On the span of Hadamard products of vectors

Let A₁, … , A_k be positive semidefinite matrices and B₁, … , B_k arbitrary complex matrices of order n. We show that

span{(A₁x)°(A₂x)°?°(A_kx)|x∈Cⁿ}=range(A₁°A₂°?°A_k)     

High quality YBCO superconductive thin films fabricated by laser molecular beam epitaxy

High quality YBa₂.Cu₃O_{6 +x}(YBCO) superconductive thin films have been fabricated on the SrTiO₃(100) substrate using laser molecular beam epitaxy (laser-MBE). The active oxygen source was used, which made the necessary ambient oxygen pressure be 2–3 orders lower than that in pulsed laser deposition (PLD). T_c0 is 85–87 K, and J_c, 1.0 × 10⁶ A/cm². Atomic force microscopy (AFM) measurements show that no obvious particulates can be observed and the root mean square roughness is 7.8 nm. High stability DC superconducting quantum interference devices (DC-SQUID) was fabricated using this YBCO thin film.     

A note on symbolic and ordinary powers of homogeneous ideals

In this note we are interested in the graded modulesM _k=I^(k)/I^k and , whereI is a saturated ideal in the homogeneous coordinate ringS=K[x₀,…,x_n] of ℙⁿ,I ^(k) is the symbolic power and is the saturation of the ordinary power. Very little is known about these modules, and we provide a bound on their diameters, we compute the Hilbert functions and we study some characteristic submodules in the special case ofn+1 general points in ℙⁿ.

---

Sunto In questa nota siamo interessati ai moduli graduatiM _k=I(k)/I^k e , doveI è un ideale saturato nell'anello delle coordinate omogeneeS:=K[x₀,…,x_n] di ℙⁿ,I ^(k) è la potenza simbolica e è la saturazione della potenza ordinaria. Poco è noto su questi moduli e qui viene fornito un limite superiore ai loro diametri. Ne calcoliamo inoltre le funzioni di Hilbert e studiamo alcuni sottomoduli caratteristici nel caso speciale din+1 punti in posizione generale, in ℙⁿ.

     

Periodic subgroups of projective linear groups in positive characteristic

We classify the maximal irreducible periodic subgroups of PGL(q, ), where is a field of positive characteristic p transcendental over its prime subfield, q = p is prime, and ^× has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q, ) containing the centre ^×1 _q of GL(q, ), such that G/ ^×1 _q is a maximal periodic subgroup of PGL(q, ), and if H is another group of this kind then H is GL(q, )-conjugate to a group in the list. We give criteria for determining when two listed groups are conjugate, and show that a maximal irreducible periodic subgroup of PGL(q, ) is self-normalising.      

Flip-chip-type high-T c gradiometer for biomagnetic measurements in unshielded environment

A flip-chip-type gradiometer has been constructed with a 10 mm × 5 mm planar DCSQUID gradiometer fabricated on a SrTiO₃ bicrystal substrate and a flux transformer made from a YBCO*/YBCO/CeO₂/YSZ multilayer on ?50.8 mm Si wafer. The coupling coefficient between the flux transformer and the planar gradiometer is 0.18. The transformer increases effectively the resolution of the gradiometer. A magnetic field gradient resolution of 73 fT.cm^?1Hz^?1/2 in the white region and 596 fT.cm^?1Hz^?1/2 at 1 Hz has been obtained. High quality magnetocardiogram signals have been successfully measured by using this flip-chip-type gradiometer in an unshielded environment.     

LSQR iterative common symmetric solutions to matrix equations AXB = E and CXD = F

A new matrix based iterative method is presented to compute common symmetric solution or common symmetric least-squares solution of the pair of matrix equations AXB = E and CXD = F. By this iterative method, for any initial matrix X₀, a solution X^∗ can be obtained within finite iteration steps if exact arithmetic was used, and the solution X^∗ with the minimum Frobenius norm can be obtained by choosing a special kind of initial matrix. In addition, the unique nearest common symmetric solution or common symmetric least-squares solution to given matrix in Frobenius norm can be obtained by first finding the minimum Frobenius norm common symmetric solution or common symmetric least-squares solution of the new pair of matrix equations. The given numerical examples show that the matrix based iterative method proposed in this paper has faster convergence than the iterative methods proposed in [1] and [2] to solve the same problems.     

Balanced Leonard pairs

Let K denote a field, and let V denote a vector space over K with finite positive dimension. By a Leonard pair on V we mean an ordered pair of linear transformations A : V → V and A^∗ : V → V that satisfy the following two conditions:

(i)

There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A^∗ is diagonal.

(ii)

There exists a basis for V with respect to which the matrix representing A^∗ is irreducible tridiagonal and the matrix representing A is diagonal.

