共查询到20条相似文献,搜索用时 62 毫秒
1.
T. Krick J. Sabia P. Solernó 《Applicable Algebra in Engineering, Communication and Computing》1997,8(2):125-134
Let k be a field and f
1, . . . , f
s
be non constant polynomials in k[X
1, . . . , X
n
] which generate the trivial ideal. In this paper we define an invariant associated to the sequence f
1, . . . , f
s
: the geometric degree of the system. With this notion we can show the following effective Nullstellensatz: if δ denotes the
geometric degree of the trivial system f
1, . . . , f
s
and d :=max
j
deg( f
j
), then there exist polynomials p
1, . . . , p
s
∈k[X
1, . . . , X
n
] such that 1=∑
j
p
j
f
j
and deg p
j
f
j
≦3n
2δd. Since the number δ is always bounded by (d+1)
n-1
, one deduces a classical single exponential upper bound in terms of d and n, but in some cases our new bound improves the known ones.
Received November 24, 1995, revised version January 19, 1996 相似文献
2.
R. R. Thomas R. Weismantel 《Applicable Algebra in Engineering, Communication and Computing》1997,8(4):241-256
The toric ideal I
A
of a matrix A=(a
1, . . . , a
n
)∈ℤd
×
n is the kernel of the monoid algebra map π^
A
: k[x
1, . . . , x
n
]→k[t
±1
1, . . . , t
±1
d
], defined as x
j
?t
aj
. It was shown in [4] that the reduced Gr?bner basis of I
A
, with respect to the weight vector c, can be used to solve all integer programs minimize {cx : Ax=b, x∈ℕ
n
}, denoted IP
A,b,c,=
, as b varies. In this paper we describe the construction of a truncated Gr?bner basis of I
A
with respect to c, that solves IP
A,b,c,=
for a fixed b. This is achieved by establishing the homogeneity of I
A
with respect to a multivariate grading induced by A. Depending on b, the truncated Gr?bner basis may be considerably smaller than the entire Gr?bner basis of I
A
with respect to c. For programs of the form maximize{cx : Ax≦b, x≦u, x∈ℕ
n
} in which all data are non-negative, this algebraic method gives rise to a combinatorial algorithm presented in [17].
Received: April 10, 1995; revised version: February 6, 1996 相似文献
3.
Rumen N. Daskalov T. Aaron Gulliver 《Applicable Algebra in Engineering, Communication and Computing》1999,9(6):547-558
Let [n, k, d; q]-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). Let d
5(n, k) be the maximum possible minimum Hamming distance of a linear [n, k, d; 5]-code for given values of n and k. In this paper, forty four new linear codes over GF(5) are constructed and a table of d
5(n, k) k≤ 8, n≤ 100 is presented. 相似文献
4.
Harald Niederreiter Arne Winterhof 《Applicable Algebra in Engineering, Communication and Computing》2001,12(3):265-272
Marsaglia's lattice test for congruential pseudorandom number generators modulo a prime is extended to a test for generators
over arbitrary finite fields. A congruential generator η0,η1,…, generated by η
n
=g(n), n = 0, 1,…, passes Marsaglia's s-dimensional lattice test if and only if s≤ deg(g). It is investigated how far this conditin holds true for polynomials over arbitrary finite fields F
q
, particularly for polynomials of the form g
d
(x)=α(x+β)
d
+γ, α, β, γ∈F
q
, α≠ 0, 1 ≤d≤q− 1.
Received: December 13, 1999; revised version: November 17, 2000 相似文献
5.
Eric R. Verheul Henk C. A. van Tilborg 《Applicable Algebra in Engineering, Communication and Computing》1997,8(5):425-435
In some applications of RSA, it is desirable to have a short secret exponent d. Wiener [6], describes a technique to use continued fractions (CF) in a cryptanalytic attack on an RSA cryptosystem having
a ‘short’ secret exponent. Let n=p ⋅ q be the modulus of the system. In the typical case that G=gcd(p−1, q−1) is small. Wiener’s method will give the secret exponent d when d does not exceed (approximately) n
1/4.
Here, we describe a general method to compute the CF-convergents of the continued fraction expansion of the same number as
in Wiener (which has denominator d ⋅ G) up to the point where the denominator of the CF-convergent exceeds approximately n
1/4. When d<n
1/4 this technique determines d, p, and q as does Wiener’s method. For larger values of d there is still information available on the secret key. An estimate is made of the remaining workload to determine d, p and q. Roughly speaking this workload corresponds to an exhaustive search for about 2r+8 bit, where r=ln2 d/n
1/4.
Received: September 30, 1996; revised version: March 7, 1997 相似文献
6.
Binary mixing and alloying during electron-beam fusion in bi-metal joints have been investigated and presented in this paper.
