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Search Results: 1 - 10 of 170 matches for " PP Ntumba "
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Pairings of Sheaves of $\mathcal{A}$-Modules through Bilinear $\mathcal{A}$-Morphisms
A. Mallios,PP Ntumba
Mathematics , 2008,
Abstract: It is proved that for any free $\mathcal{A}$-modules $\mathcal{F}$ and $\mathcal{E}$ of finite rank on some $\mathbb{C}$-algebraized space $(X, \mathcal{A})$ a \textit{degenerate} bilinear $\mathcal{A}$-morphism $\Phi: \mathcal{F}\times \mathcal{E}\longrightarrow \mathcal{A}$ induces a \textit{non-degenerate} bilinear $\mathcal{A}$-morphism $\bar{\Phi}: \mathcal{F}/\mathcal{E}^\perp\times \mathcal{E}/\mathcal{F}^\perp\longrightarrow \mathcal{A}$, where $\mathcal{E}^\perp$ and $\mathcal{F}^\perp$ are the \textit{orthogonal} sub-$\mathcal{A}$-modules associated with $\mathcal{E}$ and $\mathcal{F}$, respectively. This result generalizes the finite case of the classical result, which states that given two vector spaces $W$ and $V$, paired into a field $k$, the induced vector spaces $W/V^\perp$ and $V/W^\perp$ have the same dimension. Some related results are discussed as well.
Abstract Geometric Algebra. Orthogonal and Symplectic Geometries
PP Ntumba,Ac Orioha
Mathematics , 2008,
Abstract: Our main interest in this paper is chiefly concerned with the conditions characterizing \textit{orthogonal and symplectic abstract differential geometries}. A detailed account about the sheaf-theoretic version of the \textit{symplectic Gram-Schmidt theorem} and of the \textit{Witt's theorem} is also given.
Cofibrations in the Category of Frolicher Spaces. Part I
B. Dugmore,PP. Ntumba
Mathematics , 2007,
Abstract: Cofibrations are defined in the category of Fr\"olicher spaces by weakening the analog of the classical definition to enable smooth homotopy extensions to be more easily constructed, using flattened unit intervals. We later relate smooth cofibrations to smooth neighborhood deformation retracts. The notion of smooth neighborhood deformation retract gives rise to an analogous result that a closed Fr\"olicher subspace $A$ of the Fr\"olicher space $X$ is a smooth neighborhood deformation retract of $X$ if and only if the inclusion $i: A\hookrightarrow X$ comes from a certain subclass of cofibrations. As an application we construct the right Puppe sequence.
On the endomorphisms of some sheaves of functions
Patrice P. Ntumba
Mathematics , 2013,
Abstract: Given a $C^\infty$ real manifold $X$ and $\mathcal{C}^m_X$ its sheaf of $m$-times differentiable real-valued functions, we prove that the sheaf $\mathcal{D}^{m, r}_X$ of differential operators of order $\leq m$ with coefficient functions of class $C^r$ can be obtained in terms of the sheaf $\mathcal{H}om_{\mathbb{R}_X}(\mathcal{C}^m_X, \mathcal{C}^r_X)$ of morphisms of $\mathcal{C}^m_X$ into $\mathcal{C}^r_X$. The superscripts $m$ and $r$ are integers.
On $\mathcal A$-Transvections and Symplectic $\mathcal A$-Modules
Patrice P. Ntumba
Mathematics , 2009,
Abstract: In this paper, building on prior joint work by Mallios and Ntumba, we show that $\mathcal A$-\textit{transvections} and \textit{singular symplectic }$\mathcal A$-\textit{automorphisms} of symplectic $\mathcal A$-modules of finite rank have properties similar to the ones enjoyed by their classical counterparts. The characterization of singular symplectic $\mathcal A$-automorphisms of symplectic $\mathcal A$-modules of finite rank is grounded on a newly introduced class of pairings of $\mathcal A$-modules: the \textit{orthogonally convenient pairings.} We also show that, given a symplectic $\mathcal A$-module $\mathcal E$ of finite rank, with $\mathcal A$ a \textit{PID-algebra sheaf}, any injective $\mathcal A$-morphism of a \textit{Lagrangian sub-$\mathcal A$-module} $\mathcal F$ of $\mathcal E$ into $\mathcal E$ may be extended to an $\mathcal A$-symplectomorphism of $\mathcal E$ such that its restriction on $\mathcal F$ equals the identity of $\mathcal F$. This result also holds in the more general case whereby the underlying free $\mathcal A$-module $\mathcal E$ is equipped with two symplectic $\mathcal A$-structures $\omega_0$ and $\omega_1$, but with $\mathcal F$ being Lagrangian with respect to both $\omega_0$ and $\omega_1$. The latter is the analog of the classical \textit{Witt's theorem} for symplectic $\mathcal A$-modules of finite rank.
IKKbeta and p53 as therapeutic targets for arthritis
PP Tak
Arthritis Research & Therapy , 2001, DOI: 10.1186/ar335
Abstract: NF-κB activation is another factor involved in the persistent activation of synovial cells and impaired apoptosis. IκB kinase β (IKKβ) is a key regulator of NF-κB. We observed the development of arthritis after intra-articular adenoviral gene transfer of IKKβ-wt into the joints of normal rats. Increased IKK activity was detectable in the Ad.IKKβ-wt injected ankle joints, coincident with enhanced NF-κB binding activity. Conversely, intra-articular gene transfer of Ad.IKKβ-dn significantly ameliorated the severity of adjuvant arthritis in Lewis rats. This effect was accompanied by a significant decrease in levels of NF-κB binding activity. Targeting IKK activity may represent a valid new strategy for the treatment of RA.
Die vrou wysheid, God, en ekobillikheid: Liggaamsideologie in Spreuke 8:1–9:18
PP Venter
HTS Theological Studies/Teologiese Studies , 2009,
Abstract: The woman Wisdom, God, and ecojustice: Ideology of the body in Proverbs 8:1–9:18 This article examines the ideology of the body, specifi cally in terms of the gender of Wisdom and God, from an ecojustice perspective. Femininity within a God construct could contribute to a value system that incorporates compassion, interrelatedness and mutual care. In Proverbs 8:1–9:18, however, the woman Wisdom does not represent an ecofriendly construct, but simply enhances and supports the patriarchal, masculine values incorporated in the God Yahweh.
Fundamentals for Symplectic $\mathcal{A}$-modules
Anastasios Mallios,Patrice P. Ntumba
Mathematics , 2007,
Abstract: Sheaf theoretically based Abstract Differential Geometry incorporates and generalizes all the classical differential geometry. Here, we undertake to partially explore the implications of Abstract Differential Geometry to classical symplectic geometry. The full investigation will be presented elsewhere.
Symplectic Reduction of Sheaves of $\mathcal{A}$-modules
A. Mallios,P. P. Ntumba
Mathematics , 2008,
Abstract: Given an arbitrary sheaf $\mathcal{E}$ of $\mathcal{A}$-modules (or $\mathcal{A}$-module in short) on a topological space $X$, we define \textit{annihilator sheaves} of sub-$\mathcal{A}$-modules of $\mathcal{E}$ in a way similar to the classical case, and obtain thereafter the analog of the \textit{main theorem}, regarding classical annihilators in module theory, see Curtis[\cite{curtis}, pp. 240-242]. The familiar classical properties, satisfied by annihilator sheaves, allow us to set clearly the \textit{sheaf-theoretic version} of \textit{symplectic reduction}, which is the main goal in this paper.
Executive of this issue

pp --: Lihua CAO,pp --: Hongri HAO,

金属学报(英文版) , 2004,
Abstract:
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