Non-symmetric Ones Research Articles

Orientation peculiarities of dc Josephson tunneling betweend-wave superconductors with charge density waves

The theory of the stationary Josephson tunnel current Ic was devised for junctions involving superconductors partially gapped by biaxial or unidirectional charge density waves (CDWs) and possessing a superconducting order parameter of d-wave symmetry. Specific calculations were carried out for symmetric junctions between two identical CDW superconducting electrodes and nonsymmetric ones composed of a CDW superconductor and a conventional isotropic s-wave superconductor. Two kinds of superconducting pairing symmetries were studied, namely, that appropriate to cuprates (dx2−y2) and the dxy one. The corresponding calculations were also carried out for the extended s-wave symmetry of the superconducting order parameter. Allowances were made for the directionality of tunneling. In all the cases studied, the dependences of Ic on the angle γ between the chosen crystal direction and the normal to the junction plane were found to be significantly influenced by CDWs. It was shown in particular that the d-wave driven periodicity of Ic(γ) in the CDW-free case is transformed into double-period beatings depending on the parameters of the system. The results of calculations testify that the orientation-dependent patterns Ic(γ) measured for CDW superconductors allow the CDW configuration (unidirectional or checkerboard) and the symmetry of superconducting order parameter to be determined. The predicted effects can be used to indirectly reveal CDWs in underdoped cuprates where pseudogaps are observed. The break-junction technique is an appropriate tool for this purpose.

Microlenses with defined contour shapes

Ink-jet printing of optical ink over SU-8 pillars is here proposed as a technology for obtaining microlenses with shape control. To demonstrate the flexibility of this method, microlenses with five different contour shapes (ranging from circular and elliptical to toric or more advanced geometries) have been fabricated. Furthermore, the optical properties of the different fabricated lenses have been experimentally investigated. Focal distance, numerical aperture (NA) and full-width at half maximum (FWHM) of the microlenses have been determined. Arrays of microlenses showed an identical behavior with a standard deviation in the total intensity of only 7%. Additionally, the focal plane of the fabricated symmetric microlenses and the Sturm interval of the non-symmetric ones have been obtained. The experimental results demonstrate the validity and flexibility of the proposed technology.

Conjugate symmetry

Conjugate symmetry is an entirely new approach to symmetric Boolean functions that can be used to extend existing methods for handling symmetric functions to a much wider class of functions. These are functions that currently appear to have no symmetries of any kind. Conjugate symmetries occur widely in practice. In fact, we show that even the simplest circuits exhibit conjugate symmetry. To demonstrate the effectiveness of conjugate symmetry we modify an existing simulation algorithm, the hyperlinear algorithm, to take advantage of conjugate symmetry. This algorithm can simulate symmetric functions faster than non-symmetric ones, but due to the rarity of symmetric functions, this optimization is of limited benefit. Because the standard benchmark circuits contain many symmetries it is possible to simulate these circuits faster than is possible with the fastest known event-driven algorithm. The detection and exploitation of conjugate symmetries makes use of GF(2) matrices. It is likely that conjugate symmetry and GF(2) matrices will find applications in many other areas of EDA.

Dissipative double-well potential: Nonlinear stationary and pulsating modes

The analysis of nonlinear modes in a complex absorbing double-well potential supported by linear gain is presented. Families of the nonlinear modes and their bifurcations are found numerically by means of the properly modified "shooting" method. Linear stability and dynamics of the modes are studied. It is shown that no stable modes exist in the case of attractive nonlinearity, while stable modes, including nonsymmetric ones, are found when the nonlinearity is repulsive. Varying a control parameter (e.g., the height of barrier between the wells) results in switching from one mode to another. Apart from stationary modes we have found pulsating solutions emergent from unstable modes.

Symmetric and non-symmetric waves in the osmosis K(2, 2) equation

We give an improved qualitative method to solve the osmosis K(2, 2) equation. This method combines several characteristics of other methods. Using this method, the existence of symmetric and non-symmetric wave solutions of the osmosis K(2, 2) equation is studied. Besides abundant symmetric forms such as smooth wave solutions, peaked waves, cusped waves, looped waves, stumpons and fractal-like waves, this equation also admits non-symmetric ones including breaking kink wave solutions, breaking anti-kink wave solutions and rampons. As regards this equation most of those solutions, either symmetric or non-symmetric solutions, have not appeared in the literature. We also study the limiting behavior of all periodic solutions as the parameters tend to some special values.

Dipolarizations in Kac–Moody Algebras

In this paper, some methods are given to construct dipolarizations in Kac–Moody algebras as well as their some subalgebras, and an illustrative example is provided. The dipolarizations found in this paper include symmetric and non-symmetric ones.