Let (respectively v₀, v₁, … , v_d) denote a basis for V that satisfies (i) (respectively (ii)). For 0 ? i ? d, let a_i denote the coefficient of , when we write as a linear combination of , and let denote the coefficient of v_i, when we write A^∗v_i as a linear combination of v₀, v₁, … , v_d.In this paper we show a₀ = a_d if and only if . Moreover we show that for d ? 1 the following are equivalent; (i) a₀ = a_d and a₁ = a_d−1; (ii) and ; (iii) a_i = a_d−i and for 0 ? i ? d. These give a proof of a conjecture by the second author. We say A, A^∗ is balanced whenever a_i = a_d−i and for 0 ? i ? d. We say A,A^∗ is essentially bipartite (respectively essentially dual bipartite) whenever a_i (respectively ) is independent of i for 0 ? i ? d. Observe that if A, A^∗ is essentially bipartite or dual bipartite, then A, A^∗ is balanced. For d ≠ 2, we show that if A, A^∗ is balanced then A, A^∗ is essentially bipartite or dual bipartite.     

Flip-chip-type high-Tc gradiometer for biomagnetic measurements in unshielded environment

A flip-chip-type gradiometer has been constructed with a 10 mm × 5 mm planar DCSQUID gradiometer fabricated on a SrTiO₃ bicrystal substrate and a flux transformer made from a YBCO*/YBCO/CeO₂/YSZ multilayer on ϕ50.8 mm Si wafer. The coupling coefficient between the flux transformer and the planar gradiometer is 0.18. The transformer increases effectively the resolution of the gradiometer. A magnetic field gradient resolution of 73 fT.cm⁻¹Hz^−1/2 in the white region and 596 fT.cm⁻¹Hz^−1/2 at 1 Hz has been obtained. High quality magnetocardiogram signals have been successfully measured by using this flip-chip-type gradiometer in an unshielded environment.     

Maximal multilinear Calderón-Zygmund operators with non-doubling measures

Under the assumption that μ is a non-doubling measure on ℝ ^d which only satisfies some growth condition, the authors prove that the maximal multilinear Calderón-Zygmund operator is bounded from (μ) × … × (μ) into L ^p (μ) for any p ₁, … p _m ∈ (1, ∞) and p with 1/p = 1/p ₁ + … + 1/p _m , and bounded from (μ) × … × (μ) into weak- ^{L p} (μ) if there exists any p _i = 1. Furthermore, the authors establish a weighted weak-type estimate for the maximal multilinear Calderón-Zygmund operator. The second (corresponding) author is supported by Tianyuan Fund of China (No. 10626055) and National Natural Science Foundation of China (No. 10701078).     

Isometries and direct decompositions of pseudo MV-algebras

In the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry f in a pseudo MV-algebra = (A, ⊕, ⁻, ^∼, 0, 1) there exists an internal direct decomposition of with commutative such that and for each x ∈ A. On the other hand, if is an internal direct decomposition of a pseudo MV-algebra = (A, ⊕, ⁻, ^∼, 0, 1) with commutative, then the mapping g: A → A defined by is an isometry in and .      

Weighted <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> boundedness for multilinear fractional integral on product spaces

For 0 < α < mn and nonnegative integers n ≥ 2, m ≥ 1, the multilinear fractional integral is defined by

Lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and its inverse

For the Hadamard product A ° A⁻¹ of an M-matrix A and its inverse A⁻¹, we give new lower bounds for the minimum eigenvalue of A ° A⁻¹. These bounds are strong enough to prove the conjecture of Fiedler and Markham [An inequality for the Hadamard product of an M-matrix and inverse M-matrix, Linear Algebra Appl. 101 (1988) 1-8].     

Vectorspacelike representation of absolute planes

The pointset E of an absolute plane can be provided with a binary operation "+" such that (E, +) becomes a loop and for each a E \ {o} the line [a] through o and a is a commutative subgroup of (E, +). Two elements a, b E \ {o} are called independent if [a] ∩ [b] = {o} and the absolute plane is called vectorspacelike if for any two independent elements we have E = [a] + [b] := {x + y | x [a], y [b]}. If is singular then (E, +) is a commutative group and is vectorspacelike iff is Euclidean. If is a hyperbolic plane then is vectorspacelike and in the continous case if a, b are independent, each point p has a unique representation as a quasilinear combination p = α · a + μ · b where α · a [a]and β · b [b] are points, α, β real numbers such that λ (o, λ · a) = |λ|· λ (o, a) and λ (o, μ · b) = |μ|. λ(o, b) and λ is the distance function. This work was partially supported by the Research Project of MIUR (Italian Ministery of Education and University) “Geometria combinatoria e sue applicazioni” and by the research group GNSAGA of INDAM. Dedicated to Walter Benz on the occasion of his 75 ^th birthday, in friendship     

A complex parabolic type monge-ampère equation

The complex parabolic type Monge-Ampère equation we are dealing with is of the form inB × (0,T),u=ϕ on Γ, whereB is the unit ball in ℂ ^d ,d>1, and Γ is the parabolic boundary ofB × (0,T). Solutionu is proved unique in the class .     

Oscillation theorems for second-order nonlinear neutral delay dynamic equations on time scales

By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation