In this paper we prove a global attractivity result for the unique positive equilibrium
point of a difference equation, which improves and generalizes some known ones in the existing literature. Especially, our results completely solve an open problem and some conjectures proposed in [1, 2, 3, 4].

The single machine parallel-batch scheduling with deteriorating jobs and rejection
is considered in this paper. A job is either rejected, in which a rejection penalty should be paid,
or accepted and processed on the machine. Each job’s processing time is an increasing linear
function of its starting time. The machine can process any number of jobs simultaneously as a
batch. The processing time of a batch is equal to the largest processing time of the jobs in the
batch. The objectives are to minimize the makespan and the total weighted completion time,
respectively, under the condition that the total rejection penalty cannot exceed a given upper
bound Q. We show that both problems are NP-complete and present dynamic programming
algorithms and fully polynomial time approximation schemes (F P T ASs) for the considered
problems.

This paper highlights some recent developments in testing predictability of asset returns with focuses on linear mean regressions, quantile regressions and nonlinear regression models. For these models, when predictors are highly persistent and their innovations are contemporarily correlated with dependent variable, the ordinary least squares estimator has a finite-sample bias, and its limiting distribution relies on some unknown nuisance parameter, which is not consistently estimable. Without correcting these issues, conventional test statistics are subject to a serious size distortion and generate a misleading conclusion in testing predictability of asset returns in real applications. In the past two decades, sequential studies have contributed to this subject and proposed various kinds of solutions, including, but not limit to, the bias-correction procedures, the linear projection approach, the IVX filtering idea, the variable addition approaches, the weighted empirical likelihood method, and the double-weight robust approach. Particularly, to catch up with the fast-growing literature in the recent decade, we offer a selective overview of these methods. Finally, some future research topics, such as the econometric theory for predictive regressions with structural changes, and nonparametric predictive models, and predictive models under a more general data setting, are also discussed.

In this paper, the approximate solutions for two different type of two-dimensional
nonlinear integral equations: two-dimensional nonlinear Volterra-Fredholm integral equations
and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre
wavelet method. To do this, these two-dimensional nonlinear integral equations are transformed
into a system of nonlinear algebraic equations in matrix form. By solving these systems, unknown coefficients are obtained. Also, some theorems are proved for convergence analysis.
Some numerical examples are presented and results are compared with the analytical solution
to demonstrate the validity and applicability of the proposed method.

X-ray imaging is the conventional method for diagnosing the orthopedic condition of a patient. Computerized Tomography(CT) scanning is another diagnostic method that provides patient's 3D anatomical information. However, both methods have limitations when diagnosing the whole leg; X-ray imaging does not provide 3D information, and normal CT scanning cannot be performed with a standing posture. Obtaining 3D data regarding the whole leg in a standing posture is clinically important because it enables 3D analysis in the weight bearing condition. Based on these clinical needs, a hardware-based bi-plane X-ray imaging system has been developed; it uses two orthogonal X-ray images. However, such methods have not been made available in general clinics because of the hight cost. Therefore, we proposed a widely adaptive method for 2D X-ray image and 3D CT scan data. By this method, it is possible to three-dimensionally analyze the whole leg in standing posture. The optimal position that generates the most similar image is the captured X-ray image. The algorithm verifies the similarity using the performance of the proposed method by simulation-based experiments. Then, we analyzed the internal-external rotation angle of the femur using real patient data. Approximately 10.55 degrees of internal rotations were found relative to the defined anterior-posterior direction. In this paper, we present a useful registration method using the conventional X-ray image and 3D CT scan data to analyze the whole leg in the weight-bearing condition.

In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle. Finally an example is given to illustrate our problem.

Suppose that $\mathcal C$ is a finite collection of patterns. Observe a Markov chain until one of the patterns in $\mathcal C$ occurs as a run. This time is denoted by $\tau$. In this paper, we aim to give an easy way to calculate the mean waiting time $E(\tau)$ and the stopping probabilities $P(\tau=\tau_A)$ with $A\in\mathcal C$, where $\tau_A$ is the waiting time until the pattern $A$ appears as a run.

K-mer can be used for the description of biological sequences and k-mer distribution
is a tool for solving sequences analysis problems in bioinformatics. We can use k-mer vector as
a representation method of the k-mer distribution of the biological sequence. Problems, such as
similarity calculations or sequence assembly, can be described in the k-mer vector space. It helps
us to identify new features of an old sequence-based problem in bioinformatics and develop new
algorithms using the concepts and methods from linear space theory. In this study, we defined
the k-mer vector space for the generalized biological sequences. The meaning of corresponding
vector operations is explained in the biological context. We presented the vector/matrix form of
several widely seen sequence-based problems, including read quantification, sequence assembly,
and pattern detection problem. Its advantages and disadvantages are discussed. Also, we
implement a tool for the sequence assembly problem based on the concepts of k-mer vector
methods. It shows the practicability and convenience of this algorithm design strategy.

In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent (NOD) random variables are investigated. Let $\{X_n, n\geq1\}$ be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable $X$. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.

In this paper, we study a Yetter-Drinfeld module $V$ over a weak Hopf algebra $\mathbb{H}$. Although the category of all left $\mathbb{H}$-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules $V$, we construct Nichols algebra $B(V)$ over the weak Hopf algebra $\mathbb{H}$, and a series of weak Hopf algebras. Some results of [8] are generalized.}

This paper concerns the minimization problem of L2 norm of curl of vector fields
prescribed full trace on the boundary of a multiconnected bounded domain. The existence of
the minimizers in H1 are shown by orthogonal decompositions of vector function spaces and a
constructed auxiliary variational problem. And the H2 estimate of the type II divergence-free
part of the minimizers is established by div-curl-gradient type estimates of vector fields.

