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Let X be a compact Kähler manifold. Let $$T_1, \ldots , T_m$$ T 1 , … , T m be closed positive currents of bi-degree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the non-pluripolar product relative to T of $$T_1, \ldots , T_m$$ T 1 , … , T m . We recover the well-known non-pluripolar product of $$T_1, \ldots , T_m$$ T 1 , … , T m when T is the current of integration along X. Our main results are a monotonicity property of relative non-pluripolar products, a necessary condition for currents to be of relative full mass intersection in terms of Lelong numbers, and the convexity of weighted classes of currents of relative full mass intersection. The former two results are new even when T is the current of integration along X.

Liquid metal batteries are an emerging and promising large-scale electrochemical energy-storage technology, the corrosion of which is a significant issue due to their high-operating temperature env...

Many fundamental results of pluripotential theory on the quaternionic space $${\mathbb {H}}^n$$ are extended to the Heisenberg group. We introduce notions of a plurisubharmonic function, the quaternionic Monge–Ampere operator, differential operators $$d_0$$ and $$d_1$$ and a closed positive current on the Heisenberg group. The quaternionic Monge–Ampere operator is the coefficient of $$ (d_0d_1u)^n$$ . We establish the Chern–Levine–Nirenberg type estimate, the existence of quaternionic Monge–Ampere measure for a continuous quaternionic plurisubharmonic function and the minimum principle for the quaternionic Monge–Ampere operator. Unlike the tangential Cauchy–Riemann operator $$ {\overline{\partial }}_b $$ on the Heisenberg group which behaves badly as $$ \partial _b{\overline{\partial }}_b\ne -{\overline{\partial }}_b\partial _b $$ , the quaternionic counterpart $$d_0$$ and $$d_1$$ satisfy $$ d_0d_1=-d_1d_0 $$ . This is the main reason that we have a good theory for the quaternionic Monge–Ampere operator than $$ (\partial _b{\overline{\partial }}_b)^n$$ .

In this paper, we use the variational method to solve the quaternionic Monge–Ampere equation when the right-hand side is a positive measure of finite energy. We introduce finite energy classes of quaternionic plurisubharmonic functions of Cegrell type and define the quaternionic Monge–Ampere operator on some Cegrell’s classes, the functions of which are not necessarily bounded. By using the theory of quaternionic closed positive current, we show that integration by parts and comparison principle are valid on some classes. This opens the door to prove results in the quaternionic pluripotential theory as in the seminal framework by Cegrell (Acta Math 180(2):187–217, 1998; Ann Inst Fourier (Grenoble) 54(1):159–179, 2004; Ann Polon Math 94(2):131–147, 2008) for the complex Monge–Ampere case.

Let $$p:X\rightarrow Y$$ be a surjective holomorphic mapping between Kahler manifolds. Let D be a smoothly bounded domain in X such that every generic fiber $$D_y:=D\cap p^{-1}(y)$$ for $$y\in Y$$ is a strongly pseudoconvex domain in $$X_y:=p^{-1}(y)$$ , which admits the complete Kahler–Einstein metric. This family of Kahler–Einstein metrics induces a smooth (1, 1)-form $$\rho $$ on D. In this paper, we prove that $$\rho $$ is positive-definite on D if D is strongly pseudoconvex. We also discuss the extension of $$\rho $$ as a positive current across singular fibers.

When an asymmetrical grid voltage drop occurs in a grid-connected modular multilevel converter (MMC) system, the influence that expanded double frequency circulating current exerts on the circulating current suppressing controller (CCSC) will be coupling to the positive current controller and lead to system instability. In this paper, the CCSC and inner current controller are modeled and the interactions between them during the transient process are studied. It shows that positive current is prone to be unstable due to improper high proportional gains of both current control loops. Finally, the circuit simulations in PSCAD/EMTDC verify the analysis results.

In this study, a second-generation positive current conveyor (CCII+)-based analog circuit is proposed for the electronic implementation of a different dynamical system which is an adaptation of the chaotic Lorenz differential equation set. The proposed circuit is more cost-effective and contains less active and passive elements than the circuit obtained by applying the classical parallel synthesis method with opamps. Mathematical analyses and SPICE simulations are performed for chaotic phase portraits and bifurcation diagrams. The proposed dynamical circuit is implemented on the board by using commercially available active and passive elements on the market and an experimental study is conducted. In order to demonstrate the usability of this proposed circuit in secure communication studies, three different synchronization methods are applied and one of them is implemented. The obtained experimental results are in good agreement with the mathematical analysis and simulation results.

