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For a normal random variable Y with mean zero and general covariance matrix [[SIGMA].sub.Y] the Wishartness of a quadratic form Q(Y) is characterized in terms of Jordan algebra representations. The framework of Jordan algebras provides a unified view since the cases where Y is a real, complex or quaternionic normal are encompassed under one general theory. A general version of Cochran's theorem is also presented. Keywords and Phrases: Cochran's Theorem, Jordan algebras, Multivariate normal distribution, Quadratic forms, Wishart distribution., 1. Introduction This paper is a sequel to Masaro and Wong (12) and, like (12), is based on Wong and Masaro (22). Consider a normally distributed random matrix Y with [...]

Due to machining errors and the effect of the longitudinal end of a stator, linear permanent magnet motors (LPMMs) produce asymmetric three-phase winding resistance and inductance. After a Park transformation of the asymmetric three-phase stator inductance, the dqaxis inductance is not constant, and the dqaxis is coupled. This leads to errors in estimating the motor position by the traditional pulse injection method. In this paper, the position estimation error caused by parameter asymmetry is analyzed to discuss the influence of LPMM asymmetric three-phase winding parameters on high frequency pulse injection sensorless method error. Moreover, a double stage filtering method is used to realize error compensation. On this basis, a simulation model was built by MATLAB/Simulink and experiments were carried out on a LPMM prototype under no-load conditions. The simulation and experimental results verify that the double stage filtering method can improve the position estimated accuracy and dynamic performance under sensorless control.

ABSTRACTIntroduction: The increasing prevalence of comorbid depression and diabetes exerts a heavy burden on global health. Co-occurrence of depression and diabetes is common, affecting 14% to 35.8% of patients with diabetes, leading to a higher mortality and morbidity rate, more micro- and macro-vascular diseases and more cognitive decline.Areas covered: In this paper, the authors address various areas from epidemiology, the association between depression and diabetes, treatment strategies and future directions based on the currently available literature to provide novel insight into the pharmacotherapeutic management of comorbid depression and diabetes.Expert opinion: Pharmacotherapy can help patients with comorbid depression and diabetes by relieving depressive symptoms and improving glycemic control. When combined with psychological therapy, as a collaborative care effort, pharmacological therapy based on selective serotonin reuptake inhibitors (SSRIs) is recommended for comorbid depression with diabetes. Furthermore, studies with larger sample sizes that can help to define different subtypes of diabetes and severity of depression are needed so that clinicians can draw up a precise and applicable management guidelines for the personalized therapy of these diseases.

This paper presents a robust nonlinear control strategy to solve the instability problem of dc-dc buck power converter with a constant power load in dc microgrid systems. Based on the passivity-based control (PBC), a nonlinear disturbance observer (NDO) is designed to improve the control robustness against both load and line variations, whereas the PBC guarantees the system stability due to its property of transient energy dissipation. By applying the disturbance estimation technique, NDO works in parallel with the PBC controller to compensate the disturbances through a feed-forward channel. This strategy ensures large signal stability as well as fast recovery performance of the system during disturbance/uncertainty as compared to other nonlinear control methods. Hardware-in-loop (HIL) experiment is performed on an OPAL-RT real-time simulator. MATLAB simulation and HIL results are provided to verify the proposed control strategy. Further validations are presented using a real hardware experiment to emphasize the robustness of the proposed controller.

In high-performance magnetic resonance imaging systems, the gradient driver is required to supply the gradient coil with a large current (>600 A) and a high voltage (>2000 V) to achieve a strong gradient field and a fast slew rate. In addition, extremely high fidelity for reproducing the current command from the central system is very critical to imaging quality. This paper presents the solutions for the different elements of the driver: 1) high-bandwidth (BW) power inverter; 2) ripple cancelation filter; 3) multioutput power supply (PS); and 4) digital control. A high-BW power inverter requires a stacked-bridges structure to achieve a high output ripple frequency with the existing commercial power semiconductor modules. The high voltage and the high frequency for large power modules can be obtained easier and with lower loss using the new silicon carbide devices. The control needs a digital implementation and a very fast processor. Digital control provides compensation and feedforward to improve the response. A capability improvement is obtained by reducing the switching frequency when large currents with a very low-frequency variation are needed. The control can handle it very well, but the filter has to be designed to eliminate more than one ripple frequency. Finally, many PS solutions have been used for multiple isolated outputs, but digital control compensation permits the use of much simpler unregulated PS and keeps the performance. A 2 MVA, 900 A/1200 V, platform has been built and fully tested. The experimental results proved the validity of the proposed structure and the modulation technique.

