Faculty and Librarian Perceptions of Librarians as Researchers: Results from Semi-Structured Interviews

Following on the results of an earlier survey, this study explores the perceptions of librarians as researchers according to academic librarians and faculty using semi-structured interviews. Conducting research is a regular part of the academic librarian role, but one that often faces challenges to its undertaking, and one that is not always recognized. Exploring perceptions of librarian research helps to understand the current state of librarian research, the barriers faced by librarian researchers, and the value of librarian research. Fifteen librarians and seven faculty members were interviewed from eight Canadian universities. The interviews were coded and analysed to identify major themes. Librarian research was found to be sometimes unsupported and therefore difficult to conduct, but valuable to librarians and the discipline of librarianship. Additionally, librarian research was found to improve relations between librarians and faculty, and more broadly, was found to create a more collegial academic climate.

Asymptotics of the principal eigenvalue of the Laplacian in 2D periodic domains with small traps

We derive and numerically implement various asymptotic approximations for the lowest or principal eigenvalue of the Laplacian with a periodic arrangement of localised traps of small \[\mathcal{O}(\varepsilon )\] spatial extent that are centred at the lattice points of an arbitrary Bravais lattice in \[{\mathbb{R}^2}\] . The expansion of this principal eigenvalue proceeds in powers of \[\nu \equiv - 1/\log (\varepsilon {d_c})\] , where d c is the logarithmic capacitance of the trap set. An explicit three-term approximation for this principal eigenvalue is derived using strong localised perturbation theory, with the coefficients in this series evaluated numerically by using an explicit formula for the source-neutral periodic Green’s function and its regular part. Moreover, a transcendental equation for an improved approximation to the principal eigenvalue, which effectively sums all the logarithmic terms in powers of v, is derived in terms of the regular part of the periodic Helmholtz Green’s function. By using an Ewald summation technique to first obtain a rapidly converging infinite series representation for this regular part, a simple Newton iteration scheme on the transcendental equation is implemented to numerically evaluate the improved ‘log-summed’ approximation to the principal eigenvalue. From a numerical computation of the PDE eigenvalue problem defined on the fundamental Wigner–Seitz (WS) cell for the lattice, it is shown that the three-term asymptotic approximation for the principal eigenvalue agrees well with the numerical result only for a rather small trap radius. In contrast, the log-summed asymptotic result provides a very close approximation to the principal eigenvalue even when the trap radius is only moderately small. For a circular trap, the first few transcendental correction terms that further improves the log-summed approximation for the principal eigenvalue are derived. Finally, it is shown numerically that, amongst all Bravais lattices with a fixed area of the primitive cell, the principal eigenvalue is maximised for a regular hexagonal arrangement of traps.

Free Boundary Regularity for Almost Every Solution to the Signorini Problem

We investigate the regularity of the free boundary for the Signorini problem in $${\mathbb {R}}^{n+1}$$ R n + 1 . It is known that regular points are $$(n-1)$$ ( n - 1 ) -dimensional and $$C^\infty $$ C ∞ . However, even for $$C^\infty $$ C ∞ obstacles $$\varphi $$ φ , the set of non-regular (or degenerate) points could be very large—e.g. with infinite $${\mathcal {H}}^{n-1}$$ H n - 1 measure. The only two assumptions under which a nice structure result for degenerate points has been established are when $$\varphi $$ φ is analytic, and when $$\Delta \varphi < 0$$ Δ φ < 0 . However, even in these cases, the set of degenerate points is in general $$(n-1)$$ ( n - 1 ) -dimensional—as large as the set of regular points. In this work, we show for the first time that, “usually”, the set of degenerate points is small. Namely, we prove that, given any $$C^\infty $$ C ∞ obstacle, for almost every solution the non-regular part of the free boundary is at most $$(n-2)$$ ( n - 2 ) -dimensional. This is the first result in this direction for the Signorini problem. Furthermore, we prove analogous results for the obstacle problem for the fractional Laplacian $$(-\Delta )^s$$ ( - Δ ) s , and for the parabolic Signorini problem. In the parabolic Signorini problem, our main result establishes that the non-regular part of the free boundary is $$(n-1-\alpha _\circ )$$ ( n - 1 - α ∘ ) -dimensional for almost all times t, for some $$\alpha _\circ > 0$$ α ∘ > 0 . Finally, we construct some new examples of free boundaries with degenerate points.

