Effect of internal stress disturbance on the stress-induced transformation toughening of an alumina/zirconia dual-phase composite

The toughening and strengthening of a dual-phase composite, consisting of alpha-alumina (α-Al₂O₃) and tetragonal-zirconia (t-ZrO₂), were investigated. The toughness of the composite was evaluated through the precise measurement of work-of-fracture (WOF), which is a measure of total fracture resistance involving the rising R-curve effect. It was found that both the WOF and flexural strength of the composite were maximized at a t-ZrO₂ volume fraction f _Z of about 0.7. The thermal degradation of the mechanical properties was also observed. The effect of the internal stresses arising from the thermoelastic mismatch between α-Al₂O₃ and t-ZrO₂ on the critical stresses of the reversible phase transformation of t-ZrO₂ was numerically examined to describe the f _Z?- and temperature-dependencies of WOF quantitatively.     

Parametrically driven pendulum and exact solutions

The parametrically driven pendulumx +f ₁(t) x +f ₂(t) sinx = 0 cannot be solved in closed form for arbitrary functionvsf ₁,f ₂. We apply the Painlevé test to obtain the constraint on the functionsf ₁, andf ₂ for which the equation passes the test. The constraint onf ₁, andf ₂, a differential equation whichf ₁ andf ₂ obey, is discussed and solutions are given. The third Painlevé transcendent plays a central role.     

Diffusion activation energy versus the favourable energy in two-order-parameter model:A molecular dynamics study of liquid Al

In the present work, we find that both diffusion activation energy E_a(D) and E_a(S^ex) increase linearly with pressure and have the same slope (0.022±0.001 eV/GPa) for liquid Al. The temperature and pressure dependence of excess entropy is well fitted by the expression -S^ex(T,P)/k_B=a(P)+b(P)T+c(P)exp(E_f/k_BT), which together with the small ratio of E_f/k_BT leads to the relationship of excess entropy to temperature and pressure, i.e. S^ex≈-cE_f/T, where c is about 12 and E_f (=Δ E-PΔV) is the favourable energy. Therefore, there exists a simple relation between E_a(S^ex) and E_f, i.e. E_a(S^ex)≈cE_f.     

Enhanced isospin dependence of the empirical particle-hole effective interaction

The separation betweenT=0 andT=1 centroids of the empirical effective interaction is fairly large for the (d ₃ ^2/−1 f _7/2)JT particle-hole interaction as compared to nearby (f _7/2)² JT and (d _5/2)² JT particle-particle interactions. This interesting feature of the empirical effective interaction is shown to arise as a consequence of renormalization of the effective interaction as one truncates the configuration space from (s−d)⁻¹(f−p)¹ to (d ₃ ^2/−1 f _7/2) and from (f−p)² and (s−d)² configurations to (f _7/2)² and (d _5/2)² respectively.     

A very strong difference property for semisimple compact connected lie groups

Let G be a topological group. For a function f: G → ℝ and h ∈ G, the difference function Δ _h f is defined by the rule Δ _h f(x) = f(xh) − f(x) (x ∈ G). A function H: G → ℝ is said to be additive if it satisfies the Cauchy functional equation H(x + y) = H(x) + H(y) for every x, y ∈ G. A class F of real-valued functions defined on G is said to have the difference property if, for every function f: G → ℝ satisfying Δ _h f ∈ F for each h ∈ G, there is an additive function H such that f − H ∈ F. Erdős’ conjecture claiming that the class of continuous functions on ℝ has the difference property was proved by N. G. de Bruijn; later on, F. W. Carroll and F. S. Koehl obtained a similar result for compact Abelian groups and, under the additional assumption that the other one-sided difference function ∇ _h f defined by ∇ _h f(x) = f(xh) − f(x) (x ∈ G, h ∈ G) is measurable for any h ∈ G, also for noncommutative compact metric groups. In the present paper, we consider a narrower class of groups, namely, the family of semisimple compact connected Lie groups. It turns out that these groups admit a significantly stronger difference property. Namely, if a function f: G → ℝ on a semisimple compact connected Lie group has continuous difference functions Δ _h f for any h ∈ G (without the additional assumption concerning the measurability of the functions of the form ∇ _h f), then f is automatically continuous, and no nontrivial additive function of the form H is needed. Some applications are indicated, including difference theorems for homogeneous spaces of compact connected Lie groups.     

