The Distribution of Eigenvance of Product Diagonal Dominance Matrix

Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.

MATHEMATICAL ANALYSIS OF DRUG RELEASE FROM A MONOLITHIC MATRIX WITH AN INITIALLY LINEAR CONCENTRATION DISTRIBUTION

Based on the principle of chemical engineering in the multisubject field—drug delivery, the release kinetics of the slab monolithic matrix with an initially linear concentration distribution is studied in this paper. It can be used to describe the later stage when drug loading is above its solubility limit. A comprehensive model is proposed and the generalized solutions are acquired by Laplace transformation, from which a special case, i.e. a perfect sink has been deduced. According to the derived equations, the concentration profiles in the matrix has been computed and illustrated and the effect of volume of extraction medium on release has been investigated.

Strengthening mechanisms based on reinforcement distribution uniformity for particle reinforced aluminum matrix composites

A modified mixed strengthening model was proposed for describing the yield strength of particle reinforced aluminum matrix composites.The strengthening mechanisms of the composites were analyzed based on the microstructures and compression mechanical properties.The distribution uniformity of reinforcements and cooperation relationship among dislocation mechanisms were considered in the modified mixed strengthening model by introducing a distribution uniformity factor u and a cooperation coefficient fc,respectively.The results show that the modified mixed strengthening model can accurately describe the yield strengths of Al3Ti/2024Al composites with a relative deviation less than1.2%,which is much more accurate than other strengthening models.The modified mixed model can also be used to predict the yield strength of Al3Ti/2024Al composites with different fractions of reinforcements.

Thermal residual stresses and stress distributions under tensile and compressive loadings of short fiber reinforced metal matrix composites

The thermal residual stresses and the stress distributions of short fiber reinforced metal matrix composite under tensile and compressive loadings were studied using large strain axisymmetric elasto plastic finite element method. It is demonstrated that the thermal residual stresses can result in asymmetrical stress distributions and matrix plasticity. The thermal residual stresses decrease the stress transfer in tension and enhance the stress transfer in compression. The fiber volume fraction has more important effects on the thermal residual stresses and the stress distributions under tensile and compressive loadings than the fiber aspect ratio and the fiber end distance. [

Distribution and relative activity of matrix metalloproteinase-2 in human coronal dentin

The presence of matrix metalloproteinase-2 （MMP-2） in dentin has been reported, but its distribution and activity level in mature human coronal dentin are not well understood. The purpose of this study was to determine the MMP-2 distribution and relative activity in demineralized dentin. Crowns of twenty eight human molars were sectioned into inner （ID）, middle （MD）, and outer dentin （OD） regions and demineralized. MMP-2 was extracted with 0.33 mol·L-1 EDTA/2 mol·L-1 guanidine-HCl, pH 7.4, and MMP-2 concentration was estimated with enzyme-linked immunoabsorbant assay （ELISA）. Further characterization was accomplished by Western blotting analysis and gelatin zymography. The mean concentrations of MMP-2 per mg dentin protein in the dentin regions were significantly different （P=0.043）： 0.9 ng （ID）, 0.4 ng （MD）, and 2.2 ng （OD）, respectively. The pattern of MMP-2 concentration was OD〉ID〉MD. Western blotting analysis detected -66 and -72 kDa immunopositive proteins corresponding to pro- and mature MMP-2, respectively, in the ID and MD, and a -66 kDa protein in the OD. Gelatinolytic activity consistent with MMP-2 was detected in all regions. Interestingly, the pattern of levels of Western blot immunodetection and gelatinolytic activity was MD〉ID〉OD. The eoneentration of MMP-2 in human coronal dentin was highest in the region of dentin that contains the dentinoenamel junction and least in the middle region of dentin. However, levels of Western blot immunodetection and gelatinolytic activity did not correlate with the estimated regional concentrations of MMP-2, potentially indicating region specific protein interactions.

