Subexponentially increasing sums of partial quotients in continued fraction expansions

We investigate from a multifractal analysis point of view the increasing rate of the sums of partial quotients $S\_n(x)=\sum\_{j=1}^n a\_j(x)$, where $x=[a\_1(x), a\_2(x), \cdots ]$ is the continued fraction expansion of an irrational $x\in (0,1)$. Precisely, for an increasing function $\varphi: \mathbb{N} \rightarrow \mathbb{N}$, one is interested in the Hausdorff dimension of the sets$$E\_\varphi = \left\{x\in (0,1): \lim\_{n\to\infty} \frac {S\_n(x)} {\varphi(n)} =1\right\}.$$Several cases are solved by Iommi and Jordan, Wu and Xu, and Xu. We attack the remaining subexponential case $\exp(n^\gamma), \ \gamma \in [1/2, 1)$. We show that when $\gamma \in [1/2, 1)$, $E\_\varphi$ has Hausdorff dimension $1/2$. Thus, surprisingly, the dimension has a jump from $1$ to $1/2$ at $\varphi(n)=\exp(n^{1/2})$. In a similar way, the distribution of the largest partial quotient is also studied.Comment: 12 pages. More details for the proof of Theorem 1.2. are adde

The torment of exile and the aesthetics of nostalgia : transnational Chinese neo-romanticism in Xu Xu’s post-war fiction

Physical exile certainly was a painful reality for Xu Xu. Restorative nostalgia might to some extent have informed his literary activity in those years. However, nostalgia in Xu Xu’s postwar fiction, I will argue in this paper, constitutes above all the expression of a quest for a purely aesthetic utopia that had already begun to take shape in his pre-war oeuvre and that came to full fruition in his post-war fiction. By analyzing a number of Xu Xu’s novellas from Hong Kong, such as Bird Talk, The Other Shore 彼岸 (1951), and The All-Souls Tree 百靈樹 (1954), I will show that nostalgia in Xu’s fiction is ultimately time and place unspecific, and that Xu himself was aware of the limits and fallacy of restorative nostalgia. Nostalgia, I will illustrate, was a way for Xu Xu to give expression both to a real sense of loss as well as a sense of metaphysical homelessness that did not directly result from his exile in Hong Kong, but that is bound up with the experience of modernity and the reality of China’s cultural post-war politics. Nostalgia thus becomes the expression of a literary aesthetic that connects Xu Xu to a number of other writers who are typically associated with a twentieth-century revival of romanticism, foremost Hermann Hesse (1877−1962). Like for Xu Xu, the expression of nostalgia was as much an aesthetic gesture for Hesse as it was a political gesture. My reading of Xu Xu’s use of nostalgia thus challenges conventional interpretations of the use of nostalgia in postwar Chinese literature and enhances our understanding of the interplay of aesthetics and politics in the work of Chinese writers in exile. In my analysis of Xu’s work in the context of neo-romanticism, I will draw on the work of Michael Löwy who understands the romantic critique of modernity as bound up with an experience of loss. “The Romantic vision,” Löwy writes, “is characterized by the painful and melancholic conviction that in the modern reality something precious has been lost, at the level of both individuals and humanity at large; certain essential human values have been alienated. This alienation, keenly sensed, is often experienced as exile […]” (Löwy 2001, 21). Löwy quotes Friedrich Schlegel as speaking of the soul, the seat of humanness, as living “under the willows of exile (unter den Trauerweiden der Verbannung),” far removed from the true hearth of homeland (Löwy 2001, 21). It is precisely this sense of metaphysical homelessness, I will argue, that lies at the root of the nostalgic longing expressed by Xu Xu’s fictional protagonists. Yet Löwy’s study on romanticism informs this paper in another way. Löwy understands romanticism as a highly diverse movement the numerous strands of which can be found in genres and literatures not usually thought to be part of the romantic canon. By drawing on Xu’s own critical writing on the role of the artist in society and by illustrating his intellectual proximity to writers and thinkers of the romantic movement, I will argue that Xu Xu’s postwar fiction contributes to a transnational romantic canon and constitutes a creative engagement with romantic aesthetics that links modern Chinese literature to global literary modernity

Intersecting Jones projections

Let M be a von Neumann algebra on a Hilbert space H with a cyclic and separating unit vector \Omega and let \omega be the faithful normal state on M given by \omega(\cdot)=(\Omega,\cdot\Omega). Moreover, let {N_i :i\in I} be a family of von Neumann subalgebras of M with faithful normal conditional expectations E_i of M onto N_i satisfying \omega=\omega\circ E_i for all i\in I and let N=\bigcap_{i\in I} N_i. We show that the projections e_i, e of H onto the closed subspaces \bar{N_i\Omega} and \bar{N\Omega} respectively satisfy e=\bigwedge_{i\in I}e_i.This proves a conjecture of V.F.R. Jones and F. Xu in \cite{JonesXu04}

Are human V\u3b42pos T cells really resistant to aging and Human Cytomegalovirus infection?