Weak electric and magnetic form factors for semileptonic baryon decays in a relativistic quark model

Weak electric and magnetic form factors for semileptonic baryon decays are calculated in a relativistic quark model based on the Dirac equation with the independent-quark confining potential of the formV _q(r)=1/2(1+γ ⁰)(a ² r+V ₀). The values obtained for (g ₂/g ₁) are not very much different from the nonrelativistic results of Donoghue and Holstein. The values of (g ₁/f ₁) extracted from our model calculations of (f ₂/f ₁) in the Cabibbo limit compare well with the experimental values. The values of (f ₂/f ₁) for various semileptonic transitions are also estimated incorporating phenomenologically the effect of nonzerog ₂ in the ratio (g ₁/f ₁). It is found that the SU(3)-symmetry breaking does not generate significant departures in (f ₂/f ₁) values from the corresponding Cabibbo predictions.     

| m | Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef _|m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off _|m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f _|m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off _|m|(θ) on the positive real |m| axis.     

Approximate Homomorphisms of Ternary Semigroups

A mapping f : (G ₁,[ ]₁)→ (G ₂,[ ]₂) between ternary semigroups will be called a ternary homomorphism if f([xyz]₁)=[f(x)f(y)f(z)]₂. In this paper, we prove the generalized Hyers–Ulam–Rassias stability of mappings of commutative semigroups into Banach spaces. In addition, we establish the superstability of ternary homomorphisms into Banach algebras endowed with multiplicative normsMathematics Subject Classifications (2000). Primary 39B52, Secondary 39B82, 46B99, 17A40     

Does entropic force always imply the Newtonian force law?

We investigate propagations of graviton and additional scalar on four-dimensional anti-de Sitter (AdS₄) space using f(R) gravity models with external sources. It is shown that there is the van Dam–Veltman–Zakharov (vDVZ) discontinuity in f(R) gravity models because f(R) gravity implies GR with additional scalar. This clearly indicates a difference between general relativity and f(R) gravity.     

Variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation

We give an integral variational characterization for the speed of fronts of the nonlinear diffusion equationu _t =u _xx +f(u) withf(0)=f(1)=0, andf>0 in (0,1), which permits, in principle, the calculation of the exact speed for arbitraryf.     

New static solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) theory

We consider the equations of motion of an anisotropic space-time in f(T) theory, where T is the torsion. New spherically symmetric solutions of black holes and wormholes are obtained with a constant torsion and for the cases for which the radial pressure is proportional to a real constant, to some algebraic functions f(T) and their derivatives f _T (T), or vanishes identically.     

Existence of Solutions of a Kinetic Equation Modeling Cometary Flows

A global existence theorem is presented for a kinetic problem of the form _t f+v· _x f=Q(f), f(t=0)=f ₀, where Q(f) is a simplified model wave–particle collision operator extracted from quasilinear plasma physics. Evaluation of Q(f) requires the computation of the mean velocity of the distribution f. Therefore, the assumptions on the data are such that vacuum regions, where the mean velocity is not well defined, are excluded. Also the initial data are assumed to have bounded total energy. As additional results conservation laws for mass, momentum, and energy are derived, as well as an entropy dissipation law and the propagation of higher order moments.     

Universality of Operator Ordering in Kinetic Energy Operator for Particles Moving on two Dimensional Surfaces

When the motion of a particle is constrained on the two-dimensional surface, excess terms exist in usual kinetic energy 1/(2m)∑ p _i ² with hermitian form of Cartesian momentum p _i (i = 1,2,3), and the operator ordering should be taken into account in the kinetic energy which turns out to be 1/(2m)∑ (1/f _i )p _i f _i p _i where the functions f _i are dummy factors in classical mechanics and nontrivial in quantum mechanics. The existence of non-trivial f _i shows the universality of this constraint induced operator ordering in quantum kinetic energy operator for the constraint systems.     

Comment on Vub from exclusive semileptonic B and D decays

The prospects for determining |V_ub| from exclusive B semileptonic decay are discussed. The double ratio of form factors (f^(B→ρ)/f^(B→K*))/(f^(D→ρ)/f^(D→K*)) is calculated using chiral perturbation theory. Its deviation from unity due to contributions that are non-analytic in the symmetry breaking parameters is very small. Combining experimental data obtainable from , and can lead to a model independent determination of |V_ub| with an uncertainty from theory of about 10%.     

