A variety of results pertaining to the elastostatic transfer **matrix** **analysis** of repetitive structures has been presented. Results previously known relate to the reciprocal eigenvalue properties as a consequence of the symplectic nature of the transfer **matrix**, bi- and symplectic orthogonality and the impossibility of complex unity eigenvalues for prismatic repetitive structures. Multiple unity eigenvalues are a particular feature of the elastostatic eigenanalysis, and the Moore–Penrose pseudo-inverse is introduced as a rational approach to the computation of principal vectors. It is shown that only the eigenvalues l Z G 1 can give rise to a non-trivial JCF, at least for the prismatic structure. An example of a structure for which the transfer **matrix** has repeating negative unity eigenvalue is one possessing a scissor-like mechanism. A planar structure, previously treated as pin-jointed, is reconsidered as rigid-jointed; the additional rotational nodal degrees of freedom give rise to new Saint-Venant decay modes—the number of transmission modes associated with unity eigenvalues is ﬁxed—while the equivalent continuum properties are practically unaffected. This is in accord with the practice of treating real, rigid-jointed structures as pin-jointed, at least for small deﬂection elastic **analysis**. Symmetry implies restriction: a variety of relationships between partitions of both the stiffness and transfer matrices of a cell possessing left-to- right symmetry are derived; in contrast, one has splitting of unity eigenvalues for a tapered cell that lacks translational symmetry. The present elastostatic results may be seen as complementary to Langley’s (1996) **analysis** of wave motion energetics using transfer matrices.

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The objectives of this thesis are developing machine learning algorithms for clustering, classification and compression, emphasis on nonnegative **matrix** factorization (NMF). Nonnegative **matrix** factorization (NMF) has becoming an increasingly popular data processing tool these years, widely used by various communities including computer vision, text mining and bioinformatics. It is able to approximate each data sample in a data collection by a linear combination of a set of nonnegative basis vectors weighted by nonnegative weights. This often enables meaningful interpretation of the data, mo- tivates useful insights and facilitates tasks such as data compression, clustering and classification. These subsequently lead to various active roles of NMF in data analy- sis, e.g., dimensionality reduction tool [11, 75], clustering tool[94, 82, 13, 39], feature engine [40], source separation tool [38], etc. In this research work, the NMF algorithm is explored, emphasis being laid on the topic of the initialization methods as well as the optimization rule for NMF, to solve some data **analysis** problems. We propose two initialization methods for NMF based on the clustering algorithm and dimensionality reduction algorithm. We also propose two NMF updating strategies, which take ad- vantage of the hybrid of different NMF initialization setups and evolves along different directions to produce NMF approximations that suits better the accuracy purposes (i.e. data clustering/classification and compression). Effectiveness of the proposed methods is demonstrated thoroughly through benchmark testing and comparison with existing approaches.

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Problems in structural **analysis** can be solved using **matrix** algebra by two methods. The force, or flexibility method takes forces and moments as unknowns. It is generally better suited for investiga tion of complex aircraft and shell structures. The strain energy method is an example of the force method. The displacement, or stiffness method considers linear and angular displacements as unknowns. This method is especially suited for the **analysis** of structural frameworks. An example is the slope deflection method.

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The provision of a transparently healthy and balanced nutrition, with consumers being fully informed of what has been supplied, is one of the main objectives to be achieved for a sustainable food chain. In the case of SMZ PDO our **analysis** confirms that the product adequately responds in terms of safety. The food chain benefits from traceability throughout the product cycle, from the farm to the packaging stage. This is possible mainly due to the industry’s small size, but which is still able to supply 3 million units of canned products sold annually in 2009.

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The substructure **analysis** using the stiffness **matrix** method includes an initial **analysis** of each substructure separately, in which the movement of the nodes that share a common boundary with an adjacent substructure is fixed; these boundaries are then relaxed simultaneously and their actual boundary displacements are determined from the equation of equilibrium of forces, and each substructure is analyzed separately, taking into account the specified displacements and loading [2]. The size of the matrixes found through the substructure **analysis** for each part, are usually of lower order than the entire structure **matrix**; hence, the determination of the displacements of the common nodes implies a less amount of unknown variables [1]-[10].

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Permanent WRAP url: http://wrap.warwick.ac.uk/61393 Copyright and reuse: The Warwick Research Archive Portal WRAP makes this work by researchers of the University of Warwick available op[r]

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For this project, a new design of cast MMC automotive wheel using aluminium A356 as binding material (**matrix**) and Silicon Carbide particles (reinforcement) will be developed and **analysis** will be conducted on the product using simulation of CAD tools. The simulated **analysis** results will be compared with the experimental results obtained from the previous studies.

