Finite Pole Research Articles

Baryon-rich QCD matter

Properties of high-density strong-interaction matter of relevance for astrophysical scenarios that involve neutron stars are discussed. It is argued that theoretical and experimental insights from the small baryo-chemical potential (µB ) and high-temperature regions of the QCD phase diagram can guide realistic model building at high density, as this regime is currently not accessible to first-principles numerical calculations of the QCD partition function. Special attention is payed to the chiral properties of high-density matter and the nature of a possible first-order chiral phase transition. In this transition hadronic parity-partners, in particular baryons, become spectrally degenerate with finite (pole) masses, as expected from general insight into the mass generation in QCD. Possible signals in heavy-ion dielectron production at beam energies of a few GeV are discussed. Based on evidence for an emergent ”chiral spin symmetry” above the pseudo-critical chiral transition temperature at small µB , speculations on the physical state of dense hadronic matter beyond the chiral phase transition are presented.

Efficient Algorithm Based on Liechtenstein Method for Computing Exchange Coupling Constants Using Localized Basis Set

For large-scale computation of the exchange coupling constants $J_{ij}$, we reconstruct the Liechtenstein formula for localized orbital representation and simplify the energy integrations by adopting the finite pole approximation of the Fermi function proposed by Ozaki [Phys. Rev. B 75, 035123 (2007)]. We calculate the exchange coupling constant $J_{\mathrm{1NN}}$ of the first-nearest-neighbor sites in body-centered-cubic Fe systems of various sizes to estimate the optimal computational parameters that yield appropriate values at the lowest computational cost. It is shown that the number of poles needed for a computational accuracy of 0.05 meV is determined as $\sim$ 60, whereas the number of necessary Matsubara poles needed to obtain similar accuracy, which was determined in previous studies, is on the order of 1000. Finally, we show $J_{ij}$ as a function of atomic distance, and compared it with one derived from Korringa-Kohn-Rostoker Green's function formalism. The distance profile of $J_{ij}$ derived by KKR formalism agrees well with that derived by our study, and this agreement supports the reliability of our newly derived formalism.

Exact partition functions for deformed N = 2 $$ \mathcal{N}=2 $$ theories with N f = 4 $$ {\mathcal{N}}_f=4 $$ flavours

We consider the $\Omega$-deformed $\mathcal{N}=2$ $SU(2)$ gauge theory in four dimensions with $N_{f}=4$ massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters $\varepsilon_{1}, \varepsilon_{2}$, the scalar field expectation value $a$, and the hypermultiplet masses ${\bf m}=(m_{1}, m_{2}, m_{3}, m_{4})$. Motivated by recent findings in the $\mathcal{N}=2^{*}$ theory, we explore the theories that are characterized by special fixed ratios $\varepsilon_{2}/\varepsilon_{1}$ and ${\bf m}/\varepsilon_{1}$ and propose a simple condition on the structure of the multi-instanton contributions to the prepotential determining the effective action. This condition determines a finite set $\Pi_{N}$ of special points such that the prepotential has $N$ poles at fixed positions independent on the instanton number. In analogy with what happens in the $\mathcal{N}=2^{*}$ gauge theory, the full prepotential of the $\Pi_{N}$ theories may be given in closed form as an explicit function of $a$ and the modular parameter $q$ appearing in special combinations of Eisenstein series and Jacobi theta functions with well defined modular properties. The resulting finite pole partition functions are related by AGT correspondence to special 4-point spherical conformal blocks of the Virasoro algebra. We examine in full details special cases where the closed expression of the block is known and confirms our Ansatz. We systematically study the special features of Zamolodchikov's recursion for the $\Pi_{N}$ conformal blocks. As a result, we provide a novel effective recursion relation that can be exactly solved and allows to prove the conjectured closed expressions analytically in the case of the $\Pi_{1}$ and $\Pi_{2}$ conformal blocks.

On instantaneous invariants of hyperbolic planes

In this study, we consider the kinematics of the hyperbolic plane and define the notions of inflection curve, circling-point curve, cubic of twice stationary curvature curve, and cubic of thrice stationary curve. We also obtain Cartesian and parametric equations of these curves and illustrate some special cases. Finally, we investigate the hyperbolic Ball point, the ordinary and the sixth-order Burmester points in the case of a finite instant pole.

