Search

We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on $n$ vertices, on each turn Proposer proposes a potential edge and Decider simultaneously decides (without knowing Proposer's choice) whether to add it to the graph. Proposer cannot propose an edge which would create a triangle in the graph. The game ends when Proposer has no legal moves remaining, and Proposer wins if the final graph has independence number at least $s$. We prove a threshold phenomenon exists for this game by exhibiting randomized strategies for both players that are optimal up to constants. Namely, there exist constants $0B\sqrt{n}\log{n}$. This is a factor of $\Theta(\sqrt{\log{n}})$ larger than the lower bound coming from the off-diagonal Ramsey number $r(3,s)$.

We derive a one-dimensional model that describes pressing of water saturated paper in the press-section of the paper machine. The model involves two nonlinear diffusion equations which are coupled across an internal boundary. Existence and uniqueness as a number of qualitative properties are demonstrated. Further, computational results for a concrete case are discussed.

A goal for the pulp and paper industry is to get a fast and reliable characterization of raw materials as wood and pulp compositions. One possibility for this is near infrared reflectance (NIR) spectroscopy combined with multivariate analysis. In the first part of this study the possibility to make predictions of mixtures of wood chips from three different wood species (Swedish pine, Swedish spruce and Polish pine) is investigated based on NIR spectroscopy. Mixture design and Partial least squares projections to latent structures (PLS) were used for the multivariate calibration modeling. The calculated model was validated both internally and with an external test set. The result was a PLS model with a Q2 = 0.91 according to cross-validation and good prediction of the test set objects, Q2test set = 0·78. In the second part NIR spectroscopy is used to characterize a series of pulp samples. The pulps were also characterized by seventeen traditionally measured pulp properties. PLS was used for the calibration model and internal as well as external validation were done. The resulting PLS model for the 17 pulp properties gave an overall Q2 = 0·61 according to cross-validation. Predictions of the test set objects show that most of the properties are well described by the model. © 1996 by John Wiley & Sons, Ltd.

This is a revision of a paper that I presented at the John Nankervis Memorial Conference in July 2013. The purposes are to describe the research produced jointly by John and I and to give some personal comments.

This paper is based on one presented to the John Nankervis Memorial Conference at the University of Essex in July 2013. It outlines John's pioneering contribution to the econometric modelling of the demand for mail.

In Sani et al. (Int. J. Numer. Meth. Fluids 2006; 50:673–682), the authors claim to provide a proof of well-posedness for certain formulations of the Navier–Stokes equations for incompressible flow. We consider the proof of their main Theorem 1 incomplete, and point out some inconsistencies in the above paper. Copyright © 2008 John Wiley & Sons, Ltd.

This note contains ramifications of results of Delbaen et al. (2002). Assuming that the price process is locally bounded and admits an equivalent local martingale measure with finite entropy, we show, without further assumption, that in the case of exponential utility the optimal portfolio process is a martingale with respect to each local martingale measure with finite entropy. Moreover, the optimal value always can be attained on a sequence of uniformly bounded portfolios.

The authors would like to correct the proof of Theorem 3(a) in the original paper “On the asymptotic behaviour of the 2D Navier-Stokes equations with Navier friction conditions towards Euler equations.” [ZAMM 89(10), 810-822, 2009].

We consider a mathematical model of the fluid indicated in the title which is useful in describing several processes of industrial interest like gas flow in lighting devices or flow of molt glass in a glass furnace. This model includes the three-dimensional Navier-Stokes equations, mass conservation, and equations for radiation intensity (differential approximation) and temperature. The problem is rewritten to define a weak solution the existence of which we re-prove following a paper by J. Forste. For unicity of the solution we give a modified proof (under suitable conditions on the solution domain). Wir betrachten das mathematische Modell eines im Titel der Arbeit gekennzeichneten Fluids, das fur die Beschreibung verschiedener Prozesse von industriellem Interesse — wie einer Gasstromung in lichtaussendenden Geraten oder der Stromung von geschmolzenem Glas in einem Glasschmelzofen — verwendet werden kann. Das Modell enthalt die dreidimensionalen Navier-Stokes-Gleichungen und die Gleichungen fur die Strahlungsintensitat (differentielle Approximation) sowie die Temperatur. Das Problem wird erneut behandelt, um eine verallgemeinerte Losung zu definieren, deren Existenz wir — einer Arbeit von J. Forste folgend — neu beweisen. Fur die Eindeutigkeit der Losung geben wir einen modifizierten Beweis (unter passenden Bedingungen uber das Losungsgebiet).

