV/$c^2$, and no evidence for structure at 1.4 GeV/$c^2$.

We report that a dimer of clusters, (${\mathrm{Na}}_{19}$${)}_2$, is energetically stable and explains the abundance of ${\mathrm{Na}}_{38}$ in sodium-cluster mass spectra. A fusion process of two ${\mathrm{Na}}_{19}$ clusters has been studied on the basis of the jellium-sphere-background model by the local-spin-density-functional method. Calculated binding energies show that the force between two clusters is attractive and that the complete fusion is preceded by the formation of a stable (${\mathrm{Na}}_{19}$${)}_2$, whose electronic structure is analogous to an alkali-metal–atom dimer, supporting the concept of ‘‘clusters of giant atoms’’ for sodium clusters.

An optical ring cavity containing distributed nonlinear elements is proposed as a promising candidate for investigation of the dynamic stability of spatial disorder in a system far from thermal equilibrium. If the interaction between the elements is unidirectional, the stability of disordered structure can be determined by the spatial Lyapunov exponent. This fact implies that spatial disorder is frozen under quite restricted conditions, and most of the spatially disordered structure is replaced by spatiotemporal chaos. However, in the case of a bidirectional interaction, the spatial disorder is self-induced over a wide range of the control parameter.

A new regime for the generation of squeezed states of the electromagnetic field is described for a collection of atoms within a high-finesse cavity. The process responsible for squeezing is a coupling-induced splitting in the normal-mode structure of the atom-field system. A theoretical analysis is presented that predicts large degrees of squeezing for modest operating conditions. An experimental investigation of this regime has produced noise reductions of 30% relative to the vacuum noise level.

In the free-electron laser the interaction between the radiation and electrons can result in radiation focusing. The radiation tends to follow the electron beam when the centroid of the electron beam is laterally displaced. Spatial modulation of the electron-beam envelope induces a similar modulation in the radiation-beam envelope. These and other phenomena are studied by use of a novel source-dependent modal representation of the fully three-dimensional radiation field. Among the merits of this approach is that few modes are needed to describe the radiation accurately.

It is shown that wave eigenmode fields can provide rf stabilization of the interchange instability. The excitation level of an m=+1 fast magnetosonic wave is controlled by tailoring of the ${\mathrm{k}}_{\mathrm{?}}$ spectrum of an axial ion-cyclotron radio-frequency antenna array in the Phaedrus-B tandem mirror system. When the ${\mathrm{k}}_{\mathrm{?}}$ spectrum is chosen to excite the wave strongly, density-fluctuation levels in the plasma are greatly reduced.

Using a forced Rayleigh light-scattering technique, we have measured the mutual diffusion coefficients in a side-chain nematic polymer in the two directions parallel and perpendicular to the director, and observed an inverted anisotropy compared to conventional nematic media. These results are interpreted in terms of the influence of the chain backbone on the nematic medium, as regards both the sign of the anisotropy and the order of magnitude of the diffusion coefficients.

We show that the c-Si→a-${\mathrm{SiO}}_2$ transformation takes place via an ordered crystalline oxide layer ≃5 Å thick. Modeling of high-resolution transmission electron-microscope lattice images in two projections suggests the crystalline oxide to be tridymite, a stable, bulk form of ${\mathrm{SiO}}_2$.

The neutron scattering function for liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at 120 mK and pressures of 9, 0.5, 1, and 2 MPa has been determined for wave vectors in the range 3 ${\mathrm{nm}}^{\mathrm{-}1}$${\mathrm{nm}}^{\mathrm{-}1}$. This represents the first experimental information on the density dependence of the zero-sound frequency and damping at finite wave vectors, and should serve as a useful test of theories on excitations in neutral Fermi liquids. The results are in qualitative agreement with extensions of the Landau Fermi-liquid thoery to finite wave vectors.