Let (X, ω) be a compact Hermitian manifold of complex dimension n. In this article, we first survey recent progress towards Grauert-Riemenschneider type criteria. Secondly, we give a simplified proof of Boucksom’s conjecture given by the author under the assumption that the Hermitian metric ω satisfies $$\partial \overline \partial {\omega ^l} = {\rm{for}}\;{\rm{all}}\;l$$ , i.e., if T is a closed positive current on X such that ∫X $$T_{ac}^n>0$$ , then the class {T} is big and X is Kahler. Finally, as an easy observation, we point out that Nguyen’s result can be generalized as follows: if $$\partial \overline \partial \omega = 0$$ , and T is a closed positive current with analytic singularities, such that ∫X $$T_{ac}^n>0$$ , then the class {T} is big and X is Kahler.

We extend certain classical theorems in pluripotential theory to a class of functions defined on the support of a $(1,1)$-closed positive current $T$, analogous to plurisubharmonic functions, called $T$-plurisubharmonic functions. These functions are defined as limits, on the support of $T$, of sequences of plurisubharmonic functions decreasing on this support. In particular, we show that the poles of such functions are pluripolar sets. We also show that the maximum principle and the Hartogs's theorem remain valid in a weak sense. We study these functions by means of a class of measures, so-called "pluri-Jensen measures", about which we prove that they are numerous on the support of $(1,1)$-closed positive currents. We also obtain, for any fat compact set, an expression of its relative Green's function in terms of an infimum of an integral over a set of pluri-Jensen measures. We then deduce, by means of these measures, a characterization of the polynomially convex fat compact sets, as well as a characterization of pluripolar sets, and the fact that the support of a closed positive $(1,1)$-current is nowhere pluri-thin. In the second part of this article, these tools are used to study dynamics of a certain class of automorphisms of $\mathbb{C}^n$ which naturally generalize H\'enon's automorphisms of $\mathbb{C}^2$. First we study the geometry of the support of canonical invariant currents. Then we obtain an equidistribution result for the convergence of pull-back of certain measures towards an ergodic invariant measure, with compact support.

Similar to current profits discussed in Chap. 2, operating revenues and total assets also follow a power-law distribution in the large-scale range and a log-normal distribution in the mid-scale range in a certain year. Also, observing such short-term changes as two consecutive years, there is a time-reversal symmetry in the joint probability density function of such firm-size variables over “a certain year” and “next year.” Furthermore, Gibrat’s law also holds, which states that the conditional growth-rate distribution of firm-size variables does not depend on the initial values in a large-scale range. However, unlike the positive current profits discussed in Chap. 2, the distribution of such growth rates as operating revenues and total assets is not linear on the logarithmic axis; it has a downward curvature. Even in this case, the initial dependence of the conditional growth-rate distribution in the mid-scale range is regular. Here we extend our discussion in Chap. 2 to present a non-Gibrat’s property that describes its regularity. We show that log-normal distribution is derived from time-reversal symmetry and the extended non-Gibrat’s property and conclude that the results are consistent with the empirical data.

Considering a double-headed Brownian motor moving with both translational and rotational degrees of freedom, we investigate the directed transport properties of the system in a traveling-wave potential. It is found that the traveling wave provides the essential condition of the directed transport for the system, and at an appropriate angular frequency, the positive current can be optimized. A general current reversal appears by modulating the angular frequency of the traveling wave, noise intensity, external driving force and the rod length. By transforming the dynamical equation in traveling-wave potential into that in a tilted potential, the mechanism of current reversal is analyzed. For both cases of Gaussian and Levy noises, the currents show similar dependence on the parameters. Moreover, the current in the tilted potential shows a typical stochastic resonance effect. The external driving force has also a resonance-like effect on the current in the tilted potential. But the current in the traveling-wave potential exhibits the reverse behaviors of that in the tilted potential. Besides, the currents obviously depend on the stability index of the Levy noise under certain conditions., Comment: 10 pages