COMPOSITION OPERATORS ON FINITE RANK MODEL SUBSPACES

AbstractWe give a complete description of bounded composition operators on model subspaces KB, where B is a finite Blaschke product. In particular, if B has at least one finite pole, we show that the collection of all bounded composition operators on KB has a group structure. Moreover, if B has at least two distinct finite poles, this group is finite and cyclic.

Diseño y Análisis de Control con Modos Deslizantes para Sistemas con Predictores de Asignación Finita de Polos

A method to control input or output delayed systems is presented using sliding modes and Smith like predictors, known as finite pole assignment. Using predictors avoids chattering caused by delay in input or output. A design means for the sliding surface with this kind of predictors is introduced, the proposed method is analyzed as well as the issues to be solved due to uncertainties in parameters estimation. Also, some numerical examples are given to illustrate the method and some aspects of the developed analysis.

Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach Spaces

We will consider a pole assignment problem for a class of linear neutral functional differential equations in Banach spaces. We will think of the neutral system studied as that of involving no time delays and reduce the study of adjoint semigroups and spectral properties of neutral equations to those of Cauchy problems. Under the assumption that both the control and eigenspace of pole are finite dimensional, we establish the rank conditions for finite pole assignability.

Laurent series for inversion of linearly perturbed bounded linear operators on Banach space

In this paper we find necessary and sufficient conditions for the existence of a Laurent series expansion with a finite order pole at the origin for the inverse of a linearly perturbed bounded linear operator mapping one Banach space to another. In particular we show that the inversion defines linear projections that separate the Banach spaces into corresponding complementary subspaces. We present two pertinent applications.

Inversion of analytically perturbed linear operators that are singular at the origin

Let H and K be Hilbert spaces and for each z ∈ C let A ( z ) ∈ L ( H , K ) be a bounded but not necessarily compact linear map with A ( z ) analytic on a region | z | < a . If A ( 0 ) is singular we find conditions under which A ( z ) −1 is well defined on some region 0 < | z | < b by a convergent Laurent series with a finite order pole at the origin. We show that by changing to a standard Sobolev topology the method extends to closed unbounded linear operators and also that it can be used in Banach spaces where complementation of certain closed subspaces is possible. Our method is illustrated with several key examples. 2 2 This paper is based on preliminary work in [P.G. Howlett, K.E. Avrachenkov, Laurent series for the inversion of perturbed lionear operators on Hilbert space, in: A. Rubinov (Ed.), Progress in Optimisation III, Contributions from Australasia, Kluwer, 2001, pp. 325–342; P.G. Howlett, V. Ejov, K.E. Avrachenkov, Inversion of perturbed linear operators that are singular at the origin, in: Proceedings of 42nd IEEE Conference on Decision and Control, Maui, Hawai, December 2003, pp. 5628–5631 (on compact disc)].

Compact Low-Pass Filter with Sharp Skirt Characteristics and Broad Stopband

A new compact microstrip low-pass filter and its equivalent-circuit model are developed. The philosophy of the structure behind this novel microstrip low-pass filter is simple as it is composed of a pair of symmetrical parallel coupled-line and an open-stub. With this configuration, a finite attenuation pole near the stopband cutoff frequency is available and adjustable by simply tuning the circuit parameters. Furthermore, the rejection bandwidth of this type of low-pass filter can be extended. In order to validate the feasibility of the proposed design method, a low-pass filter based on a microstrip structure is designed, fabricated, and measured. Experimental results agree very well with the simulation and analytical results.

