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1.
Bulk amorphous Pd41Ni10Cu28P21 alloy has been prepared by water quenching method. The system shows excellent glass forming ability (GFA) with a high value of reduced glass transition temperature Trg, 0.714. Structural analyses indicate that the Pd41Ni10Cu28P21 alloy has a dense packing structure closer to "frozen liquid" than that of amorphous Pd40Ni40P20 alloy. Experiments on crystallization reveal that several crystalline phases simultaneously precipitate in the early part of crystallization. Below 710 K, a metastable phase forms, and subsequently disappears at elevated temperatures. In addition, the influence of partial substitute of Cu for Ni on GFA has been discussed with regard to thermodynamics and kinetics. 相似文献
2.
Experiments of X-ray diffraction for liquid Cu70Ni30 alloy above and below its liquidus (l 230°C) have been carried out. By the analysis of experimental results, it is discovered
that difference between structures of liquid and undercooled Cu70Ni30 alloy is their cluster sizes. The correlation radius of cluster is 1.125 nm and the atom number of cluster is 403 at l 250—l
400°C, and they are 1.3 nm and 704 respectively at the undercooled liquid state (1 200°C). The structure of liquid Cu70Ni30 alloy is fcc short order and its solid structure, fcc, is kept from liquid fcc short order. 相似文献
3.
Xiangyi Zhang Jingwu Zhang Fuxiang Zhang Wen Yu Duanwei He Liming Cao Jianhua Zhao Riping Liu Yingfan Xu Wenkui Wang 《中国科学A辑(英文版)》1999,42(4):407-413
The formation of nanocrystalline Fe73.5 Cu1Nb3Si13.5 B9 alloy by annealing an amorphous Fe73.5Cu1Nb3Si13.5B9 alloy at a temperature of 823 K under pressures in the range of 1–5 GPa is investigated by using X-ray diffraction, electron
diffraction, and transmission electron microscopy. The high pressure experiments are carried out in belt-type pressure apparatus.
Experimental results show that the initial crystalline phase in these annealed alloys is a-Fe solid solution (named a-Fe phase
below), and high pressure has a great influence on the crystallization process of the a-Fe phase. The grain size of the a-Fe
phase decreases with the increase of pressure (P). The volume fraction of the a-Fe phase increases with increasing the pressure
as the pressure is below 2 GPa, and then decreases (Pδ2 GPa). The mechanism for the effects of the high pressure on the crystallization
process of amorphous Fe73.5Cu1Nb3Si13.5B9 alloy is discussed
Project supported by the National Natural Science Foundation of China (Grant No. 19674070) and the Natural Science Foundation
of Hebei Province. 相似文献
4.
V. Chernousov 《Mathematische Annalen》2003,326(2):297-330
We prove that for a simple simply connected quasi-split group of type 3,6
D
4
,E
6
,E
7
defined over a perfect field F of characteristic ≠=2,3 the Rost invariant has trivial kernel. In certain cases we give a formula for the Rost invariant.
It follows immediately from the result above that if cd F≤2 (resp. vcd F≤2) then Serre's Conjecture II (resp. the Hasse principle) holds for such a group. For a (C
2
)-field, in particular ℂ(x,y), we prove the stronger result that Serre's Conjecture II holds for all (not necessary quasi-split) exceptional groups of
type 3,6
D
4
,E
6
,E
7
.
Received: 27 March 2002 /
Published online: 28 March 2003
The author gratefully acknowledge the support of TMR ERB FMRX CT-97-0107 and Forschungsinstitut für Mathematik, ETH in Zürich 相似文献
5.
Given two doubling measures μ and ν in a metric space (S, ρ) of homogeneous type, let B
0⊂S be a given ball. It has been a well-known result by now (see [1–4]) that the validity of an L
1→L
1 Poincaré inequality of the following form:
for all metric balls B⊂B
0⊂S, implies a variant of representation formula of fractional integral type: for ρ-a.e. x∈B
0,
One of the main results of this paper shows that an L
1 to L
q
Poincaré inequality for some 0 < q < 1, i.e.,
for all metric balls B⊂B
0, will suffice to imply the above representation formula. As an immediate corollary, we can show that the weak-type condition,
also implies the same formula.
Analogous theorems related to high-order Poincaré inequalities and Sobolev spaces in metric spaces are also proved.
Received December 27, 2000, Accepted May 28, 2001 相似文献
6.