Cyanomethylamines and azidomethylamines: new general methods of the synthesis and transformations

Simple and efficient methods have been developed to obtain cyanomethylamines and azidomethylamines using reactions of methoxymethylamines with TMSCN and TMSN 3 , respectively. In the case of dimethylformamide dimethylacetal, only one MeO group was substituted with CN, and an unexpected direction of the subsequent azidation was found. Adducts of azidomethylamines with DMAD were studied, and the base-catalyzed isomerization of symmetric triazoles into non-symmetric ones was revealed.

Nonholonomic Ricci Flows, Exact Solutions in Gravity, and Symmetric and Nonsymmetric Metrics

We provide a proof that nonholonomically constrained Ricci flows of (pseudo) Riemannian metrics positively result into nonsymmetric metrics (as explicit examples, we consider flows of some physically valuable exact solutions in general relativity). There are constructed and analyzed three classes of solutions of Ricci flow evolution equations defining nonholonomic deformations of Taub NUT, Schwarzschild, solitonic and pp--wave symmetric metrics into nonsymmetric ones.

Synthesis of non-symmetric bisoxazoline compounds. An easy way to reach tailored chiral ligands

Bisoxazoline compounds have been used as chiral catalyst ligands in a wide variety of reactions. A great deal of effort has been aimed at the synthesis of C 2-symmetric bisoxazolines but very few references exist for non-symmetric ones. As part of our studies into the possible usefulness of non-symmetric bisoxazolines, we report an easy method for the synthesis of bisoxazoline compounds bearing different substituents in each oxazoline ring.

CONVOLUTION AND CENTRAL LIMIT THEOREM ARISING FROM ADDITION OF FIELD OPERATORS IN ONE-MODE TYPE INTERACTING FOCK SPACES

In Ref. 2 the authors introduced field operators in one-mode type Interacting Fock Spaces whose spectral measures have common symmetric Jacobi recurrence coefficients but differ in the nonsymmetric ones. We show that the convolution of measures arising from addition of such field operators is the universal convolution of Accardi and Bożejko. We also present the associated central limit theorem in a more general form than in Ref. 2 and give it a proof based on the properties of the convolution.

An efficient routine for computing symmetric real spherical harmonics for high orders of expansion

A numerically efficient method of constructing symmetric real spherical harmonics is presented. Symmetric spherical harmonics are real spherical harmonics with built-in invariance with respect to rotations or inversions. Such symmetry-invariant spherical harmonics are linear combinations of non-symmetric ones. They are obtained as eigenvectors of an appropriate operator, depending on symmetry. This approach allows for fast and stable computation up to very high order symmetric harmonic bases, which can be used in e.g. averaging of non-crystallographic symmetry in protein crystallography or refinement of large viruses in electron microscopy.

Submerged plane layered isotropic media: Properties of the scattering matrix eigenvalues with application to bilayers (L)

The plot of the transmission coefficient moduli cannot be used to analyze all the resonances of layered structures because of the overlapping of the resonances. A method using the scattering matrix eigenvalues is presented. It allows, first, to annihilate the overlapping and to recover the resonance positions and half-widths and second, to divide in two independent sets most of the resonances involved in symmetric structures as well as in nonsymmetric ones. Comparisons between the results provided by the method and those coming from the poles of the transmission coefficient agree. In many cases, the transition terms constitute a generalization of the transmission coefficients.

Yang-Baxter Graphs, Jack and Macdonald Polynomials

We describe properties of the affine graph underlying the recursions between the different varieties of nonsymmetric Macdonald and Jack polynomials. We use an arbitrary function of one variable in the definition of affine edges, and of Cherednik's elements, to unify the different theories. We describe the symmetrizing operators furnishing the symmetric polynomials from the nonsymmetric ones.

An algebraic study on theAN-1- andBN-Calogero models with bosonic, fermionic and distinguishable particles

Through an algebraic method using the Dunkl--Cherednik operators, the multivariable Hermite and Laguerre polynomials associated with the $A_{N-1}$- and $B_N$-Calogero models with bosonic, fermionic and distinguishable particles are investigated. The Rodrigues formulas of column type that algebraically generate the monic non-symmetric multivariable Hermite and Laguerre polynomials corresponding to the distinguishable case are presented. Symmetric and anti-symmetric polynomials that respectively give the eigenstates for bosonic and fermionic particles are also presented by the symmetrization and anti-symmetrization of the non-symmetric ones. The norms of all the eigenstates for all cases are algebraically calculated in a unified way.