This paper presents a current feedback operational amplifier (CFOA) based on the topology of the second-generation positive current conveyor (CCII+) and an output buffer. The CCII+ is comprised of n-input and p-input balanced current mirror load OTAs with negative feedback from X node to inverting inputs of the differential pairs. Non-inverting inputs of differential pair make Y input node. The dual-input pair with balanced load structure ensures well-matched circuit characteristic and very low-output offset. This CFOA is biased in the strong inversion region using a dual power supply of ±0.6 V with a bias current of 10 µA. It dissipates the total power of 377 µW and satisfies good CFOA characteristics up to 70 MHz frequency. The CFOA cells have been utilized to design a single input multi output (SIMO) function voltage-mode universal filter which dissipates the total power of 1.79 mW. These circuits have been simulated using cadence simulator tool in 180 nm standard n-tub bulk-CMOS process in its UMC environment.

In this paper, we generalize the definition of the quaternionic Monge–Ampere operator to some unbounded plurisubharmonic functions, and we prove that the quaternionic Monge–Ampere operator is continuous on the monotonically decreasing sequences of plurisubharmonic functions. After introducing the generalized Lelong number of a positive current, Demailly’s comparison theorems are showed. Moreover, we prove that the quaternionic Lelong–Jensen-type formula also holds for the unbounded plurisubharmonic function.

The aim of this article is to develop the theory of Kahler differentials on algebroid irreducible plane curves defined over algebraically closed fields of positive characteristic and to compare it with the theory over C . We emphasize here the study of the properties of the set of values of Kahler differentials, since they were an important invariant for the analytic classification of branches (cf. [8] ), hoping that they will play an important role in positive characteristic too. At the end, we give a counterexample in positive characteristic for the result of Zariski that asserts that if a complex algebroid irreducible plane curve has coincident Tjurina and Milnor numbers, then the curve is equivalent to a monomial curve.

In this paper, we first introduce the generalized Lelong number of an m-positive current T with respect to an m-subharmonic weight $$\varphi $$ . We also prove two Demailly’s comparison theorems of the generalized Lelong numbers. Then by establishing an estimate for m-capacity $$cap_{m,T}$$ , we show a new expression of the generalized Lelong number in terms of the $$cap_{m,T}$$ -capacity of the sublevel set of $$\varphi $$ .

In this paper, we introduce the first-order differential operators $d_0$ and $d_1$ acting on the quaternionic version of differential forms on the flat quaternionic space $\mathbb{H}^n$. The behavior of $d_0,d_1$ and $\triangle=d_0d_1$ is very similar to $\partial,\overline{\partial}$ and $\partial \overline{\partial}$ in several complex variables. The quaternionic Monge-Amp\`{e}re operator can be defined as $(\triangle u)^n$ and has a simple explicit expression. We define the notion of closed positive currents in the quaternionic case, and extend several results in complex pluripotential theory to the quaternionic case: define the Lelong number for closed positive currents, obtain the quaternionic version of Lelong-Jensen type formula, and generalize Bedford-Taylor theory, i.e., extend the definition of the quaternionic Monge-Amp\`{e}re operator to locally bounded quaternionic plurisubharmonic functions and prove the corresponding convergence theorem., Comment: 32 pages

The performance and longevity of photovoltaic (PV) modules can be severely limited by cell mismatch occurring when a solar cell in a series-connected string produces a lower current than the other cells in that string. The current output of the entire string is limited by the weakest cell in the string so shading or damage to a single cell in a module can affect the entire module’s current output. Electrolumin-escence (EL) occurs when a positive current and voltage are applied to a solar cell and is used to identify damage and defects in the cell. In this study, the cell mismatch in three single crystalline silicon modules was investigated using EL and current-voltage (I-V) characterisation techniques. Two modules have a white discolouration that affects the majority of the cells in the module and also have signs of mechanical damage, while the third module acts as a reference as it has no discolouration and appears undamaged. The EL signal intensity is related to cell performance and identifies material defects, bad contacts and broken cells. Cell mismatch in a module results in a decrease in the performance parameters obtained from the I-V characteristic curve of the module. The I-V curves indicate the presence of current mismatch in the degraded modules, which is supported by the EL images of these modules. The use of EL images, in conjunction with the I-V curves, allows the degradation in the modules to be characterised.