Prevalence estimates of depression in AD vary greatly across studies, and a reliable result is crucial for further interventions. A systematic review and meta-analysis was conducted to identify the prevalence of depression in AD patients. We searched PubMed and Embase, followed by data extraction, quality assessment, prevalence estimates and subgroup analyses. A total of 63 studies were included in the review. The prevalences of depression were 12.7% (CI, 8.8-17.8) and 42% (CI, 38-45) according to the DSM criteria for major depression and the specific criteria for dementia respectively. Subgroup analyses stratified by case identification showed that the prevalences of population-based stud ies were 5% (CI: 2-15) and 35% (CI: 29-41) according to the DSM criteria and the specific criteria respectively, while those of single source were 17% (CI: 11-25) and 43% (CI: 37-49). Subgroup analyses stratified by MMSE score revealed that the prevalences of severe AD were 8% (CI: 5-15) and 48% (CI: 41-54) according to the DSM criteria and the specific criteria respectively, while those of mild AD were 14% (CI: 8-24) and 40% (CI: 32- 47). In conclusion, the prevalence of depression according to the DSM criteria was lower than that of the specific criteria. Prevalence estimates conducted in population-based studies were lower compared with those in single-source studies irrespective of the screening tools. Patients with severe AD tended to have higher prevalence of depression according to the specific criteria, while the trend was opposite according to the DSM criteria. Thus, different settings and diagnostic approaches should be taken into account before estimates of depression and further interventions.

The parallel application program development technology and process is analyzed based on the MATLAB parallel and distributed computing toolbox. Hereby, the comparison of the serial computing and the parallel computing is done by computer simulations, and the parallel computing program design and develop method is proposed. The simulations results show that, the parallel computing technology has many advantages in the calculation of high intensive and it is convenience of the parallel application development using MATLAB.

To improve the performance of the character recognition based on wavelet neural network (WNN) with gradient descent algorithm, a new character recognition method based on WNN optimized by PSO algorithm is proposed. PSO is adopted to optimize the weights and the topological structure of WNN at the same time, which can overcome the slow convergence rate and easy to drop in the local minimum, and the WNN after optimization is used to the character recognition. The invariant moments of the license plate character image after preprocessing, such as two valued and normalized, are taken as the input of WNN to implement the character recognition. The simulation results show that, compared with WNN, the WNN optimized by PSO algorithm has better performance in character recognition, and has higher recognition ratio.

In order to maximize the solar energy harvesting capabilities, power converters for photovoltaic (PV) systems have to be designed for high efficiency, accurate maximum power point tracking (MPPT), and voltage/current performance. When many converters are used in distributed PV systems, power density also becomes an important factor since it allows for simpler system integration. In this paper, a high-power-density string-level MPPT dc-dc converter suitable for distributed medium- to large-scale PV installations is presented. A simple partial power processing topology that is implemented exclusively with silicon carbide devices provides high efficiency and high power density. A 3.5-kW, 100-kHz converter is designed and tested to verify the proposed methods.

The surface modification of superfine brucite using silane coupling agent as a modifier was studied. The results of the best modified conditions show that the treated time is 1.5h, the treated temperature is 40℃, the content of silane coupling agent is 7wt%,the stirring speed is 600r/min. In this condition, the activation index up to 93.5%; the treated brucite particles filled into polypropylene(PP), the best tensile strength of 28.63MPa and the LOI of 30% is measured.

A general easily verifiable Cochran theorem is obtained for a normal random matrix Ywith mean μand covariance ΣYwhich may be singular and may not be of the form A ⊗ Σ, where Σis the population covariance: {Y′WiY}i=1L(with nonnegative definite Wi's) is an independent family of Wishart WY(mi, Σ, λi)random matrix YiWiYif and only if for W = Σi=1LWi, (W ⊗ I) Σr(W ⊗ I)is of the form C ⊗ Σwith CW+C = Cand for all distinet i, j = 1,2,…, L, mi= r(W+CW+Wi), WiW+CW+Wj= 0and λi= μ′Wiμ = μiWiW+CW+Wiμ.

Let K(N,n) denote the set of all N × n matrices X = (Xij) where and Xij = -1.0.1 and N≥ n. Such matrices arise in designs of experiments. Certain results on A-optimal designs are obtained. Small N and n are more important for practical use. A -optimal designs in K (N,.n) are known for N <6 and are given here for N = 6.