Sociosexual behaviour in wild chimpanzees occurs in variable contexts and is frequent between same-sex partners

Many animals engage in sociosexual behaviour, including that between same-sex pairs. Bonobos (Pan paniscus) are famous for their sociosexual behaviour, but chimpanzees (Pan troglodytes) apparently do not engage in sociosexual behaviour frequently. However, sociosexual behaviour in chimpanzees may have been overlooked. We observed 584 instances of sociosexual behaviour in chimpanzees at Ngogo, Kibale National Park, Uganda during three years of study. All ages and sexes engaged in sociosexual behaviour, which included mounting, touching of genitals, and pressing genitals together. Most sociosexual behaviour was between adult males. Sociosexual behaviour was often during tense contexts, such as subgroup reunions and during territorial behaviour. Among males, grooming and dominance rank relationships do not explain patterns of sociosexual behaviour. Although sociosexual behaviour may be less frequent in chimpanzees than in bonobos, and bonobos remain distinct in their genito-genital rubbing, our findings suggest that sociosexual behaviour is a regular part of chimpanzee behaviour.

Canonical Graph Contractions of Linear Relations on Hilbert Spaces

Given a closed linear relation T between two Hilbert spaces $$\mathcal {H}$$ H and $$\mathcal {K}$$ K , the corresponding first and second coordinate projections $$P_T$$ P T and $$Q_T$$ Q T are both linear contractions from T to $$\mathcal {H}$$ H , and to $$\mathcal {K}$$ K , respectively. In this paper we investigate the features of these graph contractions. We show among other things that $$P_T^{}P_T^*=(I+T^*T)^{-1}$$ P T P T ∗ = ( I + T ∗ T ) - 1 , and that $$Q_T^{}Q_T^*=I-(I+TT^*)^{-1}$$ Q T Q T ∗ = I - ( I + T T ∗ ) - 1 . The ranges $${\text {ran}}P_T^{*}$$ ran P T ∗ and $${\text {ran}}Q_T^{*}$$ ran Q T ∗ are proved to be closely related to the so called ‘regular part’ of T. The connection of the graph projections to Stone’s decomposition of a closed linear relation is also discussed.

Uniform Approximation to the Solution of a Singularly Perturbed Boundary Value Problem with an Initial Jump

In this study, a third-order linear integro-differential equation with a small parameter at two higher derivatives was considered. An asymptotic expansion of the solution to the boundary value problem for the considered equation is constructed by considering the phenomenon of an initial jump of the second degree zeroth order on the left end of a given segment. The asymptotics of the solution has been sought in the form of a sum of the regular part and the part of the boundary layer. The terms of the regular part are defined as solutions of integro-differential boundary value problems, in which the equations and boundary conditions contain additional terms, called the initial jumps of the integral terms and solutions. Boundary layer terms are defined as solutions of third-order differential equations with initial conditions. A theorem on the existence, uniqueness, and asymptotic representation of a solution is presented along with an asymptotic estimate of the remainder term of the asymptotics. The purpose of this study is to construct a uniform asymptotic approximation to the solution to the original boundary value problem over the entire considered segment.

Teachers’ aggressive and violent behaviours towards students with mild intellectual disabilities in three forms of education

Aggression and violence has become a regular part of school reality. The ongoing legal changes in the education system have provided children with mild intellectual disabilities the opportunity to study in three forms of education: mainstream schools, integration classes and special schools. Unfortunately, the results of many studies have revealed that students with disabilities are more likely to be subject to peer victimization, particularly in various forms of inclusive education. In view of such facts, the question arises whether, and if so, how and with what frequency students with mild intellectual disabilities in various forms of education experience aggression and violence perpetrated by teachers. This seems particularly important because of the role that teachers play in building a sense of security in students, especially those with mild intellectual disabilities. The results of the study revealed a much higher level of aggression and violence experienced by students with mild intellectual disabilities perpetrated by teachers working in mainstream schools compared to those working in special schools. This fact raises great reservations regarding the teachers’ attitude towards students with mild intellectual disabilities and the level of their preparation for effective work with such students.