This paper introduces a concept of $\mathbb{V}$-time scales, and establishes the existence and uniqueness of solutions for a nonlinear $\mathbb{V}$-time scales boundary value problem of dynamic system under some non-resonance conditions. The main result is based upon the distribution of eigenvalues of the corresponding linear problem, and the main tool is the critical point theory.

Using bifurcation techniques and topological degree theory, this paper investigates the existence of positive solutions for a class of integral boundary value problems of fractional differential equations. Based on the property of the Green function, several sufficient conditions are presented for the existence of positive solutions. Finally, the study of an illustrative example shows that the obtained results are effective.

In this paper, a problem of the effects of impulsive toxicant input on survival of stagestructure single population is studied in a small polluted environment, and the thresholds of survival and extinction of population are found. By the inequality scaling techniques, the sufficient conditions for extinction and survival of population are obtained. Using numerical simulations of MATLAB, the correctness of the theoretical results are verified, the effects of the amount of the toxins enter, the cycle time of toxin enter and the time of population growth on population survival are analyzed.

The method combing the function transformation, the variables separation type solutions and the first kind of elliptic equation is presented to construct many kinds of new complexion solutions of the (2+1) dimension modified Zakharov-Kuznetsov equation. Step1, two kinds of function transformations are presented, and the (2+1) dimension mZK equation can be changed to the nonlinear evolution equation that can obtain the variables separation type solutions. Step2, the variables separation type solutions of the nonlinear evolution equation are presented, and by the relative conclusions of the first kind of elliptic equation, the two-soliton solutions and the two-period solutions and other new complexion solutions of the (2+1) dimension mZK equation are constructed.

Under the mildly integrated and the mildly explosive cases, the asymptotic distributions of composite quantile estimation for moderate deviations from a unit root model with possibly infinite variance errors are obtained, respectively. Some simulation studies are also given to show that the composite quantile estimation has a good performance.

Based on the compound LINEX asymmetric loss function, the paper studies the Bayes estimation and E-Bayes estimation of Burr XII distribution parameter, and makes a random numerical simulation test on rationality and optimality of the parameter’s estimation and E-Bayes estimation.

In this paper, by using Hoffmann-Jφrgensen type probability inequality and truncation method, the sufficient conditions for complete qth moment convergence of weighted sums for arrays of rowwise NSD random variables are obtained. By using the sufficient conditions, we not only generalize and extend the corresponding results of Liang(2010) and Guo et al.(2014), but also greatly simplify their proofs.

By using the moment inequality of negatively associated (NA, for short) random variables and the truncation method, the complete moment convergence for arrays of rowwise NA random variables are studied. Several sufficient conditions to prove the complete moment convergence for arrays of rowwise NA random variables are presented. The results obtained in this paper extend the corresponding ones for NA random variables.

In this paper some properties of $csf$-countable spaces are discussed. $csf$-countable spaces can be characterized by certain images of metrizable spaces, the first-countability of pesudocompact $csf$-countable spaces are explored, and it is proved a regular pseudo-compact paratopological group is metrizable if and only if it is a $csf$-countable Frechet space

In this paper, some characterizations of a locally (sequentially) connected rectifiable space $G$ are given under the condition that $G$ is connected, which improves the corresponding result in topological groups; some characterizations of a locally (sequentially) connected rectifiable space $G$ are given from the point of the local neighborhood base of the element e in $G$. It is also proved that if $A$ is a sequentially open subset of a rectifiable space $G$, then $H=\langle A\rangle$ is a sequentially open rectifiable subspace of $G$.

According to the denseness and the closedness of range, the point spectrum of a bounded linear operator is split into four disjoint parts, i.e., four classes of point spectra. Let $\mathcal{H}_1,\mathcal{H}_2,\mathcal{H}_3$ be infinite dimensional complex separable Hilbert spaces, and write $M_{D,E,F}=\begin{pmatrix}A &D &E\\0 &B &F\\0 &0 &C\end{pmatrix}\in \mathcal{B}(\mathcal{H}_1\oplus\mathcal{H}_2\oplus\mathcal{H}_3)$. Fixed the diagonal operators $A\in \mathcal{B}(\mathcal{H}_1)$, $B\in \mathcal{B}(\mathcal{H}_2)$, $C\in \mathcal{B}(\mathcal{H}_3)$, the perturbation descriptions of various point spectra for $M_{D,E,F}$ are given when $D, E, F$ run over $\mathcal{B}(\mathcal{H}_2, \mathcal{H}_1)$, $\mathcal{B}(\mathcal{H}_3, \mathcal{H}_1)$, $\mathcal{B}(\mathcal{H}_3, \mathcal{H}_2)$, respectively.

The concept of meet C-continuity for posets is introduced. Properties and characterizations of meet C-continuity, as well as relationships of meet C-continuity with C-continuity and QC-continuity are given. Main results are: (1) A lattice which is also meet C-continuous must be distributive; (2) A bounded complete poset (bc-poset, for short) $L$ is meet C-continuous iff $\forall x\in L$ and every none-empty Scott closed set $S$ for which $\vee S$ exists, one has $x\wedge\vee S=\vee\{x\wedge s:s\in S\}$; (3) A complete lattice is a complete Heyting algebra iff it is meet continuous and meet C-continuous; (4) A bounded complete poset is C-continuous iff it is meet C-continuous and QC-continuous; (5) Some counterexamples are constructed to show that a distributive complete lattice needn’t be a meet C-continuous lattice and a meet C-continuous lattice needn’t be a meet continuous lattice.

In this paper, the authors show that the commutators generalized by a BMO function and the intrinsic area function $S_\alpha$ and $g_{\lambda,\alpha}^{\ast}$ are bounded from the weighted weak Hardy space $WH_{b,\omega}^1$ to the weak Lebesgue spaces $WL_\omega^1$.

By using properties of harmonic function, this paper discusses the min-max property of fractal interpolation function on Sierpinski gasket with uniform vertical scaling factor, and presents a necessary and sufficient condition such that the function has the same range with its basic function.