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2.1b The tensile strength Rm of composite materials on an Al-4.5% Cu-1.5% 8 Mg **matrix** reinforced with SiC dispersion particles of 10.7mm diameter 2.2 Components in low pressure die casting process 15 2.3 Microstructure of cast A356 wheel with reference to the different 16

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The paper developed a new realized **matrix**-exponential GARCH (MEGARCH) model, which is an extension of univariate realized exponential GARCH model of Hansen and Huang (2016). We considered the Bayesian MCMC estimation technique, which gives non-normal posterior distribu- tions. Using returns and realized measures of the co-volatility **matrix** for three stocks traded on NYSE, we found that the realized MEGARCH models outperformed the BEKK and MEGARCH models for in-sample and out-of-sample performance. The news impact curves based on the pos- terior densities presented reasonable results.

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undertaken as previously described (20) but with the addition of a top-up of a further 2 ! g after 3 h. LC-MS/MS **analysis** was performed using nanoAcquityTM ultraperformance LC (Waters, Manchester, UK) on-line to an LTQ-Orbitrap Velos mass spectrometer (Thermo-Fisher Scientific, Hemel Hemp- stead) as previously described (20) via an electrospray ioniza- tion ion source containing a 10- ! m coated Pico-tip emitter (Presearch LTD, Basingstoke, UK). Aliquots of tryptic peptides equivalent to 300 ng of tendon fascicle protein were loaded onto a 180- ! m % 20-mm C18 trap column (Waters) at 5 ! l/min in 99% solvent A (water plus 0.1% formic acid) and 1% solvent B (acetonitrile plus 1% formic acid) for 5 min and sub- sequently back-flushed onto a C18 pre-equilibrated analytical column (75- ! m % 15-mm Waters) using a flow rate of 0.3 ! l/min. Xcalibur 2.0 software (Thermo-Electron, Hemel Hempstead, UK) was used to operate the LTQ-Orbitrap Velos mass spectrometer in data-dependant acquisition mode. The survey scan was acquired in the Orbitrap with a resolving power set to 30,000 (at 400 m/z). MS/MS spectra were concurrently acquired on the 20 most intense ions from the high resolution survey scan in the LTQ mass spectrometer. Charge state filter- ing & 1 was used where unassigned precursor ions were not selected for fragmentation. Fragmentation parameters in the LTQ mass spectrometer were: normalized collision energy, 30; activation, 0.250; activation time, 10 ms; minimum signal threshold, 500 counts with isolation width 2 m/z.

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• Spectral clustering approaches that generalize the eigendecomposition from single to multiple Lapla- cian matrices representing network layers. One of the state-of-the-art spectral clustering methods for multi- plex graphs is the Spectral Clustering on Multi-Layer (SC-ML) [18]. First, for each network layer, SC-ML computes a subspace spanned by the principal eigen- vectors of its Laplacian **matrix**. Then, by interpreting each subspace as a point on Grassmann manifold, SC-ML merges subspaces into a consensus subspace from which the composite clusters are extracted. The biggest drawback of this methods is the underlying spectral clustering, that always finds tight and small- scale and, in some cases, almost trivial communities. For example, SC-ML cannot adequately handle net- work layers with missing or weak connections, or layers that have disconnected parts.

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Background and aims: Potentially involved proteins which are implicated as a specific target for any diseased condition may implicate certain unusual features in several pathological conditions. Human **Matrix** metalloproteinase (MMP) family of endopeptidases is one such family responsible for many beneficial as well as several pathological critical diseases. With the advent of field of bioinformatics and computational efforts can aid researchers to comprehend their system of work. Methodology: An insilico characterization of the MMP family has been carried out to analyze their primary, secondary, structural and functional perspective . The research has been focused on specific MMPs in which the further study was based on Mutational **analysis** confirming the pathogenicity of MMPs in cancer metastasis. The basic approach was to screen large protein families which plays dual role during normal and diseased conditions. Results: Thus it is hypothesized that cysteine rich and highly thermostable MMPs might be key players in diseased conditions. Conclusion: It can also be concluded that the disease responsive MMPs might be considered as promising targets for treatment of cancer.

