The Chebyshev method has two main advantages: first, it exploits the sparsity of the Liouvillian (Hamiltonian) by expressing the propagator in terms of a sequence of L (Liouville superoperator) matrix multiples. The ma- trix multiples are conveniently performed in terms of a sparse matrix algorithm with storage and compute-**time** requirements in proportion to the number of nonzero elements of L . Second, the Chebyshev expansion of the propagator is essentially exact. The series converges so rapidly that it is easily extended to the point where the truncation error is smaller than the usual round-off errors expected in any numerical computation. Moreover, the resulting number of terms in the series is at or near the optimally small number for an orthogonal polynomial expansion of the exponential function. The method of Chebyshev approximation is frequently used in numerical quantum dynamics to compute exp ( − i H τ ) ψ 0 over very long times. This can be done with m matrix-**vector** products if the above approximation is considered with a sufficiently large truncation index m. The degree m necessary for achieving a specific accuracy depends linearly on the step size τ and the spectral radius of H , and thus an increase of the step size reduces the computational work per unit step. In a practical implementation, m can be chosen such that the accuracy is dominated by the round-off error [27]. We cannot conclude this sec- tion without bringing the attention on existing drawbacks in the Chebyshev method. The scheme is not unitary, and therefore the norm is not conserved, but the deviation from unitarity is very small due to the extreme accu- racy of the approach. Another drawback is that because of the long **time** durations ( τ is very large) of propaga- tion in the Chebyshev scheme, intermediate results are not obtained. To conclude, despite the above drawbacks, the Chebyshev approach will successfully serve the quantum spin dynamics community in establishing quantum mechanical **time** **dependent** methods as a routine tool in quantum dynamics studies.

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Stachel (1980) developed a classical theory of geometric strings. Several authors viz. Banerjee et al (1990) Wang (2003), Bali and Pradhan (2007), Reddy et al. (Reddy, 2007), Rao and Vinutha (Rao, 2010) have studied homogeneous and anisotropic string cosmological models in different physical and geometrical contexts. The **magnetic** field plays a significant role at the cosmological scale and is present in galactic and intergalactic spaces. The present day magnitude of **magnetic** energy is very small in comparison with the estimated matter density and its importance is considered. A cosmological model which contains a global **magnetic** field is necessarily anisotropic since the **magnetic** field **vector** specifies a preferred spatial direction (Bronnikov et al. (Bronnikov, 2004) Melvin (1975) in the cosmological solutions for dust and electromagnetic field, has argued that for a large part of the history of evolution of the universe, the matter was in a highly ionized state and is smoothly coupled with the field and forms a neutral matter as a result of universe expansion. Hence the presence of **magnetic** field in string-dust universe is not unrealistic. Therefore, several authors viz. Tikekar and Patel (1992), Patel and Maharaj (1996), Singh and Singh (1999), Bali and Anjali (2006), Saha and Visinescu (2008), Saha et al. (2010), Bali (2008), Singh (2014) have investigated string cosmological models with incident **magnetic** field in different contexts.

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We consider **magnetic** field CHAMP satellite measurements that were selected and processed following the procedure de- scribed by Lesur et al. (2010). The data were rotated into the solar **magnetic** (SM) Cartesian coordinate system (in this coordinate system the Z SM axis coincides with the geomag- netic dipole axis and points to the north, the Sun–Earth line lies on the x–z plane, and the Y SM axis is perpendicular to the Earth–Sun line and points towards dusk; see Laundal and Richmond, 2017); only the X and Y SM components were kept. This was done in order to avoid contamination by the ring current (see Lesur et al., 2008). In addition, data were selected only for local times between 23:00 and 05:00, when the Z component of the interplanetary **magnetic** field (IMF) was positive, the norm of the **vector** **magnetic** disturbance in- dex (VMD; Thomson and Lesur, 2007) less than 20 nT, and the norm of its derivative less than 100 nT day −1 . From the selected data, the GRIMM lithospheric field model (Lesur et al., 2013) from SH degree 17 to SH degree 80 was sub- tracted. This was done in order to avoid a spectral leakage of the lithospheric field into the secular variation model (see, e.g., Lesur et al., 2010). The residuals were used to construct a **time**-**dependent** core field model up to SH degree 18 (with splines of order 6 with a knot spacing of 6 months as the tem- poral basis function), a static lithospheric field model up to SH degree 30, an external static field model up to SH degree 20, and a **time**-varying external field model based on three different parameterizations. A slowly varying external field component was considered by solving for an axial dipole ex- ternal term in the GSM coordinate system every 10 years. The more rapidly varying external field components were considered by solving for the SH degree 1 coefficients in the SM coordinates every 100 days. The fact that these bins were 100 days large reduced the risk of leakage due to a cor- rection of a track-by-track type (see Thébault et al., 2012). Finally, the even more rapidly varying external fields were accounted for by solving for the scaling coefficients of the SVMD index, the satellite-based version of the VMD index. This index is obtained by calculating the mean value of the measured **magnetic** field over each orbit and by subsequently normalizing these values in bins of 100 days (see Kunagu et al., 2013). To the **vector** residuals of this modeling proce- dure the initially removed lithospheric field model was added back. The final CHAMP data set comprises 13 229 triplets of **vector** data varying between 266 and 475 km of altitude.