Multi-Model Based PSO Method for Burden Distribution Matrix Optimization With Expected Burden Distribution Output Behaviors

Burden distribution is one of the most important operations, and also an important upper regulation in blast furnace(BF) iron-making process. Burden distribution output behaviors(BDOB) at the throat of BF is a 3-dimensional spatial distribution produced by burden distribution matrix(BDM),including burden surface output shape(BSOS) and material layer initial thickness distribution(MLITD). Due to the lack of effective model to describe the complex input-output relations,BDM optimization and adjustment is carried out by experienced foremen. Focusing on this practical challenge, this work studies complex burden distribution input-output relations, and gives a description of expected MLITD under specific integral constraint on the basis of engineering practice. Furthermore, according to the decision variables in different number fields, this work studies optimization of BDM with expected MLITD, and proposes a multi-mode based particle swarm optimization(PSO) procedure for optimization of decision variables. Finally, experiments using industrial data show that the proposed model is effective, and optimized BDM calculated by this multi-model based PSO method can be used for expected distribution tracking.

Non-random tissue distribution of human na ve umbilical cord matrix stem cells

AIM: To determine the tissue and temporal distribution of human umbilical cord matrix stem (hUCMS) cells in severe combined immunodeficiency (SCID) mice. METHODS: For studying the localization of hUCMS cells, tritiated thymidine-labeled hUCMS cells were injected in SCID mice and tissue distribution was quantitatively determined using a liquid scintillation counter at days 1, 3, 7 and 14. Furthermore, an immunofluorescence detection technique was employed in which anti-human mitochondrial antibody was used to identify hUCMS cells in mouse tissues. In order to visualize the distribution of transplanted hUCMS cells in H&E stained tissue sections, India Black ink 4415 was used to label the hUCMS cells. RESULTS: When tritiated thymidine-labeled hUCMS cells were injected systemically (iv) in female SCID mice, the lung was the major site of accumulation at 24 h after transplantation. With time, the cells migrated to other tissues, and on day three, the spleen, stomach, and small and large intestines were the major accumulation sites. On day seven, a relatively large amount of radioactivity was detected in the adrenal gland, uterus, spleen, lung, and digestive tract. In addition, labeled cells had crossed the blood brain barrier by day 1. CONCLUSION: These results indicate that peripherally injected hUCMS cells distribute quantitatively in a tissue-specific manner throughout the body.

Measuring the flexibility matrix of an eagle’s flight feather and a method to estimate the stiffness distribution

Flight feathers stand out with extraordinary mechanical properties for flight because they are lightweight but stiff enough.Their elasticity has great effects on the aerodynamics, resulting in aeroelasticity.Our primary task is to figure out the stiffness distribution of the feather to study the aeroelastic effects.The feather shaft is simplified as a beam, and the flexibility matrix of an eagle flight feather is tested.A numerical method is proposed to estimate the stiffness distributions along the shaft length based on an optimal Broyden–Fletcher–Goldfarb–Shanno(BFGS) method with global convergence.An analysis of the compressive behavior of the shaft based on the beam model shows a good fit with experimental results.The stiffness distribution of the shaft is finally presented using a 5 th order polynomial.

A Direct Derivation of the Exact Fisher Information Matrix for Bivariate Bessel Distribution of Type I

This paper deals with a direct derivation of Fisher’s information matrix for bivariate Bessel distribution of type I. Some tools for the numerical computation and some tabulations of the Fisher’s information matrix are provided.

UHAS-MIDA Software Package: Mass Isotopomer Distribution Analysis-Applying the Inverse Matrix for the Determination of Stable Isotopes of Chromium Distribution during Red Blood Cell Labelling

Clinical assessment of fluid volume status in children during malaria can be taxing and often inaccurate. During malaria, changes in fluid volume are rather multifarious and estimating this parameter, especially in sick children is very challenging for clinicians who frequently rely on indices such as long capillary refill times, tachycardia, central venous pressure and decreased urine volume as guides. Here, we present the UHAS-MIDA, an open-source software tool that calculates the red blood cell (RBC) concentration and blood volume during malaria in children determined using a stable isotope of chromium (53Cr as the label) by gas chromatography-mass spectrometry in selective ion monitoring (GC/MS-SIM) analysis. A key component involves the determination of the compositions of the most abundant naturally occurring isotopes of Cr (50Cr, 52Cr, 53Cr), and converting the proportions into a 3 × 3 matrix. To estimate unknown proportions of chromium isotopic mixtures from the measured abundances of three ions, an inverse matrix was calculated. The inverse together with several inputs is then used to calculate the corrected MS ion abundances. Thus, we constructed the software tool UHAS- MIDA using HTML, CSS/Bootstrap, JavaScript, and PHP scripting languages. The tool enables the user to efficiently determine RBC concentration and fluid volume. The source code, binary packages and associated materials for UHAS-MIDA are freely available at https://github.com/bentil078/Abaye-et-al_UHASmida

