These are the graphs of the diffusion property change due to planter flexion of the right ankle joint. White bars are the right to left ratio of diffusion properties including FA, λ1, λ2, λ3, and ADC at resting state. Gray bars are those at the contraction in GCM (a), and passive elongation in AT (b). In GCM, statistically significant elevations are seen in FA (P<0.05 *), λ1 (P<0.01 **), λ2 (P<...

aim : to evaluate the effect of active t. gondii tachyzoites and its products on the gene expression level of ifn-yr1 and ifn-yr2 in a murine model.   background : many studies have shown that the parasite toxoplasma gondii utilizes different mechanisms to inhibit the function of ifn-?, but the parasite effect on the function of ifn-yr1 and ifn-yr2 is still unclear. patients and methods : toxop...

The condition (1.1) on λ1, . . . , λn is a well–known necessary condition for n numbers to be the eigenvalues of an n× n nonnegative matrix (see, for example, Berman and Plemmons [3]). Furthermore, from a result due to Friedland [6, Theorem 1], it is known that (1.1) implies that one of the λi’s is nonnegative and majorizes the moduli of the remaining numbers. Assume for the moment, without los...

and Applied Analysis 3 Let λ1 h denote the principle eigenvalue of the following eigenvalue problem: −d2Δu h x u λu inΩ, u 0 on ∂Ω, 2.2 and denote λ1 0 , λ1 0 by λ1, λ ∗ 1 for simplicity. It is easy to know that λ1 h , λ ∗ 1 h is strictly increasing see 23, 24 . In order to calculate the indexes at the trivial and semitrivial states by means of the fixed point index theory, we also need to intr...

Hierarchical learning machines are non-regular and non-identifiable statistical models, whose true parameter sets are analytic sets with singularities. Using algebraic analysis, we rigorously prove that the stochastic complexity of a non-identifiable learning machine is asymptotically equal to λ1 log n − (m1 − 1) log logn + const., where n is the number of training samples. Moreover we show tha...

We pursue a new method, based on lattice QCD, for determining the quantities Λ̄, λ1, and λ2 of heavy-quark effective theory. We combine Monte Carlo data for the meson mass spectrum with perturbative calculations of the short-distance behavior, to extract Λ̄ and λ1 from a formula from HQET. Taking into account uncertainties from fitting the mass dependence and from taking the continuum limit, we f...

Let G be a connected non-regular graph with n vertices, maximum degree ∆ and minimum degree δ, and let λ1 be the greatest eigenvalue of the adjacency matrix of G. In this paper, by studying the Perron vector of G, it is shown that type-I-a graphs and type-I-b (resp. type-II-a) graphs with some specified properties are not λ1-extremal graphs. Moreover, for each connected non-regular graph some l...

V = U ⊕ U ′, for some other subspace U ′ ⊂ V , by Theorem 3.21. Consider T restricted to U ′. This is a map T : U ′ →W , which is injective, since U ′∩ker(T ) = {0}. And note that injective maps, in general, preserve linear independence: if we have a linearly independent set {~x1, . . . , ~xn} ∈ X in a vector space X, a linear map of vector spaces A : X → Y , and a linear combination 0 = λ1A~x1...

In this paper, we prove two new Weyl-type upper estimates for the eigenvalues of the Dirichlet Laplacian. As a consequence, we obtain the following lower bounds for its counting function. For λ ≥ λ1, one has N(λ) > 2 n+ 2 1 Hn (λ− λ1) n/2 λ −n/2 1 , and N(λ) > „ n+ 2 n+ 4 «n/2 1 Hn (λ− (1 + 4/n) λ1) n/2 λ −n/2 1 , where Hn = 2 n j2 n/2−1,1 J2 n/2 (jn/2−1,1) is a constant which depends on n, the...

In this paper,we study global bifurcation phenomena for the following Kirchhoff type problem −M  Ω |∇u(x)|2 dx  ∆u = λf (x, u) in Ω, u = 0 on ∂Ω, where M is a continuous function. Under some natural hypotheses, we show that (λ1(a)M(0), 0) is a bifurcation point and there is a global continuum C emanating from (λ1(a)M(0), 0), where λ1(a) denotes the first eigenvalue of the above problem wit...