Productivity development of Norwegian institutions of higher education 2004–2013

Productivity growth of institutions of higher education is of interest for two main reasons: education is an important factor for productivity growth of the economy, and in countries where higher education is funded by the public sector, accountability of resource use is of key interest. Educational services consist of teaching, research and the “third mission” of dissemination of knowledge to the society at large. A bootstrapped Malmquist productivity change index is used to calculate productivity development for Norwegian institutions of higher education over the 10-year period 2004–2013. The confidence intervals from bootstrapping allow part of the uncertainty of point estimates stemming from sample variation to be revealed. The main result is that the majority of institutions have had a positive productivity growth over the total period. However, when comparing with growth in labour input, the impact on productivity varies a lot.     

A short note on the derivation of the elastic von Kármán shell theory

We derive the Γ-limit of scaled elastic energies h^?4E ^h (u ^h ) associated with deformations u ^h of a family of thin shells \({S^h} = \left\{ {z = x + t\vec n\left( x \right);x \in S, - g_1^h\left( x \right) < t < g_2^h\left( x \right)} \right\}\). The obtained von Kármán theory is valid for a general sequence of boundaries g ₁ ^h , g ₂ ^h converging to 0 in an appropriate manner as h vanishes. Our analysis relies on the techniques and extends the results in [10] and [11].     

Existence of three solutions for quasilinear elliptic equations: an Orlicz-Sobolev space setting

In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13].     

Numerical algorithm for solving multi-pantograph delay equations on the half-line using Jacobi rational functions with convergence analysis

A new spectral Jacobi rational-Gauss collocation (JRC) method is proposed for solving the multi-pantograph delay differential equations on the half-line. The method is based on Jacobi rational functions and Gauss quadrature integration formula. The main idea for obtaining a semi-analytical solution for these equations is essentially developed by reducing the pantograph equations with their initial conditions to systems of algebraic equations in the unknown expansion coefficients. The convergence analysis of the method is analyzed. The method possesses the spectral accuracy. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Indeed, the present method is compared favorably with other methods.     

Some inequalities and limit theorems under sublinear expectations

In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob’s inequality for submartingale and Kolmogrov’s inequality. By Kolmogrov’s inequality, we obtain a special version of Kolmogrov’s law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition.     

Asymptotic behaviour of hessian equation with boundary blow up

We consider the boundary blow up problem for k-hessian equation with nonlinearities of power and of exponential type, and prove their existence, uniqueness and asymptotic behaviour. Moreover we also show that their perturbed problem has a unique positive solution, which satisfies some asymptotic behaviors to unperturbed problems under appropriate structure hypotheses for perturbed terms.     

On heavy paths in 2-connected weighted graphs

A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the edges incident with it. In this paper we give three weighted degree conditions for the existence of heavy or Hamilton paths with one or two given end-vertices in 2-connected weighted graphs.     

Admissibility of linear estimators with respect to inequality constraints under some loss functions

In this paper, we study the issue of admissibility of linear estimated functions of parameters in the multivariate linear model with respect to inequality constraints under a matrix loss and a matrix balanced loss. Under the matrix loss, when the model is not constrained, the results in the class of non-homogeneous linear estimators [Xie, 1989, Chinese Sci. Bull., 1148–1149; Xie, 1993, J. Multivariate Anal., 1071–1074] showed that the admissibility under the matrix loss and the trace loss is equivalent. However, when the model is constrained by the inequality constraints, we find this equivalency is not tenable, our result shows that the admissibility of linear estimator does not depend on the constraints again under this matrix loss, but it is contrary under the trace loss [Wu, 2008, Linear Algebra Appl., 2040–2048], and it is also relative to the constraints under another matrix loss [He, 2009, Linear Algebra Appl., 241–250]. Under the matrix balanced loss, the necessary and sufficient conditions that the linear estimators are admissible in the class of homogeneous and non-homogeneous linear estimators are obtained, respectively. These results will support the theory of admissibility on the linear model with inequality constraints.     

Lanthanide-organic frameworks based on terphenyl-tetracarboxylate ligands: syntheses,structures, optical properties and selective sensing of nitro explosives

Three isostructural three-dimensional(3D) lanthanide-based metal-organic frameworks [Ln_2L(H_2L)(NMP)_2].H_2O(Ln=Sm(1), Eu(2), Gd(3); H_4L=1,1′:4′,1″-terphenyl-2′,4,4″,5′-tetracarboxylic acid; NMP=N-methyl-2-pyrrolidone) have been synthesized and structurally characterized. In 1–3, two Ln3+ ions are doubly-bridged by two oxygen atoms of two carboxylate groups to form the dinuclear Ln_2(OCOO–)_2 unit. Each Ln_2(OCOO–)_2 unit links with four H_2L~(2-) ligands and four L4. ligands to lead to the 3D framework,which can be rationalized as a new trinodal 4,4,8-connected(44.62)(45.6)(412.616) topological network by considering the dinuclear Ln_2(OCOO–)_2 units as 8-connected nodes and L~4./H_2L~(2-) ligands as planar 4-connected nodes, respectively. 1 and 3 exhibit blue emission originated from the ligand with the emission maximum at 384 nm, while 2 shows intense characteristic red emission of Eu~(3+) ions and weak ligand-centered emission. Moreover, 2 has fluorescent quenching response towards the aromatic nitro compounds, especially for the 3,4-dinitrotoluene(3,4-DNT) with the linear Stern-Volmer relationship in the concentration range of 0–1 mM and the quenching constant(Ksv) of 2.084×10~3 M~(-1).