اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMean Square Radius of EAS Electrons
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Detailed theoretical study of the mean square radius of extensive air shower electrons has been made in connection with further development of scaling formalism for electron lateral distribution function. A very simple approximation formula, which allows joint description of all our results obtained in wide primary energy range and for different observation depths is presented. The sensitivity of the mean square radius to variations of basic parameters of hadronic interaction model is discussed.
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The phenomenon of low-temperature superconductivity is intimately associated with the condensation of weakly bound, very extended, strongly overlapping Cooper pairs, and systematic experimental studies of the associated mean square radius (coherence
length) have been made. While the extension of BCS theory to the atomic nucleus has been successful beyond expectation, to our knowledge, no measurement of the nuclear coherence length (expected to be much larger than nuclear dimensions) has been reported in the literature. Recent studies of Cooper pair transfer across a Josephson-like junction, transiently established in a heavy ion collision between superfluid nuclei, have likely changed the situation, providing the experimental input for a quantitative estimate of the nuclear coherence length, as well as the basis for a nuclear analogue of the (ac) Josephson effect.
In this paper, the existence conditions of nonuniform mean-square exponential dichotomy (NMS-ED) for a linear stochastic differential equation (SDE) are established. The difference of the conditions for the existence of a nonuniform dichotomy between
an SDE and an ordinary differential equation (ODE) is that the first one needs an additional assumption, nonuniform Lyapunov matrix, to guarantee that the linear SDE can be transformed into a decoupled one, while the second does not. Therefore, the first main novelty of our work is that we establish some preliminary results to tackle the stochasticity. This paper is also concerned with the mean-square exponential stability of nonlinear perturbation of a linear SDE under the condition of nonuniform mean-square exponential contraction (NMS-EC). For this purpose, the concept of second-moment regularity coefficient is introduced. This concept is essential in determining the stability of the perturbed equation, and hence we deduce the lower and upper bounds of this coefficient. Our results imply that the lower and upper bounds of the second-moment regularity coefficient can be expressed solely by the drift term of the linear SDE.
For linear stochastic differential equations (SDEs) with bounded coefficients, we establish the robustness of nonuniform mean-square exponential dichotomy (NMS-ED) on $[t_{0},+oo)$, $(-oo,t_{0}]$ and the whole $R$ separately, in the sense that such a
n NMS-ED persists under a sufficiently small linear perturbation. The result for the nonuniform mean-square exponential contraction (NMS-EC) is also discussed. Moreover, in the process of proving the existence of NMS-ED, we use the observation that the projections of the exponential growing solutions and the exponential decaying solutions on $[t_{0},+oo)$, $(-oo,t_{0}]$ and $R$ are different but related. Thus, the relations of three types of projections on $[t_{0},+oo)$, $(-oo,t_{0}]$ and $R$ are discussed.
We investigate the magnetic phase diagram of the two-dimensional model for e_g electrons which describes layered nickelates. One finds a generic tendency towards magnetic order accompanied by orbital polarization. For two equivalent orbitals with dia
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The diffusion least mean square (DLMS) and the diffusion normalized least mean square (DNLMS) algorithms are analyzed for a network having a fusion center. This structure reduces the dimensionality of the resulting stochastic models while preserving
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