Proof of universality in one-dimensional few-body systems including anisotropic interactions

We provide an analytical proof of universality for bound states in one-dimensional systems of two and three particles, valid for short-range interactions with negative or vanishing integral over space. The proof is performed in the limit of weak pair-interactions and covers both binding energies and wave functions. Moreover, in this limit the results are formally shown to converge to the respective ones found in the case of the zero-range contact interaction.

Analytical comparison of longitudinal launching of a vessel into the water with grounding

Регулярно в мире терпит крушение большое количество крупных судов. Количество случаев крушения с каждым годом растет. Крушения происходят, в том числе, из-за значительных размеров судов, роста интенсивности движения на морских путях, роста скоростей движения, неблагоприятных метеорологических условий, недостатков современных навигационных систем. Исходя из этого, следует больше уделять внимание методикам и средствам спасения судна при крушении. В случае крушения судна, для спасения человеческих жизней и груза может быть использована преднамеренная посадка судна на мель. Актуальность исследования вопросов, связанных с преднамеренной посадкой на мель, подтверждается: разработкой новых методов стягивания судна с мели, разработкой в области создания безэкипажных судов, Международной конвенцией о подготовке и дипломировании моряков и несении вахты, которая требует от судоводителя: умения осуществлять преднамеренную посадку на мель, понимания основных действий в случае, если посадка на мель неизбежна и действий после посадки на мель. В работе рассматривается продольный спуск судна на воду вперед кормой. Приводится аналитическое доказательство того, что в первом приближении продольный спуск на воду схож с посадкой судна на мель. Приводятся соответствующие математические выкладки. Из приведенного доказательства следует вывод, что в практике судоходства, в аварийной ситуации, можно рассчитать посадку на мель так, что это может привести к спасению судна и как следствие его экипажа и пассажиров. A large number of large ships are wrecked on a regular basis in the world. The number of crash cases is growing every year. Wrecks occur, among other things, due to the significant size of ships, the growth of traffic on sea routes, the growth of traffic speeds, unfavorable meteorological conditions, and the shortcomings of modern navigation systems. Based on this, more attention should be paid to methods and means of rescuing a ship in case of a wreck. In the event of a shipwreck, deliberate grounding of the ship may be used to save lives and cargo. The relevance of the study of issues related to deliberate grounding is confirmed by: the development of new methods for pulling a ship aground, development in the field of the creation of unmanned vessels, the International Convention on the Training and Certification of Seafarers and Watchkeeping, which requires the boatmaster to: the ability to carry out deliberate grounding, an understanding of basic actions in the event that a grounding is imminent and of actions after a grounding. The paper considers the longitudinal launching of the vessel into the water forward stern. Analytical proof is given that, in the first approximation, the longitudinal launching is similar to the landing of a ship aground. The corresponding mathematical calculations are given. From the above evidence it follows that in the practice of shipping, in an emergency, it is possible to calculate the aground so that it can lead to the salvation of the vessel and, as a consequence, of its crew and passengers.

Revealing ancient gold parting with silver and copper isotopes: implications from cementation experiments and for the analysis of gold artefacts

Gold parting enabled the production of very pure gold for various purposes from the sixth century BC onwards, but analytical proof of this pyrotechnical process is difficult. We describe a new analytical approach for the identification of purified gold combining silver and copper isotopic with trace element analyses. Parting experiments were performed with gold-silver-copper alloys using the classical salt cementation process to investigate potential silver and copper isotope fractionation and changes in trace element concentrations. In addition, we provide the first comprehensive dataset of silver isotope ratios of archaeological gold objects from the Mediterranean and Central Europe to test whether or not gold refining can be identified on the basis of isotope systematics. The results show that very heavy silver and copper isotopic compositions are clear evidence for parted gold, but that the application of copper isotopes might be limited.

Real-time Nonlinear Parameter Estimation and Tracking Control of Unmanned Aerial Vehicles in Closed-Loop

The real-time unknown parameter estimation and adaptive tracking control problem are investigated in this paper for a six degrees of freedom (6-DOF) of under-actuated quadrotor unmanned aerial vehicle (UAV). A virtual proportional derivative (PD) is designed to maintain the translational dynamics. Two adaptive schemes are developed to handle the attitude dynamics of UAV with several unknown parameters. In the beginning, a classical adaptive scheme using the certainty equivalence principle is proposed and designed. The idea is to design a controller for an ideal situation by assuming the unknown parameter was known. Then the unknown parameter is replaced by its estimation. A theoretical analysis is provided to ensure the trajectory tracking of the adaptive controller. However, an inherent drawback of this scheme is that there is no guarantee for the estimated parameters to converge to the actual values. To address this issue, a new adaptive approach is developed as the next step by adding a continuous function to the control structure. The proposed technique guarantees handling of parametric uncertainties with an appropriate design manifold. The rigorous analytical proof and numerical simulation analyses are presented to show the effectiveness of the proposed control design.

