关于矩阵的迹的不等式

指出了关于正定矩阵的迹中几个主要结论的错误并加以修正,得到了关于可正对角 化矩阵的迹的等式tr(AB)n=[tr(AB)]n=tr(AnBn)成立的条件．

The Solvability of the Degenerate Differential Systems with Delay

In this paper we study the degenerate differential system with delay:E(t)=Ax(t)+Bx(t-1)+f(t),give the canonical form of this systems and study this form of degeneration system with delay,have some results for the solvability of such systems and the uniqueness of their solutions.

Some Opinions on the Paper “Several Inequalities of Matrix Traces”

In this paper,we find some mistakes in the paper “Several Inequalities of Matrix Traces” which was published in Chinese Quarterly Journal of Mathematics,Vol.10,No.2.

Scalable transcoding for video transmission over space-time OFDM systems

A new scheme combining a scalable transcoder with space time block codes （STBC） for an orthogonal frequency division multiplexing （OFDM） system is proposed for robust video transmission in dispersive fading channels. The target application for such a scalable transcoder is to provide successful access to the pre-encoded high quality video MPEG-2 from mobile wireless terminals. In the scalable transcoder, besides outputting the MPEG-4 fine granular scalability （FGS） bitstream, both the size of video frames and the bit rate are reduced. And an array processing algorithm of layer interference suppression is used at the receiver which makes the system structure provide different levels of protection to different layers. Furthermore, by considering the important level of scalable bitstream, the different bitstreams can be given different level protection by the system structure and channel coding. With the proposed system, the concurrent large diversity gain characteristic of STBC and alleviation of the frequency-selective fading effect of OFDM can be achieved. The simulation results show that the proposed schemes integrating scalable transcoding can provide a basic quality of video transmission and outperform the conventional single layer transcoding transmitted under the random and bursty error channel conditions.

Three-dimensional tensor controlled-source electromagnetic modeling based on the vector finite-element method

Scalar CSAMT is only suitable for measurements in one and two dimensions perpendicular to geological structures. For complex 3D geoelectric structure, tensor CSAMT is more suitable. In this paper, we discuss 3D tensor CSAMT forward modeling using the vector finite-element method. To verify the feasibility of the algorithm, we calculate the electric field, magnetic field, and tensor impedance of the 3D CSAMT far-zone field in layered media and compare them with theoretical solutions. In addition, a three-dimensional anomaly in half-space is also simulated, and the response characteristics of the impedance tensor and the apparent resistivity and impedance phase are analyzed. The results suggest that the vector finite-element method produces high-precision electromagnetic field and impedance tensor data, satisfies the electric field discontinuity, and does not require divergence correction using the vector finite-element method.

New scale factor correction scheme for CORDIC algorithm

To overcome the drawbacks such as irregular circuit construction and low system throughput that exist in conventional methods, a new factor correction scheme for coordinate rotation digital computer（ CORDIC） algorithm is proposed. Based on the relationship between the iteration formulae, a new iteration formula is introduced, which leads the correction operation to be several simple shifting and adding operations. As one key part, the effects caused by rounding error are analyzed mathematically and it is concluded that the effects can be degraded by an appropriate selection of coefficients in the iteration formula. The model is then set up in Matlab and coded in Verilog HDL language. The proposed algorithm is also synthesized and verified in field-programmable gate array （FPGA）. The results show that this new scheme requires only one additional clock cycle and there is no change in the elementary iteration for the same precision compared with the conventional algorithm. In addition, the circuit realization is regular and the change in system throughput is very minimal.

1-D Controlled source electromagnetic forward modeling for marine gas hydrates studies

We discuss the feasibility of using controlled-source electromagnetic （CSEM） in the frequency domain for prospecting marine gas hydrates. Based on the Ocean Drilling Program （ODP） Leg 164 log data, we have established several 1-D resistivity models which have different gas hydrate concentrations. Meanwhile, we analyzed the electromagnetic response of marine gas hydrates in the frequency domain based on these models. We also studied the relationship between electrical field magnitude or phase and parameters such as receiver-transmitter distance and frequency. Our numerical modeling results provide us with a quantitative reference for exploration and resource evaluation of marine gas hydrates.