Riping Liu Liling Sun Duanwei He Xiangyi Zhang Jianhua Zhao Zhicheng Qin Yingfan Xu Wenkui Wang 《中国科学A辑(英文版)》1997,40(6):662-667
The microstructure and solute distribution of Pd40Ni40P20 alloy solidified both on board a Chinese retrievable satellite (μg) and on the earth (1g) were studied. It was found that the dendritic primary phase formed under microgravity condition was finer and shorter. In the central area of the sample some asteroidal patterns of the primary phase were present in the microstructure. The primary spacing of the dendrites at the cooling rate of 0. 056 K/s was smaller than that measured in the ground-based experiments at the same cooling rate, but almost the same as that cooled at 0.67 K/s on the ground. With these experimental results, mass transport coefficients both in space and on the earth were evaluated. 相似文献
7.
Let λK
m,n be a bipartite multigraph with two partite sets having m and n vertices, respectively. A P
v-factorization of λK
m,n is a set of edge-disjoint P
v
-factors of λK
m,n which partition the set of edges of λK
m,n. When v is an even number, Ushio, Wang and the second author of the paper gave a necessary and sufficient condition for the existence
of a P
v
-factorization of λK
m,n. When v is an odd number, we proposed a conjecture. However, up to now we only know that the conjecture is true for v = 3. In this paper we will show that the conjecture is true when v = 4k − 1. That is, we shall prove that a necessary and sufficient condition for the existence of a P
4k−1-factorization of λK
m,n is (1) (2k − 1)m ⩽ 2kn, (2) (2k − 1)n ⩽ 2km, (3) m + n ≡ 0 (mod 4k − 1), (4) λ(4k − 1)mn/[2(2k − 1)(m + n)] is an integer. 相似文献
8.
Ming-Chang Kang 《Israel Journal of Mathematics》2005,146(1):77-92
LetK be any field which may not be algebraically closed,K(x
1
,x
2
,x
3
) be the rational function field of three variables overK, and σ:K(x
1
,x
2
,x
3
) → K(x
1
,x
2
,x
3
) be aK-automorphism defined by
wherea
i
,b
i
,c
i
,d
i
∈K anda
i
d
i
−b
i
c
i
≠0. Let
,f
i
(T)=T
2
−(a
i
+d
i
)T+(a
i
d
i
−b
i
c
i
)∈K[T] be the “characteristic polynomial” of σ
i
.
Theorem:Assume that charK≠2.Then the fixed field K(x
1
,x
2
,x
3
)
<σ>
is not rational (=purely transcendental) over K if and only if (i) for each 1≤i≤3, f
i
(T) is irreducible; (ii) the Galois group of f
1
(T)f
2
(T)f
3
(T) over K is of order 8; and (iii) for each 1≤i≤3,ord (σ
[itn]
)is an even integer. 相似文献
9.
Most results on the crossing number of a graph focus on the special graphs, such as Cartesian products of small graphs with
paths Pn, cycles Cn or stars Sn. In this paper, we extend the results to Cartesian products of complete bipartite graphs K2,m with paths Pn for arbitrary m ≥ 2 and n ≥ 1.
Supported by the NSFC (No. 10771062) and the program for New Century Excellent Talents in University. 相似文献
10.
Andrea Vietri 《Graphs and Combinatorics》2007,23(1):111-121
We analyse 3-subset difference families of Z2d+1⊕Z2d+1 arising as reductions (mod 2d+1) of particular families of 3-subsets of Z⊕Z. The latter structures, namely perfect d-families, can be viewed as 2-dimensional analogues of difference triangle sets having the least scope. Indeed, every perfect d-family is a set of base blocks which, under the natural action of the translation group Z⊕Z, cover all edges {(x,y),(x′,y′)} such that |x−x′|, |y−y′|≤d. In particular, such a family realises a translation invariant (G,K3)-design, where V(G)=Z⊕Z and the edges satisfy the above constraint. For that reason, we regard perfect families as part of the hereby defined translation designs, which comprise and slightly generalise many structures already existing in the literature. The geometric context allows
some suggestive additional definitions. The main result of the paper is the construction of two infinite classes of d-families. Furthermore, we provide two sporadic examples and show that a d-family may exist only if d≡0,3,8,11 (mod 12). 相似文献
11.