Joint transform correlator: expansion of the aberration function for a compact design

A method to compute the aberrations of any order introduced into an optical system which performs the first Fourier transform in a joint transform correlator is described. The optical system considered is illuminated by a quasimonochromatic axial point source and it optically processes a structure placed between two centred optical systems, A and B. The structure acts as an aperture stop, its plane is perpendicular to the optical axis of A and B and it consists of two rectangular displays (object and sample) placed symmetrically with respect to this axis. Each display can be considered as a superposition of sinusoidal gratings of different spatial frequencies and orientations. The aberrations which correspond to each spatial frequency must be evaluated separately for the object (scene) and for the sample (target) and then the device is neither centred nor symmetric. Here it is shown that the aberration function for one of the displays and a given spatial frequency can be expanded in Zernike's polynomials considering both the usual symmetric terms and the non-symmetric ones and assuming that the aperture stop is the circle which contains the display. Moreover, if the optical system which performs the second Fourier transform in the correlator is free from aberrations, it is shown that a criterion which can be used to ensure that an accurate correlation signal is obtained is that the difference between the wavefront aberrations introduced in both displays is less than a quarter of a wavelength.

Cover times for words in symmetric and nonsymmetric cases: A comparison

Considering an infinite string of i.i.d. random letters drawn from a finite alphabet X, we are interested in the number of letters needed until one or more given words are observed as a substring. Given a large subset of words of length n (typically the whole Xn), one can define the corresponding cover time as the maximum of the waiting times associated with each of the words considered, that is, the number of random letters needed until each word appears at least once. The symmetric case of uniformly distributed random letters has been studied throughly, but it is less well known how the results change if the distribution of random letters is no longer uniform. In the paper, a comparison is made between results in the symmetric and nonsymmetric cases, both known and new ones.

The Limiting Values of Added Masses of a Partially Submerged Cylinder of Arbitrary Shape

Using Schwarz's integral formula, new series expressions are obtained for the low-and high-frequency limiting values of the added-mass tensor of partially submerged cylinders of arbitrary shape, including nonsmooth and non-symmetric ones. These series contain the Fourier coefficients of simple geometric quantities of the body contour, and their rate of convergence is controlled by geometrical parameters reflecting the smoothness of the double-body contour. Alternative expressions of a more usual form, in terms of the conformal mapping coefficients of the body contour, are also presented. The off-diagonal elements of the limiting added-mass tensors as well as the low-frequency added moment of inertia for nonsymmetric sections are apparently given for the first time. As an application, closed-form expressions for the limiting added-mass coefficients of an extended-Lewis family of ship sections are obtained. Numerical results are also presented for an extended-Lewis, a rectangular, and three ogival sections. The convergence of the frequency-dependent elements of the added-mass tensors towards their limiting values is also discussed in detail, and it is numerically illustrated for a heeled ship-like section.

Quantum field theory and the antipodal identification of black-holes

The antipodal points ( U, V, θ, ϕ) and (− U, − V, π − θ, ϕ + π) of the Schwarzchild-Kruskal manifold, usually interpreted as two different events (in two different worlds) are considered here as physically identified (to give one single world). This has fundamental consequences for the QFT formulated on this manifold. The antipodal symmetric fields have (globally) zero norm. The usual particle-antiparticle Fock space definition breaks down. There is no quantum operator (unitary, antiunitary or projection) giving antipodal symmetric states from the usual Kruskal ones. The antipodal symmetric Green functions have the same periodicity β = 8 π M in imaginary (Schwarzschild) time as the usual (non-symmetric) ones. (Identification with “conical singularity” would give a period 1 2 β ). In any case, no usual thermal interpretation is possible for T = β −1 (nor for T 0 = 2 β or any other value) in the theory. In the light of these results we discuss “old” ideas and more recent ones on identification.

Algebraic multigrid theory: The symmetric case

A rigorous two-level theory is developed for general symmetric matrices (and nonsymmetric ones using Kaczmarz relaxation), without assuming any regularity, not even any grid structure of the unknowns. The theory applies to algebraic multigrid (AMG) processes, as well as to the usual (geometric) multigrid. It yields very realistic estimates and precise answers to basic algorithmic questions, such as: In what algebraic sense does Gauss-Seidel (or Jacobi, Kaczmarz, line Gauss-Seidel, etc.) relaxation smooth the error? When is it appropriate to use block relaxation? What algebraic relations must be satisfied by the coarse-to-fine interpolations? What is the algorithmic role of the geometric origin of the problem? The theory helps to rigorize local mode analyses and locally analyze cases where the latter is inapplicable.

Energy consumption of three-link manipulators as a function of geometric features and trajectory parameters

SUMMARYThe method of parametric optimization is applied to the energy analysis of the motion of three-link manipulators. The quality criterion is the energy consumption along 1 m of the path. It consists of two parts: 1) The sum of the products of joint moments and relative joint velocities (an equivalent of the mechanical work); 2) a quadratic form of joint velocities (an analogue of dissipation losses). Typical spatial motions are studied: the hand of the robot moves along a straight line from an initial position to another one, and returns to the start. Several velocity function shapes (parabolic, sinusoidal, and triangular), both symmetric and non-symmetric ones, are considered. The dependence of the energy consumption on the velocity form, on the trajectory parameters and on mechanical and geometrical characteristics of links is discussed.