We investigate the transport of active matter system in the presence of a disordered square lattice of half-circles, which is built by removing a fraction of them from the initial full lattice. We consider no external field. We observe a spontaneous inversion of the net current, compared to the usual sense of such a current reported in previous papers, if the obstacle has the same diameter as the unit cell of the square lattice. If this diameter is smaller, there is no inversion. We show a calculation that reproduces our numerical results qualitatively, based on the argument that such effects are the results of the imbalance of particles traveling in the positive and the negative directions due to traps formed by the obstacles: for positive travelers the traps are the spaces between neighboring obstacles, while for negative travelers, they are the flat side of the obstacles., Comment: 7 pages, 7 figures

Let $p:X\to Y$ be an holomorphic surjective map between compact K\"ahler manifolds and let $D$ be an effective divisor on $X$ with generically simple normal crossings support and coefficients in $(0,1)$. Provided that the adjoint canonical bundle $K_{X_y}+D_y$ of the generic fiber is ample, we show that the current obtained by glueing the fiberwise conic K\"ahler-Einstein metrics on the regular locus of the fibration is positive. Moreover, we prove that this current is bounded outside the divisor and that it extends to a positive current on $X$., Comment: 24 pages; v2: there was a gap in section 5 which led us to weaken the statement on the regularity of the current outside D (bounded instead of smooth)

The hybrid direct-current circuit breaker (DCCB) consists of a mechanical switch (MS) branch and a static DCCB branch. Once a short-circuit fault is detected, the current should commutate from the MS branch to the static DCCB branch first. In this paper, two current commutation measures have been investigated. A hybrid DCCB prototype with current commutated by the arc voltage of the SF ${}_{6}$ switch is developed. Based on the prototype, current commutation and interruption tests have been carried out. The results show the current of 3.4 kA can be commutated within 2.4 ms, and be interrupted within 6 ms. Then, a current commutation drive circuit (CCDC) is proposed as the other current commutation measure. Equivalent current commutation tests have been carried out. The results show with the CCDC, both positive current and negative current can be commutated within tens of microseconds. Using a CCDC in series with a mechanical vacuum switch as the MS branch, a 44 kV/3.4 kA hybrid DCCB prototype is developed. Based on the prototype, current commutation and interruption tests are carried out. According to the results, the current of 3.4 kA can be commutated within 100 $\mu $ s, and be interrupted within 2 ms.

Positive leader current spikes were observed in long air gap discharge. However, there has been no explanation on this phenomenon so far, and some leader advancement models can only produce the current without spikes. Therefore, it is necessary to figure out this phenomenon in order to deepen the understanding of leader discharge. In this paper, experiments of leader development were carried out in a 10 m rod-plane gap under positive switching impulse. The discharge current and high speed photographs of discharge process were recorded synchronously. Then the high speed photographs during the period when the leader current fluctuated were carefully analyzed. The experimental results showed that the leader current spikes were with leader branching. Finally, the effect of branching on the spikes of positive current was explained qualitatively and a hypothesis on leader branching was proposed.

In this paper, we study the existence of Lelong numbers of negative plurisubharmonic currents. We prove first that if T is a negative plurisubharmonic current of bidimension (p, p) on a neighbourhood of the origin in where , then the projective mass of T satisfies for r small enough. Then we study the case of the Lelong–Skoda potential associated with a positive closed current to prove that the set is not analytic in general for a positive pluriharmonic current R.Nombres de Lelong des potentiels associes a des courants positifs fermes et applicationsResume Dans cet article, on s’interesse a l’etude des nombres de Lelong des courants negatifs plurisousharmoniques. On montre tout d’abord que si T est un courant negatif plurisousharmonique de bidimension (p, p) sur un voisinage de l’origine de , alors la masse projective de T satisfait pour r assez petit. En suite on etudie le cas du potentiel de Lelong-Skoda associe a un courant positif ferme pour conclure que, pour un courant positif pluriharmonique R, l’e...

In this paper, we firstly introduce the concepts of capacity and Cegrell’s classes of m-subharmonic functions , , associated to any m-positive closed current T. Next, we investigate some m-potential properties associated to T and we study a generalization of the Demailly and Xing results about the definition and the continuity of the complex hessian operator. We also prove a Xing-type comparison principle for the class . Finally, we generalize the work of Ben Messaoud–El Mir on the complex Monge–Ampere operator and the Lelong–Skoda potential associated to a positive closed current.