Dumitru Popa 《Proceedings Mathematical Sciences》2009,119(2):221-230
Let Ω be a compact Hausdorff space, X a Banach space, C(Ω, X) the Banach space of continuous X-valued functions on Ω under the uniform norm, U: C(Ω, X) → Y a bounded linear operator and U
#, U
# two natural operators associated to U. For each 1 ≤ s < ∞, let the conditions (α) U ∈ Π
s
(C(Ω, X), Y); (β)U
# ∈ Π
s
(C(Ω), Π
s
(X, Y)); (γ) U
# ε Π
s
(X, Π
s
(C(Ω), Y)). A general result, [10, 13], asserts that (α) implies (β) and (γ). In this paper, in case s = 2, we give necessary and sufficient conditions that natural operators on C([0, 1], l
p
) with values in l
1 satisfies (α), (β) and (γ), which show that the above implication is the best possible result. 相似文献
12.
Mariya Ishteva Lieven De Lathauwer P.-A. Absil Sabine Van Huffel 《Numerical Algorithms》2009,51(2):179-194
An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric
Newton method for computing the best rank-(R
1, R
2, R
3) approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate
the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order
orthogonal iteration (De Lathauwer et al., SIAM J Matrix Anal Appl 21(4):1324–1342, 2000). This kind of algorithms are useful for many problems.
This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by
the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility
rests with its authors. Research supported by: (1) Research Council K.U.Leuven: GOA-Ambiorics, CoE EF/05/006 Optimization
in Engineering (OPTEC), (2) F.W.O.: (a) project G.0321.06, (b) Research Communities ICCoS, ANMMM and MLDM, (3) the Belgian
Federal Science Policy Office: IUAP P6/04 (DYSCO, “Dynamical systems, control and optimization”, 2007–2011), (4) EU: ERNSI.
M. Ishteva is supported by a K.U.Leuven doctoral scholarship (OE/06/25, OE/07/17, OE/08/007), L. De Lathauwer is supported
by “Impulsfinanciering Campus Kortrijk (2007–2012)(CIF1)” and STRT1/08/023. 相似文献
13.
Let (Ω,
,P) be a measurable space and
a sub-σ-lattice of the σ-algebra
. For XL1(Ω,
,P) we denote by P
X the set of conditional 1-mean (or best approximants) of X given L1(
) (the set of all
-measurable and integrable functions). In this paper, we obtain characterizations of the elements in P
X, similar to those obtained by Landers and Rogge for conditional s-means with 1<s<∞. Moreover, using these characterizations we can extend the operator P
to a bigger space L0(Ω,
,P). When, in certain sense,
n goes to
∞, we will be able to prove theorems about convergence and we will obtain bounds for the maximal function supnP
nX. A sharper characterization of conditional 1-means for certain particular σ-lattice was proved in previous papers. In the last section of this paper we generalize those results to all totally ordered σ-lattices. 相似文献
14.
A. F. Barabanov A. V. Mikheenkov A. V. Shvartsberg 《Theoretical and Mathematical Physics》2011,168(3):1192-1215
In the framework of a spherically symmetric self-consistent approach to two-time retarded spin-spin Green’s functions, we
develop the theory of a two-dimensional frustrated J
1
-J
2
-J
3
quantum S=1/2 antiferromagnet. We show that taking the damping of spin fluctuations into account is decisive in forming both the spin-liquid
state and the state with long-range order. In particular, the existence of damping allows explaining the scaling behavior
of the susceptibility χ(q, ω) of the CuO
2
cuprate plane, the behavior of the spin spectrum in the two-plane case, and the occurrence of an incommensurable χ(q, ω) peak. In the case of the complete J1-J
2
-J
3
model, in a single analytic approach, we find continuous transitions between three phases with long-range order (“checkerboard,”
stripe, and helical (q, q) phases) through the spin-liquid state. We obtain good agreement with cluster computations for the
J
1
-J
2
-J
3
model and agreement with the neutron scattering data for the J
1
-J
2
model of cuprates. 相似文献
15.
