Abstract:
Efficient radio resource management is essential in Quality-of-Service (QoS) provisioning for wireless communication networks. In this paper, we propose a novel priority-based packet scheduling algorithm for downlink OFDMA systems. The proposed algorithm is designed to support heterogeneous applications consisting of both real-time (RT) and non-real-time (NRT) traffics with the objective to increase the spectrum efficiency while satisfying diverse QoS requirements. It tightly couples the subchannel allocation and packet scheduling together through an integrated cross-layer approach in which each packet is assigned a priority value based on both the instantaneous channel conditions as well as the QoS constraints. An efficient suboptimal heuristic algorithm is proposed to reduce the computational complexity with marginal performance degradation compared to the optimal solution. Simulation results show that the proposed algorithm can significantly improve the system performance in terms of high spectral efficiency and low outage probability compared to conventional packet scheduling algorithms, thus is very suitable for the downlink of current OFDMA systems.

Abstract:
The degree distance of a graph G is , where and are the degrees of vertices , and is the distance between them. The Wiener index is defined as . An elegant result (Gutman; Klein, Mihali?,, Plav?i? and Trinajsti?) is known regarding their correlation, that
for a tree T with n vertices. In this note, we extend this study for more general graphs that have frequent appearances in the study of these indices. In particular, we develop a formula regarding their correlation, with an error term that is presented with explicit formula as well as sharp bounds for unicyclic graphs and cacti with given parameters.

Abstract:
Economic dispatch problem lies at the kernel among different issues in GTCC units’ operation, which is about minimizing the fuel consumption for a period of operation so as to accomplish optimal load dispatch among units. This paper has analyzed the load dispatch model of gas turbine combined-cycle (GTCC) units and utilizes a quantum genetic algorithm to optimize the solution of the model. The performance of gas turbine combined-cycle units varies with many factors and this directly leads to variation of model parameters. To solve the dispatch problem, variable constraints are adopted to correct the parameters influenced by ambient conditions. In the simulation, comparison of dispatch models for GTCC units considering and not considering the influence of ambient conditions indicates that it is necessary to adopt variable constraints for the dispatch model of GTCC units. To optimize the solution of the model, a Quantum Genetic Algorithm is used considering its advantages in searching performance. QGA combines the quantum theory with evolutionary theory of genetic algorithm. It is a new kind of intelligence algorithm which has been successfully employed in optimization problems. Utilizing quantum code, quantum gate and so on, QGA shows flexibility, high convergent rate, and global optimal capacity and so on. Simulations were performed by building up models and optimizing the solutions of the models by QGA. QGA shows better effect than equal micro incremental method used in the previous literature. The operational economy is proved by the results obtained by QGA. It can be concluded that QGA is quite effective in optimizing economic dispatch problem of GTCC units.

Abstract:
We apply the I-method to prove that the Cauchy problem of a higher-order Schrodinger equation is globally well-posed in the Sobolev space $H^{s}(mathbb{R})$ with s>6/7.

Abstract:
We will obtain the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley -function, and -function on the weighted Herz spaces with general weights. 1. Introduction and Main Results Let and . The classical square function (Lusin area integral) is a familiar object. If is the Poisson integral of , where denotes the Poisson kernel in , then we define the classical square function (Lusin area integral) by (see [1, 2]) where denotes the usual cone of aperture one: Similarly, we can define a cone of aperture for any : and corresponding square function The Littlewood-Paley -function (could be viewed as a “zero-aperture” version of ) and the -function (could be viewed as an “infinite aperture” version of ) are defined, respectively, by (see, e.g., [3, 4]) The modern (real-variable) variant of can be defined in the following way (here we drop the subscript if ). Let be real, radial and have support contained in , and let . The continuous square function is defined by (see, e.g., [5, 6]) In 2007, Wilson [7] introduced a new square function called intrinsic square function which is universal in a sense (see also [8]). This function is independent of any particular kernel , and it dominates pointwise all the above-defined square functions. On the other hand, it is not essentially larger than any particular . For , let be the family of functions defined on such that has support containing in , , and for all , For and , we set Then we define the intrinsic square function of (of order ) by the following formula: We can also define varying-aperture versions of by the formula The intrinsic Littlewood-Paley -function and the intrinsic -function will be given, respectively, by In [8], Wilson showed the following weighted boundedness of the intrinsic square functions. Theorem A. Let , , and . Then there exists a constant independent of such that Moreover, in [9], Lerner obtained sharp norm inequalities for the intrinsic square functions in terms of the characteristic constant of for all . For further discussions about the boundedness of intrinsic square functions on various function spaces, we refer the readers to [10–17]. Before stating our main results, let us first recall some definitions about the weighted Herz and weak Herz spaces. For more information about these spaces, one can see [18–22] and the references therein. Let and let for any . Denote for , if , and , where is the characteristic function of the set . For any given weight function on and , we denote by the space of all functions satisfying

