Journal of Advances in Applied Mathematics

8

Authors: Ren Gao, Yun Zhang, Long Tang

How to get quality of service (QoS) support in the MAC layer is a hot topic in wireless ad hoc network (MANET). In this paper, a novel adaptive QoS model is presented in MANET, and its feasibility and reliability is analyzed and verified. Compared with traditional SWAN model, the proposed approach is improved by differentiated services in MAC layer in order to achieve high control rate of low-priority transactions. The simulations of the presented model are carried out and the results show that can improve the bandwidth utilization and increase the network throughput, as well as reduce transmission delay in MANET.

12

Authors: Lucian M. Ionescu

The current research regarding the Riemann zeros suggests the existence of a non-trivial algebraic/analytic structure on the set of Riemann zeros [1,2,3]. The duality between primes and Riemann zeta function zeros suggests some new goals and aspects to be studied: adelic duality and the POSet of prime numbers. The article presents computational evidence of the structure of the imaginary parts t of the non-trivial zeros of the Riemann zeta function ρ = 1/2 + it, called in this article the Riemann Spectrum, using the study of their distribution, as in [3]. The novelty represents in considering the associated characters pit, towards an algebraic point of view, than rather in the sense of Analytic Number Theory. This structure is tentatively interpreted in terms of adelic characters, and the duality of the rationals. Second, the POSet structure of prime numbers studied in [4], is tentatively mirrored via duality in the Riemann spectrum. A direct study of the convergence of their Fourier series, along Pratt trees, is proposed. Further considerations, relating the Riemann Spectrum, adelic characters and distributions, in terms of Hecke idelic characters, local zeta integrals (Mellin transform) and !-eigen-distributions, are explored following [5].

6

Authors: Jochen Merker

In supervised machine learning, a support vector machine (SVM) constructs from binary classified training data a linear classifier by solving a linearly constrained convex optimization problem. Depending on the number N of training data and the dimension D of the feature space, it either is advantageous to solve the primal problem or the dual problem. In this article, the case D >> N is discussed where D is so large that even a calculation of the dot product of fully occupied vectors in dimension D is too slow for the desired (e.g. real-time) application. Then a way to speed up the classification is to use an SVM which constructs a sparse linear classifier by solving an optimization problem involving the 1-norm, i.e. many components of the classifying vector are zero so that much less than D multiplications are neccessary to calculate the dot product. For a soft-margin SVM, in this article a theorem on the number of non-zero components is shown.

12

Authors: Farhana Alam, M. H. Rashid, M. A. Alom

Let X and Y be Banach spaces. We study a Regula-falsi-type method for solving the generalized equations 0 ∈ f(x) + g(x) + F(x), where f : X → Y is Fréchet differentiable in a neighborhood of a solution x¯, g : X → Y is Fréchet differentiable at x¯ and F : X ⇒ 2 Y is a set valued mapping with closed graph. Under some suitable assumptions, we prove the existence of any sequence generated by the Regula-falsi-type method and establish the local convergence results of the sequence generated by this method. Indeed, we will show that the sequence generated by this method converges linearly and super-linearly

16

Authors: Lingying Teng, Xiaohu Wang

The main aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs) with non-Lipschitz coefficients. Firstly, we show that Peano’s theorem holds for SFDEs, that is, the continuity alone is sufficient to prove the local existence of the initial value problem of SFDEs. Secondly, some new uniqueness theorems are established by the comparison methods proposed by Xu et al. And then, continuation theorems and global existence theorems for SFDEs with non-Lipschitz coefficients are obtained. Finally, an example is given to illustrate the efficiency of the obtained results.

7

Authors: Richard H. Warren

This paper illustrates fundamental principles about small traveling salesman problems (TSPs) which are a current application for quantum annealing computers. The 2048 qubit, quantum annealing computer manufactured by D-Wave Systems is estimated to be able to solve all TSPs on 8 cities, which advances a recent 4-city result on a quantum simulator. Additionally, the D-Wave quantum computer is expected to find all optimal tours for each TSP. To prepare for this, we show the expected quantum output for 5,000 randomly generated TSPs on 6, 8 and 10 cities. The examples in the TSPLIB have 14 or more cities. These are too large for the current quantum annealing processors. We have included an annotated bibliography about solving the TSP on a quantum computer.

18

Authors: ANDRÉS VIÑA

Given a Calabi-Yau manifold and considering the B-branes on it as objects in the derived category of coherent sheaves, we identify the vertex operators for strings between two branes with elements of the cohomology groups of Ext sheaves. We define the correlation functions for these general vertex operators. Strings stretching between two coherent sheaves are studied as homological extensions of the corresponding branes. In this context, we relate strings between different pairs of branes when there are maps between these pairs. We also interpret some strings with ghost number k as obstructions for lifts or extensions of strings with ghost number k − 1.

8

Authors: Fei Yang, Yuanjian Lin

In this paper, by the use of a new fixed point theorem and the Boundary Value Problem’s Green function. the existence of at least one positive solutions for the fourth-order two point boundary value problem with all order derivatives  u (4)(t) + u 00 (t) = λf(t, u(t), u 0 (t), u 00 (t), u 000 (t)), t ∈ [0, 1], u(0) = u(1) = u 00 (0) = u 00 (1) = 0. is considered, where f is a nonnegative continuous function and λ > 0, 0 < A < π2 .

8

Authors: Yan Feng, Luping Xu, Minghui Wang

The nonlinear matrix equation ( ) t X AI X C A Q m − ∗ + ⊗− = is considered in this paper. A sufficient and necessary condition for Hermite positive definite (HPD) solutions of this equation is presented by using properties of the Kronecker product. Two iterative methods for solving the equation are constructed by making use of the principle of the bounded sequence. The feasibility and effectiveness of the iterative methods are verified by numerical example.

14

Authors: John Guenther, Herbert Lee

The black box functions found in computer experiments often have multiple optima. When there are multiple optima, the goal of a computer experiment should be to determine the best optimum for the purposes of the experiment. This brings up the concept of the utility of an optimum: The degree to which the optimum fulfills the purposes of the experiment. The utility of an optima is based on measures of the variability of the surface in the tolerance region (region of interest around the optima) defined by the accuracy with which influential variables can be specified. This tolerance region can be symmetric or asymmetric. For symmetric optima the tolerance region that provides maximum utility is centered at the optimum point. For asymmetric optima, it may be advantageous to displace the center of the tolerance region from the optimum point. For example, a very skewed optimum (minimum in this case) can increase significantly in one direction but only slightly in the opposite direction from the minimum point. For such an optimum the center point of the tolerance region that provides maximum utility for the optimum is displaced from the optimum point along the direction that only slightly increases. The algorithm discussed in this paper locates the center point for the tolerance region to achieve the best utility for any optimum, symmetric or asymmetric. Making use of the surface predictions of the emulator around the minimum point, it employs pattern search to find the best center point for any optimum and for any dimensionality.