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Stabilization is one of the central themes of control theory. It was shown in [1–4] that the class of continuous stationary feedbacks is too restrictive for the purposes of stabi- lization of nonlinear systems. In other words, in order to design a continuous feedback stabilizer one needs to use functions depending on **time** and state [6, 8]. To stay with the class of stationary feedbacks one has to deal with piecewise continuous functions [5]. The synthesis procedures for both continuous and piecewise continuous stabilizers are devel- oped only for some special types of systems. For example, in [5, 4] it is shown how to construct stationary piecewise continuous stabilizers for generic two-dimensional aﬃne nonlinear systems. On the other hand, the papers [6, 8, 9] show how to design feedbacks for certain types of nonholonomic systems. Both approaches (nonstationary continuous and stationary discontinuous) are quite complicated as far as the feedback synthesis is concerned. The statement of the problem considered in this paper is not new. There are many publications related to the problems that are similar in nature to the stabilization of a single **time**-**dependent** **vector**. Similar equations arise naturally in learning systems, repetitive, and adaptive control systems. That underlines the importance of the approach presented here. Not only the main result but especially the technique employed in this publication might have consequences of significant magnitude for various branches of applied mathematics. Novelty of the approach developed in this paper is due to averag- ing the **time**-**dependent** **vector** field over a **time** interval. By its nature this approach does not impose any unnatural restrictions on the **vector** field in question. That strongly ad- vocates its advantage and power. The **time**-averaging technique is not new itself. In fact equity traders use it daily comparing dynamics of 200- and 50-day moving averages for

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Summaries of the marginal posterior distributions are shown in table 3, while figure 1 compares the probability of the U.S. economy being in recession resulting from the estimated model with the official NBER dating: the signal “probability of being in re- cession” extracted by the model here presented matches the official dating rather well, and is less noisy than the signal extracted by Hamilton (1989), based on the IP series only. The NBER dating seems to be best matched if, every **time** the model’s probability of being in recession exceeds 0.5, the peak date is set equal the **time** the line crosses a low probability level (say 0.1) from below and the trough date is set equal the **time** the probability line crosses a high probability level (say 0.9) from above. NBER trough dates seem to be matched more frequently by the model than the peaks.

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The derivation described here for intrinsic spin takes evidence from dominant data obtained from atomic and chemical physics, but it extends to isospin in atomic nuclei and **magnetic** moments in elementary particles. The same transverse motion exists there with similar outcomes on different scales. Likewise, uncharged mesons and hadrons contain charged quarks and have **magnetic** moments [15]. Less is known about the neutrino [16]. Furthermore, any theory for intrinsic spin should provide a physical explanation for Pauli exclusion: here it is represented by indegeneracy of Fermionic states, consequential on residual ambient magnetism. If otherwise, uncertainties in angular momentum of degenerate states would cause those states having identical orbital and spin quantum numbers to interfere de- structively. Bosons, by contrast, are not so constrained because their wave func- tions are real—notably in the photon—so that phases can lock coherently onto ex- ternal influence. Interference is then constructive. Superconducting Cooper pairs, containing both chiralities in phase ( e k + e −k ), do the same.

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partial pressure of 1.1×10 -2 Torr. Once cooled, Ni films were then deposited in vacuum. Two different temperatures were chosen for the Ni deposition in order to produce both Volmer- Weber (island) and Frank-van der Merwe (2D layer) growth. The island Ni samples were deposited at 282°C, whereas the 2D layer Ni samples were deposited at 148°C. All films were confirmed to be continuous. Table 7.1 provides the growth parameters for all films uses in this study. X-ray diffraction (XRD) 𝜃 − 2𝜃 and φ-scans were performed, using a Rigaku X-ray diffractometer with a Cu Kα source (λ = 1.5418 Å), to verify that the films were fully epitaxial. Microstructural examination using a JEOL 2010 high-resolution, field emission transmission electron microscope (HR-TEM) and selected-area-electron diffraction (SAED) provided confirmation of the Ni growth mode as well as confirmation of crystallinity. **Magnetic** hysteresis measurements were then performed on the Ni/VO 2 heterostructures

