Magnetic properties and microstructure of HDDR isotropic Nd-Dy-Fe-Co-B bonded magnets with high coercivity

The effect of small amount of Co and Dy addition on the magnetic properties of HDDR isotropic Nd-Dy-Fe-Co-B bonded magnets was investigated. The experimental results show that the intrinsic coercivity H_cj and the reversible temperature coefficient of remanence of (Nd_0.65 Dy_0.35)_12.5-(Fe_0.9Co_0.1)₈₁B_6.5 magnet were 1.53 MA·m^-1(19.3 kOe) and -0.059%/°C (25–155°C), respectively. The high coercivity and low temperature coefficient of the magnet are due to the enhanced anisotropy field, increased Curie temperature and improved microstructure by Dy and Co addition.     

The bicompletion of an asymmetric normed linear space

A biBanach space is an asymmetric normed linear space (X,‖·‖) such that the normed linear space (X,‖·‖^s) is a Banach space, where ‖x‖^s= max {‖x‖,‖-x‖} for all x∈X. We prove that each asymmetric normed linear space (X,‖·‖) is isometrically isomorphic to a dense subspace of a biBanach space (Y,‖·‖_Y). Furthermore the space (Y,‖·‖_Y) is unique (up to isometric isomorphism). This revised version was published online in August 2006 with corrections to the Cover Date.     

Design and performance of a thin magnetic lens β-ray spectrometer

Construction of a thin magnetic lens β-ray spectrometer is described. A baffle system which takes advantage of the ring focus has been designed on the basis of the calculations of electron trajectories limited to an angle of acceptance of 9–10·5 degrees. The results of the study of the β-ray spectra of Sr⁹⁰ and Y⁹⁰, Pm¹⁴⁷, Tm¹⁷⁰ are presented.     

Boundedness of Marcinkiewicz integrals and their commutators in H1 (?n × ?m)

The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H ¹ (ℝ ⁿ × ℝ ^m ) to the Lebesgue space L ¹(ℝ ⁿ × ℝ ^m ) and their commutators with Lipschitz functions from the Hardy space H ¹ (ℝ ⁿ × ℝ ^m ) to the Lebesgue space L ^q (ℝ ⁿ × ℝ ^m ) for some q > 1.     

Boundedness of Hausdorff operators on some product Hardy type spaces

We study Hausdorff operators on the product Besov space B01,1 (Rn × Rm) and on the local product Hardy space h1 (Rn × Rm).We establish some boundedness criteria for Hausdorff operators on these functio...     

On the laws of large numbers for double arrays of independent random elements in Banach spaces

For a double array of independent random elements {Vmn,m ≥ 1,n ≥ 1} in a real separable Banach space,conditions are provided under which the weak and strong laws of large numbers for the double sums mi=1 nj=1Vij,m ≥ 1,n ≥ 1 are equivalent.Both the identically distributed and the nonidentically distributed cases are treated.In the main theorems,no assumptions are made concerning the geometry of the underlying Banach space.These theorems are applied to obtain Kolmogorov,Brunk–Chung,and Marcinkiewicz–Zygmund type strong laws of large numbers for double sums in Rademacher type p(1 ≤ p ≤ 2) Banach spaces.     

Ratio of pions to protons and ratio of neutral to charged interacting particles at mountain altitude of 800 gm/cm2

Using a combined set-up of a multiplate cloud chamber, an air Cerenkov counter and a total absorption spectrometer, the ratio of pions to protons not associated with large air showers has been determined to be 0·50 ± ·07 in the energy region 20–40 GeV at an altitude of 800 gm/cm². In the same energy region the ratio of neutral to charged particles is found to be 0·66 ± ·07. From the ratio of neutrons to protons deduced from these measurements (i.e., 0·99 ± ·11), it is concluded that most of the charge excess of nuclear active particles of energies > 20 GeV at mountain altitudes and sea-level is due to pions.     

Ordered representations of spaces of integrable functions

Let X be a Banach space, (Ω,Σ) a measurable space and let m : Σ → X be a (countably additive) vector measure. Consider the corresponding space of integrable functions L¹(m). In this paper we analyze the set of (countably additive) vector measures n satisfying that L¹(n) = L¹(m). In order to do this we define a (quasi) order relation on this set to obtain under adequate requirements the simplest representation of the space L¹(m) associated to downward directed subsets of the set of all the representations. This research has been partially supported by La Junta de Andalucía. The support of D.G.I. under project MTM2006–11690–C02 (M.E.C. Spain) and FEDER is gratefully acknowledged.     