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Recently, variational Bayesian (VB) techniques have been applied to probabilistic **matrix** factor- ization and shown to perform very well in experiments. In this paper, we theoretically elucidate properties of the VB **matrix** factorization (VBMF) method. Through finite-sample **analysis** of the VBMF estimator, we show that two types of shrinkage factors exist in the VBMF estimator: the positive-part James-Stein (PJS) shrinkage and the trace-norm shrinkage, both acting on each sin- gular component separately for producing low-rank solutions. The trace-norm shrinkage is simply induced by non-flat prior information, similarly to the maximum a posteriori (MAP) approach. Thus, no trace-norm shrinkage remains when priors are non-informative. On the other hand, we show a counter-intuitive fact that the PJS shrinkage factor is kept activated even with flat priors. This is shown to be induced by the non-identifiability of the **matrix** factorization model, that is, the mapping between the target **matrix** and factorized matrices is not one-to-one. We call this model-induced regularization. We further extend our **analysis** to empirical Bayes scenarios where hyperparameters are also learned based on the VB free energy. Throughout the paper, we assume no missing entry in the observed **matrix**, and therefore collaborative filtering is out of scope.

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Reinforcements such as Graphite and Boron Carbide were preheated at a specified temperature 30 min in order to remove moisture or any other gases present within reinforcement. The preheating of also promotes the wetability of reinforcement with **matrix**. Reinforcements are added as 5% and 10% composition with Aluminium 2024. The Preheating of Reinforcements in furnace is shown below.

MMC materials have a combination of different superior properties to an unreinforced **matrix** which are; increased strength, higher elastic modulus, higher service temperature, improved wear resistance, high electrical and thermal conductivity, low coefficient of thermal expansion and high vacuum environmental resistance. These properties can be attained with the proper choice of **matrix** and reinforcement. The **matrix** can be selected on the basis of oxidation and corrosion resistance or other properties. Generally Al, Ti, Mg, Ni, Cu, Pb, Fe, Ag, Zn, Sn and Si are used as the **matrix** material, but Al, Ti, Mg are used widely. Now a day’s researchers all over the world are focusing mainly on aluminum because of its unique combination of good corrosion resistance, low density and excellent mechanical properties. The unique thermal properties of aluminum composites such as metallic conductivity with coefficient of expansion that can be tailored down to zero.

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Excess amount of potassium permanganate has often been used in-situ for chemical oxidation of contaminated sites. The consequences are not limited to secondary contamination and cost but also inefficient remediation. Encapsulation of permanganate using PMMA enables controlled dissolution of the oxidant and aids long-term processes. This paper focuses on the oxidant release efficiency from polymer **matrix** and **analysis** of data using existing models for glassy polymers. The efficiency profile obtained using mass ratios of 2:1, 4:1, and 8:1 of PMMA to KMnO 4 showed a

Learning word representations to capture the semantics and compositionality of language has received much research interest in natu- ral language processing. Beyond the popu- lar vector space models, **matrix** representations for words have been proposed, since then, ma- trix multiplication can serve as natural com- position operation. In this work, we investi- gate the problem of learning **matrix** representa- tions of words. We present a learning approach for compositional **matrix**-space models for the task of sentiment **analysis**. We show that our approach, which learns the matrices gradually in two steps, outperforms other approaches and a gradient-descent baseline in terms of quality and computational cost.

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Random glass fibre reinforced (33%) LDPE was selected because there were successful cases of welding the composite with high density polyethylene (HDPE) as **matrix** using microwave energy and it was believed that LDPE will couple better to microwaves as its cyrstallinity is lower than the HPDE (Wu and Benatar, 1992; NRC, 1994; Ku et al., 1997a; 1997b). The composite is not readily available in the market and it was specially manufactured in Plastic and Rubber Technical Education Centre (PARTEC) in Brisbane, Australia. The length of the reinforcing fibre was 6 mm or less and the test pieces were injection-moulded to shape. However, typical lengths of fibres used in reinforced injection moulding materials were 0.8 to 25 mm (Strong, 1989).

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In this paper design a **matrix** converter which is a AC- AC power converter which is composed of an array of mxn bidirectionalsemiconductor switches, connecting each phase of the input to each phase of the output using venturini and space vector method which provides sinusoidal input and output waveforms, with minimal higher order harmonics and no sub harmonics. The output is tested for different load condition.

In Mongolia, planting and harvesting sea buckthorn is a new way of farming, contrasting with the traditional way of simply harvesting the berries from the wild. Sea buck- thorn farming benefits the environment by combatting deser- tification and it generates income for poor rural households. However, the methodology used lacks an in-debt **analysis** of externalities of sea buckthorn production, which merits fu- ture research. Our data, nevertheless indicate that the private competitiveness level was lower than the social one. This may have been a ff ected by the assumption of using SCF to estimate social output and input prices.

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