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the charged **vector** ρ meson the **magnetic** polarizability and hyperpolarizability have been calculated depending on the spin projection on the the **magnetic** field. We have estimated the intervals of the **magnetic** field for which the nonlinear terms in field give a significant contribution to the meson energy.

flasks, a safe concentration of nanoparticles, ie, 250 μ g/mL, was added to each flask to ensure that the Dex-LSMO nanoparticles per se do not cause cell death. The flasks were exposed to an optimized RF condition (365 kHz, input cur- rent 700 A, power 8,000 W) for a total **time** of 6, 8.5, and 11 minutes to increase the temperature from 37 ° C to 43 ° C, 45 ° C, and 47 ° C, respectively. After reaching the desired temperature, RF was switched off. To determine the effect of repeated cycles of hyperthermia, additional groups of cells were subjected to three cycles of hyperthermia at 15-minute intervals. All experiments were performed in triplicates.

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purpose of cultivation, the suspension was diluted to an optical density of 0.5 Absorbance Unit (UA) at the light wavelength λ = 620 nm. 200 µl of this suspension were then pipetted into each of the 96 wells of the microtitra- tion plate A. Pipetting was performed columnwise, using a multi-channel pipette. To rule out the possibility that pipetting might affect the results obtained (e.g. suspen- sion sedimentation), the luminescence of all samples was measured for a period of three cycles (the **time** necessary for one cycle of measuring the bacteria luminescence in all the 96 wells is 132 seconds) using the LM01-T lumi- nometer (Immunotech, Czech Republic). The measure- ment was carried out prior to the beginning of each test for the initial luminescence values of all wells to exhibit only minimum differences. Subsequently, half the 96 wells of plate A (4 rows - 48 wells) containing the bacte- rial suspension were taken out and put into plate B, which was placed outside the range of applicator action. Plate A with half the wells with bacterial suspension was placed in the inner space of the coils, as shown in Figure 4(a).

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where i , j and k are the unit vectors in the x , y and z directions, respectively. For clarity, the dependence of the electric and **magnetic** components on the fre- quency ƒ is not explicitly shown in Equation (10). A common assumption made is that the horizontal spatial variations of the fields are much less than the varia- tion with depth ( i.e. the skin depth in the Earth is much smaller than the hori- zontal spatial scales of the fields). This assumption is generally valid when “large-scale” ionospheric-magnetospheric sources are considered or the points of observation are far from the sources, and there are no significant lateral varia- tions in the Earth’s conductivity. In this case, the terms with the variation in the vertical direction ( z ) dominate on the left-hand side of Equation (10), and so Equation (10) reduces to

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Figure 5 shows spectrograms for 3 selected days. The spectrograms are overlain with **time** series of the field (black line). Panels (a) and (c) are directly comparable as both cover the 2 February 2016. Panel (a) is based on merged data and panel (c) on fluxgate data only. Whereas in panel (a) the spectral content is clearly resolved up to the Nyquist fre- quency of 0.5 Hz in panel (c) only the strongest activity sur- pass the noise level in the frequency band from 30 mHz up to 0.5 Hz. These are possibly field line resonances and their lowering frequencies towards the nighttime is clearly visible in the merged data in panel (a). Panel (a) also shows with help of the overlain magnetogram that irregular pulsations (Pi-1 pulsation, no clear frequency) are related to the begin- ning of substorms. Panel (b) shows around 18:00 an example of a pulsation event with a clearly defined center frequency of about 300 mHz (Pc-1 pulsation) and panel (d) shows an example of a pulsation whose main frequency rises from about 20 mHz at 15:30 to 400 mHz at 16:30. Additionally, panel (b) shows horizontal structures from 06:00 to 17:00 (16.2 s square wave) and sweeps with falling frequency start- ing at 06:30 and 09:00. Both are manmade contaminations. We found a lot of other remarkable signals revealed in such spectrograms, but discussing them is beyond the scope of this paper.

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word-embeddings took care of the right trans- lation for relationships between objects and **time**-dependencies. Yet, we noticed a common misbehavior for all our multimodal models: if the attention loose track of the objects in the picture and ”gets lost”, the model still takes it into account and somehow overrides the information brought by the text-based annotations. The translation is then totally mislead. We illustrate with an example:

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Phrase-based Machine Translation We used a standard PBMT system built using Moses toolkit (Koehn et al., 2007). At training **time**, we extract and score phrase sentences up to the size of 9 to- kens. All the feature functions were trained using the gold-standard alignments from the training set and their weights were tuned on the development data using k-batch MIRA with k = 60 (Cherry and Foster, 2012) with BLEU as the evaluation metric. A distortion limit of 6 was used for the reordering models. Lexicalised reordering models were bidi- rectional. At decoding **time**, we use a stack size of 1000.