Let T be a self-mapping on a complete metric space (X, d). Then T has a fixed point if there exist self-mappings $ {\alpha _1},{\alpha _2},{\alpha _3},{\alpha _4},{\alpha _5}$ $ [0,\infty ]$ $ {\alpha _1}(t) + {\alpha _2}(t) + {\alpha _3}(t) + {\alpha _4}(t) + {\alpha _5}(t) &lt; t$, (b) each $ {\alpha _1}$

$\displaystyle d(T(x),T(y)) \leqq {a_1}d(x,T(x)) + {a_2}d(y,T(y)) + {a_3}d(x,T(y)) + {a_4}d(y,T(x)) + {a_5}d(x,y)$ for all pairs of distinct x, y in X, where . Related results are obtained for two mappings and mappings on a bounded convex subset of a uniformly convex Banach space.

Characterizations of sequentially complete and of countably compact subsets of a uniform space are obtained. Applications to fixed point theory and coincidence theory are given.

The linear model Y - N(Xb, σ2∑) with a restriction R'b = M'u + c is considered, where X, R, M, ∑ and c are known. Explicit formulae are obtained for the best linear unbiased estimator of K'b, for the F-test of the hypothesis K'b = W'v + a, and for the simultaneous confidence intervals of the parameters K'i b' s, where K = [K1,K2,…Ks], w, and a are known, none of the matrices X, ∑, R, M, K, and W is required to have full ranks, and the design X can be one - or multi-way,complete or incomplete, balanced or not balanced, connected or disconnected.

A capture-recapture model that depends on the catchability of the individuals in a closed population is considered. An asymptotic result on the distribution of a pivtal quantity is proved. This result was used previously to construct confidence intervals for the population size N. Certain other confidence intervals for N are obtained by using the normal approximatin for the maximum likelihood esimator of functions of N. A simulation study is carried out to compare the actal confidence levels of these intervals

Dugundji's notion of positive definiteness is generalized to nonnegative real-valued functions on a uniform space. Its relations with completeness and various notions of compactness are investigated. For an arbitrary uniform space $ X$ and so a further generalization of Dugundji's notion of positive definiteness is needed for the development of the fixed point (or coincidence) theory. With such an extension, a very general fixed point theorem is obtained to include a recent result of the author, which contains, as special cases, some results of S. Banach, F.E. Browder, D. W. Boyd and J. S. W. Wong, M. Edelstein and R. Kannan.

Let $ K$. Let $ T$ such that for all $ x,y$ $ K,\vert\vert T(x) - T(y)\vert\vert \leqslant (\vert\vert x - T(x)\vert\vert + \vert\vert y - T(y)\vert\vert)/2$ and Zorn's lemma that $ T$ $ \inf \{ \vert\vert x - T(x)\vert\vert:x \in K\} = 0$ is obtained in terms of close-to-normal structure. As consequences, the following results are obtained: (i) $ T$ is locally uniformly convex or more generally if $ B$ $ {\mathbf{A}}$ $ \{ {x_n}\} $ $ B,\{ {x_n}\} $ in $ B$ and $ \{ \vert\vert x\vert\vert\} $; (ii) $ T$ is separable.

Let $ K$ is compact, then the fixed points of a continuous generalized nonexpansive self-mapping $ T$ can be approximated by the iterates of $ {T_t}$ $ t \in (0,1),{T_t}(x) = (1 - t)x + tT(x),x \in K;{T_t}$ has a fixed point.

Let dithe degree of the ith vertex of a mutigraph and λijbe the number of edges between vertex iand vertex j.A multigraph is called nearly balanced if |di− di| ≤1 for all i≠i′ and |λij−λij| for all iand all j,j′ Let be the collection of all the multigraphs with vvertices and e edges. It is shown that for any v, there is an e* such that if, then any nearly balanced graph in ζv, ehas more spanning trees than any non‐nearly‐balanced graph in ζv, e.

Let S, Tbe self-mappings on a (non-empty) complete metric space (X, d). Let ai, i = 1, 2, ?, 5, be non-negative real numbers such that < 1 and for any x, yin X,

A technique is developed for finding optimum designs for weighing nobjects in Nweighings $( N\geqq n )$ on a chemical balance. Certain designs are shown to be optimal with respect to a large class of criteria (including the A- and D-criteria) for sufficiently large $ N \equiv 2 \,\text{or}\, 3 (\bmod 4)$. For small N, the result allows the elimination of a large number of competitors, and those that remain can be checked by a computer.

Let $ X$ be a Hausdorff topological semigroup which is either left amenable or left reversible. Then for any generalised nonexpansive (jointly) continuous action of $ S$ contains a common fixed point of .

Let T be a self map on a bounded interval [a, b] with $ a,b \in T([a,b])$x, y in [a, b],

A refinement of the proof of a recent fixed point theorem of Caristi is obtained.