Transform methods, together with the fast Fourier transform algorithm, can be used to compute various quantities of interest in risk theory and insurance mathematics. These include the total claim size distribution at a fixed time, the mean and variance of the claim size process as a function of time in the Sparre-Andersen model, and the probability of ruin. The associated discretization error can be reduced by applying Richardson's deferred approach to the limit. A theorem is given that puts the use of this technique on a mathematical basis in the context of compound distributions.

van Lenthe, Broer, and Rashid made comments on our 2009 paper [Song et al., J. Comput. Chem. 2009, 30, 399] by criticizing that we did not properly reference the work by Broer and Nieuwpoort in 1988 [Broer and Nieuwpoort, Theor. Chim. Acta. 1988, 73, 405], and we favorably compared our valence bond self-consistent field (VBSCF) algorithm with theirs. However, both criticisms are unjustified insignificant. The Broer–Nieuwpoort algorithm, properly cited in our paper, is for the evaluations of matrix elements between determinants of nonorthogonal orbitals. Stating that this algorithm “can be used for an orbital optimization” afterwards [van Lenthe et al., submitted] is not a plausible way to require more credits or even criticize others. While we stand by our statement that our algorithms scales at O(m4) and van Lenthe et al.'s approximate Newton Raphson algorithm scales at O(mN5) (here m and N are the numbers of basis functions and electrons), as we discussed in our original paper, it becomes obvious that any strict comparison among different algorithms is difficult, unproductive, and counteractive. © 2012 Wiley Periodicals, Inc.

Schneider misinterpreted the rhetorical question about the second law, which the authors firmly believe not violated. Their main purpose is to show, under the Boussinesq approximation and the Navier-Stokes, there exist non-trivial solutions even for quiescent boundary conditions.

The recent paper [1] presents a formula for an interval containing all eigenvalues of a real symmetric matrix. The formula requires only the trace of the matrix and the trace of its square. This formula is here generalised to complex matrices.

The preeminent target of present study is to reveal the speed characteristic of ongoing outbreak COVID-19 due to novel coronavirus. On January 2020, the novel coronavirus infection (COVID-19) detected in India, and the total statistic of cases continuously increased to 7 128 268 cases including 109 285 deceases to October 2020, where 860 601 cases are active in India. In this study, we use the Hermite wavelets basis in order to solve the COVID-19 model with time- arbitrary Caputo derivative. The discussed framework is based upon Hermite wavelets. The operational matrix incorporated with the collocation scheme is used in order to transform arbitrary-order problem into algebraic equations. The corrector scheme is also used for solving the COVID-19 model for distinct value of arbitrary order. Also, authors have investigated the various behaviors of the arbitrary-order COVID-19 system and procured developments are matched with exiting developments by various techniques. The various illustrations of susceptible, exposed, infected, and recovered individuals are given for its behaviors at the various value of fractional order. In addition, the proposed model has been also supported by some numerical simulations and wavelet-based results.

Summary Recently Theodoresu and Wolff have proposed a sequence of random variables for estimating a sequence of constants satisfying a certain recurrence equation. Their problem, which is similar to some arising in stochastic approximation theory, was solved by using techniques from this theory. The present paper shows that the theory of sums of independent random variables is a more natural tool for tackling this problem.

This work comments on a recent paper by J. C. Strikwerda in SIAM Journal on Scientific and Statistical Computing, in an attempt to clear up the evident confusion regarding the use of a Poisson equation for pressure in incompressible Navier-Stokes solutions.

n/a

Before the standard affinity of dyeing — Δu± can be determined, it is necessary to develop a theory of the dyeing process. This theory should indicate clearly the measurements that must be made and the manner in which they must be interpreted in order to determine — Δμ±. Each existing theory of dyeing provides a theoretical model of the dyeing process with which the behaviour of the real dyeing system may be compared. Only when the theoretical model is correct in every respect is — Δμ±, calculated with the aid of the model, a true thermodynamic variable, and only then can reliance be placed upon the values that are obtained for this parameter. From the variation of — Δμ± with the absolute temperature T, it is possible to determine the standard heat of dyeing ΔH±, which then enables the standard entropy of dyeing ΔS± to be derived. The measurement and the significance of the thermodynamic variables — Δμ±, ΔH±, and ΔS± are discussed in detail, with particular reference to the mechanism of dyeing of synthetic-polymer fibres with disperse dyes.

A recent paper by W. Zijl, which reformulated the Navier–Stokes and Boussinesq equations in terms of Clebsch potentials, has an error that greatly reduces the generality of the results. Some other recent efforts to use such potentials in fluid and plasma dynamics are briefly discussed.

In a recent paper, Dr. Frind has formulated a two-dimensional isoparametric finite element based upon the Hermite bicubic interpolation scheme. The present discussion focuses upon certain simplifications in the derivation which appear to have diminished the accuracy of the resulting element, and suggests a simpler approach to the element formulation. This author agrees strongly with Dr. Frind's recommendation of the Hermite parametric element as an efficient and useful tool for general field problems; the present comments are offered to point out that, in fact, the accuracy comparisons presented by Dr. Frind are biased against the Hermite finite element.

The paper shows a procedure for estimating the shape parameter of a Gamma distribution from a sample. This procedure uses a rapidly converging iteration to solve the maximum-likelihood equation and suggests a simple formula for determing the starting value.