Distribution and engulfment behavior of TiB_2 particles or clusters in wedge-shaped copper casting ingot

Wedge-shaped copper casting experiment was conducted to study the engulfment behavior of TiB2 particle and the interaction between particle or cluster and the solid/liquid front in commercial pure aluminum matrix. The experimental results show that the particle size distribution obeys two separate systems in the whole wedge-cast sample. Furthermore, it is found that the big clusters are pushed to the center of the wedge shaped sample and the single particle or small clusters consisting of few particles are engulfed into the α-Al in the area of the sample edge. The cluster degree of particles varies in different areas, and its value is 0.2 and 0.6 for the cluster fraction in the edge and in the center of the wedge sample, respectively. The cluster diameter does not obey the normal distribution but approximately obeys lognormal distribution in the present work. More importantly, in the whole sample, the particle size obeys two separate log-normal distributions.

Thermal conductivity of diamond/copper composites with a bimodal distribution of diamond particle sizes prepared by pressure infiltration method

The thermal conductivity of diamond/copper composites with bimodal particle sizes was studied. The composites were prepared through pressure infiltration of liquid copper into diamond preforms with a mixture of 40 and 100 pm-size diamonds. The permeability of the preforms with different coarse-to-fine volume ratios of diamonds was investigated. The thermal conductivity of the diamond/copper composites with bimodal size distribution was compared to the theoretical value derived from an analytical model developed by Chu. It is predicted that the diamond/copper composites could reach a higher thermal conductivity and their surface roughness could be improved by applying bimodal diamond particle sizes.

Effect of tool rotational speed on the particle distribution in friction stir welding of AA6092/17.5 SiCp-T6 composite plates and its consequences on the mechanical property of the joint

This study investigates the effect of tool rotational speed(TRS)on particle distribution in nugget zone(NZ)through quantitative approach and its consequences on the mechanical property of friction stir welded joints of AA6092/17.5 SiCp-T6 composite.6 mm thick plates are welded at a constant tool tilt angle of 2°and tool traverse speed of 1 mm/s by varying the TRS at 1000 rpm,1500 rpm and 2000 rpm with a taper pin profiled tool.Microstructure analysis shows large quantity of uniformly shaped smaller size SiC particle with lower average particle area which are homogeneously distributed in the NZ.The fragmentation of bigger size particles has been observed because of abrading action of the hard tool and resulting shearing effect and severe stress generation due to the rotation of tool.The particles occupy maximum area in the matrix compared to that of the base material(BM)due to the redistribution of broken particles as an effect of TRS.The migration of particles towards the TMAZ-NZ transition zone has been also encountered at higher TRS(2000 rpm).The microhardness analysis depicts variation in average hardness from top to bottom of the NZ,minimum for 1500 rpm and maximum for 2000 rpm.The impact strength at 1000 rpm and 1500 rpm remains close to that of BM(21.6 J)while 2000 rpm shows the accountable reduction.The maximum joint efficiency has been achieved at 1500 rpm(84%)and minimum at 1000 rpm(68%)under tensile loading.Fractographic analysis shows mixed mode of failure for BM,1000 rpm and 1500 rpm,whereas 2000 rpm shows the brittle mode of failure.

On Graphs with Same Distance Distribution

In the present paper we investigate the relationship between Wiener number W, hyper-Wiener number R, Wiener vectors WV, hyper-Wiener vectors HWV, Wiener polynomial H, hyper-Wiener polynomial HH and distance distribution DD of a (molecular) graph. It is shown that for connected graphs G and G*, the following five statements are equivalent:?;and if G and G* have same distance distribution DD then they have same W and R but the contrary is not true. Therefore, we further investigate the graphs with same distance distribution. Some construction methods for finding graphs with same distance distribution are given.

Distributions of Ratios: From Random Variables to Random Matrices

The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric positive definite random matrices, this ratio can take various forms and its distribution, and even its definition, can offer many challenges. However, for the distribution of its determinant, Meijer G-function often provides an effective analytic and computational tool, applicable at any division level, because of its reproductive property.

