Showing papers on "Projection (relational algebra) published in 1994"

Squeezed Atomic States and Projection Noise in Spectroscopy

Abstract: We investigate the properties of angular-momentum states which yield high sensitivity to rotation. We discuss the application of these ``squeezed-spin'' or correlated-particle states to spectroscopy. Transitions in an ensemble of N two-level (or, equivalently, spin-1/2) particles are assumed to be detected by observing changes in the state populations of the particles (population spectroscopy). When the particles' states are detected with 100% efficiency, the fundamental limiting noise is projection noise, the noise associated with the quantum fluctuations in the measured populations. If the particles are first prepared in particular quantum-mechanically correlated states, we find that the signal-to-noise ratio can be improved over the case of initially uncorrelated particles. We have investigated spectroscopy for a particular case of Ramsey's separated oscillatory method where the radiation pulse lengths are short compared to the time between pulses. We introduce a squeezing parameter ${\ensuremath{\xi}}_{\mathit{R}}$ which is the ratio of the statistical uncertainty in the determination of the resonance frequency when using correlated states vs that when using uncorrelated states. More generally, this squeezing parameter quantifies the sensitivity of an angular-momentum state to rotation. Other squeezing parameters which are relevant for use in other contexts can be defined. We discuss certain states which exhibit squeezing parameters ${\ensuremath{\xi}}_{\mathit{R}}$\ensuremath{\simeq}${\mathit{N}}^{\mathrm{\ensuremath{-}}1/2}$. We investigate possible experimental schemes for generation of squeezed-spin states which might be applied to the spectroscopy of trapped atomic ions. We find that applying a Jaynes-Cummings--type coupling between the ensemble of two-level systems and a suitably prepared harmonic oscillator results in correlated states with ${\ensuremath{\xi}}_{\mathit{R}}$1.

Defect-induced Raman spectra in doped CeO 2

Abstract: Polarized Raman-scattering spectra are obtained from oriented single crystals of yttria-doped ${\mathrm{CeO}}_{2}$. The temperature and dopant dependencies of Raman spectra strongly suggest that many structures in the Raman spectra of yttria-doped ${\mathrm{CeO}}_{2}$ are induced by the defect space including an ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ vacancy. The contribution to the frequency distributions of Raman-active modes from the whole Brillouin zone are estimated from the imaginary part of the simple projection of the phonon displacement-displacement Green's functions of undoped ${\mathrm{CeO}}_{2}$ crystals onto several defect spaces. The observed spectra are well explained by the linear combination of the calculated frequency distributions from the defect space consisting of the four metal ions and from that consisting of the six next-nearest-neighbor ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ions surrounding an ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ vacancy. Brillouin-scattering spectra of ${\mathrm{CeO}}_{2}$ are also measured in order to calculate the phonon-dispersion curves of ${\mathrm{CeO}}_{2}$. The dependencies of type and concentration of defect space on dopant concentration in doped ${\mathrm{CeO}}_{2}$ are also discussed.

A projection method for l p norm location-allocation problems

Abstract: We present a solution method for location-allocation problems involving thel p norm, where 1

The z=0.8596 Damped Lyman Alpha Absorbing Galaxy Toward PKS 0454+039

Abstract: We present {\it Hubble Space Telescope} and ground--based data on the $z_{abs}=0.8596$ metal line absorption system along the line of sight to PKS 0454+0356. The system is a moderate redshift damped Lyman alpha system, with ${\rm N(HI)}=(5.7\pm0.3)\times10^{20}$~cm$^{-2}$ as measured from the {\it Faint Object Spectrograph} spectrum. We also present ground--based images which we use to identify the galaxy which most probably gives rise to the damped system; the most likely candidate is relatively underluminous by QSO absorber standards ($M_B \sim -19.0$ for $q_0=0.5$ and $H_0=50$ \kms Mpc$^{-1}$), and lies $\sim 8.5h^{-1}$ kpc in projection from the QSO sightline. Ground--based measurements of Zn~II, Cr~II, and Fe~II absorption lines from this system allow us to infer abundances of [Zn/H]=$-1.1$, [Cr/H]=$-1.2$, and [Fe/H]=$-1.2$, indicating overall metallicity similar to damped systems at $z >2$, and that the depletion of Cr and Fe onto dust grains may be even {\it less} important than in many of the high redshift systems of comparable metallicity. Limits previously placed on the 21-cm optical depth in the $z=0.8596$ system, together with our new N(H~I) measurement, suggest a very high spin temperature for the H~I, $T_S >> 580$ K.

