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This Article provides an analysis of how the UK's withdrawal from the European Union is going to impact on EU criminal procedural laws. From the EU's perspective, the loss of a \"critical\" partner may lead to more harmonised cooperation between the remaining Member States and thus less intergovernmental features in this area in the long term. More crucially however, the future relationship between the EU and the UK poses certain difficulties as the procedural arrangements to be put in place cannot simply replicate the pre-Brexit status of the UK's membership. According to the Draft Agreement on the New Partnership with the UK, mechanisms such as the European Arrest Warrant are to be replaced by new \"streamlined\" procedures and other \"simplified\" arrangements for the exchange of information and cooperation. This raises questions as regards the possibility for monitoring the UK's compliance as well as the enforceability of any procedural guarantees given. In addition, the inherent danger of the UK's departure comes in the shape of a discontinuity of upholding similar values as those applied by the EU (e.g., fundamental rights) and thus a further drifting apart of both sides. Essentially, it is argued in this contribution that this constitutes the opposite of the relationship with other third countries, which is usually characterised with progressive alignment, and should therefore be approached with great caution from an EU perspective for the conclusion of the negotiations on the future relationship.

In this study, we demonstrate studies on two types of solutions linear fuzzy functional integration and differential equation under two kinds Hukuhara derivative by using the concept of generalized differentiability. Various types of solutions to are generated by applying of two separate concepts of fuzzy derivative in formulation of differential problem. Some patterns are presented to describe these results.

Low Earth Orbit (LEO) satellite navigation signal can be used as an opportunity signal in the case of a Global Navigation Satellite System (GNSS) outage, or as an enhancement by means of traditional GNSS positioning algorithms. No matter which service mode is used, signal acquisition is a prerequisite for providing enhanced LEO navigation services. Compared with the medium orbit satellite, the transit time of the LEO satellite is shorter. Thus, it is of great significance to expand the successful acquisition time range of the LEO signal. Previous studies on LEO signal acquisition are based on simulation data. However, signal acquisition research based on real data is crucial. In this work, the signal characteristics of LEO satellites: power space density in free space and the Doppler shift of LEO satellites are individually studied. The unified symbolic definitions of several integration algorithms based on the parallel search signal acquisition algorithm are given. To verify these algorithms for LEO signal acquisition, a Software Defined Receiver (SDR) is developed. The performance of these integration algorithms on expanding the successful acquisition time range is verified by the real data collected from the Luojia-1A satellite. The experimental results show that the integration strategy can expand the successful acquisition time range, and it will not expand indefinitely with the integration duration. The performance of the coherent integration and differential integration algorithms is better than the other two integration algorithms, so the two algorithms are recommended for LEO signal acquisition and a 20 ms integration duration is preferred. The detection threshold of 2.5 is not suitable for all integration algorithms and various integration durations, especially for the Maximum-to-Mean Ratio indicator.

Computer simulations of electrical behaviour in the whole ventricles have become commonplace during the last few years. The goals of this article are (i) to review the techniques that are currently employed to model cardiac electrical activity in the heart, discussing the strengths and weaknesses of the various approaches, and (ii) to implement a novel modelling approach, based on physiological reasoning, that lifts some of the restrictions imposed by current state-of-the-art ionic models. To illustrate the latter approach, the present study uses a recently developed ionic model of the ventricular myocyte that incorporates an excitation-contraction coupling and mitochondrial energetics model. A paradigm to bridge the vastly disparate spatial and temporal scales, from subcellular processes to the entire organ, and from sub-microseconds to minutes, is presented. Achieving sufficient computational efficiency is the key to success in the quest to develop multiscale realistic models that are expected to lead to better understanding of the mechanisms of arrhythmia induction following failure at the organelle level, and ultimately to the development of novel therapeutic applications.

The Global Positioning System (GPS) plays an important role in navigation and positioning services. When GPS signals propagate through a complex space environment, they are susceptible to interference of ionospheric scintillation. As one of the biggest interference sources on GPS navigation and positioning, ionospheric scintillation will lead to signal intensity decline and carrier phase fluctuation, making signal acquisition of the GPS receiver challenging. Thus, an acquisition algorithm based on differential coherent integration combining accumulation correlation and bit sign transition estimation is proposed. The coherent accumulation is applied to reduce computational loads and contribution by the Gaussian white noise in the signal. Moreover, the differential coherence integration is utilized to eliminate data blocks with bit transition, prolonging the coherence integration time and improving the data utilization rate. Experimental results show that under severe ionospheric scintillation condition, weak GPS signals can be acquired successfully after improving the acquisition algorithm, with the acquisition probability reaching 50% when the signal-to-interference ratio (SIR) drops to −34 dB. Comparing to the differential coherence integration, the complexity of the calculation reduces to only 21.75% effectively after the improvement. The execution time is less than half of the differential coherence integral.

The purpose of the present memoir is two-fold. First, we obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, we deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, we use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar in the Hamiltonian case, and we obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the multiplicities of the index of general

The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,\\mathsf d,\\mathfrak m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong \\mathrm {CD}^{*}(K,N) condition of Bacher-Sturm.

With the modernization of global navigation satellite systems (GNSS), secondary codes, also known as the Neumann–Hoffman (NH) codes, are modulated on the satellite signal to obtain a better positioning performance. However, this leads to an attenuation of the acquisition sensitivity of classic integration algorithms because of the frequent bit transitions that refer to the NH codes. Taking weak BeiDou navigation satellite system (BDS) signals as objects, the present study analyzes the side effect of NH codes on acquisition in detail and derives a straightforward formula, which indicates that bit transitions decrease the frequency accuracy. To meet the requirement of carrier-tracking loop initialization, a frequency recalculation algorithm is proposed based on verified fast Fourier transform (FFT) to mitigate the effect, meanwhile, the starting point of NH codes is found. Then, a differential correction is utilized to improve the acquisition accuracy of code phase. Monte Carlo simulations and real BDS data tests demonstrate that the new structure is superior to the conventional algorithms both in detection probability and frequency accuracy in a degraded channel.

The authors develop a degree theory for compact immersed hypersurfaces of prescribed K-curvature immersed in a compact, orientable Riemannian manifold, where K is any elliptic curvature function. They apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where K is mean curvature, extrinsic curvature and special Lagrangian curvature and show that in all these cases, this number is equal to -\\chi(M), where \\chi(M) is the Euler characteristic of the ambient manifold M.

An integration method based on Runge-Kutta-Chebyshev (RKC) methods is discussed which has been designed to treat moderately stiff and nonstiff terms separately. The method, called partitioned Runge-Kutta-Chebyshev (PRKC), is a one-step, partitioned RK method of second order. It belongs to the class of stabilized methods, namely explicit RK methods possessing extended real stability intervals. The aim of the PRKC method is to reduce the number of function evaluations of the nonstiff terms and to get a nonzero imaginary stability boundary.