Remark on the well-posedness of the problem of minimization of integral functionals

In this note, we study the well-posedness of the problem of constrained minimization of an integral functional and show that global well-posedness is equivalent to pointwise well-posedness almost everywhere. Our result extends an earlier one by Zolezzi.This research was supported by NSF Grant No. DMS 88-02688.     

Elliptic Solutions of Dynamical Lucas Sequences

We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler–Cassini identity.     

Pairwise entanglement in the Heisenberg XX model with three-site interactions

We investigate the effects of three-site interactions on the pairwise entanglement in a three-qubit Heisenberg XX model. We find the three-site interactions only in favor of the thermal entanglement and benefit the teleportation between the next-to-nearest neighbor qubits. In addition, we also study the stationary entangled state in the model with intrinsic decoherence taken into account. The influence of different types of three-site interactions on the stationary entangled state is then examined.     

PSEUDOHYPERBOLIC METRIC AND UNIFORMLY DISCRETE SEQUENCES IN THE REAL UNIT BALL

We present an overview of the properties of the pseudohyperbolic metric in several real dimensions and study uniformly discrete sequences for the real unit ball in R^n.     

An intelligent decomposition of pairwise comparison matrices for large-scale decisions

A Pairwise Comparison Matrix (PCM) has been used to compute for relative priorities of elements and are integral components in widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, PCMs suffer from several issues limiting their applications to large-scale decision problems. These limitations can be attributed to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker. This issue results to inconsistent preferences due to the limited cognitive powers of decision makers. To address these limitations, this research proposes a PCM decomposition methodology that reduces the elicited pairwise comparisons. A binary integer program is proposed to intelligently decompose a PCM into several smaller subsets using interdependence scores among elements. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets to derive the global weights of the elements from the original PCM. As a result, the number of pairwise comparison is reduced and consistency is of the comparisons is improved. The proposed decomposition methodology is applied to both AHP and ANP to demonstrate its advantages.     

Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics简

In this paper, the complicated dynamics is studied near a double homoclinic loops with bellows configuration for general systems. For the non-twisted multiple homoclinics, the existence of periodic orbit with the specified route and the existence of shift-invariant curve sequences defined on the cross sections of multiple homoclinics corresponding to any specified one-side infinite sequences are given. In addition, the existence regions are also located.     

Low-cost addition–subtraction sequences for the final exponentiation in pairings

In this paper, we address the problem of finding low cost addition–subtraction sequences for situations where a doubling step is significantly cheaper than a non-doubling one. One application of this setting appears in the computation of the final exponentiation step of the reduced Tate pairing defined on ordinary elliptic curves. In particular, we report efficient addition–subtraction sequences for the Kachisa–Schaefer–Scott family of pairing-friendly elliptic curves, whose parameters involve computing the multi-exponentiation of relatively large sequences of exponents with a size of up to 26 bits.     

Proofs of some conjectures on monotonicity of number-theoretic and combinatorial sequences

In 2012,Zhi-Wei Sun posed many conjectures about the monotonicity of sequences of form {n√zn},where {zn} is a familiar number-theoretic or combinatorial sequence. We show that if the sequence {zn+1/zn}is increasing(resp.,decreasing),then the sequence {n√zn} is strictly increasing(resp.,decreasing) subject to a certain initial condition. We also give some sufficient conditions when {zn+1/zn} is increasing,which is equivalent to the log-convexity of {zn}. As consequences,a series of conjectures of Zhi-Wei Sun are verified in a unified approach.     

关于两两NQD随机变量部分和强大数律的注记

In this paper, the authors study the strong law of large numbers for partial sums of pairwise negatively quadrant dependent （NQD） random variables. The results obtained improve the corresponding theorems of Hu et al. （2013）, and Qiu and Yang （2006） under some weaker conditions.