The geometry of the quantum correction for topological σ-models

The ring (Frobenius algebra) of local observables for topological -models on ¹ with values in the grassmannianG(s, n) is known to be the same as the quotient of the homology ring of the target space by the (inhomogeneous) ideal generated by the so-called quantum correction. While the need for a quantum correction comes from algebraic motivations in field theory, the aim of this paper is to understand its geometric meaning. The simple examples of ^{1 n} models tell us that the quantum correction comes by restriction on the boundary of the moduli spaces which allows to compute intersections on moduli spaces of lower degrees. We will check this point of view for the case of ¹ G(s,n) models, yielding a proof of the algebraic result from physics in terms of the geometry of the -model itself.Work partially supported by National Project 40% Probabilistic and geometrical methods in Mathematical Physics and by CNR-Gruppo Nazionale di Fisica Matematica.     

An iteration method for correcting the located coordinates of an underwater target

An iteration method for correcting the target coordinates deter-mined by a locating system with a Cartesian array is reported.Under thecomplex hydrological condition,the method can give the target position notonly accurately but also quickly.The preliminary experimental results showthat the correction is effective.An application of the method has been com-pleted.     

The design of the apodizing functions for guided-wave EOTF

A design method of the apodizing functions for guided-wave four-port electrooptic tunable filter (EOTF) is proposed. As an example, the specific form of Gaussian apodizing function is designed by analyzing the crosstalk performance of EOTF. Crosstalk is calculated based on the transient response of the filter to an input optical pulse. It is concluded that crosstalk level below -30 dB for 20-Gb/s data rates and 100-GHz channel spacing is achievable with presently available substrate dimensions.     

Quantum geometric tensor and the topological characterization of the extended Su–Schrieffer–Heeger model

We investigate the quantum metric and topological Euler number in a cyclically modulated Su–Schrieffer–Heeger(SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss–Bonnet theorem on the topologic...     

Variational iteration method for solving the mechanism of the Equatorial Eastern Pacific El Nino-Southern Oscillation

A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.     

The topological quantum field theory of Riemann’s theta functions

In this paper we prove the existence and uniqueness of a topological quantum field theory that incorporates, for all Riemann surfaces, the corresponding spaces of theta functions and the actions of the Heisenberg groups and modular groups on them.     

Nonperturbative effect in the β functions and the equations of motion for the string

We study systematically how to calculate the β functions nonperturbatively in the sigma model which describes the string propagation in arbitrary background fields. In particular, we calculate explicity the β functions for a tachyon and massless background fields up to the three-string tree interactions and also the four-tachyon tree interactions.     

Differential-Geometric Invariants of the Hamiltonian Systems of pde’s

Differential-geometric invariants of Hamiltonian systems of partial differential equations are introduced on the basis of the Schouten (2,1)-tensor . Algebraic identities for the corresponding Schouten, Nijenhuis and Haantjes tensors are found. The necessary conditions for existence of Hamiltonian structures for systems of hydrodynamic type are derived.     

Unified treatment for accurate and fast evaluation of the Fermi-Dirac functions

A new analytical approach to the computation of the Fermi-Dirac(FD) functions is presented,which was suggested by previous experience with various algorithms.Using the binomial expansion theorem,these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions.This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation,should such limits be required in practice.Some numerical results are presented for significant mapping examples and they are briefly discussed.     

Loci of extrema of thermodynamic response functions for the Lennard–Jones fluid

Lines of extrema along isotherms and isobars for the residual isochoric heat capacity, the residual isobaric heat capacity, the isobaric thermal expansivity, and the isothermal compressibility of the Lennard–Jones fluid have been studied from popular equations of state due to Johnson et al. [Mol. Phys. 78, 591 (1993)], Kolafa and Nezbeda [Fluid Phase Equilib. 100, 1 (1994)], and Mecke et al. [Int. J. Thermophys. 17, 391 (1996)]. On depicting such loci in the pressure–temperature plane, the characteristic behaviour of thermodynamic response functions in the ideal-gas limit (at high enough temperatures or low enough pressures), the close-packed-fluid limit (at low enough temperatures or high enough pressures) as well as in the liquid, critical, and supercritical regions is identified. The present analysis is informative itself, but it also stimulates further work in order to tackle more complicated cases of study including associated fluids.     