From the Gla domain to a novel small-molecule detector of apoptosis

Apoptosis plays a pivotal role in the etiology or pathogenesis of numerous medical disorders, and thus, target- ing of apoptotic cells may substantially advance patient care. In our quest for novel low-molecular-weight probes for apoptosis, we focused on the uncommon amino acid T-carboxyglutamic acid （Gla）, which plays a vital role in the binding of clotting factors to negatively charged phospholipid surfaces. Based on the alkyl-malonic acid motif of Gla, we have developed and now present ML-10 （2-（5-fluoro-pentyl）-2-methyl-malonic acid, MW=206 Da）, the pro- totypical member of a novel family of small-molecule detectors of apoptosis. ML-10 was found to perform selective uptake and accumulation in apoptotic cells, while being excluded from either viable or necrotic cells. ML-10 uptake correlates with the apoptotic hallmarks of caspase activation, Annexin-V binding and disruption of mitochondrial membrane potential. The malonate moiety was found to be crucial for ML-10 function in apoptosis detection. ML- 10 responds to a unique complex of features of the cell in early apoptosis, comprising irreversible loss of membrane potential, permanent acidification of cell membrane and cytoplasm, and preservation of membrane integrity. ML-10 is therefore the most compact apoptosis probe known to date. Due to its fluorine atom, ML-10 is amenable to radio- labeling with the lSF isotope, towards its potential future use for clinical positron emission tomography imaging of apoptosis.

A new variable step-size LMS method and its application in DOA estimation of OFDMA signals

To meet the requirements of quick positioning of mobile terminals from base stations(BSs)or third-party devices,as well as to improve the convergence speed and reduce the steady state maladjustment of the least mean square(LMS)method,a new logarithmic-sigmoid variable step-size LMS(LG-SVSLMS)was proposed and applied to estimate the direction of arrival(DOA)of orthogonal frequency division multiple access(OFDMA)signals.Based on the proposed LG-SVSLMS,a non-blind DOA estimation system for OFDMA signals was constructed.The proposed LG-SVSLMS adopts a new multi-parameter step-size update function which combines the sigmoid function and the logarithmic function.It controls the adjustment magnitude of step-size during the initial and steady state phases of the LMS method to achieve both a high convergence speed and low steady state maladjustment.Finally,simulation was conducted to verify the performance of the LG-SVSLMS.The simulation results show that the non-blind DOA estimation system based on the LG-SVSLMS can accurately estimate the DOA of the target signal in the scenario where interference signals from multi-source and multi-path fading signals arrive at the third-party devices asynchronously with the target signal,and the estimation deviation is within±3°.The non-blind DOA estimation for OFDMA signals with the proposed LG-SVSLMS is of great significance for the instant positioning technology of mobile terminals based on the adaptive antenna array.

A general version of the Morse-Sard theorem

Let k, m, n be positive integers, and k≥2, α∈(0,1], 0<r<min{m,n} an integer, d=r+(m?r)/(k+α), and if f∈Ck (Rm, ,α Rn), A=Cr(f)={x∈Rm |rank(Df(x))≤r}, then f(A) is d-null. Thus the statement posed by Arthur Sard in 1965 can be completely solved when k≥2.

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance Under the General Linear Model

Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.

Semi-empirical modeling of volumetric efficiency in engines equipped with variable valve timing system

Volumetric efficiency and air charge estimation is one of the most demanding tasks in control of today's internal combustion engines.Specifically,using three-way catalytic converter involves strict control of the air/fuel ratio around the stoichiometric point and hence requires an accurate model for air charge estimation.However,high degrees of complexity and nonlinearity of the gas flow in the internal combustion engine make air charge estimation a challenging task.This is more obvious in engines with variable valve timing systems in which gas flow is more complex and depends on more functional variables.This results in models that are either quite empirical(such as look-up tables),not having interpretability and extrapolation capability,or physically based models which are not appropriate for onboard applications.Solving these problems,a novel semi-empirical model was proposed in this work which only needed engine speed,load,and valves timings for volumetric efficiency prediction.The accuracy and generalizability of the model is shown by its test on numerical and experimental data from three distinct engines.Normalized test errors are 0.0316,0.0152 and 0.24 for the three engines,respectively.Also the performance and complexity of the model were compared with neural networks as typical black box models.While the complexity of the model is less than half of the complexity of neural networks,and its computational cost is approximately 0.12 of that of neural networks and its prediction capability in the considered case studies is usually more.These results show the superiority of the proposed model over conventional black box models such as neural networks in terms of accuracy,generalizability and computational cost.

New Exact Solutions for （2＋1）-Dimensional Breaking Soliton Equation

New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutionsand triangular periodic wave solutions are obtained.

On Inverse Limits of Normal δθ-refinable Spaces

This paper proves the following results: Le t X= lim ←｛X σ,π σ ρ,Λ｝,｜Λ｜=λ, and every p rojection π σ: X→X σ be an open and onto mapping. (A) If X is λ-paracompact and every X σ is normal and δθ-refinable, then X is normal and δθ-refinable; (B) If X is hereditarily λ-pa racompact and every X σ is hereditarily normal and hereditarily δθ- refinable, then X is hereditarily normal and hereditarily δθ-refiable .