This paper investigates double sampling series derivatives for bivariate functions defined on $\mathbb{R}^{2}$ that are in the Bernstein space.
For this sampling series, we estimate some of the pointwise and uniform bounds when the function satisfies some decay conditions. The truncated series of this formula allow us to approximate any order of partial derivatives for function from Bernstein space using only a finite number of samples from the function itself.
This sampling formula will be useful in the approximation theory and its applications, especially after having the truncation error well-established. Examples with tables and figures are given at the end of the paper to illustrate the advantages of this formula.

By using the geometric constraints on the control polygon of a Pythagorean hodograph (PH) quartic curve, we propose a sufficient condition for this curve to have monotone curvature and provide the detailed proof. Based on the results, we discuss the construction of spiral PH quartic curves between two given points and formulate the transition curve of a $G^2$ contact between two circles with one circle inside another circle. In particular, we deduce an attainable range of the distance between the centers of the two circles and summarize the algorithm for implementation. Compared with the construction of a PH quintic curve, the complexity of the solution of the equation for obtaining the transition curves is reduced.

We develop a data driven method (probability model) to construct a composite shape descriptor by combining a pair of scale-based shape descriptors. The selection of a pair of scale-based shape descriptors is modeled as the computation of the union of two events, i.e., retrieving similar shapes by using a single scale-based shape descriptor. The pair of scale-based shape descriptors with the highest probability forms the composite shape descriptor. Given a shape database, the composite shape descriptors for the shapes constitute a planar point set. A VoR-Tree of the planar point set is then used as an indexing structure for efficient query operation. Experiments and comparisons show the effectiveness and efficiency of the proposed composite shape descriptor.

Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random matrices which can also be used to serve as the measurement matrices. Hence, Weibull random matrices induce extensive interest. In this paper, we first propose the $l_{2,q}$ robust null space property that can weaken the $D$-RIP, and show that Weibull random matrices satisfy the $l_{2,q}$ robust null space property with high probability. Besides, we prove that Weibull random matrices also possess the $l_q$ quotient property with high probability. Finally, with the combination of the above mentioned properties, we give two important approximation characteristics of the solutions to the $l_q$-minimization with Weibull random matrices, one is on the stability estimate when the measurement noise $e \in \mathbb{R}^n$ needs a priori $\|e\|_2\leq \epsilon$, the other is on the robustness estimate without needing to estimate the bound of $\|e\|_2$. The results indicate that the performance of Weibull random matrices is similar to that of Gaussian random matrices in sparse recovery.

Modeling log-mortality rates on O-U type processes and forecasting life expectancies are explored using U.S. data. In the classic Lee-Carter model of mortality, the time trend and the age-specific pattern of mortality over age group are linear, this is not the feature of mortality model. To avoid this disadvantage, O-U type processes will be used to model the log-mortality in this paper. In fact, this model is an AR(1) process, but with a nonlinear time drift term. Based on the mortality data of America from Human Mortality database (HMD), mortality projection consistently indicates a preference for mortality with O-U type processes over those with the classical Lee-Carter model. By means of this model, the low bounds of mortality rates at every age are given. Therefore, lengthening of maximum life expectancies span is estimated in this paper.

In this paper, in terms of Wiener index, hyper-Wiener index and Harary index, we
first give some sufficient conditions for a nearly balance bipartite graph with given minimum
degree to be traceable. Secondly, we establish some conditions for a k-connected graph to be
Hamilton-connected and traceable for every vertex, respectively.

Under linear expectation (or classical probability), the stability for stochastic differential
delay equations (SDDEs), where their coefficients are either linear or nonlinear but
bounded by linear functions, has been investigated intensively. Recently, the stability of highly
nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper,
by using Peng’s G-expectation theory, we first prove the existence and uniqueness of solutions
to SDDEs driven by G-Brownian motion (G-SDDEs) under local Lipschitz and linear growth
conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs
are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs.

In this paper, we introduce a new extension of the power Lindley distribution, called
the exponentiated generalized power Lindley distribution. Several mathematical properties of
the new model such as the shapes of the density and hazard rate functions, the quantile function,
moments, mean deviations, Bonferroni and Lorenz curves and order statistics are derived.
Moreover, we discuss the parameter estimation of the new distribution using the maximum
likelihood and diagonally weighted least squares methods. A simulation study is performed to
evaluate the estimators. We use two real data sets to illustrate the applicability of the new
model. Empirical findings show that the proposed model provides better fits than some other
well-known extensions of Lindley distributions.

Tracy-Widom distribution was first discovered in the study of largest eigenvalues
of high dimensional Gaussian unitary ensembles (GUE), and since then it has appeared in a
number of apparently distinct research fields. It is believed that Tracy-Widom distribution
have a universal feature like classic normal distribution. Airy2 process is defined through finite
dimensional distributions with Tracy-Widom distribution as its marginal distributions. In this
introductory survey, we will briefly review some basic notions, intuitive background and fundamental properties concerning Tracy-Widom distribution and Airy2 process. For sake of reading,
the paper starts with some simple and well-known facts about normal distributions, Gaussian
processes and their sample path properties.