Studies in the logic of trees with applications to grammar formalisms

Abstract: We present a series of studies in which we employ the machinery of mathematical logic in exploring the formal properties of trees. These are connected by a common core logical language and by the fact that they address issues related to the precise meaning of descriptions of trees and of sets of trees that arise in formal grammars of natural language. Our initial study is an exploration of quasi-trees--partial descriptions of trees arising in recent research in Tree-Adjoining Grammars. We formalize the notion of quasi-trees in the quantifier-free fragment of our language. On this foundation, we develop mechanisms that decide if such a description is satisfiable and, if it is, to produce the linguistically appropriate representatives of the trees that it describes. Such mechanisms are presupposed by the TAG applications that employ quasi-trees. We then turn to the monadic second-order variant of our language ($L\sbsp{K,P}{2}$), and show that it is equivalent in expressive power to the language of SnS--the monadic second-order theory of multiple successor functions. This gives us a descriptive complexity result for the recognizable sets: a set of finite trees is recognizable (a projection of a set of derivation trees generated by some context-free grammar) iff it is definable in $L\sbsp{K,P}{2}$. The final two studies apply this result. First, we explore definability of the principles of Government and Binding Theory. We show that free-indexation, as it is usually employed in GB, is not definable in $L\sbsp{K,P}{2}$, and therefore not enforceable by CFGs. We go on to show, however, that the language licensed by a set of principles describing substantially all of English syntax is definable in $L\sbsp{K,P}{2}$, and thus strongly context-free. This gives an indication of the strength of this technique, since prior to this it has been difficult to show that such languages are even recursive. Finally, we use definability in $L\sbsp{K,P}{2}$ in identifying a decidable class of Tree-Adjoining Grammars that is strongly context-free. This class provides a normal form for TAGs that generate local sets and serves to lexicalize CFGs in a way that is more flexible than previous means.

Improved modeling of excitons in type-II semiconductor heterostructures by use of a three-dimensional variational function

Abstract: Binding energies and oscillator strengths of excitons in staggered-lineup heterostructures such as type-II quantum wells are calculated by a variational method, using a single parameter. This method involves the effective attractive potential imposed by the confined carrier to its unconfined companion. Contrary to previous comparable works, a three-dimensional trial function of the variable r (r=\ensuremath{\Vert}${\mathbf{r}}_{\mathit{e}}$-${\mathbf{r}}_{\mathit{h}}$\ensuremath{\Vert}) is used, instead of a two-dimensional function of the in-plane projection \ensuremath{\rho}. Due to the large spatial extension along z of the wave function of the unconfined carrier, the latter approximation commonly used up to date, is too drastic, even though it works reasonably well for type-I systems. This is demonstrated by comparison of both hypotheses for GaAs-AlAs systems: when using the 3D function, binding energies are increased by up to 52%, while electron-hole overlap integrals can be enhanced by one order of magnitude.

R-Matrix Formulation of the Quantum Inhomogeneous Groups Iso_qr(N) and Isp_qr(N)

Abstract: The quantum commutations $RTT=TTR$ and the orthogonal (symplectic) conditions for the inhomogeneous multiparametric $q$-groups of the $B_n,C_n,D_n$ type are found in terms of the $R$-matrix of $B_{n+1},C_{n+1},D_{n+1}$. A consistent Hopf structure on these inhomogeneous $q$-groups is constructed by means of a projection from $B_{n+1},C_{n+1},D_{n+1}$. Real forms are discussed: in particular we obtain the $q$-groups $ISO_{q,r}(n+1,n-1)$, including the quantum Poincar\'e group.

Asymptotic theory of s-->p charge exchange: Extended Demkov model

Abstract: The asymptotic theory is developed for the calculation of the charge-exchange amplitudes for large impact parameters \ensuremath{\rho}. The case of the small energy defect is considered which corresponds to the Demkov model (nonadiabatic transitions induced by the switching of the wave functions from the atomic states to the molecular-orbital regime). The effect of electron momentum transfer is included. The initial and final states with nonzero orbital momentum are considered with a special emphasis on the simplest case of s\ensuremath{\rightarrow}p charge exchange. The large-\ensuremath{\rho} asymptote of the charge-exchange amplitude is calculated both for the transitions induced by radial and rotational couplings. One-center depolarization transitions (changing the projection of the angular momentum) are also incorporated in the general theory. The orientation and alignment parameters characterizing the asymmetry created in the s\ensuremath{\rightarrow}p process are obtained in a simple analytical form for large \ensuremath{\rho} (or small scattering angles). They include contributions both from the one-center depolarization and from the competition of the charge exchange induced by radial and rotational coupling. The relative role of both mechanisms is analyzed and a strong dependence of the asymmetry parameters on the sign of the process energy defect is predicted. The theory is applied to the process Na(3p)+${\mathrm{H}}^{+}$\ensuremath{\rightarrow}${\mathrm{Na}}^{+}$+H(n=2).