Plate motion on Europa and nonrigid behavior of the Icy lithosphere: The Castalia Macula region

We have developed a generalized quantitative technique for determining the finite pole of rotation between two rigid plates and use it to critically examine differing reconstructions of a region surrounding a prominent dark spot on Europa, Castalia Macula. This region is located near the equator of Europa's trailing hemisphere and has been suggested as a site where crustal convergence may have occurred. Previous reconstructions of the region have indicated that a ridge set and/or a band-like complex that define a collection of tectonic plates in the region accommodated surface contraction. However, a critical examination of the differences between these reconstructions has been complicated by the lack of a finite pole of rotation for the plates involved in either reconstruction. We have applied our modeling technique, coupled with a detailed examination of the morphology and cross-cutting relationships involving this ridge set and band-like complex, to determine if a unique reconstruction exists for several tectonic plates in this region. The cross-cutting relationships involving the ridge set also allow us to test the general assumption that plates behave rigidly on Europa. Assuming rigid behavior, our results suggest that a unique reconstruction does exist, indicating the ridge set accommodated surface contraction. However, analysis performed to test the assumption of plate rigidity indicates that one or more of the plates in the region did not behave rigidly. This does not rule out surface contraction along the ridge set but does indicate that a component of nonrigid behavior must be considered.

Miniaturized microstrip lowpass filter with wide stopband using double equilateral U-shaped defected ground structure

A compact double equilateral U-shaped defected ground structure (DGS) unit is proposed. In contrast to a single finite attenuation pole characteristic offered by the conventional dumbbell DGS, the proposed DGS unit provides dual finite attenuation poles that can be independently controlled by the DGS lengths. A 2.4-GHz microstrip lowpass filter using five cascaded double U-shaped DGS units is designed and compared with conventional DGS lowpass filters. This low pass filter achieves a wide stopband with overall 30-dB attenuation up-to10 GHz and more than 42% size diminution.

Regularization of Linear Discrete-Time Periodic Descriptor Systems by Derivative and Proportional State Feedback

In this paper, we consider the regularization problem for the linear time-varying discrete-time periodic descriptor systems by derivative and proportional state feedback controls. Sufficient conditions are given under which derivative and proportional state feedback controls can be constructed so that the periodic closed-loop systems are regular and of index at most one. The construction procedures used to establish the theory are based on orthogonal and elementary matrix transformations and can, therefore, be developed to a numerically efficient algorithm. The problem of finite pole assignment of periodic descriptor systems is also studied.

A New Precession Formula

We adapt J. G. Williams' expression of the precession and nutation using the 3-1-3-1 rotation to an arbitrary inertial frame of reference. The modified formulation avoids a singularity caused by finite pole offsets near the epoch. By adopting the planetary precession formula numerically determined from DE405 and by using a recent theory of the forced nutation of the nonrigid Earth by Shirai & Fukishima, we analyze the celestial pole offsets observed by VLBI for 1979-2000 and determine the best-fit polynomials of the lunisolar precession angles. We then translate the results into classical precession quantities and evaluate the difference due to the difference in the ecliptic definition. The combination of these formulae and the periodic part of the Shirai-Fukishima nutation theory serves as a good approximation of the precession-nutation matrix in the International Celestial Reference Frame. As a by-product, we determine the mean celestial pole offset at J2000.0 as 0 = -(17.12 ± 0.01) mas and 0 = -(5.06 ± 0.02) mas. Also, we estimate the speed of general precession in longitude at J2000.0 as p = 50287955 ± 00003 per Julian century, the mean obliquity at J2000.0 in the inertial sense as (0)I = 8438140621 ± 000001 and in the rotational sense as (0)R = 8438140955 ± 000001, and the dynamical flattening of Earth as Hd = (3.2737804 ± 0.0000003) × 10-3. Furthermore, we establish a fast way to compute the precession-nutation matrix and provide a best-fit polynomial of an angle to specify the mean Celestial Ephemeris Origin.

