On the potential functions for a link diagram

Cho and Murakami defined the potential function for a link [Formula: see text] in [Formula: see text] whose critical point, slightly different from the usual sense, corresponds to a boundary-parabolic representation [Formula: see text]. They also showed that the volume and Chern–Simons invariant of [Formula: see text] can be computed from the potential function with its partial derivatives. In this paper, we extend the potential function to a representation that is not necessarily boundary-parabolic. We show that under a mild assumption it leads us to a combinatorial formula for computing the volume and Chern–Simons invariant of a [Formula: see text]-representation of a closed 3-manifold.

An explicit extragradient algorithm for solving variational inequality problem with application

In this paper, we introduce a new explicit extragradient algorithm for solving Variational Inequality Problem (VIP) in Banach spaces. The proposed algorithm uses a linesearch method whose inner iterations are independent of any projection onto feasible sets. Under standard and mild assumption of pseudomonotonicity and uniform continuity of the VIP associated operator, we establish the strong convergence of the scheme. Further, we apply our algorithm to find an equilibrium point with minimal environmental cost for a model in electricity production. Finally, a numerical result is presented to illustrate the given model. Our result extends, improves and unifies other related results in the literature.

An Inertial Iterative Algorithm with Strong Convergence for Solving Modified Split Feasibility Problem in Banach Spaces

In this paper, we propose an iterative scheme for a special split feasibility problem with the maximal monotone operator and fixed-point problem in Banach spaces. The algorithm implements Halpern’s iteration with an inertial technique for the problem. Under some mild assumption of the monotonicity of the related mapping, we establish the strong convergence of the sequence generated by the algorithm which does not require the spectral radius of A T A. Finally, the numerical example is presented to demonstrate the efficiency of the algorithm.

Recurrence Properties of Generalized Hexanacci Sequence

In this paper, we investigate the recurrence properties of the generalized Hexanacci sequence under the mild assumption that the roots of the corresponding characerteristic polynomial are all distinct, and present how the generalized Hexanacci sequence at negative indices can be expressed by the sequence itself at positive indices.

Covering Rational Surfaces with Rational Parametrization Images

Let S be a rational projective surface given by means of a projective rational parametrization whose base locus satisfies a mild assumption. In this paper we present an algorithm that provides three rational maps f,g,h:A2⇢S⊂Pn such that the union of the three images covers S. As a consequence, we present a second algorithm that generates two rational maps f,g˜:A2⇢S, such that the union of its images covers the affine surface S∩An. In the affine case, the number of rational maps involved in the cover is in general optimal.

Output feedback disturbance rejection control for building structure systems subject seismic excitations

In this paper, the output feedback disturbance rejection control (OFDRC) problem is considered for buildings structures subject seismic excitations. First, based on a mild assumption and a linear transformation, the addressed problem of building structure system is translated into the output feedback disturbance rejection control problem large-scale system with disturbances. Then, by utilizing generalized-proportional-integral observer (GPIO) technique and output feedback domination approach, an output feedback decentralized disturbance rejection control law is derived via a systematic design manner. The multi-overlapping output feedback disturbance rejection controller is obtained according to the inverse transformation of a linear transformation. Strict theory analysis demonstrates that the states of the structure system will be stabilized to a small bounded region. Finally, an 8-story structure system is employed to evaluate the effectiveness of the proposed control strategy. Simulation results demonstrate that the proposed OFDRC exhibits better seismic loads attenuation ability and strong robustness against model uncertainties.

Isogenies Between K3 Surfaces Over

We generalize Mukai and Shafarevich’s definitions of isogenies between K3 surfaces over ${\mathbb{C}}$ to an arbitrary perfect field and describe how to construct isogenous K3 surfaces over $\bar{{\mathbb{F}}}_p$ by prescribing linear algebraic data when $p$ is large. The main step is to show that isogenies between Kuga–Satake abelian varieties induce isogenies between K3 surfaces, in the context of integral models of Shimura varieties. As a byproduct, we show that every K3 surface of finite height admits a CM lifting under a mild assumption on $p$.

Strong Convergent Theorems Governed by Pseudo-Monotone Mappings

The purpose of this paper is to introduce two different kinds of iterative algorithms with inertial effects for solving variational inequalities. The iterative processes are based on the extragradient method, the Mann-type method and the viscosity method. Convergence theorems of strong convergence are established in Hilbert spaces under mild assumption that the associated mapping is Lipschitz continuous, pseudo-monotone and sequentially weakly continuous. Numerical experiments are performed to illustrate the behaviors of our proposed methods, as well as comparing them with the existing one in literature.

Schneider–Siegel theorem for a family of values of a harmonic weak Maass form at Hecke orbits

Let {j(z)} be the modular j-invariant function. Let τ be an algebraic number in the complex upper half plane {\mathbb{H}}. It was proved by Schneider and Siegel that if τ is not a CM point, i.e., {[\mathbb{Q}(\tau):\mathbb{Q}]\neq 2}, then {j(\tau)} is transcendental. Let f be a harmonic weak Maass form of weight 0 on {\Gamma_{0}(N)}. In this paper, we consider an extension of the results of Schneider and Siegel to a family of values of f on Hecke orbits of τ. For a positive integer m, let {T_{m}} denote the m-th Hecke operator. Suppose that the coefficients of the principal part of f at the cusp {i\infty} are algebraic, and that f has its poles only at cusps equivalent to {i\infty}. We prove, under a mild assumption on f, that, for any fixed τ, if N is a prime such that {N\geq 23} and {N\notin\{23,29,31,41,47,59,71\}}, then {f(T_{m}.\tau)} are transcendental for infinitely many positive integers m prime to N.

Volume lemmas and large deviations for partially hyperbolic endomorphisms

We consider partially hyperbolic attractors for non-singular endomorphisms admitting an invariant stable bundle and a positively invariant cone field with non-uniform cone expansion at a positive Lebesgue measure set of points. We prove volume lemmas for both Lebesgue measure on the topological basin of the attractor and the SRB measure supported on the attractor. As a consequence, under a mild assumption we prove exponential large-deviation bounds for the convergence of Birkhoff averages associated to continuous observables with respect to the SRB measure.