Bernhard Burgstaller 《Monatshefte für Mathematik》2009,265(4):1-11
There exists a separable exact C*-algebra A which contains all separable exact C*-algebras as subalgebras, and for each norm-dense measure μ on A and independent μ-distributed random elements x
1, x
2, ... we have
limn ? ¥\mathbb P(C*(x1,?,xn) is nuclear)=0{\rm {lim}}_{n \rightarrow \infty}\mathbb {P}(C^*(x_1,\ldots,x_n) \mbox{ is nuclear})=0. Further, there exists a norm-dense non-atomic probability measure μ on the Cuntz algebra O2{\mathcal {O}_2} such that for an independent sequence x
1, x
2, ... of μ-distributed random elements x
i
we have
lim infn ? ¥\mathbb P(C*(x1,?,xn) is nuclear)=0{\rm {lim\, inf}}_{n \rightarrow \infty}\mathbb {P}(C^*(x_1,\ldots,x_n) \mbox{ is nuclear})=0. We introduce the notion of the stochastic rank for a unital C*-algebra and prove that the stochastic rank of C([0, 1]
d
) is d. 相似文献
16.
Alexander Nenashev 《K-Theory》2005,34(3):219-232
We interpret the Steinberg symbols xi,j(a) as homotopies contracting the elementary matrices ei,j(a), the latters being represented by certain arcs in a simplicial model of the K-theory. We further prove the Steinberg relations for these homotopies. This provides an explicit map from K2 of a ring, defined classically as ker(St(R) → GL(R)), to π2 of the G-construction assigned to R. Though the two groups are known to be isomorphic, a certain work is to be done to prove that this explicit map is an isomorphism.
Mathematics Subject Classification 1991: Primary 19B99, 19D99; secondary 18E10, 18F25. 相似文献
17.
S. John 《Annals of the Institute of Statistical Mathematics》1973,25(1):363-372
Summary Let the two alternative populationsP
1 andP
2 from which the individual with measurements χ may have come beN(μ(1), Σ) andN(μ(2), Σ). Then the classification rule with minimum risk is to assign the individual toP
1 orP
2 according as (μ(2)-μ(1))′Σ-1
x≶(1/2)(μ(2)-μ(1))′Σ-1(μ(1)+μ(2))+c wherec is a constant depending on the prior probabilities ofP
1 andP
2 and the costs of the two kinds of misclassification. The probability of misclassifying an individual fromP
2 by this rule is π21=Φ(-δ/2+cδ-1), where Φ(.) is the distribution function of anN(0, 1) and
. (Since we are free to choose which population we shall callP
2, it is not necessary to consider separately the probability of misclassifying an individual fromP
1.) LetP
21 denote the probability of misclassification of an individual fromP
2 by the rule derived from the one mentioned by fixing μ(1), μ(2) and Σ at estimates
andV and letP
21
*
be the probability of misclassification of an individual fromP
2 when the classification rule is the one with minimum risk among those based on
. The fiducial distributions of π21,P
21 andP
21
*
are determined. Point estimates and confidence intervals for π21,P
21 andP
21
*
are derived. Only easily available tables are needed to make fiducial inferences. An incidental result of some interest elsewhere
as well is the distribution of a linear combination of a chi and an independent normal variable. 相似文献
18.
Giovanni Mongardi 《Central European Journal of Mathematics》2012,10(4):1472-1485
Let X be a hyperk?hler manifold deformation equivalent to the Hilbert square of a K3 surface and let φ be an involution preserving the symplectic form. We prove that the fixed locus of φ consists of 28 isolated points and one K3 surface, and moreover that the anti-invariant lattice of the induced involution on H 2(X, ℤ) is isomorphic to E 8(−2). Finally we show that any couple consisting of one such manifold and a symplectic involution on it can be deformed into a couple consisting of the Hilbert square of a K3 surface and the involution induced by a symplectic involution on the K3 surface. 相似文献
19.
A. Kopotowski M G. Nadkarni K. P. S. Bhaskara Rao 《Proceedings Mathematical Sciences》2003,113(1):77-86
We discuss subsetsS of ℝn such that every real valued functionf onS is of the formf(x1, x2, ..., xn) =u
1(x1) +u
2(x2) +...+u
n(xn), and the related concepts and situations in analysis. 相似文献
20.
LetS be a semigroup andE the set of all idempotents inS. LetS-Act be the category of allS-acts. LetC be a full subcategory ofS-Act which containss
S and is closed under coproducts and summands. It is proved that, inC, anS-actP is projective and unitary if and only ifP≅ ∐
jϕ
I
Se
i
,e
i
ϕE. In particular,P is a projective, indecomposable and unitary object if and only ifP ≅Se for somee ∈E. These generalize some results obtained by Knauer and Talwar.
Research partially supported by a UGC (HK) (Grant No. 2160092). 相似文献