Consider a Hamiltonian system with Hamiltonian of the form H(x, t, p) where H is convex in p and periodic in x, and t and x ∈ R. It is well-known that its smooth invariant curves correspond to smooth Z-periodic solutions of the PDE ut +H(x, t, u)x = 0 . In this paper, we establish a connection between the Aubry-Mather theory of invariant sets of the Hamiltonian system and Z-periodic weak soluti...

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ord...

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

The rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. The rational bi-cubic function involves six parameters in each rectangular patch. Data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

Convex polygonal lines with vertices in Z+2 and endpoints at 0=(0,0) n=(n1,n2)→∞, such that n2/n1→c∈(0,∞), under the scaling n1−1, have limit shape γ* respect to uniform distribution, identified as parabola arc c(1−x1)+x2=c. This is universal a large class of so-called multiplicative ensembles random lines. The present paper concerns inverse problem shape. In contrast aforementioned universalit...

Background & Aims: Precise muscle activity pattern is required to maintain normal shoulder function and any alteration in muscle activity can result in movement impairment. The purpose of this study was to assess normalized electromyography (EMG) of shoulder muscles during selected functional tasks of upper limb in patients with shoulder impingement syndrome. Methods: Test group consisted of 15...

This paper shows the existence of Lur’e-Postkinov Lyapunov functions for the generalized multivariable discrete-time Popov criterion. The nonlinearities in the Lur’e system considered here are monotonic, sectorand slope-restricted. We discuss the cases where the nonlinearities are diagonal and non-diagonal. Our derivation is based on the discrete-time Kalman-Yakubovich-Popov (KYP) lemma and the...

Using the ζ functional equation and the Hadamard product, an analytical expression for the sum of the reciprocal of the ζ zeros is established. We then demonstrate that on the critical line, |ζ| is convex, and that in the region 0 < <(s) ≤ 0.5, |ζ| has a negative slope, given the RH. In each case, analytical formulae are established, and numerical examples are presented to validate these formulae.

Ve study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function. The likelihood ratio test for this hypothesis is derived in the particular case of interval censoring (or current status data) and its limiting distribution is obtained. The limiting distribution is that of the integral of the difference of the squared slope processes...