The measuring current effect on low-temperature resistivity of Bi1.9Lu0.1Te3 has been analyzed. Values of currents correspond to weak electric fields with strength of several V·m−1. Temperature behavior of the resistivity is connected to two mechanisms. High-temperature mechanism (above 35 K) is due to acoustic phonon scattering. For this mechanism, the resistivity is growing with both increasing temperature and increasing current (positive current effect). Low-temperature mechanism (below 35 K) results in appearance of resistivity minimum at low temperatures. Below the minimum, the resistivity is growing with decreasing temperature. This feature is originated from contribution from variable-range hopping conductivity. With increasing current, the resistivity is falling (negative current effect). Crossover from positive to negative current effect on the resistivity occurs with decreasing temperature. Positive effect is originated from saturation of drift velocity of electrons under electric field. Negative effect is due to activation of hopping conductivity via electric field.

Recently, lithium-ion battery system appears to be an effective approach for energy storage due to their excellent performances. The internal structure of the lithium-ion pouch cell is laminated and is composed of several repeated units, and the unit includes five parts of positive current collector, positive electrode, separator, negative electrode and negative current collector. This structure brings great difficulties for simulator to develop full-scale model of the battery due to the complex calculation. In this paper, three kinds of three-dimensional layered electrochemical-thermal models with different unit numbers, one unit model (OUM), two unit model (TUM), and half-scale model (HSM) are established to study the effect of number of units on lithium-ion battery thermal behavior and electrochemical characteristics under adiabatic condition. The corresponding experimental procedure is performed for model validation, the simulation and experiment are in good agreement with temperature and discharge curves at four different discharge rates (0.5 C, 1 C, 1.5 C and 2 C). The results show that the temperature distribution and heat generation rate per volume as well as the representative electrochemical properties are almost the same of the three models; it is also found that each unit of the TUM and HSM is uniform and symmetrical distributed. Therefore, the HSM and full-scale model can be replaced by the OUM for lithium-ion pouch cell under adiabatic condition. The OUM can save 1/140 of computing time and greatly reduce the computational resources compared to HSM, which can facilitate the related research under adiabatic.

This paper proposes a novel drive circuit for three-phase switched reluctance motors (SRMs) with bipolar current drive. Asymmetric H-bridge drive circuit is often used as a SRM drive circuit, and only positive current flows through windings in the SRMs. The SRMs can also generate positive torque even if the motor current is negative during positive torque generation angles.In this paper, a bipolar current drive and a suitable drive circuit for SRMs are discussed, and the effectiveness of the proposed drive system is confirmed by some simulations and experimental results.

We often call an extremal Kahler metric with finite singularities on a compact Riemann surface an HCMU (the Hessian of the Curvature of the Metric is Umbilical) metric. In this paper we consider the following question: if we give $N$ points $p_1, \ldots, p_N$ on $S^2$ and $N$ positive real numbers $2\pi \alpha_1, \ldots, 2\pi \alpha_N$ with $\alpha_n \neq 1$, $n = 1, \ldots, N$, what condition can guarantee the existence of a non-CSC HCMU metric which has conical singularities $p_1, \ldots, p_N$ with singular angles $2\pi \alpha_1, \ldots, 2\pi \alpha_N$ respectively. We prove that if there are at least $N-2$ integers in $\alpha_1, \ldots, \alpha_N$ then there exists one non-CSC HCMU metric on $S^2$ satisfying the condition stated above no matter where the given points are.

We investigate Andreev transport through a quantum dot attached to two external ferromagnetic leads and one superconducting electrode. The transport properties of the system are studied by means of the real-time diagrammatic technique in the sequential tunneling regime. To distinguish various contributions to Andreev current we calculate the current cross-correlations, i.e. correlations between currents flowing through two junctions with normal leads. We analyze dependence of current cross-correlations on various parameters of the considered model, both in linear and nonlinear transport regimes. The processes and mechanisms leading to enhancement, suppression or sign change of current cross-correlations are examined and discussed. Interestingly, our results show that for specific transport regimes splitted Cooper pair results in two uncorrelated electrons. However, utilizing ferromagnetic leads instead of non-magnetic electrodes can result in positive current cross-correlations., Comment: 9 pages, 6 figures