Code Design and Latency Analysis of Distributed Matrix Multiplication with Straggling Servers in Fading Channels

This paper exploits coding to speed up computation offloading in a multi-server mobile edge computing(MEC)network with straggling servers and channel fading.The specific task we consider is to compute the product between a user-generated input data matrix and a large-scale model matrix that is stored distributively across the multiple edge nodes.The key idea of coding is to introduce computation redundancy to improve robustness against straggling servers and to create communication redundancy to improve reliability against channel fading.We utilize the hybrid design of maximum distance separable(MDS)coding and repetition coding.Based on the hybrid coding scheme,we conduct theoretical analysis on the average task uploading time,average edge computing time,and average output downloading time,respectively and then obtain the end-to-end task execution time.Numerical results demonstrate that when the task uploading phase or the edge computing phase is the performance bottleneck,the hybrid coding reduces to MDS coding;when the downlink transmission is the bottleneck,the hybrid coding reduces to repetition coding.The hybrid coding also outperforms the entangled polynomial coding that causes higher uplink and downlink communication loads.

A METHOD OF CALCULATING PRESSURE DISTRIBUTION OF PERIODIC PULSATION FLUID TRANSPORTED IN PIPING NETWORK

The pressure pulsation induced by the pumped periodic pulsation fluid is the main factor of causing fluid resonance and stimulating pipelines vibrations and noise. In order to reduce the faults caused by the vibrations of pipelines, two aspects have been researched: one is to develop high quality filters, weaken and restrain the crest of pulsation pressure; the other is to design structural parameters of the piping network and eliminate the fluid resonance. Both need calculating the pressure pulsations of different structural parameters and frequencies, and knowing the amplitude frequency. In this paper the stiffness matrix technique is used for treating the coupling of subsystems of pipelines and calculating the pressure distribution of the piping network and it is tested by simulation and experiments.

Data-Driven Control of Distributed Event-Triggered Network Systems

The present paper deals with data-driven event-triggered control of a class of unknown discrete-time interconnected systems(a.k.a.network systems).To this end,we start by putting forth a novel distributed event-triggering transmission strategy based on periodic sampling,under which a model-based stability criterion for the closed-loop network system is derived,by leveraging a discrete-time looped-functional approach.Marrying the model-based criterion with a data-driven system representation recently developed in the literature,a purely data-driven stability criterion expressed in the form of linear matrix inequalities(LMIs)is established.Meanwhile,the data-driven stability criterion suggests a means for co-designing the event-triggering coefficient matrix and the feedback control gain matrix using only some offline collected state-input data.Finally,numerical results corroborate the efficacy of the proposed distributed data-driven event-triggered network system(ETS)in cutting off data transmissions and the co-design procedure.

In situ(α-Al_2O_3+ZrB_2)/Al composites with network distribution fabricated by reaction hot pressing

In situ（α-Al2O3+ZrB2）/Al composites with network distribution were fabricated using low-energy ball milling and reaction hot pressing. Differential thermal analysis（DTA） was used to study the reaction mechanisms in the Al–Zr O2–B system. X-ray diffraction（XRD） and scanning electron microscopy（SEM） in conjunction with energy-dispersive X-ray spectroscopy（EDX） were used to investigate the composite phases, morphology, and microstructure of the composites. The effect of matrix network size on the microstructure and mechanical properties was investigated. The results show that the optimum sintering parameters to complete reactions in the Al–Zr O2–B system are 850°C and 60 min. In situ-synthesized α-Al2O3 and Zr B2 particles are dispersed uniformly around Al particles, forming a network microstructure; the diameters of the α-Al2O3 and Zr B2 particles are approximately 1–3 μm. When the size of Al powder increases from 60–110 μm to 150–300 μm, the overall surface contact between Al powders and reactants decreases, thereby increasing the local volume fraction of reinforcements from 12% to 21%. This increase of the local volume leads to a significant increase in microhardness of the in situ（α-Al2O3–Zr B2）/Al composites from Hv 163 to Hv 251.

Biexponential distribution of open times of a toy channel model

The biexponential distributions of open times are observed in various types of ion channels. In this paper, by discussing a simple channel model, we show that there are two different schemes to understand the biexponential distribution of open times. One scheme is mathematically strict based on generator matrix theory, while the other one has a clear physical explanation according to an approximation process with numerical simulation of Markovian channel dynamics. Our comparison results suggest that even for biologically complex channels, in addition to carrying out a stochastic simulation, the strict theoretical analysis should be considered to understand the multiple exponential distributions of open times.