Discrepant Cretaceous paleomagnetic poles between Eastern China and Indochina: a consequence of the extrusion of Indochina

A paleomagnetic study of Cretaceous and Paleocene red-beds has been carried out in the Yunlong area (Yunnan province of China) of the Northern Indochina block. A high-temperature component with dual polarities was isolated from both Lower Cretaceous and Paleocene rocks, and of solely polarity for upper Early Cretaceous and lower Late Cretaceous rocks. Thirteen magnetic polarity zones are found along the Pijiang section. The primary nature of Cretaceous magnetic remanence is ascertained by positive and reversal fold tests. These results, combined with previous Cretaceous results from the Yunlong and Yongping areas of the Lanping basin, indicate that these areas behaved as a relatively rigid block, and rotated 37.2±17° clockwise relative to Eurasia since the Paleocene. Comparing available Early Cretaceous paleomagnetic results obtained both from Indochina and Eastern China, a statistically significant paleolatitude difference of 9.6±5.7° is inferred. This difference is consistent with an estimated 1000±400km extrusion of Indochina relative to South China, through a counter-clockwise rotation of 14° of Indochina around a finite rotation pole inferred from the stage poles of rotation derived from the magnetic isochrons in the South China Sea. The reconstruction is fully consistent between, the Cretaceous pole obtained from the Khorat basin of the stable core of the Indochina block and the coeval pole of Eastern China.

A Behavioral Approach to the Pole Structure of One-Dimensional and Multidimensional Linear Systems

We use the tools of behavioral theory and commutative algebra to produce a new definition of a (finite) pole of a linear system. This definition agrees with the classical one and allows a direct dynamical interpretation. It also generalizes immediately to the case of a multidimensional (nD) system. We make a natural division of the poles into controllable and uncontrollable poles. When the behavior in question has latent variables, we make a further division into observable and unobservable poles. In the case of a one-dimensional (1D) state-space model, the uncontrollable and unobservable poles correspond, respectively, to the input and output decoupling zeros, whereas the observable controllable poles are the transmission poles. Most of these definitions can be interpreted dynamically in both the 1D and nD cases, and some can be connected to properties of kernel representations. We also examine the connections between poles, transfer matrices, and their left and right matrix fraction descriptions (MFDs). We find behavioral results which correspond to the concepts that a controllable system is precisely one with no input decoupling zeros and an observable system is precisely one with no output decoupling zeros. We produce a decomposition of a behavior as the sum of subbehaviors associated with various poles. This is related to the integral representation theorem, which describes every system trajectory as a sum of integrals of polynomial exponential trajectories.

Algebraic conditions of robust decentralized impulse elimination for descriptor systems

In this paper, problems associated with robust impulse elimination for descrip-tor systems under a decentralized control structure are considered. First, the concept of impulse margin of the system is defined to give a measure from an impulse-free descriptor system to an impulsive descriptor system. Then a robust decentralized impulse-eliminating controller is designed, from which necessary and sufficient conditions for impulse margin assignment (singular value assignment) are derived. This result may be thought of as counterpart of finite pole assignment for a R-decentralized controllable system. Finally, a numerical example is employed to illustrate the mam results.

New method of designing pole profile in combined function magnets of high field quality

Combined function magnets are often used in synchrotrons and beam lines. The field quality of such magnets depends mainly on the pole profile. A new method is described for determining the finite pole shapes of such magnets for obtaining field qualities of 1×10−4 or better. Profiles of the typical quadrupole-sextupole and dipole-quadrupole magnets are presented.

The effect of finite pole lengths of replay heads on the signal and noise characteristics of thin film recording media

The effect the finite pole lengths of thin film heads on signal and noise properties of thin film recording media was investigated. In addition to the experimental data, theoretical signal and medium-noise analyses were developed incorporating available analytical head sensitivity functions and, where appropriate, gapped head image fields. Overall, predictions compare well with observations of signal roll-off curves, noise spectra and total noise power.

Pole assignment and controllability subspaces in descriptor systems

The development, by Wonham and co-workers, of the concept of a controllability subspace and elucidation of its relationship with pole assignment have profoundly influenced the geometric control theory of state-space systems. This paper develops the corresponding theory for linear systems described by a mixture of algebraic and differential equations. The proofs given use eigenstructure assignment and include necessary and sufficient conditions for the assignability of a given eigenstructure, including the so-called infinite eigenstructure. This approach provides some simplifications of the state-space theory, such as an intrinsic characterization of controllability subspaces, and a very general result concerning finite pole assignment in descriptor systems. Throughout, care is taken to ensure the existence and uniqueness of classical solutions of the underlying differential equations, which cannot be taken for granted.