In case of beam-power densities greater than about 1010 Wm−2, rapid fusion of metals is accompanied by violent agitation of the melts. The resulting mass transport in the melt is described
here from an enhanced mass diffusion coefficientD =D
s(W′/a
0
η)1/2, whereD
s is mass diffusivity in solid,W′ is beam-power density,a
0 is acceleration in melt growth andη is the coefficient of viscosity. Moreover, a uniformly mixed central-widthw′ is predicted in the fusion zone (total widthw), where,w′ is significantly dependent onη andw throughW′. For these conditions, the continuity of mass transport in stationary and travel modes of the source has been solved using
line and plane source models and conservation principles. The predictions from these calculations have been validated through
quantitative analyses of experiments. 相似文献
7.
V. Pilla E. F. Chillcce A. A. R. Neves E. Munin T. Catunda C. L. Cesar L. C. Barbosa 《Journal of Materials Science》2007,42(7):2304-2308
Mode-mismatched Thermal Lens (TL) measurements were performed in 70TeO2–19WO3–7Na2O–4Nb2O5 (% mol) tellurite glasses doped with either Er3+ or Tm3+ and co-doped with Er3+/Tm3+ ions. Thermo-optical parameters (D, K, ds/dQ and ds/dT) were obtained in function of thulium concentrations (0.39–1.6) × 10 20 ions/cm3. For Er3+/Tm3+ co-doped tellurite glasses, D and K values are practically independent of the Tm3+ concentrations used in this study. The average values of D and ds/dT obtained for tellurite glasses are: (3.1 ± 0.2) × 10−3 cm2/s and (16 ± 3) × 10−6 K−1, respectively. 相似文献
8.
Tor Helleseth Daniel Sandberg 《Applicable Algebra in Engineering, Communication and Computing》1997,8(5):363-370
Differentially uniform power mappings of the form f (x)=x
d
over GF(p
n
) are considered. We construct an infinite family of 2-uniform mappings in the binary case. In the nonbinary case we give
two large families of k-uniform mappings with low values of k. We also show how to construct families of sequences from differentially 1-uniform power mappings, which have parameters
as good as the best presently known comparable families of sequences.
Received: November 4, 1996; revised version: February 14, 1997 相似文献
9.
M. Weger 《Journal of Superconductivity and Novel Magnetism》1997,10(4):435-440
We consider the role of the enormous ionic dielectric constant ε0≈ 30–50 in the cuprates. The ionically-screened Thomas-Fermi screening parameter ~qTF
= [4θe2N(EF)/εin0
1/2 is extremely small, namely 0.2-0.3 A-1. The electron-phonon coupling constant I(q,w) is found to be anomalously large forq ≈ ~qTF and smallco, accounting for the CDW observed in overdoped BSCCO with wavevector 0.24 A-1. Using the Eliashberg theory we derive from this I(q,w) a maximumT
c
of about 200 K. The small electron-phonon scattering angle △θ = ~q
F ≈
0.3 rad acounts for the observedd-wave pairing, as originating from a phonon-mediated mechananism. 相似文献
10.
M. K. Savushkina A. M. Fedoseev V. P. Shilov V. A. Kravchenko I. E. Polyakov 《Radiochemistry》2009,51(4):354-358
The kinetics of the reaction of Np(V) with Fe(II) in dilute perchloric and nitric acid solutions containing H2C2O4 was studied by spectrophotometry. In the range pH 1–2, the reaction rate is described by the equation d[Np(V)]/dt = k[Np(V)][Fe(II)][H2C2O4]2[H+]−1.6, k = 182 mol−1.4 l1.4 s−1. The activation energy in the range 25–45°C is 26 kJ mol−1. The reaction mechanism involves formation of Fe(II) and Np(V) oxalate complexes, followed by their reaction with the participation
of the H+ ion. 相似文献
11.
S. D. Cohen D. Hachenberger 《Applicable Algebra in Engineering, Communication and Computing》1999,9(5):383-403
Let E be a finite degree extension over a finite field F = GF(q), G the Galois group of E over F and let a∈F be nonzero. We prove the existence of an element w in E satisfying the following conditions:
- w is primitive in E, i.e., w generates the multiplicative group of E (as a module over the ring of integers).
- the set {w
g
∣g∈G} of conjugates of w under G forms a normal basis of E over F.
- the (E, F)-trace of w is equal to a.
This result is a strengthening of the primitive normal basis theorem of Lenstra and Schoof [10] and the theorem of Cohen on primitive elements with prescribed trace [3]. It establishes a recent conjecture of Morgan and Mullen [14], who, by means of a computer search, have verified the
existence of such elements for the cases in which q≤ 97 and n≤ 6, n being the degree of E over F. Apart from two pairs (F, E) (or (q, n)) we are able to settle the conjecture purely theoretically.
Received: June 15, 1998; revised version: December 2, 1998 相似文献
12.
