In this contribution, we study scalar nonlocal conservation laws with the p-norm. Here, "nonlocal" means that the velocity of the conservation law depends on an integral term in space. Typically, the nonlocal term is an L1-type weighted average of the solution whereas here we study the case when the solution is integrated in the Lp-norm. We also consider the case of the Lp-quasi-norm when p is an element of (0, 1) and establish, for an initial datum which is uniformly bounded away from zero, the existence and uniqueness of weak solutions. We then demonstrate that weak solutions also exist for initial data that may vanish under more restrictive assumptions. Furthermore, we investigate the singular limit, i.e., what happens when the nonlocal kernel converges to a Dirac distribution. Indeed, for the one-sided exponential kernel, we recover the (entropy) solution of the corresponding local conservation law for all p is an element of (0, infinity) with further restrictions for p is an element of (0, 1). This generalizes the celebrated singular limit result for nonlocal conservation laws for p = 1 significantly and showcases the robustness of the approximation of local conservation laws by nonlocal ones. We also investigate the monotonicity of the solution when assuming that the initial datum is monotone. Finally, we prove the convergence of solutions for p -> 0, resulting in a different kind of nonlocal conservation law. The paper concludes with numerical studies illustrating the effect of p on singular-limit convergence and related phenomena. (c) 2026 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
In optimal control, extending the class of admissible controls is a common strategy to guarantee the existence of optimal solutions. However, such extensions may introduce a gap between the infimum of the original problem and the minimum of the extended one, especially in the presence of endpoint constraints. Since Warga’s seminal work – where the extension consisted of the convexification of the dynamics –, normality of first-order necessary conditions for extended minimizers has been recognized as a sufficient condition to avoid the gap phenomenon, though it is far from being necessary. In this paper, we consider impulsive extensions of control-affine systems with unbounded controls. We prove that a notion of higher-order normality, based on iterated Lie brackets of the system’s vector fields, is sufficient to prevent an infimum gap. Our main contribution is to establish this result for local minimizers with respect to the L1-distance between controls, rather than the L∞-topology on trajectories considered in previous higher-order no-gap results. This significantly strengthens the theory, since L1-control-local optimality is a weaker notion. However, this generalization does not apply to arbitrary extensions: indeed, Vinter exhibited a counterexample for relaxation-based extensions where first-order normality with respect to the L1-topology on controls does not exclude an infimum gap. Our method relies on a set-separation approach, which allows us to derive higher-order conditions and exploit the corresponding notion of higher-order normality.
We investigate consensus formation and flocking behavior in multi-agent systems subject to two distinct types of delay: a transmission delay accounting for information exchange between agents, and a reaction delay representing the processing time before agents adjust their states. For a simplified linear two-agent system, we analyze how these delays affect asymptotic stability. We then derive sufficient conditions for asymptotic consensus and flocking in the general multi-agent setting with a nonlinear, globally positive influence function. These conditions require the delays to be sufficiently small relative to the initial data and the decay rate of the influence function. The analysis is based on a Lyapunov functional approach combined with a Gr & ouml;nwall-Halanay-type inequality. Our results establish rigorous sufficient conditions under which collective behavior emerges in delayed multi-agent systems where both communication and reaction lags are non-negligible, with applications to biological, social, and engineered systems.
Amid the global push for sustainable construction, bamboo has been widely studied as a rapidly renewable, high-performance building material. This paper reviews the published literature on bamboo’s journey from plant to structural component. The review first examines the fundamental botanical characteristics of bamboo, explaining the relationship between its hierarchical structure—from molecular to cellular levels—and its mechanical properties. It then transitions to an analysis of sustainable forestry, harvesting practices, the structural uses of round bamboo, and the manufacturing processes for engineered bamboo products, such as glued laminated bamboo and bamboo scrimber. Critical performance challenges are addressed by evaluating modern treatment methods that enhance durability, dimensional stability, and fire resistance. Structural applications are explored in detail, covering traditional building typologies, innovative connection systems, and the emerging potential for bamboo in mid- and high-rise as well as long-span structures. The life cycle perspective is completed by examining end-of-life scenarios, including reuse, recycling, and energy recovery. Ultimately, the review situates bamboo within the global context by examining resource distribution, trade, and the policy frameworks required to promote its widespread adoption. By consolidating research across multiple disciplines, this paper highlights the significant potential of bamboo to contribute to a low-carbon built environment. It concludes that a holistic, science-based approach is essential for overcoming remaining challenges and fully integrating this versatile material into modern construction practices.
The increasing and widespread use of Business Process Model and Notation (BPMN) business processes, which also incorporate Decision Model and Notation (DMN) tables, necessitates tools and methodologies to verify their correctness. However, most commonly used frameworks to build BPMN + DMN models only allow designers to detect syntactical errors, thus ignoring semantic (behavioral) faults. This forces business processes designers to manually run single executions of their BPMN + DMN processes using proprietary tools in order to detect failures. Furthermore, how proprietary tools translate a BPMN + DMN process to a computer simulation is left unspecified. In this paper, we advance this state of the art by designing a tool, named BDTransTest, providing: (i) a translation from a BPMN + DMN process (13, D) to a Java program P; ii) the synthesis and execution of a verification plan for (13, D); iii) the analysis of the coverage achieved by the verification plan in terms of nodes and edges of 13, as well as of rows in the DMN tables D. Finally, we evaluate our methodology on BPMN + DMN processes from the literature, obtaining over 60% coverage with more than 2000 test cases and negligible resource requirements.
