Matricial Structure Research Articles

Spectral enclosures for Dirac operators perturbed by rigid potentials

In this paper we are interested in generalizing Keller-type eigenvalue estimates for the non-selfadjoint Schrödinger operator to the Dirac operator, imposing some suitable rigidity conditions on the matricial structure of the potential, without necessarily requiring the smallness of its norm.

Polynomials in operator space theory: matrix ordering and algebraic aspects

We extend the $\lambda$-theory of operator spaces given by Defant and Wiesner (2014), that generalizes the notion of the projective, Haagerup and Schur tensor norm for operator spaces to matrix ordered spaces and Banach $*$-algebras. Given matrix regular operator spaces and operator systems, we introduce cones related to $\lambda$ for the algebraic tensor product that respect the matricial structure of matrix regular operator spaces and operator systems, respectively. The ideal structure of $\lambda$-tensor product of $C^*$-algebras has also been discussed.

ALMOST INVARIANT HALF-SPACES FOR OPERATORS ON HILBERT SPACE

The theory of almost invariant half-spaces for operators on Banach spaces was begun recently and is now under active development. Much less attention has been given to almost invariant half-spaces for operators on Hilbert space, where some techniques and results are available that are not present in the more general context of Banach spaces. In this note, we begin such a study. Our much simpler and shorter proofs of the main theorems have important consequences for the matricial structure of arbitrary operators on Hilbert space.

EXPLOITING THE VERSATILITY OF CHOLESTEROL IN NANOPARTICLES FORMULATION

The biocompatibility of polymers, lipids and surfactants used to formulate is crucial for the safe and sustainable development of nanocarriers (nanoparticles, liposomes, micelles, and other nanocarriers). In this study, Cholesterol (Chol), a typical biocompatible component of liposomal systems, was formulated in Chol-based solid nanoparticles (NPs) stabilized by the action of surfactant and without the help of any other formulative component. Parameters as type (Solutol HS 15, cholic acid sodium salt, poly vinyl alcohol and Pluronic-F68), concentration (0.2; 0.5 and 1% w/v) of surfactant and working temperature (r.t. and 45°C) were optimized and all samples characterized in terms of size, zeta potential, composition, thermal behavior and structure. Results demonstrated that only Pluronic-F68 (0.5% w/v) favors the organization of Chol chains in structured NPs with mean diameter less than 400nm. Moreover, we demonstrated the pivotal role of working temperature on surfactant aggregation state/architecture/stability of Chol-based nanoparticles. At room temperature, Pluronic-F68 exists in solution as individual coils. In this condition, nanoprecipitation of Chol formed the less stable NPs with a 14±3% (w/w) of Pluronic-F68 prevalently on surface (NP-Chol/0.5). On the contrary, working near the critical micelle temperature (CMT) of surfactant (45°C), Chol precipitates with Pluronic-F68 (9±5% w/w) in a compact stable matricial structure (NP-Chol/0.5-45). In vitro studies highlight the low toxicity and the affinity of NP-Chol/0.5-45 for neuronal cells suggesting their potential applicability in pathologies with a demonstrated alteration of neuronal plasticity and synaptic communication (i.e. Huntington⿿s disease).

Icarus ignored: Riffaterre and Eagleton on Auden’s Musée des Beaux Arts

AbstractIn his 2007 book dealing with poetry in English, Terry Eagleton sacrifices integrity on the altar of the popularizing impulse. His partial analysis of an Auden poem also treated by Michael Riffaterre reveals the advantages of a semiotic approach, which can show how images on the textual surface signify indirectly by pointing to an underlying matricial structure. The author’s expanded version of Riffaterrian theory accounts for the added complexity conferred by two matrices, each founded on a proposition. In sum, Eagleton’s employment of a traditional “lit-crit” approach – with its prose-based preoccupation with surface details – fails to identify the semiotic structure of the poem as a signifying totality.

Non-Commutative Resistance Networks

In the setting of finite-dimensional $C^*$-algebras ${\mathcal A}$ we define what we call a Riemannian metric for ${\mathcal A}$, which when ${\mathcal A}$ is commutative is very closely related to a finite resistance network. We explore the relationship with Dirichlet forms and corresponding seminorms that are Markov and Leibniz, with corresponding matricial structure and metric on the state space. We also examine associated Laplace and Dirac operators, quotient energy seminorms, resistance distance, and the relationship with standard deviation.

