Flower-shaped nanoparticles improve sensitivity of chemical detection

What you need to know: Raman spectroscopy can be enhanced to be more sensitive in detecting chemicals through the use of nanoparticles with sharper edges and cavities. Silver nanoparticle “flowers” developed at Laurier show the most promising results for the optimal enhancement of this diagnostic testing

Singleton mesh patterns in multidimensional permutations

This paper introduces the notion of mesh patterns in multidimensional permutations and initiates a systematic study of singleton mesh patterns (SMPs), which are multidimensional mesh patterns of length 1. A pattern is avoidable if there exist arbitrarily large permutations that do not contain it. As our main result, we give a complete characterization of avoidable SMPs using an invariant of a pattern that we call its rank. We show that determining avoidability for a $d$-dimensional SMP $P$ of cardinality $k$ is an $O(d\cdot k)$ problem, while determining rank of $P$ is an NP-complete problem. Additionally, using the notion of a minus-antipodal pattern, we characterize SMPs which occur at most once in any $d$-dimensional permutation. Lastly, we provide a number of enumerative results regarding the distributions of certain general projective, plus-antipodal, minus-antipodal and hyperplane SMPs.Comment: Theorem 12 and Conjecture 1 are replaced by a more general Theorem 12; the paper is to appear in JCT

Implementation of Federal Research Projects as a Tool to Enhance the Training Quality of Master's Program

Analytical study of the impact of Federal target programs (FTP) implementation with involvement of master's program students for the purpose of obtaining practical skills, identifying and developing organizational skills, increasing motivation to the educational process and competitiveness in the labor market. The result of a parallel implementation of the Federal program and training of students in the master's program has significantly improved the performance of students. The average point increased from 4.23 in 2014 to 4.55 in 2015. The publication activity increased by 64%, the number of conferences with participation of students in the master's program increased by 75%. The growth of these criteria is caused by a large number of experiments carried out, analytical review, the practical relevance of the studied material and level of motivation due to payments to students from the Federal program funds

Expectation values of local fields in Bullough-Dodd model and integrable perturbed conformal field theories

Exact expectation values of the fields e^{a\phi} in the Bullough-Dodd model are derived by adopting the ``reflection relations'' which involve the reflection S-matrix of the Liouville theory, as well as special analyticity assumption. Using this result we propose explicit expressions for expectation values of all primary operators in the c<1 minimal CFT perturbed by the operator \Phi_{1,2} or Phi_{2,1}. Some results concerning the $\Phi_{1,5}$ perturbed minimal models are also presented.Comment: 27 pages, harvmac.tex, one epsf figur

Form factor expansions in the 2D Ising model and Painlev\'e VI

We derive a Toda-type recurrence relation, in both high and low temperature regimes, for the $\lambda$ - extended diagonal correlation functions $C(N,N;\lambda)$ of the two-dimensional Ising model, using an earlier connection between diagonal form factor expansions and tau-functions within Painlev\'e VI (PVI) theory, originally discovered by Jimbo and Miwa. This greatly simplifies the calculation of the diagonal correlation functions, particularly their $\lambda$-extended counterparts. We also conjecture a closed form expression for the simplest off-diagonal case $C^{\pm}(0,1;\lambda)$ where a connection to PVI theory is not known. Combined with the results for diagonal correlations these give all the initial conditions required for the \l-extended version of quadratic difference equations for the correlation functions discovered by McCoy, Perk and Wu. The results obtained here should provide a further potential algorithmic improvement in the \l-extended case, and facilitate other developments.Comment: 23 pages, references added, introduction extended, abstract modified, misprints correcte

The space group classification of topological band insulators

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice symmetries in the physics of these topological states remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: (a) Gamma-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs.Comment: Accepted in Nature Physic