Electrons magnetic fields and background radio emission in the galaxy

Extensive data now available on the non-thermal background radio emission from different celestial directions, and recent measurements on the energy spectrum of cosmic ray electrons in the vicinity of the earth permit one to deduce information on the mean magnetic fields and cosmic electron spectra needed to exist in different regions of the Galaxy. It is found that in order to explain quantitatively the background radio brightness distributions from the Galaxy one needs (i) the same or nearly same electron spectrum that exists in the near interstellar space, to exist in almost all regions of Galactic space, (ii) a mean magnetic field close to 6×10^?6 Gauss in the Disc in the direction of the Anti-centre, (iii) a mean magnetic field close to 2·5×10^?6 Gauss in the radio Halo and (iv) a mean magnetic field probably close to 9·5×10^?6 Gauss towards the Galactic Ridge in the direction of the Centre. Some inferences are also drawn on the confinement of cosmic rays in the Galaxy.     

Best Constants in the Miranda-Agmon Inequalities for Solutions of Elliptic Systems and the Classical Maximum Modulus Principle for Fluid and Elastic Half-spaces

The Dirichlet problem for elliptic systems of the second order with constant real and complex coefficients in the half-space  ^k ₊ = {x = (x ₁,…,x_k ): x_k > 0} is considered. It is assumed that the boundary values of a solution u = (u ₁,…,u _m) have the form ψ ₁ ξ ₁ + · · · + ψ _n ξ _n, 1 ≤ n ≤ m, where ξ ₁,· · ·,ξ _n is an orthogonal system of m-component normed vectors and ψ ₁,· · ·,ψ _n are continuous and bounded functions on ? ^k ₊. We study the mappings [C(? ^k ₊)] ⁿ ? (ψ ₁,…,ψ _n) → u(x) ?  ^m and [C(? ^k ₊)] ⁿ ? (ψ ₁,…,ψ _n) → u(x) ?  ^m generated by real and complex vector valued double layer potentials. We obtain representations for the sharp constants in inequalities between |u(x)| or |(z, u(x))| and ∥u| _xk =₀∥, where z is a fixed unit m-component vector, | · | is the length of a vector in a finite-dimensional unitary space or in Euclidean space, and (·,·) is the inner product in the same space. Explicit representations of these sharp constants for the Stokes and Lamé systems are given. We show, in particular, that if the velocity vector (the elastic displacement vector) is parallel to a constant vector at the boundary of a half-space and if the modulus of the boundary data does not exceed 1, then the velocity vector (the elastic displacement vector) is majorised by 1 at an arbitrary point of the half-space. An analogous classical maximum modulus principle is obtained for two components of the stress tensor of the planar deformed state as well as for the gradient of a biharmonic function in a half-plane.     

The regularity of bidimensional solutions of the third grade fluids equations

It was recently proved in [1,2] that the third grade fluids equations have a unique global bidimensional solution provided that the initial velocity belongs to the Sobolev space H². Here, we complete this result by proving that this solution preserves the Sobolev regularity of the initial data, i.e., if the initial velocity belongs to H^m, m ≥ 2, then the evolved velocity v(t, ·) also belongs to H^m for every time t.     

Non-Existence of Stable Currents in Hypersurfaces

Let M^m be a compact hypersurface in the Euclidean space E^m+1. In this paper, we study the non-existence of stable integral currents in M^m and its immersed submanifolds. Some vanishing theorems concerning the homology groups of these manifolds are established.AMS Subject Classification (1991): 49Q15 53C40 53C20     

Radioactive decay of Eu154

The radioactive decay of Eu¹⁵⁴ (t _1/2=16y), obtained from thermal neutron irradiations of 95% enriched Eu¹⁵³, has been studied by using the Seigbahn-Slätis intermediate image spectrometer, a thin lens magnetic spectrometer and a coincidence scintillation spectrometer. The following gamma-rays (energy in kev.) have been identified as belonging to this isotope: 123, 248, 585, 717, 759, 875, 998, 1007, 1285, 1600. Beta end points of Eu¹⁵⁴ were measured at 275 (20%), 590 (45%), 890 (23%) and 1860 (12%). The K-conversion coefficient of 123 kev. gamma-ray has been experimentally determined to be ～0·5. On the basis of gamma-gamma and beta-gamma coincidences, the decay scheme of Eu¹⁵⁴ has been deduced: the resulting level-structure of Gd¹⁵⁴ conforms well with the predictions of the unified nuclear model.     