Early radiological assessment of locally advanced pancreatic cancer treated with electrochemotherapy

To report early imaging assessment of ablated area post electrochemotherapy (ECT) in patients with locally advanced pancreatic cancer (LAPC). METHODSECT was performed in 19 LAPC patients enrolled in an approved ongoing clinical phase I/II study. Before and after ECT, 18 patients underwent computed tomography (CT) scan, 11 patients underwent morphological and functional magnetic resonance (MR) scan (dynamic contrast enhanced-MRI) calculating wash-in slope (WIS) and wash-out slope (WOS); diffusion weighted imaging calculating pseudo-diffusivity (Dp), perfusion fraction (fp) and tissue diffusivity (Dt); 10 patients underwent positron emission tomography (PET). Response evaluation criteria in solid tumour (RECIST) on MR and CT were used to assess tumour therapy response. Choi on CT, PET response criteria in solid tumors (PERCIST) on PET and functional parameters on MR were used to evaluate treatment response. RESULTSFor each patient no significant reduction was measurable by CT and MR using RECIST. According Choi criteria a partial response was obtained in 18/18 (100.0%) patients. According PERCIST criteria 6/10 (60.0%) patients showed a partial response, 3/10 (30.0%) stable disease and 1/10 (10.0%) progression disease. Moreover, using functional MR parameters, a significant reduction of viable tumour after ECT can be observed. According ΔWIS and ΔWOS 9/11 (81.8%) patients exhibited a partial response and 2/11 (18.2%) stable disease; 8/11 (72.7%) patients were considered in partial response by ΔDp evaluation and 3/11 (27.3%) in stable disease; according ΔDt 7/11 (63.6%) patients showed a partial response, 1/11 (9.1%) showed progression of disease and 3/11 (27.3%) were stable. Perfusion fraction fp showed a significant reduction after ECT only in four patients. No significant difference was observed after ECT in signal intensity of T1-weighted images and T2-weighted images, and in equilibrium-phase of contrast study, according to χ2 test was observed. A good correlation was reported between ΔHounsfield unit and Δmaximum standardized uptake value and between Δfp and ΔWOS, with a significant statistically difference (P < 0.05) using Spearman correlation coefficient. CONCLUSIONPerfusion and diffusion MR derived parameters, Choi, PERCIST criteria are more performant than morphological MR and CT criteria to assess ECT treatment response.

Two Sequences of Operator Monotone Functions and Strictly Chaotic Order

In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k＋1t/（tlogt）k-（t-1）^k（k=1,2…）,gk（t）=t^klog^k＋1t/（t-1）^k-log^kt（k=1,2…）defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-t＋1/log^2t which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].

Bayesian prestack seismic inversion with a self-adaptive Huber-Markov random-field edge protection scheme

Seismic inversion is a highly ill-posed problem, due to many factors such as the limited seismic frequency bandwidth and inappropriate forward modeling. To obtain a unique solution, some smoothing constraints, e.g., the Tikhonov regularization are usually applied. The Tikhonov method can maintain a global smooth solution, but cause a fuzzy structure edge. In this paper we use Huber-Markov random-field edge protection method in the procedure of inverting three parameters, P-velocity, S-velocity and density. The method can avoid blurring the structure edge and resist noise. For the parameter to be inverted, the Huber- Markov random-field constructs a neighborhood system, which further acts as the vertical and lateral constraints. We use a quadratic Huber edge penalty function within the layer to suppress noise and a linear one on the edges to avoid a fuzzy result. The effectiveness of our method is proved by inverting the synthetic data without and with noises. The relationship between the adopted constraints and the inversion results is analyzed as well.

Test case generation based on orthogonal table for software black-box testing

Software testing is an important means to assure the software quality. This paper presents a practicable method to generate test cases of software testing, which is operational and high efficient. We discuss the identification of software specification categories and choices and make a classification tree. Based on the orthogonal array, it is easy to generate test cases. The number of this method is less than that of all combination of the choices.

Study of Vertical Breakwater Reliability Based on Copulas

The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.

The State Equations Methods for Stochastic Control Problems

The state equations of stochastic control problems,which are controlled stochastic differential equations,are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain approximation approach. Local consistency of the methods are proved.Numerical tests on a simplified Merton's portfolio model show better simulation to feedback control rules by these two methods, as compared with the weak Euler-Maruyama discretisation used by Krawczyk.This suggests a new approach of improving accuracy of approximating Markov chains for stochastic control problems.