共查询到20条相似文献，搜索用时 475 毫秒
1.
Alfred Landé 《Journal of The Franklin Institute》1940,229(6):767-774
In order to quantize Dirac's classical point electron1 we supplement Einstein's classical equation (E/c)2 ? p2 = b2 with a reciprocal classical equation (CΔt)2 ? (Δr)2 = a2 where b = mc and a is Dirac's signal radius. Δt is the time saved by a light signal in various states of motion of the electron, and a/c is the rest time saved. Our former efforts2 of obtaining an integral equation for the probability amplitude have been rectified by Born.3 There is no solution of the integral equation, however, unless advanced and retarded phases are introduced simultaneously, along with Dirac's advanced and retarded potentials. We have obtained a transcendental equation for the eigen-value μ = αγ where α is the Sommerfeld fine-structure constant, and γ is the numerical factor in Dirac's signal radius a = γe2/mc2. The smallest eigen-value is μ = 0.0299.That is, ab = hγ = h/210. 相似文献
2.
This paper investigates a stability problem for linear systems with time-varying delays. By constructing suitable augmented Lyapunov–Krasovskii functionals, improved stability criteria under various conditions of time-varying delays are derived within the framework of linear matrix inequalities (LMIs). Moreover, to reduce the computational burden caused by the non-convex term including h2(t), how to deal with it is applied by estimating it to the convex term including h(t). Finally, three illustrative examples are given to show the effectiveness of the proposed criteria. 相似文献
3.
This paper focuses on input-to-state stability of a class of switched stochastic delayed systems which are drived by Lévy noise. By multiple Lyapunov function and average dwell time approach, the sufficient conditions of the ψλ(t)-weighted input-to-state stability can be obtained if all the subsystems are input-to-state stable. Then utilizing comparison principle and the method of constant variation, the sufficient criteria of the eλt-weighted input-to-state stability of the switched stochastic delayed systems containing both input-to-state stable subsystems and non-input-to-state stable subsystems can also be derived. Finally, an example is given to illustrate the effectiveness of the proposed results. 相似文献
4.
By means of Mawhin's continuation theorem, we study a kind of fourth-order p-Laplacian neutral functional differential equation with a deviating argument in the form:
(φp(x(t)−cx(t−δ))″)″=f(x(t))x′(t)+g(t,x(t−τ(t,|x|∞)))+e(t). 相似文献
5.
A method of using orthogonal shifted Legendre polynomials for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials is presented. It is based on the repeated integration of the differential equation and the representations of s(τ) dτ = Ps(t) and ts(t) = Rs(t), where P and R are constant matrices and s(t) is a shifted Legendre vector whose elements are shifted Legendre polynomials. The differential input-output equation is converted into a set of overdetermined linear algebraic equations for a least squares solution. The results of simulation studies are included to illustrate the applicability of the method. 相似文献
6.
C.C.H. Tang 《Journal of The Franklin Institute》1973,296(2):137-149
In this paper we attempt to obtain approximate solutions of improved accuracy for a class of differential equations of the form , where ε is a real parameter less than unity, ωc is a positive real constant of order unity and μ(x) is a singular function of x in the region of interest. It does not appear to be possible to find a general analytic expression for the error estimate of the approximate solution. For the case μ(x) = x?2, however, it is shown that the approximate solution is accurate to 0(ε2), as x → 0? from negative values, by comparing it with the numerically integrated solution. For the same case, the approximate solution is orders of magnitude more accurate than Poincaré's first-order perturbation solution, which is accurate to as x → 0?. This work arose in search of analytic solutions to a linearized form of the restricted three-body problem. 相似文献
7.
L.W. Blau 《Journal of The Franklin Institute》1928,206(3):355-378
The solution of the differential equation y″ + 2Ry′ + n2y = E cos pt is written in a new form which clearly exhibits many important facts thus far overlooked by theoretical and experimental investigators. Writing s = n ? p, and Δn = n ? √n2 ? R2, it is found: (a) When s ≠ Δn, there are “beats,” and the first “beat” maximum is greater than any later maximum while the first “beat” minimum is less than any later “beat” minimum. The “beat” frequency is . (b) When n2 ? p2 = R2, there are no “beats,” and the resultant amplitude grows monotonically from zero to the amplitude of the forced vibration, (c) At resonance, when n = p, we still have maxima which occur with a frequency in a damped system. (d) The absence of “beats” is neither a sufficient nor a necessary condition for resonance in a damped system.In the experimental investigation the upper extremity of a simple pendulum was moved in simple harmonic motion and photographic records obtained of the motion of the pendulum bob. Different degrees of damping were used, ranging from very small to critical.The experimental results are in excellent agreement with theory. 相似文献
8.