J. A. Sánchez-gil A. A. Maradudin Jun Q. Lu V. D. Freilikher M. Pustilnik I. Yurkevich 《Journal of Modern Optics》2013,60(3):435-452
Abstract The diffuse scattering of p-polarized light from a one-dimensional, randomly rough dielectric film deposited on a planar, perfectly conducting surface is studied by means of small-amplitude perturbation theory. The dielectric constant εd and the thickness d of the dielectric film are chosen in such a way that in the absence of roughness the scattering system supports N (≥ 2) guided modes whose wavenumbers are q 1 (ω), …,q N(ω) at the frequency ω of the light incident at an angle θo. We investigate the occurrence of satellite peaks, in addition to the enhanced back-scattering peak, in the angular distribution of the intensity of the diffusely scattered light, at angles θs(n, m) given by sin θs(n, m)= ? sin θ0± (c/ω) [Qn(ω) ? qm(ω)] for n, m=1, …, N(n ≠ m). These satellite peaks are multiple-scattering effects due to degenerate timereversal symmetry. 相似文献
13.
New lead zirconate titanate/zinc oxide nanowhisker (PZT/ZnOw) ceramics were fabricated by a conventional solid state processing and their structures, piezoelectric, ferroelectric and
mechanical properties were studied. Both the PZT perovskite and ZnO phases can be observed from the X-ray diffraction patterns.
The grain size of ceramics is reduced due to the ZnOw addition. The incorporation of ZnOw into the PZT ceramics improves the strength and toughness, while deteriorates the piezoelectric and ferroelectric properties.
For the PZT/ZnOw ceramics with 1–2 wt% ZnOw, the mechanical properties become optimum, meanwhile maintain good piezoelectric and ferroelectric properties: σ
c = 376–484 MPa, σ
f = 115–121 MPa, K
IC = 1.41–1.54 MPa m1/2, d
33 = 442–490 pC/N, k
p = 0.54–0.55, ε
r = 3,322–3,980, Q
m = 99–101, tanδ = 1.6%–1.7%, P
r = 21.5–26.9 μC/cm2 and E
c = 8.1–8.6 kV/cm. 相似文献
14.
J. H. Merkin 《Journal of Engineering Mathematics》2007,59(2):195-206
The existence of solutions to the travelling-wave equations governed by an autocatalytic reaction of order p (p ≥ 1) and an autocatalytic decay step of order q (q ≥ 1) are examined in the limit of large p. Two cases are treated, q of O(1) and . In the first case, an upper bound k
crit is found for k for the existence of a solution, where k is a dimensionless measure of the strength of the decay step. In the second case, an upper bound on k is also found when q < p. For q ≥ p, there is no upper bound on k and solutions exist for all (positive) values of k. 相似文献
15.
Consider a heteroscedastic regression model Y=m(X)+σ(X)ε, where m(X)=E(Y|X) and σ
2(X)=Var (Y|X) are unknown, and the error ε is independent of the covariate X. We propose a new type of test statistic for testing whether the regression curve m(⋅) belongs to some parametric family of regression functions. The proposed test statistic measures the distance between the
empirical distribution function of the parametric and of the nonparametric residuals. The asymptotic theory of the proposed
test is developed, and the proposed testing procedure is illustrated by means of a small simulation study and the analysis
of a data set. 相似文献
16.
Juan Sabia Pablo Solernó 《Applicable Algebra in Engineering, Communication and Computing》1995,6(6):353-376
In this paper we obtain an effective Nullstellensatz using quantitative considerations of the classical duality theory in complete intersections. Letk be an infinite perfect field and let f1,...,f n–rk[X1,...,Xn] be a regular sequence with d:=maxj deg fj. Denote byA the polynomial ringk [X1,..., Xr] and byB the factor ring k[X1,...,Xn]/(f1,...,fn
r); assume that the canonical morphism AB is injective and integral and that the Jacobian determinant with respect to the variables Xr+1,...,Xn is not a zero divisor inB. Let finally B*:=HomA(B, A) be the generator of B* associated to the regular sequence.We show that for each polynomialf the inequality deg (¯f) dn
r(+1) holds (¯fdenotes the class off inB and is an upper bound for (n–r)d and degf). For the usual trace associated to the (free) extensionA B we obtain a somewhat more precise bound: deg Tr(¯f) dn
r degf. From these bounds and Bertini's theorem we deduce an elementary proof of the following effective Nullstellensatz: let f1,..., fs be polynomials in k[X1,...,Xn] with degrees bounded by a constant d2; then 1 (f1,..., fs) if and only if there exist polynomials p1,..., psk[X1,..., Xn] with degrees bounded by 4n(d+ 1)n such that 1=ipifi. in the particular cases when the characteristic of the base fieldk is zero ord=2 the sharper bound 4ndn is obtained.Partially supported by UBACYT and CONICET (Argentina) 相似文献
17.