Spherical harmonics and cartesian tensor scalar product expansions of the distribution function

On the basis of the expansion of the distribution function in a sum of the spherical harmonics, the distribution functionf(v, r, t) is expanded in a series of scalar products of two Cartesian tensors term by term, i.e. The tensors and ^(l) (l=2, 3) are constructed in dependence on the spherical harmonic expansion coefficients (the tensors and ^(l) (l=0, 1) have been constructed by Jancel and Kahan [3]). On the basis of the knowledge of the analytic form off ₂ andf ₃ the equations forf ₁ f ₂ andf ₃ for the case of the Boltzmann's equation are determined.Technická 2, Praha 6, Czechoslovakia.     

掺Er光纤飞秒激光器中高信噪比载波包络位相偏移频率获取的实验研究

在实验上分析了掺Er光纤光学频率梳中激光器与一级放大器之间光纤长度、 光纤扰动以及放大器抽运功率对倍频程光谱和载波包络位相偏移频率(f₀)信噪比的影响. 通过系统优化, 实现了40 dB信噪比的f₀输出, 为f₀的长期锁定和光纤光学频率梳的实现提供了技术保障.     

Future cosmological evolution in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity using two equations of state parameters

We investigate the issues of future oscillations around the phantom divide (FOPD) for f(R) gravity. For this purpose, we introduce two types of energy density and pressure arisen from the f(R)-higher order curvature terms. One has the conventional energy density and pressure even in the beginning of the Jordan frame, whose continuity equation defines the native equation of state w _DE. On the other hand, the other has the different energy density and pressure which do not obviously satisfy the continuity equation. This needs to introduce the effective equation of state w _eff to describe the f(R)-fluid, in addition to the native equation of state [(w)\tilde]_DE\tilde{w}_{\mathrm{DE}}. We show that the FOPD occur in f(R) gravities by introducing two types of equation of state. Finally, we point out that the singularity appears ar x=x _c because the stability condition of f(R) gravity violates.     

Electrical and magnetic properties of [(CoFeZr)x(Al2O3)1 ? x/(α-SiH)]n multilayer structures

The concentration dependences of the electrical resistivity and complex permeability of [“(Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} ”/“α-Si: H”] _n multilayer structures and (Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} composites have been studied. It has been established that introduction of a semiconductor interlayer into the (Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} composites substantially decreases the electrical resistivity of [“(Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} ”/“α-Si: H”] _n multilayer structures. The concentration dependences of the real and imaginary parts of the complex permeability of the [“(Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} ”/“α-Si: H”] _n nanomultilayer structures substantially differ from those of the (Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} composites. The real part of the complex permeability of the [“(Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} ”/“α-Si: H”] _n nanomultilayer structures follows the curve with a minimum near the percolation threshold of the composite, and the imaginary part smoothly decreases as the ferromagnetic phase concentration increases. The results obtained are explained by the increase in the bifurcation temperature due to the conduction electrons of the semiconductor interlayer, which favor magnetic ordering of ferromagnetic grains.     

L p -Boundedness of Wave Operators for¶Two Dimensional Schrödinger Operators

Let be the two dimensional Schr?dinger operator with the real valued potential V which satisfies the decay condition at infinity for . We show that the wave operators , , are bounded in for any 1<p<∞ under the condition that H has no zero bound states or zero resonance, extending the corresponding results for higher dimensions. As W _± intertwine H ₀ and the absolutely continuous part H P _ac of H : f(H)P _ac=W _± f(H ₀ )W _± ^* for any Borel function f on ℝ¹, this reduces the various L ^p -mapping properties of f(H)P _ac to those of f(H)₀), the convolution operator by the Fourier transform of the function f(ξ²). Received: 5 April 1999 / Accepted: 26 May 1999     

Expectation values of unbounded observables

For an unbounded quantum mechanical observableA, the expectation value A _f and the mean square deviation _f A cannot be denned for all (pure) statesf by A _f = (f,Af) and ( _f A)² = (f,A ² f)-(f,Af)², respectively. More general definitions are given here, which are also valid for state mixtures (density matrices). A general uncertainty relation for unbounded observables is derived.