In this paper the scattering of plane electromagnetic waves from eccentrically coated metallic spheres is considered. Inhomogeneous, surface, singular integral equations are used to formulate the problem. Their solution is obtained in terms of spherical vector wave functions in conjunction with related addition theorems. Analytical, closed-form results are obtained in the case of small eccentricities kd, where d is the distance between the two centers and k the wave number of the dielectric coating. Thus the scattered field and the various scattering cross-sections of the problem are given by expressions of the form: S(d) = S(0)[1+g’(kd)+g”(kd)2+0(kd)3]. Numerical and graphical results for various values of the parameters are also discussed. 相似文献
9.
The periodic differential equation (1+ε cos t)y̋ + py = 0, hereby termed the Carson–Cambi equation, is the simplest second-order differential equation having a periodic coefficient associated with the second derivative. Provided |ε|<1, which is the case we examine, then the differential equation is a Hill's equation and thus possesses regions of stability and instability in the p–ε plane. Ordinary perturbation theory is employed to obtain the stable (periodic) solutions to ε3. Two-timing theory is employed to obtain solutions for values of k near the critical points k = ±, ±, ±. Three-timing is employed to extend the solution near k = ±. The solutions of the Carson–Cambi equation are compared with the solutions of the corresponding Mathieu equation. 相似文献
10.
In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Rayleigh equation with two deviating arguments of the form
x″+f(x′(t))+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=p(t). 相似文献
11.
J.M. Lowerre 《Journal of The Franklin Institute》1977,303(6):517-526
For the linear statistical model y = Xb + e, X of full column rank estimates of b of the form (C + X′X)+X′y are studied, where C commutes with X′X and Q+ is the Moore-Penrose inverse of Q. Such estimators may have smaller mean square error, component by component than does the least squares estimator. It is shown that this class of estimators is equivalent to two apparently different classes considered by other authors. It is also shown that there is no C such that (C + X′X)+X′Y = My, in which My has the smallest mean square error, component by component. Two criteria, other than tmse, are suggested for selecting C. Each leads to an estimator independent of the unknown b and σ2. Subsequently, comparisons are made between estimators in which the C matrices are functions of a parameter k. Finally, it is shown for the no intercept model that standardizing, using a biased estimate for the transformed parameter vector, and retransforming to the original units yields an estimator with larger tmse than the least squares estimator. 相似文献
12.
Huaqing Li Hao Zhang Zheng Wang Yifan Zhu Qi Han 《Journal of The Franklin Institute》2019,356(6):3733-3761
This paper considers solving a class of optimization problems over a network of agents, in which the cost function is expressed as the sum of individual objectives of the agents. The underlying communication graph is assumed to be undirected and connected. A distributed algorithm in which agents employ time-varying and heterogeneous step-sizes is proposed by combining consensus of multi-agent systems with gradient tracking technique. The algorithm not only drives the agents’ iterates to a global and consensual minimizer but also finds the optimal value of the cost function. When the individual objectives are convex and smooth, we prove that the algorithm converges at a rate of if the homogeneous step-size does not exceed some upper bound, and it accelerates to O(1/t) if the homogeneous step-size is sufficiently small. When at least one of the individual objectives is strongly convex and all are smooth, we prove that the algorithm converges at a linear rate of O(λt) with 0?<?λ?<?1 even though the step-sizes are time-varying and heterogeneous. Two numerical examples are provided to demonstrate the efficiency of the proposed algorithm and to validate the theoretical findings. 相似文献
13.
A system of differential equations A(d/dt) x = Bx+f, along with the initial condition x(0) = k, is considered where A and B are m x n matrices. Generalized inverses of the matrix A are used to derive algebraic conditions for the existence and uniqueness of a solution. An example is presented to illustrate application of the results to circuit theory. 相似文献
14.
John Grist Brainerd 《Journal of The Franklin Institute》1942,233(2):135-142
Numerous relatively simple physical systems give rise under appropriate circumstances to oscillations which obey the equation y″ + ?(1 + k cos t)y = 0 (Mathieu's equation). These oscillations may be either stable, periodic, or unstable, depending upon parameters of the physical system as expressed by the parameters ? and k in the basic equation. It has been customary to distinguish between the stable and unstable states by diagrams of the type of Fig. 1, from which it is possible to tell whether a given set of values of the parameters ?, k will yield a stable or unstable solution. In this paper are given curves which not only present this information, but in addition give for an important part of the stable state the values of the characteristic exponent μ. The solution of the equation y″ + ?(1 + k cos t)y = 0 depends to a large extent on this exponent, and the availability of values of μ should greatly facilitate the practical application of the equation. 相似文献
15.
By means of Mawhin's continuation theorem, we study a third-order p-Laplacian differential equation
(?p(u″(t)))′+f(t,u′(t),u″(t))+g(t,u(t-τ(t)))=e(t). 相似文献
16.