Tensorial Function Theory: From Berezin Transforms to Taylor’s Taylor Series and Back

Let H ∞(E) be the Hardy algebra of a W*-correspondence E over a W*-algebra M. Then the ultraweakly continuous completely contractive representations of H ∞(E) are parametrized by certain sets $${{\mathcal{AC}}(\sigma)}$$ indexed by NRep(M)—the normal *-representations σ of M. Each set $${{\mathcal{AC}}(\sigma)}$$ has analytic structure, and each element $${F \in H^{\infty}(E)}$$ gives rise to an analytic operator-valued function $${\widehat{F}_{\sigma}}$$ on $${{\mathcal{AC}}(\sigma)}$$ that we call the σ-Berezin transform of F. The sets $${\{{\mathcal{AC}}(\sigma)\}_{\sigma\in\Sigma}}$$ and the family of functions $${\{\widehat{F}_{\sigma}\}_{\sigma\in\Sigma}}$$ exhibit “matricial structure” that was introduced by Joeseph Taylor in his work on noncommutative spectral theory in the early 1970s. Such structure has been exploited more recently in other areas of free analysis and in the theory of linear matrix inequalities. Our objective here is to determine the extent to which the matricial structure characterizes the Berezin transforms.

Security constrained optimal active power flow via network model and interior point method

This paper presents a new formulation for the security constrained optimal active power flow problem which enables the representation of three basic constraints: branch outage, generator outage and multiple equipment congestion. It consists of a network model with additional linear equality and inequality constraints and quadratic separable objective function, which is efficiently solved by a predictor-corrector interior point method. Sparsity techniques are used to exploit the matricial structure of the problem.Case studies with a 3,535-bus and a 4,238-branch Brazilian power system are presented and discussed, to demonstrate that the proposed model can be efficiently solved by an interior point method, providing security constrained solutions in a reasonable time.

GAPS BETWEEN CLASSES OF MATRIX MONOTONE FUNCTIONS

We prove the existence of gaps between all the different classes of matrix monotone functions defined on an interval, provided the interval is non trivial and different from the whole real line. We then show how matrix monotone functions may be used in the characterization of certain C*-algebras as an alternative to the study of the matricial structure by positive linear maps.

Semiclassical resolvent estimates for Schrödinger matrix operators with eigenvalues crossing

AbstractFor semiclassical Schrödinger 2×2–matrix operators, the symbol of which has crossing eigenvalues, we investigate the semiclassical Mourre theory to derive bounds O(h−1) (h being the semiclassical parameter) for the boundary values of the resolvent, viewed as bounded operator on weighted spaces. Under the non–trapping condition on the eigenvalues of the symbol and under a condition on its matricial structure, we obtain the desired bounds for codimension one crossings. For codimension two crossings, we show that a geometrical condition at the crossing must hold to get the existence of a global escape function, required by the usual semiclassical Mourre theory.

<b>O reflexo da mudança organizacional sobre o desempenho de uma empresa de autopeças: um estudo de caso</b>

Many researchers have developed some studies in the area of change organizational structure. But, there are some questions about this subject. On this way, this article aimed to get a case study about the consequence of organizational change on the performance of a manufacturing industry that was functional and now it has a matricial structure. The industry was broken down in five mini factories with base on its line product and each mini factory is management by a boss with a multiskil group. The firm was evaluated on two aspects: management human resource and quality process. The results show that the quality of products and the organizational enviroment improved. Keywords: organizational framework, human resource, quality.

Finite element formulation for Maxwell's equations with space dependent electric properties

ABSTRACT The Time Domain Reflectometry—TDR- probe is a new technique applied to moisture measurement. It is a wave guide constituted by two or three parallel metallic rods stuck in the ground. An electromagnetic wave propagates all along the wave guide and crosses a variable electric properties medium. In that way the reflecting wave is disrupted and we detect the electric singularities. We study the transverse magneti- mode. We simulate this wave guide in this medium thanks to the Finite Element Method and present the used matricial structure. For time integration we compare a semi-implicit or Runge-Kutta method with variable time-step. This process is driven by the Automatic Multigrid System with an unknown time-dependent number.

Linear Analysis of Quadrature Domains, III

The linear data of a quadrature domain, introduced in the first paper in this series, is further investigated. The matricial structure of all hyponormal operators with finite rank self-commutators, which is inductively constructed from such linear data, is discussed. In particular, a conservation law (of a determinantal function) in the iterative process of defining these matrices is exploited. The spectrum of the determining left upper corner of some of these operators is analyzed in connection with the existence of generalized quadrature formulas on planar domains.

An immunohistochemical study of the apocrine type of cutaneous mixed tumors with special reference to their follicular and sebaceous differentiation.

