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ABSTRACT As modern agriculture faces increasing demands for efficiency and automation, this study presents a novel, untethered soft gripper system designed for autonomous and efficient harvesting. At the core of this innovation is a piston‐driven, pneumatically actuated gripper embedded with flexible tactile sensors, enabling operation without an external air source. The system integrates a compact motorized syringe, forming a closed‐loop fluid circuit that provides precise pressure control for adaptive grasping. The pneumatic actuation mechanism regulates air pressure from −30 to 180 kPa, allowing the gripper to perform delicate and adaptive handling, particularly suited for tree fruits and other fragile crops. A key feature of the system is its intelligent control mechanism, which seamlessly combines pneumatic and electrical systems to enhance autonomy and versatility in agricultural applications. The integration of size recognition and adaptive grasping, enabled by force feedback from embedded tactile sensors, ensures safe, efficient, and damage‐free harvesting. Demonstrating exceptional potential for autonomous agricultural operations, the untethered soft gripper system offers enhanced independence, maneuverability, and adaptability across diverse harvesting environments. Its ability to optimize crop handling while minimizing damage highlights its significance as a pioneering solution for the future of automated agriculture. 

Let $E/\mathbf{Q}$be an elliptic curve and let $p$be an odd prime of good reduction for $E$. Let $K$be an imaginary quadratic field satisfying the classical Heegner hypothesis and in which $p$splits. The goal of this paper is two-fold: (1) we formulate a $p$-adic BSD conjecture for the $p$-adic $L$-function $L_{\mathfrak{p}}^{\mathrm{B}\mathrm{D}\mathrm{P}}$introduced by Bertolini–Darmon–Prasanna [Duke Math. J. 162 (2013), pp. 1033–1148]; and (2) for an algebraic analogue $F_{\stackrel{¯<\#comment/>}{\mathfrak{p}}}^{\mathrm{B}\mathrm{D}\mathrm{P}}$of $L_{\mathfrak{p}}^{\mathrm{B}\mathrm{D}\mathrm{P}}$, we show that the “leading coefficient” part of our conjecture holds, and that the “order of vanishing” part follows from the expected “maximal non-degeneracy” of an anticyclotomic $p$-adic height. In particular, when the Iwasawa–Greenberg Main Conjecture $\left(F_{\stackrel{¯<\#comment/>}{\mathfrak{p}}}^{\mathrm{B}\mathrm{D}\mathrm{P}}\right)=\left(L_{\mathfrak{p}}^{\mathrm{B}\mathrm{D}\mathrm{P}}\right)$is known, our results determine the leading coefficient of $L_{\mathfrak{p}}^{\mathrm{B}\mathrm{D}\mathrm{P}}$at $T=0$up to a $p$-adic unit. Moreover, by adapting the approach of Burungale–Castella–Kim [Algebra Number Theory 15 (2021), pp. 1627–1653], we prove the main conjecture for supersingular primes $p$under mild hypotheses. In the $p$-ordinary case, and under some additional hypotheses, similar results were obtained by Agboola–Castella [J. Théor. Nombres Bordeaux 33 (2021), pp 629–658], but our method is new and completely independent from theirs, and apply to all good primes. 

Abstract We derive precise formulas for the archimedean Euler factors occurring in certain standard Langlands 𝐿-functions for unitary groups.In the 1980s, Paul Garrett, as well as Ilya Piatetski-Shapiro and Stephen Rallis (independently of Garrett), discovered integral representations of automorphic 𝐿-functions that are Eulerian but, in contrast to the Rankin–Selberg and Langlands–Shahidi methods, do not require that the automorphic representations to which the 𝐿-functions are associated are globally generic.Their approach, thedoubling method, opened the door to a variety of applications that could not be handled by prior methods.For over three decades, though, the integrals occurring in the Euler factors at archimedean places for unitary groups eluded precise computation, except under particular simplifications (such as requiring certain representations to be one-dimensional, as Garrett did in the first major progress on this computation and only prior progress for general signatures).We compute these integrals for holomorphic discrete series of general vector weights for unitary groups of any signature.This has consequences not only for special values of 𝐿-functions in the archimedean setting, but also for 𝑝-adic 𝐿-functions, where the corresponding term had remained open.