Analysis of sulphonated phthalocyanine dyes by capillary electrophoresis

Sulphonated phthalocyanine dyes may be prepared either by direct sulphonation or by mixed condensation methods. Both syntheses will produce mixtures of products. Such mixtures may be analysed by capillary electrophoresis to identify the various degrees of substitution and to indicate the approximate composition of the mixtures.     

Optical mode crossings and the low temperature anomalies of SrTiO3

Optical mode crossing is not a plausible explanation for the new broad Brillouin doublet nor for the strong acoustic anomalies observed at low temperatures in SrTiO₃. Data presented to support that explanation are also inconclusive.     

The constrained minimum weighted sum of job completion times problem

We consider the problem of minimizing the weighted sum of job completion times on a single machine (subject to certain job weights) with an additional side constraint on the weighted sum of job completion times (with respect to different job weights). This problem is NP-hard, and we provide a polynomial time approximation scheme for this problem. Our method is based on Lagrangian relaxation mixed with carefully guessing the positions of certain jobs in the schedule. An earlier version of this paper appeared in the Proceedings of the 10th International IPCO Conference.     

Packing,counting and covering Hamilton cycles in random directed graphs

In this paper we study the chaotic behavior of the heat semigroup generated by the Dunkl-Laplacian on weighted L ^p spaces. In the case of the heat semigroup associated to the standard Laplacian we obtain a complete picture on the spaces L ^p (R ⁿ , (φ _iρ (x))² dx) where φ _iρ is the Euclidean spherical function. The behavior is very similar to the case of the Laplace–Beltrami operator on non-compact Riemannian symmetric spaces studied by Pramanik and Sarkar.     

Development of a rapid-scan fiber-integrated terahertz spectrometer

Scientists in terahertz (THz) wave technologies have benefited from the recent developments in ultrafast laser technologies and RF technologies and applied these new gained techniques into characterizing a wide variety of phenomena. Undoubtedly, the most successful of these applications has been in the development of time-domain terahertz spectroscopic and imaging systems which has been utilized in the characterization of dielectrics and semiconductors. This pulsed technique has allowed users to characterize dynamical behavior inside materials under illumination with picosecond resolution. Typically pump/probe or similar dynamical measurements require the use of amplified pulses derived from free-space solid state lasers in the $\upmu $ J–mJ range and since interferometric techniques are typically used in pulsed measurements the measurement time of a THz spectrum can last at least tens of minutes. Better systems can be realized based on fiber laser technologies. Here we discuss the advantages of a THz spectrometer driven by an ultrafast Ytterbium doped fiber laser whose repetition rate can be tuned rapidly allowing for rapid dynamical measurements. The efficient gain medium, robust operation and compact design of the system opens up the possibility of exploring rapid detection of various materials as well as studying dynamical behavior using the high brightness source.     

A Note About Critical Percolation on Finite Graphs

In this note we study the geometry of the largest component C₁\mathcal {C}_{1} of critical percolation on a finite graph G which satisfies the finite triangle condition, defined by Borgs et al. (Random Struct. Algorithms 27:137–184, 2005). There it is shown that this component is of size n ^2/3, and here we show that its diameter is n ^1/3 and that the simple random walk takes n steps to mix on it. By Borgs et al. (Ann. Probab. 33:1886–1944, 2005), our results apply to critical percolation on several high-dimensional finite graphs such as the finite torus \mathbbZ_n^d\mathbb{Z}_{n}^{d} (with d large and n→∞) and the Hamming cube {0,1} ⁿ .     

Is the critical percolation probability local?

We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. We also prove a finite analogue of this statement, valid for expander graphs, without any girth assumption.     

Ramsey Theory,integer partitions and a new proof of the Erdős–Szekeres Theorem

Let H be a k  -uniform hypergraph whose vertices are the integers 1,…,N$1,\dots ,N$. We say that H contains a monotone path of length n   if there are _x1<_x2<?<_xn+k−1$x_1<x_2<?<x_{n+k-1}$ so that H contains all n   edges of the form {_xi,_xi+1,…,_xi+k−1}$\{x_i,x_{i+1},\dots ,x_{i+k-1}\}$. Let _Nk(q,n)$N_k(q,n)$ be the smallest integer N so that every q-coloring of the edges of the complete k-uniform hypergraph on N vertices contains a monochromatic monotone path of length n  . While the study of _Nk(q,n)$N_k(q,n)$ for specific values of k and q   goes back (implicitly) to the seminal 1935 paper of Erd?s and Szekeres, the problem of bounding _Nk(q,n)$N_k(q,n)$ for arbitrary k and q was studied by Fox, Pach, Sudakov and Suk.     

Biased games on random boards

In this paper we analyze biased Maker‐Breaker games and Avoider‐Enforcer games, both played on the edge set of a random board . In Maker‐Breaker games there are two players, denoted by Maker and Breaker. In each round, Maker claims one previously unclaimed edge of G and Breaker responds by claiming b previously unclaimed edges. We consider the Hamiltonicity game, the perfect matching game and the k‐vertex‐connectivity game, where Maker's goal is to build a graph which possesses the relevant property. Avoider‐Enforcer games are the reverse analogue of Maker‐Breaker games with a slight modification, where the two players claim at least 1 and at least b previously unclaimed edges per move, respectively, and Avoider aims to avoid building a graph which possesses the relevant property. Maker‐Breaker games are known to be “bias‐monotone”, that is, if Maker wins the (1,b) game, he also wins the game. Therefore, it makes sense to define the critical bias of a game, b ^*, to be the “breaking point” of the game. That is, Maker wins the (1,b) game whenever and loses otherwise. An analogous definition of the critical bias exists for Avoider‐Enforcer games: here, the critical bias of a game b ^* is such that Avoider wins the (1,b) game for every , and loses otherwise. We prove that, for every is typically such that the critical bias for all the aforementioned Maker‐Breaker games is asymptotically . We also prove that in the case , the critical bias is . These results settle a conjecture of Stojakovi? and Szabó. For Avoider‐Enforcer games, we prove that for , the critical bias for all the aforementioned games is . © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 46,651–676, 2015     

Low energy phonon spectrum and its parameterization in pure KTaO<Subscript>3</Subscript> below 80 K

High resolution data on low energy phonon branches (acoustic and soft optic) along the three principal symmetry axes in pure KTaO₃ were obtained by cold neutron inelastic scattering between 10 and 80 K. Additional off-principal axis measurements were performed to characterize the dispersion anisotropy (away from the and axes). The parameters of the phenomenological model proposed by Vaks [28] are refined in order to successfully describe the experimental low temperature (10 < T < 100 K) dispersion curves, over an appreciable reciprocal space volume around the zone center ( rlu). The refined model, which involves only 4 temperature-independent adjustable parameters, is intended to serve as a basis for quantitative computations of multiphonon processes. Received: 29 September 1999 and Received in final form 6 January 2000