Abstract:
In an Ambient Assisted Living (AAL) project the activities of the user will be analyzed. The raw data is from a motion detector. Through data processing the huge amount of dynamic raw data was translated to state data. With hidden Markov model, forward algorithm to analyze these state data the daily activity model of the user was built. Thirdly by comparing the model with observed activity sequences, and finding out the similarities between them, defined the best adapt routine in the model. Furthermore an activity routine net was built and used to compare with the hidden Markov model.

Abstract:
Two types of framework for blurred image classification based on adaptive dictionary are proposed. Given a blurred image, instead of image deblurring, the semantic category of the image is determined by blur insensitive sparse coefficients calculated depending on an adaptive dictionary. The dictionary is adaptive to the Point Spread Function (PSF) estimated from input blurred image. The PSF is assumed to be space invariant and inferred separately in one framework or updated combining with sparse coefficients calculation in an alternative and iterative algorithm in the other framework. The experiment has evaluated three types of blur, naming defocus blur, simple motion blur and camera shake blur. The experiment results confirm the effectiveness of the proposed frameworks.

A kind of direct numerical simulation method suitable for supercritical carbon dioxide jet flow has been discussed in this paper. The form of dimensionless nonconservative compressible Navier-Stokes equations in a two-dimensional cartesian coordinate system is derived in detail. High accurate finite difference compact schemes based on non-uniform grid system are introduced to solve the equations. The simulation results of the three vortex pairing phenomenon of plane mixing layer and a compressible axisymmetric jet flow field show that the discussed numerical simulation method is feasible to calculate the supercritical carbon dioxide jet fluid. And it is found that the difficulties of splitting the convective terms in conservation Navier-Stokes equations, which are brought by the supercritical carbon dioxide fluid pressure state equation, can be avoided by solving the nonconservative compressible Navier-Stokes equations.

Abstract:
Based on Nehari manifold, Schwarz symmetric methods and critical point theory, we prove the existence of positive radial ground states for a class of Schrodinger-Poisson systems in , which doesn’t require any symmetry assumptions on all potentials. In particular, the positive potential is interesting in physical applications.

Abstract:
In this paper, a group of Gauss-Legendre iterative methods with cubic convergence for solving nonlinear systems are proposed. We construct the iterative schemes based on Gauss-Legendre quadrature formula. The cubic convergence and error equation are proved theoretically, and demonstrated numerically. Several numerical examples for solving the system of nonlinear equations and boundary-value problems of nonlinear ordinary differential equations (ODEs) are provided to illustrate the efficiency and performance of the suggested iterative methods.

Abstract:
In this paper, the author is concerned with the following fractional equation \[ { }^CD_{0+}^\alpha u(t)=f(t,u(t),{}^CD_{0+}^{\alpha _1 } u(t),{ }^CD_{0+}^{\alpha _2 } u(t)),t\in (0,1) \] with the anti-periodic boundary value conditions \[ u(0)=-u(1), \;\; t^{\beta _1 -1}\; {}^CD_{0+}^{\beta _1 } u(t)_{\vert t\to 0}=-t^{\beta _1 -1}\; {}^CD_{0+}^{\beta_1 } u(t)_{\vert t=1}, \] \[ t^{\beta _2 -2}\; {}^CD_{0+}^{\beta _2 } u(t)_{\vert t\to 0} =-t^{\beta _2-2}\; {}^CD_{0+}^{\beta _2 }u(t)_{\vert t=1}, \] where ${ }^CD_{0+}^\gamma $ denotes the Caputo fractional derivative of order $\gamma $, the constants $\alpha ,\alpha _1 ,\alpha _2 ,\beta _1 ,\beta _2 $ satisfy the conditions that $2<\alpha \leq3,0<\alpha _1 \leq1<\alpha _2 \leq2,0<\beta _1 <1<\beta _2 <2$. Differing from the recent researches, the function $f$ involves Caputo fractional derivative ${}^CD_{0+}^{\alpha _1 } u(t)$ and ${}^CD_{0+}^{\alpha _2 } u(t)$. In addition, the author put forward a new anti-periodic boundary value conditions, which are more suitable than that were studied in the recent literature. By applying Banach contraction mapping principle, and Leray-Schauder degree theory, some existence results of solution are obtained.

Abstract:
Let $\mathcal{S}$ be a finite commutative semigroup. The Davenport constant of $\mathcal{S}$, denoted ${\rm D}(\mathcal{S})$, is defined to be the least positive integer $\ell$ such that every sequence $T$ of elements in $\mathcal{S}$ of length at least $\ell$ contains a proper subsequence $T'$ ($T'\neq T$) with the sum of all terms from $T'$ equaling the sum of all terms from $T$. Let $q>2$ be a prime power, and let $\F_q[x]$ be the ring of polynomials over the finite field $\F_q$. Let $R$ be a quotient ring of $\F_q[x]$ with $0\neq R\neq \F_q[x]$. We prove that $${\rm D}(\mathcal{S}_R)={\rm D}(U(\mathcal{S}_R)),$$ where $\mathcal{S}_R$ denotes the multiplicative semigroup of the ring $R$, and $U(\mathcal{S}_R)$ denotes the group of units in $\mathcal{S}_R$.

Abstract:
Let $\mathcal{S}$ be a finite semigroup, and let $E(\mathcal{S})$ be the set of all idempotents of $\mathcal{S}$. Gillam, Hall and Williams in 1972 proved that every sequence of terms from the semigroup $\mathcal{S}$ of length at least $|\mathcal{S}|-|E(\mathcal{S})|+1$ contains a nonempty subsequence whose product is idempotent, which affirmed a question proposed by Erd\H{o}s. They also gave a sequence of terms from a particular semigroup to show the value $|\mathcal{S}|-|E(\mathcal{S})|+1$ is best possible. Motivated by this work, in this paper we completely determined the structure of the extremal sequence $T$ provide that $T$ is a sequence of terms from any finite commutative semigroup $\mathcal{S}$ of length exactly $|\mathcal{S}|-|E(\mathcal{S})|$ such that $T$ contains no nonempty subsequence whose product is idempotent. Moreover, we introduced two combinatorial constants for finite semigroups associated with this Erd\H{o}s' question.

Abstract:
Let $\mathcal{S}$ be a commutative semigroup, and let $T$ be a sequence of terms from the semigroup $\mathcal{S}$. We call $T$ an (additively) {\sl irreducible} sequence provided that no sum of its some terms vanishes. Given any element $a$ of $\mathcal{S}$, let ${\rm D}_a(\mathcal{S})$ be the largest length of the irreducible sequence such that the sum of all terms from the sequence is equal to $a$. In case that any ascending chain of principal ideals starting from the ideal $(a)$ terminates in $\mathcal{S}$, we found the sufficient and necessary conditions of ${\rm D}_a(\mathcal{S})$ being finite, and in particular, we gave sharp lower and upper bounds of ${\rm D}_a(\mathcal{S})$ in case ${\rm D}_a(\mathcal{S})$ is finite. We also applied the result to commutative unitary rings. As a special case, the value of ${\rm D}_a(\mathcal{S})$ was determined when $\mathcal{S}$ is the multiplicative semigroup of any finite commutative principal ideal unitary ring.