An immunohistochemical analysis of 8 cases of the apocrine type of cutaneous mixed tumor is reported. Histologically, 7 cases of the tumor were suggested to have follicular and/or sebaceous differentiation. Carcinoembryonic antigen (CEA), epithelial membrane antigen and gross cystic disease fluid protein-15 were present in the inner surface and/or in the luminal cell bodies of the tubular structures. CEA and non-specific cross-reacting antigen were also detected in the keratinous cysts. Positive reactions for S-100 protein and vimentin were observed in the solid nests, the outer layer of the tubular structures and some stromal cells. However, smooth muscle actin was only focally expressed in the outer cells of the tubular nests in one case. Involucrin was positive in the inner layers of the keratinous cysts. Various staining patterns were observed in the keratin immunohistochemistry. The solid nests showed heterogeneous expressions of CK1/5/10/14, CK7, CK10/11, CK14, CK8/18 and CK19. The inner cells of the tubular structures were constantly positive for CK7, CK8/18 and CK19, and heterogeneously for CK1/5/10/14, CK10/11 and CK14. The outer cells were heterogeneously positive for CK1/5/10/14 and CK14. The keratinous cysts showed positive reactions for CK1/5/10/14 throughout the whole cell layers, and for CK14 in the basal layer. The inner layers in some keratinous cysts expressed CK6, CK10/11 and CK17, but only CK10 in others. CK13 was positively stained in the transitional portion between the matricial structure and the column of shadow cells in the cyst wall in only one case. When compared with the immunohistochemistry of the normal skin, the apocrine type of cutaneous mixed tumor can show various immunophenotypical patterns similar to those of entire structures of hair follicles, sebaceous glands and all components of apocrine glands, that is to say, the folliculosebaceous-apocrine unit.

Matrix Regular Operator Spaces

The concept of the regular (or Riesz) norm on ordered real Banach spaces is generalized to matrix ordered complex operator spaces in a way that respects the matricial structure of the operator space. A norm on an ordered real Banach spaceEis regular if: (1) −x⩽y⩽ximplies that ‖y‖⩽‖x‖; and (2) ‖y‖<1 implies the existence ofx∈Esuch that ‖x‖<1 and −x⩽y⩽x. A matrix ordered operator space is called matrix regular if, at each matrix level, the restriction of the norm to the self-adjoint elements is a regular norm. In such a space, elements at each matrix level can be written as linear combinations of four positive elements. The concept of the matrix ordered operator space is made specific in such a way as to be a natural generalization of ordered real and complex Banach spaces. For the case whereVis a matrix ordered operator space, a natural cone is defined on the operator spaceX*⊗hV⊗hX, with ⊗hindicating the Haagerup tensor product, so as to make it a matrix ordered operator space. Exploiting the advantages gained by takingXto be the column Hilbert spaceHc, an equivalence is established between the matrix regularity of a space and that of its operator dual. This concept of matrix regularity also provides for more accessible proofs of the Christensen–Sinclair Multilinear Representation and Multilinear Decomposition theorems.

A characterization of operator algebras

An operator algebra is a uniformly closed algebra of bounded operators on a Hilbert space. In this paper we give a characterization of unital operator algebras in terms of their matricial norm structure. More precisely if A is an L ∞-matricially normed space and also an algebra with a completely contractive multiplication and an identity of norm 1, then there is a completely isometric isomorphism of A onto a unital operator algebra. Indeed the multiplication on A need not be assumed to be associative for this conclusion to follow. Examples are given to show that the condition on the identity is necessary. It follows from the above that the quotient of an operator algebra by a closed two-sided ideal (with the natural matricial structure) is again an operator algebra up to complete isometric isomorphism.

Studies on chromatin organization in a nucleolus without fibrillar centres

In embryonic cell-line derivative KCo of Drosophila melanogaster, the nucleolus, like most nucleoli, contains a small proportion of ribosomal DNA (1-2% of the total nucleolar DNA). The ribosomal DNA is virtually the only active gene set in the nucleolus and is found among long stretches of inactive supercoiled heterochromatic segments. We have demonstrated by use of a Feulgen-like ammine-osmium staining procedure that, depending on the state of growth, more or less fibres of decondensed DNA emanating from the intra-nucleolar chromatin (which is in continuity with the nucleolus-associated chromatin) ramify and unravel within the central nucleolar core to be transcribed. The nucleolus expands or contracts with the variation of activity and could belong to a supramolecular matricial structure such as is shown after extraction of the nuclei. After a long period of exposure to high doses of actinomycin D, the central nucleolar core became an homogeneous fibrous structure that could be interpreted as an aggregate of protein skeletal elements. The mechanism of repression and derepression of the nucleolar chromatin could thus be explained by a mechanism involving in part a sub-nucleolar structure. We propose a schematic organization of the nucleolar chromatin in KCo cells of Drosophila and discuss it in relation with other nucleolar organizations.

Separable Functions and the Generalization of Matricial Structure

Separable Functions and the Generalization of Matricial Structure

Separable Functions and the Generalization of Matricial Structure

Separable Functions and the Generalization of Matricial Structure