Universal conditions for algebraic travelling salesman problems to be efficiently solvable

We consider Travelling Salesman Problems (TSPs) where the cost of a tour is an algebraic composition of the cost coefficients that are elements of a totally ordered, commutative semigroup. Conditions for the cost matrix are stated which allow to solve these problems in polynomial time. In particular, we investigate conditions which guarantee that an optimal tour is pyramidal and can therefore be determined in O(n ²) time. Furthermore, we discuss TSP_s with Brownian as well as those with left-upper-triangular cost matrices.     

High Sensitive Electrochemiluminescence Biosensor Based on Ru(phen)32+-loaded Double Strand DNA as Signal Tags use to Detect DNA Methyltransferase Activity

DNA methyltransferase (DNA MTase) can act as biomarker for many diseases and it is important to develop some new methods for sensitive detection of DNA MTase. In this work, a highly efficient electrochemiluminescence (ECL) sensor had been designed for detection of DNA MTase based on Ru(phen)₃²⁺ loaded double strand DNA (dsDNA- Ru(phen)₃²⁺) as signal tags. Ru(phen)₃²⁺ had been efficiently embed in the dsDNA produced through a simple hybridization chain reaction. First, a hairpin probe was designed, which can be specifically recognized by Dam MTase and modified with -SH at one end. It was modified on the surface of gold electrode by -SH as an immobilization probe (IP). This IP will be methylated in the present of Dam MTase and digested by DpnI following. Results in the release of capture probe (CP) which remains on the surface of gold electrode. The CP can hybridize with the single stand part of the dsDNA- Ru(phen)₃²⁺ and make the immobilization of ECL tags on the electrode surface, which results in a strong ECL signals detected. However, without the effect of Dam MTase, the hairpin structure of IP remains stable and cannot capture signal tags, and can only detecte weak ECL signals. The biosensor can detect the activity of Dam MTase in the concentration range of 0.01 U/mL to 20 U/mL with the ECL intensity and the logarithm of the concentration have a linear relationship, and the detection limit is calculated to be 7.6 mU/mL. The developed sensor has the ability to specifically detect Dam MTase, which can be differentiated from other types of DNA MTase. In addition, the designed method has good applicability to detect Dam MTase activity in serum samples and been applied to detect its inhibitor with high efficiency.     

New solutions for charge distribution on conductor surface

In the paper, a problem of electrostatics for charge distribution on a conductor surface is analytically solved for three new particular cases of conducting surfaces with complicated shape and specified value of electrostatic potential. The exact analytical expressions for surface charge density for the bodies are obtained. All the solutions are represented in a clear view of 3D graphs. It is shown that the proposed method of electrostatic problem for conductors allows to obtain infinitely many numerical solutions for the problem but only several special cases can be solved analytically.     

Mathematical Analysis of caching policies and cooperation in YouTube-like services

Currently, most video on-demand services offered over the Internet do not exploit the idle resources available from end-users. We discuss the benefits of user-assistance in video on-demand systems, where users are both clients and servers, helping with the task of video distribution. The mathematical machinery for the systematic analysis of video on-demand services is not mature yet. In this paper we develop a deterministic fluid model to determine the expected evolution of user-assisted on-demand video streaming services. We theoretically prove that cooperative systems always outperform non-cooperative solutions. A combinatorial optimization problem is proposed, where the goal is to distribute a set of video items into repositories trying to offer the minimum waiting times to end-users. This combinatorial problem is proved to be in the class of NP-Complete computational problem, and is heuristically solved with a GRASP methodology. Predictions inspired in YouTube scenarios suggest the introduction of cooperation is both robust and extremely attractive from an economical viewpoint as well.     

Separable programming/duality approach to solving the multi-product Newsboy/Gardener Problem with linear constraints

The Gardener Problem is an extension of the multi-product Newsboy Problem with constraints. It deals with situations where not only the demand is random but also the yield (the supply). Separable programming and duality approaches are utilized to solve the constrained Newsboy/Gardener Problem. The solution methodologies are developed for the common probability distribution functions for the demand, and uniform distribution for the supply, rendering exact and approximate solutions to the problem. Numerical examples are given and when applicable, the performance of the developed approach is compared to those of existing works in this arena. The results reveal that the developed solution methods efficiently converge to the optimal or near optimum solutions. Also, a salient feature of the proposed methodologies is that they can utilize readily available commercial software to solve the considered problems. This feature facilitates the portability of the developed models to the classroom environment.     

LOCALLY STABILIZED FINITE ELEMENT METHOD FOR STOKES PROBLEM WITH NONLINEAR SLIP BOUNDARY CONDITIONS

Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.     

Entropy, independent sets and antichains: A new approach to Dedekind's problem

For -regular, -vertex bipartite graphs with bipartition , a precise bound is given for the sum over independent sets of the quantity . (In other language, this is bounding the partition function for certain instances of the hard-core model.) This result is then extended to graded partially ordered sets, which in particular provides a simple proof of a well-known bound for Dedekind's Problem given by Kleitman and Markowsky in 1975.

     

Three Classes of Reaction-Diffusion Systems with Neumann Boundary Condition

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Computational experience with the Chow—Yorke algorithm

The Chow—Yorke algorithm is a nonsimplicial homotopy type method for computing Brouwer fixed points that is globally convergent. It is efficient and accurate for fixed point problems. L.T. Watson, T.Y. Li, and C.Y. Wang have adapted the method for zero finding problems, the nonlinear complementarity problem, and nonlinear two-point boundary value problems. Here theoretical justification is given for applying the method to some mathematical programming problems, and computational results are presented.This work was partially supported by NSF Grant MCS 7821337.     

A numerical technique for three-dimensional compressible boundary layers

The non-linear two-point boundary value problem for three-dimensional compressible boundary layers is solved through the application of a boundary value technique for a range of parameters characterizing the nature of stagnation point flows. The analytical boundary conditions, at infinity, are applied at the edge of the computational mesh with iterations on the size of the domain. The solutions obtained show excellent agreement with the established similarity solutions for three-dimensional flows. The present method has the potential advantage of yielding the wall values of f″_w, g″_w and θ′_w as a part of the solution, contrary to the previously used ‘shooting’ methods. The algorithm is computationally simple and numerically stable and extremely suitable for engineering design applications.