Compact Homogeneous Hypersurfaces in Hyperbolic Space

In this paper we prove that an n-dimensional compact homogeneous Riemannian manifold isometrically immersed in the hyperbolic space Hⁿ⁺¹ is isometric to a sphere.AMS Subject Classification (1990): 53A07, 53C42, 57S15     

On (2<Superscript><Emphasis Type="Italic">m</Emphasis></Superscript> + 1)-variable symmetric Boolean functions with submaximum algebraic immunity 2<Superscript><Emphasis Type="Italic">m</Emphasis>−1</Superscript>

All (2 ^m + 1)-variable symmetric Boolean functions with submaximal algebraic immunity 2 ^m−1 are described and constructed. The total number of such Boolean functions is 3² · 2^2m−3 +3 ^m−2 · 2⁴ − 2 for m ⩾ 2. This work was supported by the Major State Basic Research Development Program of China (Grant No. 2004CB3180004) and National Natural Science Foundation of China (Grant No. 60433050)     

Noncommutative correction to the Cornell potential in heavy-quarkonium atoms

We investigate the effect of space–time noncommutativity on the Cornell potential in heavy-quarkonium systems. It is known that the space–time noncommutativity can create bound states, and we therefore consider the noncommutative geometry of the space–time as a correction in quarkonium models. Furthermore, we take the experimental hyperfine measurements of the bottomium ground state as an upper limit on the noncommutative energy correction and derive the maximum possible value of the noncommutative parameter θ, obtaining θ ≤ 37.94 · 10^?34 m². Finally, we use our model to calculate the maximum value of the noncommutative energy correction for energy levels of charmonium and bottomium in 1S and 2S levels. The energy correction as a binding effect in quarkonium system is smaller for charmonium than for bottomium, as expected.     

New large sets of t‐designs

Abstact: We introduce generalizations of earlier direct methods for constructing large sets of t‐designs. These are based on assembling systematically orbits of t‐homogeneous permutation groups in their induced actions on k‐subsets. By means of these techniques and the known recursive methods we construct an extensive number of new large sets, including new infinite families. In particular, a new series of LS[3](2(2 + m), 8·3^m ? 2, 16·3^m ? 3) is obtained. This also provides the smallest known ν for a t‐(ν, k, λ) design when t ≥ 16. We present our results compactly for ν ≤ 61, in tables derived from Pascal's triangle modulo appropriate primes. © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 40–59, 2001     

Studies on efficiencies of electrochemiluminescence of rubrene

The electrochemiluminescence efficiencies of rubrene system has been obtained by using the transient method in a variety of solvents. The efficiencies are in the range of 0·11 × 10^?3?4·1×10^?2. The mixed system efficiencies are less at least by an order of magnitude in all the solvents except in dimethylsulphoxide. The variation in efficiencies of the pure and mixed systems is explained on the basis of mechanistic differences. In the applied magnetic field, the electrochemiluminescence efficiency of the pure system increases by about 7% and of the mixed system by about 18–25%.     

Robust stabilization of some class of uncertain systems

Consider an uncertain system $$ \dot x = A( \cdot )x + B( \cdot )u, $$ where A(·) ∈ ? ^{n × n} , B(·) ∈ ? ^{n × m} , and the elements of matrices A(·) and B(·) are arbitrary functionals. It is assumed that all elements are uniformly bounded, and that the first r elements counted from above and situated on a certain fixed upper superdiagonal are alternating. It is also assumed that m = n ? r, and that a matrix formed by the last m rows of matrix B(·) is nonsingular. The control u = S(·)x is synthesized, and conditions on the admissible matrix B(·) ensuring the global asymptotical stability of the system are obtained. We consider the case when modulation of the components of the vector u is realized by means of synchronous amplitude-frequency pulse modulators of the first kind. A lower estimate for the pulse frequency under which the pulse system is globally asymptotically stable is obtained.     

Grassmannians of 2-Sided Vector Spaces

Let k ? K be an extension of fields, and let A ? M _n (K) be a k-algebra. We study parameter spaces of m-dimensional subspaces of K ⁿ which are invariant under A. The space  _A (m, n), whose R-rational points are A-invariant, free rank m summands of R ⁿ , is well known. We construct a distinct parameter space,  _A (m, n), which is a fiber product of a Grassmannian and the projectivization of a vector space. We then study the intersection  _A (m, n) ∩  _A (m, n), which we denote by  _A (m, n). Under suitable hypotheses on A, we construct affine open subschemes of  _A (m, n) and  _A (m, n) which cover their K-rational points. We conclude by using  _A (m, n),  _A (m, n), and  _A (m, n) to construct parameter spaces of 2-sided subspaces of 2-sided vector spaces.