Distinguished Boundary Research Articles

Magnetoresistance in bicrystal Fe 3O 4 thin films

An epitaxial magnetite (Fe 3O 4) film has been deposited by the pulsed laser deposition (PLD) technique on a bicrystal substrate. Magnetoresistance measurements on patterned stripes (width=20 μm) across the bicrystal grain boundary have not revealed a distinguishable grain boundary contribution. Post-annealing of the film has a strong influence on the relaxation degree of the film and on the density of antiphase boundaries. Magnetotransport measurements of the micrometer-patterned annealed film show significantly enlarged high-field magnetoresistance values at low temperatures.

Solution of the $\bar{\partial}$-Neumann problem on a bi-disc

In this paper we study the behavior of the solution to the ¯ ∂-Neumann problemfor (0 , 1)-forms on a bi-disc in C 2 . We show singularities which arise at the distinguished boundary are of logarithmic and arctangent type.

ON CAUCHY-POMPEIU FORMULA FOR FUNCTIONS WITH VALUES IN A UNIVERSAL CLIFFORD ALGEBRA

This paper obtains the Cauchy-Pompeiu formula on certain distinguished boundary for functions with values in a universal Clifford algebra. This formula is just an extension of the Cauchy's integral formula obtained in [11].

A Cauchy's Integral Formula for Functions with Values in a Universal Clifford Algebra and its Applications

In this paper, we obtain Cauchy's integral formula on certain distinguished boundary for functions with values in a universal Clifford algebra, which is similar to the classical Cauchy's integral formula on the distinguished boundary of polycylinder for several complex variables. By using it, both the mean value theorem and the maximum modulus theorem are given.

A tangential interpolation problem on the distinguished boundary of the polydisk for the Schur–Agler class

We study a tangential interpolation problem with an arbitrary set of interpolating points on the distinguished boundary of the unit polydisk for Schur–Agler class. The description of all solutions is parametrized in terms of a linear fractional transformation.

Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces

In this paper we define a distinguished boundary for the complex crowns $\Xi \subseteq G_{\mathbb {C}} /K_{\mathbb {C}}$ of non-compact Riemannian symmetric spaces $G/K$. The basic result is that affine symmetric spaces of $G$ can appear as a component of this boundary if and only if they are non-compactly causal symmetric spaces.

Detection of edaphic discontinuities with ground-penetrating radar and electromagnetic induction

Quantification of edaphic properties which may regulate the spatial distribution of vegetation is often limited by the expense and labor associated with collecting and analyzing soil samples. Here we evaluate the utility of two technologies, ground-penetrating radar (GPR) and electromagnetic induction (EMI), for rapid, extensive and nondestructive mapping of diagnostic subsurface features and soil series map unit boundaries. Strong reflectance from fine-textured, near-surface soils obscured radar signal reflectance from deeper horizons at our field test site in the Rio Grande Plains of southern Texas, USA. As a result, ground-penetrating radar did not delineate known edaphic contrasts along catena gradients. In contrast, EMI consistently distinguished boundaries of soil map units. In several instances, gradients or contrasting inclusions within map units were also identified. In addition, the location and boundary of calcic or cambic-horizon inclusions embedded within a laterally coextensive and well-developed argillic horizon were consistently predicted. Correlations between EMI assessments of apparent conductivity (ECa) and soil properties such as CEC, pH, particle size distribution and extractable bases were low (i.e., explained <6% of the variance), or non-significant. As a result, EMI has a high prospecting utility, but cannot necessarily be used to explain the basis for edaphic contrasts. Results suggest EMI can be a cost-effective tool for soil survey and exploration applications in plant ecology. As such, it is potentially useful for rapidly locating and mapping subsurface discontinuities, thereby reducing the number of ground truth soil samples needed for accurate mapping of soil map unit boundaries. An application, addressing hypotheses proposed to explain the role of edaphic heterogeneity in regulating woody plant distribution in a savanna parkland landscape, is presented.

Operators having the symmetrized bidisc as a spectral set

AbstractWe characterize those commuting pairs of operators on Hubert space that have the symmetrized bidisc as a spectral set in terms of the positivity of a hermitian operator pencil (without any assumption about the joint spectrum of the pair). Further equivalent conditions are that the pair has a normal dilation to the distinguished boundary of the symmetrized bidisc, and that the pair has the symmetrized bidisc as a complete spectral set. A consequence is that every contractive representation of the operator algebra A(Γ) of continuous functions on the symmetrized bidisc analytic in the interior is completely contractive. The proofs depend on a polynomial identity that is derived with the aid of a realization formula for doubly symmetric hereditary polynomials, which are positive on commuting pairs of contractions.

A Simple Least-Squares Design of M-D IIR Filters with Fixed Separable Denominator Based on Multivariate Division Algorithm

In this paper, we propose a simple algorithmic solution to the best approximation problem of finding the nearest multivariate rational function, with a fixed separable denominator polynomial, from a given multivariate polynomial, where the numerator polynomial is desired to minimize the integral of the squared error over the distinguished boundary of the unit polydisc. The proposed algorithm does not require any numerical integration or numerical root finding technique because this is realized based on the standard multivariate division algorithm. A simple observation of the proposed algorithm leads to an ideal membership problem characterizing the solution to the problem. A relation of this characterization and a multivariate generalization of the Walsh's Theorem is also discussed with another ideal membership problem derived by applying a corollary of the Hilbert Nullstellensatz to the Walsh's Theorem. Although the discussion to derive the latter ideal membership problem seems to be roundabout, such a characterization would be useful for further generalization, for example to some weighted least-squares approximation. Numerical examples demonstrate the practical applicability of the proposed method to design problems of multidimensional IIR filters.

Evolution of local electronic structure in cubic Mg 1− xFe xS by S K-edge XANES spectroscopy

Synchrotron radiation S K-edge XANES spectra are reported for rocksalt (B1) structure Mg 1− x Fe x S, with x=0–0.68. The edge peak for pure MgS is at 2474.5 eV, consistent with that of a large (3.7 eV) band gap monosulfide semiconductor. XANES spectra of all Fe-bearing compositions contain a pre-edge shoulder or peak which progressively evolves with increase in Fe content into a feature analogous to the edge peak of the S K-edge XANES spectrum of FeS (NiAs-type; B8 structure). The pre-peak is, therefore, assigned to transition of S 1 s electrons to unoccupied hybridized S 3 p σ ∗ antibonding and Fe 3 d(e g) states. Evolution of S K-edge XANES spectra in MgS–FeS binary compositions with increase in Fe content shows: (1) increasing probability of a transition from the S 1 s core level to unoccupied S 3 p σ ∗ antibonding states hybridized with Fe 3 d(e g β) states, and (2) a distinguishable phase boundary at ∼68 mol% FeS, for B1 phase coexisting with B8, consistent with previous P-XRD studies. The S K-edge XANES spectrum of the hypothetical cubic (B1) FeS phase has been derived from the spectrum of Mg 0.375Fe 0.625S.

Complex-Analytic Theory of the μ-Function

In this paper, we consider the determinant of the multivariable return difference Nyquist map, crucial in defining the complex μ-function, as a holomorphic function defined on a polydisk of uncertainty. The key property of holomorphic functions of several complex variables that is crucial in our argument is that it is an open mapping. From this single result only, we show that, in the diagonal perturbation case, all preimage points of the boundary of the Horowitz template are included in the distinguished boundary of the polydisk. In the block-diagonal perturbation case, where each block is norm-bounded by one, a preimage of the boundary is shown to be a unitary matrix in each block. Finally, some algebraic geometry, together with the Weierstrass preparation theorem, allows us to show that the deformation of the crossover under (holomorphic) variations of “certain” parameters is continuous.

On the dilatation of extremal quasiconformal mappings of polygons

A polygon PN is the unit disk {\Bbb D} with n distinguished boundary points, 4\le n \le N . An extremal quasiconformal mapping f_0\: {\Bbb D}_z\to {\Bbb D}_w maps each polygon P_N inscribed in {\Bbb D}_z onto a polygon P_N' inscribed in {\Bbb D}_w . Let fN be the extremal quasiconformal mapping of PN onto P'N. Let KN be its dilatation and let K0 be the maximal dilatation of f0. Then, evidently \sup K_N\le K_0 . The problem is, when equality holds. This is completely answered, if f0 does not have any essential boundary points. For quadrilaterals Q and Q' = f0(Q) the problem is sup(M'/M) = K0, with M and M' the moduli of Q and Q' respectively.

Algebraic multidimensional phase unwrapping and zero distribution of complex polynomials-characterization of multivariate stable polynomials

We define the multidimensional unwrapped phase for any finite extent multidimensional signal that may have its zero on the distinguished boundary of the unit polydisc. By using this definition, we deduce that multivariate stable polynomials can be simply characterized in terms of the proposed unwrapped phase. A rigorous symbolic algebraic solution to the exact phase unwrapping problem for multidimensional finite extent signals is also proposed. This solution is based on a newly developed general Sturm sequence and does not need any numerical root finding or numerical integration technique. Furthermore, it is shown that the proposed algebraic phase unwrapping algorithm can be used to determine the exact zero distribution of any univariate complex polynomial without suffering the so-called singular case problem.

Annealing twins in nominally pure Al

Classic examples of annealing twins were observed in Al which was sufficiently pure due to Fe precipitation such that continuous recrystallization could occur. The twin formation at triple junctions is due to energy reduction on both sides bounding the twinned grain. The low frequency of such twins illustrates that twin boundary energy in Al is indeed comparable to large angle boundary energy. The observation of many {Sigma}3 oriented grains without readily distinguishable planar boundaries supports this conclusion. The formation of parallel twins is assisted by stored work whereby the dislocated structure is eliminated by the migration of incoherent twin boundaries. If the bounding recrystallized region envelops the twin band, the driving force is lost and the twin band shrinks.

Slice Maps and Multipliers of Invariant Subspaces

AbstractLet be the closed bidisc and T2 be its distinguished boundary. For be a slice map, that is, and Then ker Φαβ is an invariant subspace, and it is not difficult to describe ker Φαβ and In this paper, we study the set of all multipliers for an invariant subspace M such that the common zero set of M contains that of ker Φαβ.

On the Bifurcation Structure of Nonlinear Perturbations of Hill’s Equations at Boundary Points of the Continuous Spectrum

Nonlinear perturbations of Hill’s equations have been studied as a first application of a general operator-theoretic approach for treating bifurcation at boundary points of the continuous spectrum. It has been established that there is bifurcation into the gap at distinguished boundary points of the spectrum; moreover, for fixed parameters in the gap there are m distinct solutions where m can be characterized by the number of negative eigenvalues of an associated linear eigenvalue problem. For a class of nonlinear Hill equations with a nonlinearity concentrated on a finite inverval $[ - N,N]$, we are able to reduce the problem to an auxiliary nonlinear Sturm–Liouville problem with parameter dependent boundary conditions. The reduction is based on the knowledge of the stable/unstable spaces of the linearized problem. Although the reduced problem is of a complicated nature, we can analyze its bifurcation structure by a modified Lyapunov–Schmidt procedure. In that way we provide a detailed analysis of both the reduced and the original problem and we can explain various phenomena which occur in connection with bifurcation from the continuous spectrum. In particular, we detect global effects of the presence of continuous spectrum and we provide a mechanism to understand results on the various numbers of solutions.

The peak-interpolation sets in polydiscs

According to one of Noell's results, there are no peak-interpolation manifolds for A ∞(D). if domain Dhas smooth boundary. But a C ∞-submanifold M ⊂ T nwhere Tn is the distinguished boundary of polydisc U n , is locally a peak-interpolation manifold for A ∞(U n ) if it satisfies the “open cone” condition. This gives the answer to a problem by Saerens.

Möbius-invariant Hilbert spaces in polydiscs

We define the Dirichlet space 31 on the unit polydisc of . 2 is a semi-Hilbert space of of holomorphic functions, contains the holomorphic polynomials densely, is invariant under compositions with the biholomorphic automorphisms of , and its semi-norm is preserved under such compositions. We show that 2 is unique with these properties. We also prove 3ί is unique if we assume that the semi-norm of a function in 3f composed with an automorphism is only equivalent in the metric sense to the semi-norm of the original function. Members of a subclass of 3f given by a norm can be written as potentials of «5 5>2-functions on the «-torus . We prove that the functions in this subclass satisfy strong-type inequalities and have tangential limits almost everywhere on dVn . We also make capacitory estimates on the size of the exceptional sets on f)Vn . 1. Introduction. Mόbius-invariant spaces. Let U be the open unit disc in C and T be the unit circle bounding it. The open unit polydisc Vn and the torus Tn in Cn are the cartesian products of n unit discs and n unit circles, respectively. Ίn is the distinguished boundary of Uw and forms only a small part of the topological boundary dVn of Un . We denote by Jΐ the group of all biholomorphic automorphisms of Vn (the Mδbius group). The subgroup of linear automorphisms in Jf is denoted by %. The space of holomorphic functions with domain Un will be called ^(ϋn) and will carry the topology of uniform convergence on compact subsets of Vn. A semi-inner product on a complex vector space β? is a sesquilinear functional on β(? x %? with all the properties of an inner product except that it is possible to have {(a, a)) = 0 when a Φ 0. IWI = \/(( α> a)) *s the associated semi-norm. We assume ((• , •)) is

Finite word-length effects in m-D digital filters with singularities on the stability boundary

The author addresses stability robustness with respect to finite word-length conditions for multidimensional (m-D) digital filters with singularities on the distinguished boundary. In particular, it is shown that all purely first-order digital filters with nonessential singularities of the second kind (NSSKs) are asymptotically stable under certain types of nonlinearities. Even bounded-input, bounded-output (BIBO)-unstable m-D digital filters with singularities on the distinguished boundary proved to be asymptotically stable in the first-order case. The results are then extended to certain classes of higher-order m-D digital filters. It is demonstrated that, although linear m-D digital filters with NSSKs on the distinguished boundary have no margin of stability in the l/sub 1/, l/sub 2/ or asymptotic sense, they might exhibit a rather robust asymptotic behavior with respect to nonideal effects such as finite word-length conditions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Surface tension and buoyancy‐driven flow in a non‐isothermal liquid bridge

AbstractThe Navier–Stokes–Boussinesq equations governing the transport of momentum, mass and heat in a non‐isothermal liquid bridge with a temperature‐dependent surface tension are solved using a vorticity‐stream‐function formulation together with a non‐orthogonal co‐ordinate transformation. The equations are discretized using a pseudo‐unsteady semi‐implicit finite difference scheme and are solved by the ADI method. A Picard‐type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary‐driven flow situations and mixed thermocapillary‐ and bouyancy‐driven flow.