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An exact analytical model for performance prediction in surface inset permanent magnet machines considering slotting effects and magnet segmentation has been developed in this paper. Fourier analysis method based on sub-domain method is applied to derive analytical expressions for calculation of **magnetic** **vector** potential, **magnetic** flux density, cogging torque and electromagnetic torque in surface inset permanent magnet machines. This model is applied for performance computation of two prototype motors and the results of proposed model are verified by using FEM method.

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After an rf pulse, the precessing transverse magnetization is very small but de- tectable, since it oscillates at a well deﬁned frequency. A rotating **magnetic** moment generates a rotating **magnetic** ﬁeld. A changing **magnetic** ﬁeld is asso- ciated with an electric ﬁeld. If a wire-coil is placed near the sample, this electric ﬁeld induces a voltage which causes an oscillating electric current in the wire. This oscillating current can be detected using a radiofrequency detector. The oscillating electric current induced by the precessing nuclear transverse magne- tization is called the NMR signal or free induction decay (FID). It is plotted in terms of amplitude as function of **time**. This may be converted into the frequency domain, the spectrum, by a mathematical procedure called a Fourier Transfor- mation (FT) [162]. It is represented by amplitude as function of frequency.

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Abstract —Due to the agile maneuverability, unmanned aerial vehicles (UAVs) have shown great promise for on-demand com- munications. In practice, UAV-aided aerial base stations are not separate. Instead, they rely on existing satellites/terrestrial systems for spectrum sharing and efficient backhaul. In this case, how to coordinate satellites, UAVs and terrestrial systems is still an open issue. In this paper, we deploy UAVs for coverage enhancement of a hybrid satellite-terrestrial maritime communication network. Using a typical composite channel model including both large-scale and small-scale fading, the UAV trajectory and in-flight transmit power are jointly optimized, subject to constraints on UAV kinematics, tolerable interference, backhaul, and the total energy of the UAV for communications. Different from existing studies, only the location-**dependent** large- scale channel state information (CSI) is assumed available, because it is difficult to obtain the small-scale CSI before takeoff in practice and the ship positions can be obtained via the dedicated maritime Automatic Identification System. The optimization problem is non-convex. We solve it by using prob- lem decomposition, successive convex optimization and bisection searching tools. Simulation results demonstrate that the UAV fits well with existing satellite and terrestrial systems, using the proposed optimization framework.

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An obvious first step to achieving a high S/N ratio in a particle-in-cell code is ensur- ing that a sufficient number of markers are used in the simulation. However, simu- lations become more computationally expensive with increasing number of markers and so care must be taken to find a balance between a marker number high enough to accurately represent the gyrokinetic model of ORB5 and low enough to run com- plete simulations within a reasonable **time**. The scaling of noise to marker number is given to be N −1/2 , where N is marker number. Therefore, increasing the signal to noise ratio by a factor of 2 would theoretically require a 4 times increase in the number of particles. From this relation, it can be seen how increasing the accuracy of simulations can quickly become extremely computationally expensive.

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Ferric chloride hexahydrate (FeCl 3 ⋅ 6H 2 O), ferrous chloride tetrahydrate (FeCl 2 ⋅ 4H 2 O), and ammonium hydroxide (25 wt%) were purchased from Fluka (Buchs, Switzerland). D, L-lactide and glycolide were purchased from Sigma-Aldrich (St Louis, MO) and recrystallized with ethyl acetate. Stannous octoate (Sn (Oct) 2 :stannous 2-ethylhexanoate), PEG (molecu- lar weight 2000, 3000, and 4000), and dimethyl sulfoxide were purchased from Sigma-Aldrich. PEGs were dehydrated under vacuum at 70 ° C for 12 hours and used without further purification. Doxorubicin hydrochloride was purchased from Sigma-Aldrich. X-ray diffraction, Rigaku D/MAX-2400 x-ray diffractometer with Ni-filtered Cu K α radiation, and scanning electron microscopy (SEM) measurements were conducted using VEGA/TESCAN. DSC measurements were conducted using the Perkin Elmer 7 series. The drug-loading capacity and release behavior were determined using an ultraviolet- visible 2550spectrometer (Shimadzu, Tokyo, Japan). Infrared spectra were recorded in real-**time** with a Perkin Elmer series FTIR. The **magnetic** property was measured on a vibrating sample magnetometer (Meghnatis Daghigh Kavir, Iran) at room temperature. 1 H NMR spectra was recorded in real-

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A cross section of the stator windings of a two-pole, three-phase machine is shown in Fig. 1. The phase windings are shown to be displaced from each other by 120 0 and the positive direction of current flowing through each winding is upwards through the non-primed side and downwards through the primed side. Using this convention of current flow through the windings, positive **magnetic** axes were developed for each phase winding, along which all **magnetic** quantities exists.