On the Existence and Uniqueness of the ODE Solution and Its Approximation Using the Means Averaging Approach for the Class of Power Electronic Converters

Power electronic converters are mathematically represented by a system of ordinary differential equations discontinuous right-hand side that does not verify the conditions of the Cauchy-Lipschitz Theorem. More generally, for the properties that characterize their discontinuous behavior, they represent a particular class of systems on which little has been investigated over the years. The purpose of the paper is to prove the existence of at least one global solution in Filippov’s sense to the Cauchy problem related to the mathematical model of a power converter and also to calculate the error in norm between this solution and the integral of its averaged approximation. The main results are the proof of this theorem and the analytical formulation that provides to calculate the cited error. The demonstration starts by a proof of local existence provided by Filippov himself and already present in the literature for a particular class of systems and this demonstration is generalized to the class of electronic power converters, exploiting the non-chattering property of this class of systems. The obtained results are extremely useful for estimating the accuracy of the averaged model used for analysis or control of the effective system. In the paper, the goodness of the analytical proof is supported by experimental tests carried out on a converter prototype representing the class of power electronics converter.

Analytical Proof of Origin for Raw Materials

Growing public interest in getting information on the origin of raw materials used to manufacture goods for daily life has triggered the development of concepts to increase the transparency of raw material supply chains. Analytical proofs of origin (APOs) for raw materials may support those transparency concepts by giving evidence about the origin of a specific raw material shipment. For a variety of raw materials like gemstones, TTT (tantalum, tin, tungsten) minerals, and others, APOs have been developed. The identification of features that distinguish different origins, databases of those features from reliable reference samples, and a data evaluation strategy adopted to the envisaged application scenario are the key aspects of APO methods. Here, an overview is given on APO methods developed for different raw materials and application cases.

On the Scaling Law of Phase Drift in Coupled Nonlinear Oscillators for Precision Timing

Computational and experimental works reveal that the coupling of similar crystal oscillators leads to a variety of collective patterns, mainly various forms of discrete rotating waves and synchronization patterns, which have the potential for developing precision timing devices through phase drift reduction. Among all observed patterns, the standard traveling wave, in which consecutive crystals oscillate out of phase by [Formula: see text], where [Formula: see text] is the network size, leads to optimal phase drift error that scales down as [Formula: see text] as opposed to [Formula: see text] for an uncoupled ensemble. In this manuscript, we provide an analytical proof of the scaling laws, for uncoupled and coupled symmetric networks, and show that [Formula: see text] is the fundamental limit of phase-error reduction that one can obtain with a symmetric network of nonlinear oscillators of any type, not just crystals.

Methyl-4-Hydroxybutyrate and Ethyl-4-Hydroxybutyrate as Potential Markers for Simultaneous Consumption of GHB/GBL and Alcohol: Preliminary Investigations

γ-Hydroxybutyric acid (GHB) and its corresponding lactone γ-butyrolactone (GBL) are misused as knock out (k.o.) drugs. The short detection window and the major inter- and intra-individual variations of endogenous GHB concentrations in commonly used matrices such as blood and urine complicate the analytical proof of an exogenous GHB/GBL administration. We searched for an alternative way to prove an exogenous GHB/GBL administration via detection of methyl- and ethyl-4-hydroxybutyrate, which could arise in alcoholic solutions after spiking with GHB/GBL. A liquid chromatographic–triple quadrupole mass spectrometric method was developed and validated to quantitatively determine methyl- and ethyl-4-hydroxybutyrate in alcoholic beverages (limit of detection [LoD]: 5.8 and 3.4 ng/mL, respectively). A sample collective of alcoholic beverages (n = 47) revealed natural occurring amounts of ethyl-4-hydroxybutyrate (<LoD—approx. 3980 ng/mL) with higher concentrations particularly found in wine samples. Nearly no ethyl-4-hydroxybutyrate was observable in spirits/liqueurs and no methyl-4-hydroxybutyrate was detectable at all. A moderate correlation was shown between the ethyl-4-hydroxybutyrate concentration and the pH-value in wine samples (pH 2.9–3.7, n = 29) as well as between the ethyl-4-hydroxybutyrate concentration and the GHB concentration in all measured beverages (GHB: < limit of quantification [LoQ]—11.4 µg/mL, n = 47). A dependency on alcohol content could not be observed. A voluntary intake (n = 1) of 750-mL wine naturally containing high amounts of ethyl-4-hydroxybutyrate (approx. 2010 ng/mL) revealed no observable GHB-ester concentrations in blood and urine. Furthermore, an experiment simulating a beverage that could potentially be used in a drug-facilitated crime (DFC) case showed ethyl-4-hydroxybutyrate concentrations exceeding the concentrations naturally observed in beverage samples. However, in order to evaluate whether ethyl-4-hydroxybutyrate could be useful as marker for the co-consumption of GHB/GBL and alcohol and to prolong the detection window of unintended GHB/GBL intake, further experiments have to be performed.

Upper bounds on the compactness at the innermost light ring of anisotropic horizonless spheres

In the background of isotropic horizonless spheres, Hod recently provided an analytical proof of a bound on the compactness at the innermost light ring with the dominant energy condition. In this work, we extend the discussion of isotropic spheres to anisotropic spheres. With the dominant energy and non-negative trace conditions, we prove that Hod’s bound also holds in the case of anisotropic horizonless spheres.