Applicability of chemical derivatization – X-ray photoelectron spectroscopy (CD–XPS) to the characterization of complex matrices: case of electrosynthesized polypyrroles

Problems arising in the application of XPS coupled with derivatization reactions (CD-XPS) to the characterization of complex matrices are stressed by considering the case of polypyrroles electrosynthesized from aqueous solution. In these materials oxygen– and nitrogen–carbon functionalities are contemporaneously present, as well as acidic, basic, charged and reducible groups. The derivatizing agents titanium di-isopropoxide-bis(2,4-pentanedionate) (TAA), trifluoroethanol (TFE) and pentafluorophenylhydrazine (PFPH) were used to label the C–OH, COOH and CO groups, respectively, in the pristine (PPY) and in the overoxidized (PPYox) polymer. The case shows that, when real samples are analysed, only the correlation among the information present in all the available spectra can supply the key to the interpretation of CD-XPS data, such as the actual stoichiometry and secondary effects. In particular, it is showed that PFPH cannot be used as a reliable derivatizing agent for CO groups in PPYox, due to the competition of a side reaction (already reported for hydrazines) occurring on this particular substrate. This effect may be disregarded if a thorough control of the stoichiometry is not performed.     

A New Type of Non-Noether Adiabatic Invariants for Disturbed Lagrangian Systems： Adiabatic Invariants of Generalized Lutzky Type

For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the basis of the invariance of disturbed Lagrangian systems under general infinitesimal transformations, the determining equations of Lie symmetries of the system are constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariant, i.e. generalized Lutzky adiabatic invariants, of a disturbed Lagrangian system are obtained by investigating the perturbation of Lie symmetries t＇or a Lagrangian system with the action of small disturbance. Finally, an example is given to illustrate the application of the method and results.     

New aspects of the plastic deformation of silicon – prerequisites for the reshaping of silicon microelements

New shapes of silicon microelements which can be partially situated outside the wafer plane can be created by the combination of wet anisotropic etching and plastic deformation at high temperatures. Therefore new applications become possible. In order to characterize the plastic behaviour of the silicon microelements bending tests in the 3-point manner were carried out at monocrystalline, differently orientated beams with variation of temperature, bending rate and maximum bending. Additionally the fracture strength at room temperature of deformed and undeformed beams was determined. The dislocation content introduced during the deformation was analysed by the etch pit technique. The deformation is characterized by the formation of dislocations, a pronounced yield point effect, and an orientation-dependent strengthening. The yield points depend strongly on temperature. Because of the strong dependence on the deformation parameters it is possible to create the same amount of irreversible deformation at different stages of the stress–bend diagrams resulting in different dislocation contents and therefore different properties. The analysis of the fracture strength values by means of the Weibull statistics shows a slightly decreased average fracture strength of the deformed material in comparison to the undeformed silicon but a strongly increased Weibull modulus. Received: 22 September 1998 / Accepted: 29 January 1999 / Published online: 28 April 1999     

Quantization of the space－time with topological defect

We present the classical solution of Lagrange equations for the black hole with a global monopole or with a cosmic string. Then we obtain the wavefunction of the space－time by solving the Wheeler－De Witt equation. De Broglie－Bohm interpretation applied to the wavefunction gives the quantum solution of the space－time. In the end, the quantum effect on Hawking radiation is studied.     

Gauge Theoretical Equivariant Gromov–Witten Invariants and the Full Seiberg–Witten Invariants¶of Ruled Surfaces

Let F be a differentiable manifold endowed with an almost K?hler structure (J,ω), α a J-holomorphic action of a compact Lie group on F, and K a closed normal subgroup of which leaves ω invariant. The purpose of this article is to introduce gauge theoretical invariants for such triples (F,α,K). The invariants are associated with moduli spaces of solutions of a certain vortex type equation on a Riemann surface Σ. Our main results concern the special case of the triple