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We obtain an upper bound for the dimension of the cuspidal automorphic forms for $\mathrm{GL}_2$ over a number field, whose archimedean local representations are not tempered. More precisely, we prove the following result. Let $F$ be a number field and $\mathbb{A}_{F}$ be the ring of adeles of $F$. Let $\mathcal{O}_{F}$ be the ring of integers of $F$. Let $\mathfrak{X}_{F,\mathrm{ex}}$ be the set of irreducible cuspidal automorphic representations $\pi$ of $\mathrm{GL}_2(\mathbb{A}_{F})$ with the trivial central character such that for each archimedean place $v$ of $F$, the local representation of $\pi$ at $v$ is an unramified principal series and is not tempered. For an ideal $J$ of $\mathcal{O}_{F}$, let $\mathrm{K}_{0}(J)$ be the subgroup of $\mathrm{GL}_2(\mathbb{A}_{F})$ corresponding to $\Gamma_0(J) \subset \mathrm{SL}_2(\mathcal{O}_F)$. Let $r_1$ be the number of real embeddings of $F$ and $r_2$ be the number of conjugate pairs of complex embeddings of $F$. Using the Arthur-Selberg trace formula, we have \begin{equation*} \sum_{\pi\in \mathfrak{X}_{F,\mathrm{ex}}} \dim \pi^{\mathrm{K}_0(J)} \ll_{F} \frac{[\mathrm{SL}_2(\mathcal{O}_{F}) : \Gamma_0(J)]}{(\log (N_{F/\mathbb{Q}}(J)))^{2r_1+3r_2}} \quad \text{ as } \quad |N_{F/\mathbb{Q}}(J)|\to \infty. \end{equation*} From this result, we obtain the result on an upper bound for the number of Hecke-Maass cusp forms of weight $0$ on $\Gamma_0(N)$ which do not satisfy the Selberg eigenvalue conjecture.

Let $M$ be a positive integer and $p(n)$ be the number of partitions of a positive integer $n$. Newman's conjecture asserts that for each integer $r$, there are infinitely many positive integers $n$ such that \[ p(n)\equiv r \pmod{M}. \] For an integer $d$, let $B_{d}$ be the set of positive integers $M$ such that the number of prime divisors of $M$ is $d$. In this paper, we prove that for each positive integer $d$, the density of the set of positive integers $M$ for which Newman's conjecture holds in $B_{d}$ is $1$. Furthermore, we study an analogue of Newman's conjecture for weakly holomorphic modular forms on $\Gamma_0(N)$ with nebentypus, and this applies to $t$-core partitions and generalized Frobenius partitions with $h$-colors., Comment: 24 pages

We report exchange bias (EB) effect in the Au-Fe3O4 composite nanoparticle system, where one or more Fe3O4 nanoparticles are attached to an Au seed particle forming dimer and cluster morphologies, with the clusters showing much stronger EB in comparison with the dimers. The EB effect develops due to the presence of stress in the Au-Fe3O4 interface which leads to the generation of highly disordered, anisotropic surface spins in the Fe3O4 particle. The EB effect is lost with the removal of the interfacial stress. Our atomistic Monte-Carlo studies are in excellent agreement with the experimental results. These results show a new path towards tuning EB in nanostructures, namely controllably creating interfacial stress, and open up the possibility of tuning the anisotropic properties of biocompatible nanoparticles via a controllable exchange coupling mechanism., Comment: 28 pages, 6 figures, submitted to Nanotechnology

Many researchers have paid attention to the potentiality and possibility of the shared mental model because it enables teammates to perform their job better by sharing team knowledge, skills, attitudes, dynamics and environments. Even though theoretical and experimental evidences provide a close relationship between the shared mental model and successful team performance, there has not been much consideration of the factors of the shared mental model that can show a causal relationship between it and team performance. Based on the reviews of existing studies, the purpose of this study is to specify what factors affect the shared mental model. For further research, it is necessary to conduct empirical studies that validate the causal relationship among the identified factors of shared mental models that affect team performance.

The articles published in four prominent distance education journals between 1997 and 2002 were categorized and the references cited were tallied. The study provides an opportunity to examine research topics, methods, and citation trends. The results can be used to review current research trends and to explore potential research directions. (Contains 2 figures and 7 tables.)