Abstract:
We will obtain the strong type and weak type estimates for vector-valued analogues of classical Hardy-Littlewood maximal function, weighted maximal function, and singular integral operators in the weighted Morrey spaces when and , and in the generalized Morrey spaces for , where is a growth function on satisfying the doubling condition. 1. Introduction The classical Hardy-Littlewood maximal function is defined for a locally integrable function on by where the supremum is taken over all balls containing . It is well known that the maximal operator maps into for all and into . Let be a sequence of locally integrable functions on . For any , we define and This nonlinear operator was introduced by Fefferman and Stein in [1], and since then it has played an important role in the development of modern harmonic analysis. In this remarkable paper [1], Fefferman and Stein extended the classical maximal theorem to the case of vector-valued functions. Theorem 1 (see [1]). Let . Then, for every , there exists a constant independent of such that Theorem 2 (see [1]). Let . Then, for every , there exists a constant independent of such that A weight is a nonnegative, locally integrable function on ; denotes the ball with the center and radius . For , a weight function is said to belong to , if there is a constant such that, for every ball (see [2, 3]), For the case ,？？ , if there is a constant such that, for every ball , A weight function if it satisfies the condition for some . We say that , if for any ball there exists an absolute constant such that It is well known that if with , then . Moreover, if , then, for all balls and all measurable subsets of , there exists such that Given a ball and , denotes the ball with the same center as whose radius is times that of . For a given weight function and a measurable set , we also denote the Lebesgue measure of by and the weighted measure of by , where . Given a weight function on , for , the weighted Lebesgue space is defined as the set of all functions such that We also denote by the weighted weak space consisting of all measurable functions such that In particular, when equals to a constant function, we will denote and simply by and . In [4], Andersen and John considered the weighted version of Fefferman-Stein maximal inequality and showed the following. Theorem 3 (see [4]). Let and . Then, for every , there exists a constant independent of such that Theorem 4 (see [4]). Let and . Then, for every , there exists a constant independent of such that Given a weight , the weighted maximal function is defined as where the

Abstract:
The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate achemical compound's molecular graph with experimentally gathered data regarding the compound's characteristics. The tree that minimizes the Wiener index among trees of given maximal degree was studied. We characterize trees that achieve the maximum and minimum Wiener index, given the number of vertices and the degree sequence.

Abstract:
Let $T$ be a Calder\'on-Zygmund singular integral operator. In this paper, we will show some weighted boundedness properties of commutator $[b,T]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under appropriate conditions on the weight $w$, where the symbol $b$ belongs to weighted $BMO$ or Lipschitz space or weighted Lipschitz space.

Abstract:
In this paper, we first introduce $L^{\sigma_1}$-$(\log L)^{\sigma_2}$ conditions satisfied by the variable kernels $\Omega(x,z)$ for $0\leq\sigma_1\leq1$ and $\sigma_2\geq0$. Under these new smoothness conditions, we will prove the boundedness properties of singular integral operators $T_{\Omega}$, fractional integrals $T_{\Omega,\alpha}$ and parametric Marcinkiewicz integrals $\mu^{\rho}_{\Omega}$ with variable kernels on the Hardy spaces $H^p(\mathbb R^n)$ and weak Hardy spaces $WH^p(\mathbb R^n)$. Moreover, by using the interpolation arguments, we can get some corresponding results for the above integral operators with variable kernels on Hardy--Lorentz spaces $H^{p,q}(\mathbb R^n)$ for all $p