Manuel A. Duarte-Mermoud Jorge L. Estrada Juan C. Travieso-Torres 《Journal of The Franklin Institute》2009,346(8):752-767
The problem of adaptive stabilization of a class of continuous-time and time-varying nonlinear plants is treated in this paper. The control scheme guarantees that the state of the plant, with bounded time-varying parameters, asymptotically converges to zero. For the nonlinear case with n2+n unknown parameters (n time-varying and n2 constant), when the control matrix B is unknown the controller has to adjust n2+1 parameters providing only local stability results. On the contrary, when the control matrix B is known only one parameter has to be adjusted and the proposed scheme provides global stability results. The general methodology is particularized for the linear case with 2n2 unknown parameters (n2 time-varying and n2 constant), adjusting n2+1 parameters when the control matrix B is unknown and guarantees only local stability results, whereas in the case when the control matrix B is known only one parameter has to be adjusted and the proposed scheme provides global stability results. 相似文献
17.
A well-known discrete stability test is used to derive from the denominator D(z) of a given stable high-order transfer function G(z), the denominator of a low-order approximant of G(z). The proposed method, based on the truncation and inversion of a continued fraction formed with the coefficients of D(z), yields a reduced denominator d(z) of degree, say m, which is always stable. Furthermore, depending on the neglected parts of the continued fraction, d(z) approximates m1 and m2 = m−m1 zeros of D(z), located very near the points z=1 and z=-1, respectively. In the special case m1=m, d(z) is identical to the polynomial obtained by applying to D(z) the indirect technique, which combines the bilinear transformation with the Routh or the Schwarz approximation method. 相似文献
18.
Using Lu's continuation theorem, the extension one of Manásevich-Mawhin, we study the existence of periodic solutions for p-Laplacian neutral Liénard equation of the form
(?p(x(t)-cx(t-σ))′)′+f(x(t))x′(t)+β(t)g(x(t-τ(t))=e(t). 相似文献
19.
Identification and characterization of a novel 2R,3R-Butanediol dehydrogenase from Bacillus sp. DL01
Background2R,3R-butanediol dehydrogenase (R-BDH) and other BDHs contribute to metabolism of 3R/3S-Acetoin (3R/3S-AC) and 2,3-butanediol (2,3-BD), which are important bulk chemicals used in different industries. R-BDH is responsible for oxidizing the hydroxyl group at their (R) configuration. Bacillus species is a promising producer of 3R/3S-AC and 2,3-BD. In this study, R-bdh gene encoding R-BDH from Bacillus sp. DL01 was isolated, expressed and identified.ResultsR-BDH exerted reducing activities towards Diacetyl (DA) and 3R/3S-AC using NADH, and oxidizing activities towards 2R,3R-BD and Meso-BD using NAD+, while no activity was detected with 2S,3S-BD. The R-BDH showed its activity at a wide range of temperature (25°C to 65°C) and pH (5.0–8.0). The R-BDH activity was increased significantly by Cd2+ when DA, 3R/3S-AC, and Meso-BD were used as substrates, while Fe2+ enhanced the activity remarkably at 2R,3R-BD oxidation. Kinetic parameters of the R-BDH from Bacillus sp. DL01 showed the lowest Km, the highest Vmax, and the highest Kcat towards the racemic 3R/3S-AC substrate, also displayed low Km towards 2R,3R-BD and Meso-BD when compared with other reported R-BDHs.ConclusionsThe R-BDH from Bacillus sp. DL01 was characterized as a novel R-BDH with high enantioselectivity for R-configuration. It considered NAD+ and Zn2+ dependant enzyme, with a significant affinity towards 3R/3S-AC, 2R,3R-BD, and Meso-BD substrates. Thus, R-BDH is providing an approach to regulate the production of 3R/3S-AC or 2,3-BD from Bacillus sp. DL01.How to cite: Elmahmoudy M, Elfeky N, Zhongji P, et al. Identification and characterization of a novel 2R,3R-Butanediol Dehydrogenase from Bacillus sp. DL01. Electron J Biotechnol 2021;49. https://doi.org/10.1016/j.ejbt.2020.11.002 相似文献
20.
Ross Gunn 《Journal of The Franklin Institute》1943,236(4):373-390
The deformation of a strong elastic lithosphere supported by an underlying weak magma is calculated for a long mountainous load. The deformations, produce vertical superposed stresses in the lithosphere that contribute to the support of the mountain and distribute its weight over a large area.Employing the principle of isobaric equilibrium, the distribution of the vertical supporting stress and the associated gravity anomalies may be determined by analysis.The results of the analysis are applied to the Hawaiian chain and it is shown that the calculated physical properties and gravity anomalies are remarkably like those observed. It is inferred from the study that: (a) a strong lithosphere underlies the Hawaiians and this section is practically identical with those underlying other regions; (b) the lithosphere will support one-sided stresses approximating 109 dynes/cm.2 for long periods of time; (c) the distribution of gravity anomaly may be described quantitatively in terms of the calculated deformations; (d) the principle of isobaric equilibrium is obeyed throughout the region whereas the isostatic principle is generally violated; and (e) the distribution of compensating masses is not at all like that demanded by the principle of isostasy.It is concluded that isostasy leads to results that are clearly wrong when applied to mountains or other deformed regions. The principle of isobaric equilibrium appears, however, to be well established by the investigation. 相似文献