The Future of Institutional Repositories at Small Academic Institutions: Analysis and Insights

Institutional repositories (IRs) established at universities and academic libraries over a decade ago, large and small, have encountered challenges along the way in keeping faith with their original objective: to collect, preserve, and disseminate the intellectual output of an institution in digital form. While all institutional repositories have experienced the same obstacles relating to a lack of faculty participation, those at small universities face unique challenges. This article examines causes of low faculty contribution to IR content growth, particularly at small academic institutions. It also offers a first-hand account of building and developing an institutional repository at a small university. The article concludes by suggesting how institutional repositories at small academic institutions can thrive by focusing on classroom teaching and student experiential learning, strategic priorities of their parent institutions

ON NEWTON-RAPHSON METHOD

Recent versions of the well-known Newton-Raphson method for solving algebraic equations are presented. First of these is the method given by J. H. He in 2003. He reduces the problem to solving a second degree polynomial equation. However He’s method is not applicable when this equation has complex roots. In 2008, D. Wei, J. Wu and M. Mei eliminated this deficiency, obtaining a third order polynomial equation, which has always a real root. First of the authors of present paper obtained higher order polynomial equations, which for orders 2 and 3 are reduced to equations given by He and respectively by Wei-Wu-Mei, with much improved form. In this paper, we present these methods. An example is given.newton-raphson

Longitudinal analysis on AQI in 3 main economic zones of China

textIn modern China, air pollution has become an essential environmental problem. Over the last 2 years, the air pollution problem, as measured by PM 2.5 (particulate matter) is getting worse. My report aims to carry out a longitudinal data analysis of the air quality index (AQI) in 3 main economic zones in China. Longitudinal data, or repeated measures data, can be viewed as multilevel data with repeated measurements nested within individuals. I arrive at some conclusions about why the 3 areas have different AQI, mainly attributed to factors like population, GDP, temperature, humidity, and other factors like whether the area is inland or by the sea. The residual variance is partitioned into a between-zone component (the variance of the zone-level residuals) and a within-zone component (the variance of the city-level residuals). The zone residuals represent unobserved zone characteristics that affect AQI. In this report, the model building is mainly according to the sequence described by West et al (2007) with respect to the bottom-up procedures and the reference by Singer, J. D., & Willett, J. B (2003) which includes the non-linear situations. This report also compares the quartic curve model with piecewise growth model with respect to this data. The final model I reached is a piece wise model with time-level and zone-level predictors and also with temperature by time interactions.Statistic

Incompatibility of different customary kaon phase convention

The conventions that Wu and Yang assumed for the kaon phases in the context of $CP$ symmetrical two-pion decay channels fix the relative kaon phase. This fact, apparently not emphasized sufficiently in the past, has recently been overlooked by Hayakawa and Sanda. In particular, Wu and Yang fix the relative phase to a different value than the one resulting from the convention $CP|K^{0}\rangle = |\overline{K^{0}}\rangle$. The difference between the two values is made up of possible contributions from $CPT$- and direct $CP$-violations during the decay of a kaon into a two-pion state of isospin zero.Comment: 5 pages, LaTe

The McCoy-Wu Model in the Mean-field Approximation

We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents $\beta \approx 3.6$ and $\beta_1 \approx 4.1$ in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent $\alpha \approx -3.1$. The samples reduced critical temperature $t_c=T_c^{av}-T_c$ has a power law distribution $P(t_c) \sim t_c^{\omega}$ and we show that the difference between the values of the critical exponents in the pure and in the random system is just $\omega \approx 3.1$. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.Comment: LaTeX file with iop macros, 13 pages, 7 eps figures, to appear in J. Phys.

Relatively Congruence-free Regular Semigroups

Yu, Wang, Wu and Ye call a semigroup S τ -congruence-free, where τ is an equivalence relation on S, if any congruence ρ on S is either disjoint from τ or contains τ . A congruence-free semigroup is then just an ω-congruence-free semigroup, where ω is the universal relation. They determined the completely regular semigroups that are τ -congruence-free with respect to each of the Green’s relations. The goal of this paper is to extend their results to all regular semigroups. Such a semigroup is J –congruence-free if and only if it is either a semilattice or has a single nontrivial J -class, J, say, and either J is a subsemigroup, in which case it is congruence-free, or otherwise its principal factor is congruence-free. Given the current knowledge of congruence-free regular semigroups, this result is probably best possible. When specialized to completely semisimple semigroups, however, a complete answer is obtained, one that specializes to that of Yu et al. A similar outcome is obtained for L and R. In the case of H, only the completely semisimple case is fully resolved, again specializing to those of Yu et al

NEW METHODS FOR SOLVING ALGEBRAIC EQUATIONS

Iteration methods are very useful in solving nonlinear algebraic equations. The most famous such method is Newton’s method deduced by first order Taylor expansion. In 2003, J. H. He gives a new faster convergent method, based on second order Taylor expansion, that gives a quadratic equation for the iterations difference xn+1-xn . However He’s method is not applicable when this equation has complex roots. In 2008, D. Wei, J. Wu and M. Mei eliminated this deficiency, obtaining from third order Taylor expansion a cubic equation, that always has a real root. In this paper, we present the three methods and their applications to some particular equations.equations

Power Partial Isometry Index and Ascent of a Finite Matrix

We give a complete characterization of nonnegative integers $j$ and $k$ and a positive integer $n$ for which there is an $n$-by-$n$ matrix with its power partial isometry index equal to $j$ and its ascent equal to $k$. Recall that the power partial isometry index $p(A)$ of a matrix $A$ is the supremum, possibly infinity, of nonnegative integers $j$ such that $I, A, A^2, \ldots, A^j$ are all partial isometries while the ascent $a(A)$ of $A$ is the smallest integer $k\ge 0$ for which $\ker A^k$ equals $\ker A^{k+1}$. It was known before that, for any matrix $A$, either $p(A)\le\min\{a(A), n-1\}$ or $p(A)=\infty$. In this paper, we prove more precisely that there is an $n$-by-$n$ matrix $A$ such that $p(A)=j$ and $a(A)=k$ if and only if one of the following conditions holds: (a) $j=k\le n-1$, (b) $j\le k-1$ and $j+k\le n-1$, and (c) $j\le k-2$ and $j+k=n$. This answers a question we asked in a previous paper.Comment: 11 page