Search results for "Matrix"
showing 10 items of 3205 documents
Single Molecules Probing the Freezing of Polymer Melts: A Molecular Dynamics Study for Various Molecule-Chain Linkages
2010
8 pages; International audience; We present molecular dynamics simulations of coarse-grained model systems of a glassforming polymer matrix containing fluorescent probe molecules. These probe molecules are either dispersed in the matrix or covalently attached to the center or the end of a dilute fraction of the polymer chains. We show that in all cases the translational and rotational relaxation of the probe molecules is a faithful sensor for the glass transition of the matrix as determined from a mode-coupling analysis or Vogel-Fulcher analysis of their R-relaxation behavior. Matrix and dumbbell related relaxation processes show a clear violation of the Stokes-Einstein-Debye laws. In accor…
Encapsulation of aroma compounds in biopolymeric emulsion based edible films to control flavour release
2010
Abstract Flavour loss strongly affects food quality. In order to decrease flavour changes during food conservation, different strategies could be used. Aroma compound encapsulation allows the protection of food flavour from loss and degradative reactions, like oxidation. Edible films could be an encapsulation matrix: in the case of emulsified film, lipid globules incorporated can act as carriers of active molecules, such as aroma compounds. Edible films prepared from ι-carrageenans are interesting for good mechanical and gas barrier properties. The aim of this study was to encapsulate different aroma compounds in an ι-carrageenan emulsion based edible film. Release of ten aroma compounds wa…
Aroma behaviour during steam cooking within a potato starch-based model matrix.
2012
To help understand the organoleptic qualities of steam cooked foods, the kinetics of aroma release during cooking in a potato starch based model matrix was studied. Behaviour of components having a major impact in potato flavour were studied using solid phase micro extraction-gas chromatography (SPME-GC). Evolution of microstructure of potato starch model-matrix during steam cooking process was analyzed using environmental scanning electron microscopy (ESEM). Both aroma compounds that are naturally present in starch matrix and those that were added were analyzed. Both the aroma compounds naturally presented and those added had different behaviour depending on their physico-chemical properti…
Defining relations of the noncommutative trace algebra of two 3×3 matrices
2006
The noncommutative (or mixed) trace algebra $T_{nd}$ is generated by $d$ generic $n\times n$ matrices and by the algebra $C_{nd}$ generated by all traces of products of generic matrices, $n,d\geq 2$. It is known that over a field of characteristic 0 this algebra is a finitely generated free module over a polynomial subalgebra $S$ of the center $C_{nd}$. For $n=3$ and $d=2$ we have found explicitly such a subalgebra $S$ and a set of free generators of the $S$-module $T_{32}$. We give also a set of defining relations of $T_{32}$ as an algebra and a Groebner basis of the corresponding ideal. The proofs are based on easy computer calculations with standard functions of Maple, the explicit prese…
The Lie algebra of polynomial vector fields and the Jacobian conjecture
1998
The Jacobian conjecture for polynomial maps ϕ:Kn→Kn is shown to be equivalent to a certain Lie algebra theoretic property of the Lie algebra\(\mathbb{D}\) of formal vector fields inn variables. To be precise, let\(\mathbb{D}_0 \) be the unique subalgebra of codimensionn (consisting of the singular vector fields),H a Cartan subalgebra of\(\mathbb{D}_0 \),Hλ the root spaces corresponding to linear forms λ onH and\(A = \oplus _{\lambda \in {\rm H}^ * } H_\lambda \). Then every polynomial map ϕ:Kn→Kn with invertible Jacobian matrix is an automorphism if and only if every automorphism Φ of\(\mathbb{D}\) with Φ(A)\( \subseteq A\) satisfies Φ(A)=A.
Polynomial Fuzzy Models for Nonlinear Control: A Taylor Series Approach
2009
Classical Takagi-Sugeno (T-S) fuzzy models are formed by convex combinations of linear consequent local models. Such fuzzy models can be obtained from nonlinear first-principle equations by the well-known sector-nonlinearity modeling technique. This paper extends the sector-nonlinearity approach to the polynomial case. This way, generalized polynomial fuzzy models are obtained. The new class of models is polynomial, both in the membership functions and in the consequent models. Importantly, T-S models become a particular case of the proposed technique. Recent possibilities for stability analysis and controller synthesis are also discussed. A set of examples shows that polynomial modeling is…
Matrix algebras with degenerate traces and trace identities
2022
In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of a degenerate trace, all its trace identities follow by the commutativity law and by pure trace identities. Moreover we relate the trace identities of $D_{n+1}$ endowed with a degenerate trace, to those of $D_n$ with the corresponding trace. This allows us to determine the generators of the trace T-ideal of $D_3$. In the second part we study commutative subalgebras of $M_k(F)$, denoted by $C_k$ of the type $F + J$ that can be endowed with the so-called st…
New background correction approach based on polynomial regressions for on-line liquid chromatography-Fourier transform infrared spectrometry.
2008
Abstract In the present study a new approach for the chemometric background correction in on-line gradient LC–FTIR is introduced. For this purpose, the spectral changes of the elution mixture during gradient elution were analyzed applying 2D correlation spectroscopy. The fundamentals of the new background correction algorithm, based on polynomial fits calculated from a reference spectra matrix (Polyfit-RSM method) are explained. The Polyfit-RSM approach was applied on blank gradient runs as well as on LC–FTIR data obtained from the injection of a soft drink sample using acetonitrile:water as eluent. Results found were critically assessed and compared to those obtained by two previous backgr…
New Results in Generalized Minimum Variance Control of Computer Networks
2014
In this paper new results in adaptive (generalized) minimum variance control of packet switching computer networks are presented. New solutions, corresponding to the new inverses of the nonsquare polynomial matrices, can be used for design of robust control of multivariable systems with different number of inputs and outputs. Application of polynomial matrix inverses with arbitrary degrees of freedom creates the possibilities to optimal control of computer networks in terms of usage their maximal bandwidth. Simulation examples made in Matlab environment show big potential of presented approach. DOI: http://dx.doi.org/10.5755/j01.itc.43.3.6268
A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering
2021
<p style='text-indent:20px;'>Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Beside…