Fabrication of sub-40-nm p-n junctions for 0.18-μm MOS device applications using a cluster-tool-compatible, nanosecond thermal doping technique

Abstract: In this paper, we introduced an alternative deep-submicrometer doping technology, Projection Gas Immersion Laser Doping (P-GILD). Representing the marriage of lithography and diffusion, P-GILD is a resistless, step-and-repeat doping process that utilizes excimer laser light patterned by a dielectric reticle to selectively heat and, thereby, dope regions of an integrated circuit. Results of physical and electrical characterization are presented for ultra-shallow p{sup +} {minus}n and n{sup +} {minus}p junctions produced by gas immersion laser doping (GILD), a phenomenologically identical technique that utilizes an aluminum contact mask rather than a dielectric reticle to pattern the beam. Junctions produced using GILD exhibit uniformly-doped, abrupt impurity profiles with no apparent defect formation in the silicon. Electrically, sheet and contact resistivities of the ultra-shallow junctions are less than 100{Omega}/sheet and 1 {times} 10{sup {minus}6} {Omega}{sm_bullet}cm{sup 2}, respectively, while n{sup +} {minus}p and p{sup +} {minus}n diodes exhibit nearly ideal forward bias behavior and reverse leakage current densities less than 5 nA/cm{sup 2} at {minus}5V. Uniformity of both diode characteristics and sheet resistance for junctions produced by the step-and-repeat process is also shown to be better than {plus_minus}5% across a 4-inch wafer.

Generalized information-lossless automata of finite order. II

Abstract: The notion of generalized information-lossless automaton was introduced elsewhere. The mathematical model for our analysis is a structured weakly-initialized minimal Mealy automaton A = (S, X, Y, {delta}, {lambda}, S{sub 0}), where S is the finite state set, X the finite input alphabet, Y the finite output alphabet, {alpha} and {lambda} are the transition and output functions that define the mappings {delta}: S x X{yields}S, {lambda}: S x X{yields}Y, S{sub 0} is the set of allowed initial states (1 {le} {vert_bar} S{sub 0} {vert_bar} {le} {vert_bar} S {vert_bar}). Each symbol {bar x} {element_of} X is a vector (x{sub 1},...,x{sub n}), i.e., X = X{sub 1} x X{sub 2} x ... x X{sub n}, and each symbol {bar y} {element_of} Y is a vector (y{sub 1},...,y{sub m}), Y = Y{sub 1} x Y{sub 2} x ... x Y{sub m}. Suppose that in input word {bar v} is applied to the automaton A which is in one of the states of the set S{sub 0} (the exact state is not known), and the response {bar w} to this word is observed in output channels j{sub 1} < j{sub 2} < ... < j{sub {mu}}, where 1 {le} j{sub i} {le} m. Ifmore » an integer N(A) exists for the automaton A such that the protection of the initial section of length N(A) of the word {bar w} is always sufficient for unique determination of the projection of the first symbol of the word {bar v} in input channels i{sub 1} < i{sub 2} < ... < i{sub v}, where 1 {le} i{sub j} {le} n, independently of the input sequence and the initial state of the automaton, then A is called a generalized information-lossless automaton of finite order (GILFO). The ensure single-valued determination of the number N(A), we assume that it is the least number among all possible numbers of this kind for the automaton A. As previously, we assume without loss of generality that the automaton response is observed in the first u output channels 1,2,...,{mu}, and the unknown word is reconstructed for the first v input channels 1,2,...,v.« less

On n -column 0,1-matrices with all k -projections surjective

Abstract: This paper presents a new approach to construct a smalln-column 0, 1-matrix for two given integersn andk(k

The Algebra of Hamiltonian Systems

Abstract: It is well known that the projective space ℂP n carries a canonical symplectic structure (see, for instance, Arnol’d [1974] or Arnol’d and Givental’ [1985]). We consider a representation ρ: G →GL(V) of a Lie group G on a finite-dimensional complex vector space V. There is an induced action of G on the projective space P(V) associated with V. We denote by G(z) the orbit of this action passing through a point z ϵ P(V). It is now natural to ask when the symplectic structure of P(V) induces a symplectic structure on the orbits of G in P(V). Let us assume that G is compact, let T be a maximal torus in G, let g and t be the Lie algebras of G and T, respectively, and let L ℂ denote the complexification of a vector space L. We then have the root space decomposition \( {g^C} = {t^C} + \sum\limits_{\alpha e 0} {\mathbb{C}{E_\alpha }{H_\alpha }} = \left[ {{E_\alpha }{E_{ - \alpha }}} \right] \) (see, for instance, Helgason [1962], Jacobson [1962] or the Appendix). Let n: V\0 → P(V) be the natural projection which maps a vector υ ∊ V\0 into the straight line passing through υ and the origin.

Strange properties of early time evolution of the projection of a state vector

Abstract: Using the equation for a projection of a state vector, the exponent of a damping factor for a given state, corresponding to the effective decay width $$\overline {\gamma _\alpha (t)} $$ appearing in the case of multiple measured unstable states, is obtained numerically in some models for early time period t → 0. $$\overline {\gamma _\alpha (t)} $$ is found to be nonzero (even for stable states) at this time period; thus, for early times, this damping factor is always smaller than unity. It is shown that at finitet's $$\overline {\gamma _\alpha (t)} $$ may be smaller or greater than the standard decay width γα in Weisskopf-Wigner theory depending on the parameters of a model considered.