Often, the objectives in a computational analysis involve characterization of system performance based on some function of the computed response. In general, this characterization includes (at least) an estimate or prediction for some performance measure and an estimate of the associated uncertainty. Surrogate models can be used to approximate the response in regions where simulations were not performed. For most surrogate modeling approaches, however, (1) estimates are based on smoothing of available data and (2) uncertainty in the response is specified in a point-wise (in the input space) fashion. These aspects of the surrogate model construction might limit their capabilities.One alternative is to construct a probability measure, G(r), for the computer response, r, based on available data. This “response-modeling” approach will permit probability estimation for an arbitrary event, E(r), based on the computer response. In this general setting, event probabilities can be computed: prob(E)=∫rI(E(r))dG(r) where I is the indicator function. Furthermore, one can use G(r) to calculate an induced distribution on a performance measure, pm. For prediction problems where the performance measure is a scalar, its distribution Fpm is determined by: Fpm(z)=∫rI(pm(r)z)dG(r). We introduce response models for scalar computer output and then generalize the approach to more complicated responses that utilize multiple response models. 相似文献
18.
The purpose of this paper is to compute the relaxation and creep functions from the data of shear complex modulus, G
∗(iν). The experimental data are available in the frequency window ν∈[νmin ,νmax ] in terms of the storage G′(ν) and loss G″(ν) moduli. The loss factor
h( n) = \fracG"( n)G¢(n)\eta( \nu) = \frac{G'( \nu )}{G'(\nu )} is asymmetrical function. Therefore, a five-parameter fractional derivative model is used to predict the complex shear modulus,
G
∗(iν). The corresponding relaxation spectrum is evaluated numerically because the analytical solution does not exist. Thereby,
the fractional model is approximated by a generalized Maxwell model and its rheological parameters (G
k
,τ
k
,N) are determined leading to the discrete relaxation spectrum G(t) valid in time interval corresponding to the frequency window of the input experimental data. Based on the deterministic
approach, the creep compliance J(t) is computed on inversing the relaxation function G(t). 相似文献
19.
Lead-free ceramics [(Bi0.98La0.02Na1−x
Li
x
)0.5]0.94Ba0.06TiO3 have been prepared by an ordinary sintering technique and their ferroelectric and piezoelectric properties have been studied.
The results of X-ray diffraction reveal that Li+, Ba2+, and La3+ diffuse into the Bi0.5Na0.5TiO3 lattices to form a new solid solution with a pure perovskite structure. The partial substitution of Li+ lowers the coercive field E
c and improves the remanent polarization P
r. Because of the larger P
r and lower E
c, the ceramic with x = 0.10 exhibits optimum piezoelectric properties: d
33 = 212 pC/N and k
P = 36.1%. The partial substitution of Li+ for Na+ shifts the depolarization temperature T
d toward low temperature. The ceramics exhibit relaxor characteristic, which is probably resulted from the cation disordering
in the 12-fold coordination sites. The temperature dependences of the ferroelectric and dielectric properties suggest that
the ceramics contain both the polar and non-polar regions near/above T
d, which cause the polarization hysteresis loop become deformed and the ceramics become depolarized. 相似文献
20.
A. M. Saleh M. M. Abu-Samreh G. M. Al-Awaysa R. M.-L. Kitaneh 《Journal of Superconductivity and Novel Magnetism》2008,21(4):229-235
The ac susceptibility data was employed to extract the temperature dependence of the critical current density, J
c(T), as well as the variation of flux-creep exponent n(T,H
ac) with temperature and ac field amplitude in bulk samples of polycrystalline magnetic superconductor RuSr2GdCu2O8 (Ru-1212). The critical state models and the collective flux-creep approximation model were successfully accounted to describe
such behavior below the transition temperature. The calculated values of n(T,H) are well fitted to a power law of the following form: n(T,H)=n
0(H)T
−s(H), where s is field dependent exponent whose values varied from −2.4, −1.01 for field amplitudes ranging from 0.5 G and 3.8 G. The power
law describing the frequency dependence of χ′ is found to be consistent with the results of the current-dependent effective activation energy of the form U(J)=U
0ln (J
c/J).
Additionally, the dependence of the current density is found to scale according as: J
c(T)=J
c0(1−T/T
c)
n
, where the exponent n values varied from 1.05 to 1.25. Such dependence is an indication of intergrain coupling that could be ascribed in terms
of superconductor–insulator–superconductor junctions. The derived temperature dependence of J
c(T) is in good agreement with the data obtained from the measurements using the traditional “loss-maximum” approach. Furthermore,
the flux-creep effect increased with increasing both ac fields and temperatures except at about 15–25 K below the onset of
T
c, where a slowing down of the flux creep was observed. 相似文献