In this article, certain classes of homeomorphisms on the complex plane have been considered. Specifically, we investigate ring and lower Q-homeomorphisms with respect to the p-module, as well as homeomorphisms of finite distortion. The behavior at infinity of these mappings is investigated, and sharp estimates for their lower power $\alpha $-order are obtained.

In view of the post-stroke finger contracture period, the patient’s muscle weakness causes the fingers to bend and not be extended, and the fingers are in a contracture state. A new hand rehabilitation exoskeleton with a cable and leaf spring hybrid drive is designed. The high-stiffness leaf spring helps the patient complete the extension movement, and the flexion and grasping movement is completed under the action of the cable. The exoskeleton combines the cable and the leaf spring in the driving form. It is flexible and can generate enough grasping force to meet daily activities. The workspace when wearing the exoskeleton is analyzed, and the simulation verifies that the exoskeleton has a high movement space. The stiffness of the finger module is analyzed to determine the appropriate size parameters of the leaf spring. The experimental prototype is built, and the structural performance test is carried out. A prosthetic hand model is made to simulate the hand of a patient without motor ability. The position control is carried out to complete the gesture experiment and grasping experiment, which verifies that the exoskeleton can meet the rehabilitation needs and daily grasping movements. Finally, a variety of performance parameters are designed to evaluate a variety of exoskeletons. The comparison shows that the exoskeleton in this paper has significant advantages, and the area coverage rate of the performance evaluation map can reach 70.4% of the ideal exoskeleton.

In this article, we generalize Andrews’ partitions separated by parity to overpartitions in two ways. We investigate the generating functions for $16$ overpartition families whose parts are separated by parity, and we prove various q-series identities for these functions. These identities include relations to modular forms, q-hypergeometric series, and mock modular forms.

We prove a reciprocity-type formula for the fourth moment of L-functions associated with holomorphic primitive cusp forms of level one and large weight which relates it to the eighth moment of the Riemann zeta function and the dual weighted fourth moments of automorphic L-functions (both holomorphic and Maass). The main objective of the article is to study the structure of the main term for possible generalization of the method to higher moments.

This article presents an examination of the utilization of a conceptual metaphor that maps the art of poetry onto the craft of lapidary in the works of Niẓāmī Ganjavī (1141–1209), a prominent Persian poet known for his innovative use of poetic imageries and literary devices. This conceptual metaphor, as defined in cognitive linguistics, originates from the Persian cultural context and serves as a tangible way for Niẓāmī to express his abstract ideas regarding poetry’s beauty, elegance, and worth. This study contributes to a more comprehensive understanding of the efficacy of this prevalent metaphorical framework in explicating the art of poetry and its related subjects through close reading and textual analysis of excerpts from Niẓāmī’s works, in which this metaphor operates as an underlying element. Additionally, this examination illuminates some aspects of Niẓāmī’s distinctive literary style. More broadly, relying on Niẓāmī’s poetry, this article delivers a perspective on the literary conventions of medieval Iranian courts, particularly with regard to the perception of poetry and the societal status of those who engaged in poetic production.

In this study, a Holling–Tanner type predator–prey model with a discrete time delay is investigated, where the functional response of the predator dynamics is ratio-dependent. We first analyze the local stability of the equilibrium point and examine the existence of Hopf bifurcations. The Hopf bifurcation, also known as the Poincaré–Andronov–Hopf bifurcation, is named after the French mathematician Jules Henri Poincaré, the Russian mathematician Alexander A. Andronov, and the German mathematician Heinz Hopf, whose fundamental contributions laid the foundation of this theory. By treating the delay parameter $\tau $ as the bifurcation parameter, we show that a Hopf bifurcation occurs when the delay crosses certain critical values. Finally, numerical simulations are carried out to support and illustrate our theoretical results.

This essay examines five children’s homemade manuscript magazines and advances an argument that creative collaboration was an important feature of late nineteenth- and early twentieth-century childhood, especially for middle-class young people associated with artistic circles. Focusing on children connected to the Pre-Raphaelite and Bloomsbury circles, the essay shows how select children formed their own artistic circles, modeled on those of the adults in their lives. The magazines are The Scribbler (1878–80) by the children of William Morris with assistance from the children of Philip Burne-Jones; Our Paper (1870–87) by the children and cousins of the Strachey family; The Gem (1898) by Margaret Keynes with her brothers Geoffrey and John Maynard; the Hyde Park Gate News (1891–95) by the Stephen children, later Virginia Woolf and Vanessa Bell; and the Charleston Bulletin (1921–27) by Vanessa Bell’s sons, Julian and Quentin Bell. Through serialized stories, correspondence, competitions, and abundant editorial commentary, child-authors and editors asserted a textual agency as they documented and created collaborative artistic communities.

We prove rigidity and gap theorems for self-dual and even Poincaré-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincaré-Einstein metrics in terms of conformal invariants of the boundary and the topology of the bulk. As a by-product of our proof, we identify a new scalar conformal invariant of three-dimensional Riemannian manifolds.

This article places the nearly forgotten local tour guides at the forefront of the studies of Victorian travel and travel writing on semicolonial China, showing how mediating agents shaped and disrupted cross-cultural writing and history with their relational identities. It contextualizes British and American travel writing on the Five Hundred Genii Temple (in Chinese, the Hualin Temple) from 1849 to 1912 within the intertwined relations between travel writers and guides, in the local socio-spatial condition of Guangzhou (then Canton) and under the travel-to-tourism transition in China. The role played by earlier foreign expatriate guides shifted from introducers to coordinators, leading to travelers’ nuanced local understandings that challenged the temple’s presumed otherness. Later authoritative Cantonese guides manipulated local interactions, reviving stereotypical images among the tourists. The guides appropriated metropolitan baggage of the guided in different ways, cowriting the travel writing and the cross-cultural history it implied. Being mediating agents in the travel as a process of encounter with otherness, the guides significantly altered the encounter while sometimes becoming themselves the focal Other in the writing.

We report on the collection of two phaeodarian protists from the deep Fram Strait (Arctic Ocean). Specimens were collected using high-volume plankton pumps in the Long-Term Ecological Observatory HAUSGARTEN in 2021. The 18S sequences from our specimens formed two distinct clusters in a phylogenetic tree: one in the family Aulacanthidae and one in the genus Auloscena. The vast majority of phaeodarian species that have been taxonomically described do not have publicly available sequence data (≥95%), so our specimens likely represent species that have been described morphologically but not sequenced. Phaeodarians are an understudied group, despite their abundance and importance for carbon and silica flux. Further exploration will likely reveal a more thorough characterization of biodiversity in the deep Arctic Ocean.

This article problematises traditionalist thinking in constitutional adjudication in relation to the rights of same-sex couples, especially those rights that are connected to family life. It identifies two approaches, represented respectively by the case law of the Italian Constitutional Court (ItCC) and the Court of Final Appeal (CFA) of the Hong Kong SAR of the People’s Republic of China. The ItCC has expressly stated that preserving traditional family forms is a reasonable objective per se for the legislature to pursue. The CFA, on the other hand, has challenged this approach to traditionalist thinking in relation to same-sex unions. Despite some contradictory signals within its case law, the CFA has stated that justifying differential treatment based on sexual orientation with reference to tradition is circular reasoning. Drawing on historical, anthropological, and philosophical sources, this article argues that invoking the preservation of tradition, despite its rhetorical force, is empirically and conceptually criticisable and, ultimately, unpersuasive.