In their recent paper, Weili Xu et al. [1] described the different behaviors of V\u3b41pos and V\u3b42pos T cell subsets in response to lifelong stress and claimed that V\u3b42pos T cells are not affected by aging and Human Cytomegalovirus (HCMV) infection. While we agree that these two \u3b3\u3b4 T cell subsets diverge both in phenotype/function and in tissue distribution, we are somewhat surprised that authors did not take into account the several previously published and contradictory experimental evidence in regards to senescence of V\u3b42pos T cells [2,3]. These latter studies reported that HCMV infection not only induces a clonal expansion of a distinct V\u3b39neg/V\u3b42pos T cell subset, but also determines a concomitant adaptive differentiation from CD27high na\uefve cells to CD27low/neg terminal-effectors. However, Weili Xu et al. argued that the expression and kinetics of both CD27 and CD45RA surface markers do not change and follow the homeostatic changes of V\u3b42pos T cells. This statement goes in the opposite direction to previously reported findings as the CD27/CD45RA phenotype has been shown to mark the maturation and differentiation (TNa\uefve, TCentral-Memory, Teffector-Memory and TEffectory-Memory RA) of V\u3b42pos T cells. Indeed, the different surface expression of both CD27 and CD45 parallel the progressive decrease of telomere length, the proliferative capacity as well as the different effector-functions and resistance to death of V\u3b42+ T cells in response to antigens and homeostatic cytokines [4,5]. Hence, we believe that these controversial issues require further discussion beyond the unilateral conclusion given by the study of Weili Xu et al

Drugačni pristopi v obravnavi kitajske estetike: Fang Dongmei in Xu Fuguan

The article introduces Fang Dongmei’s and Xu Fuguan’s ideas about aesthetics and examines their different methodological approaches. Fang Dongmei and Xu Fuguan are both representatives of the second generation of Modern Taiwanese Confucianism. The fundamental goal of this significant movement is to re-evaluate and re-examine the profound contents of Chinese thought in contemporary socio-political conditions through a dialogue with Western philosophy. The representatives of Modern Confucianism of the 20th century hoped that the encounter with the Western intellectual tradition would serve as a platform for modernization of Chinese culture on the one hand, and as a way to achieve the recognition of the West for the profound value of the Chinese intellectual tradition on the other. Fang Dongmei was one of the first representatives of this movement who was trained in Western and Chinese philosophy, and hence built his own philosophical theory on the encounter of both, while Xu Fuguan was one of the first who engaged in a dialogue with the West in the field of Chinese aesthetics. The present article illuminates the profound differences in their basic methods: while Fang Dongmei’s elaboration upon Chinese art and aesthetics is based on philosophical and poetic approaches, Xu Fuguan’s comprehension is grounded on philological, historical and cultural analyses. The author argues that such mutual differences between their ideas show their reciprocal complementarity, which in turn provides a more profound and clear understanding of the specific spirit of Chinese art.Članek predstavi Fang Dongmeijevo in Xu Fuguanovo estetsko misel ter razišče njune različne metodološke pristope. Fang Dongmei in Xu Fuguan sta bila predstavnika druge generacije tajvanskega modernega konfucijanstva. Temeljni cilj tega pomembnega gibanja je bil na podlagi dialoga z zahodno filozofijo ponovno ovrednotiti in preučiti globoke vsebine kitajske misli v sodobnih družbeno-političnih razmerah. Predstavniki modernega konfucianizma 20. stoletja so upali, da bo srečanje z zahodno intelektualno tradicijo na eni strani služilo kot platforma za modernizacijo kitajske kulture, na drugi strani pa kot način doseganja prepoznanja vrednosti in vsebin kitajske intelektualne tradicije s strani Zahoda. Fang Dongmei je bil eden prvih predstavnikov tega gibanja, ki je bil izobražen v zahodni in kitajski filozofiji in ki je na podlagi sinteze med njima zgradil lastno filozofsko teorijo. Xu Fuguan pa je bil eden prvih, ki je vzpostavil dialog z Zahodom na področju kitajske estetike. Članek osvetli razlike v njunih osnovnih metodah: medtem ko je Fang Dongmeijevo proučevanje kitajske umetnosti in estetike temeljilo na filozofskih in poetičnih pristopih, Xu Fuguanovo temelji na filoloških, zgodovinskih in kulturnih analizah. Članek pokaže, da se razlike med njunimi idejami dopolnjujejo, kar posledično omogoča bolj poglobljeno in jasno razumevanje posebnosti duha kitajske umetnosti

Structural and optical properties of MOCVD AllnN epilayers

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Fast growth of the vorticity gradient in symmetric smooth domains for 2D incompressible ideal flow

We construct an initial data for the two-dimensional Euler equation in a bounded smooth symmetric domain such that the gradient of vorticity in $L^{\infty}$ grows as a double exponential in time for all time. Our construction is based on the recent result by Kiselev and \v{S}ver\'{a}k.Comment: 18 page