Last 10 Published Papers

• Cover pages v37n2
Vasile Staicu
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• On some inequalities with operators in Hilbert spaces
Alexandru Carausu
Operators deﬁned on Hilbert spaces represent a major subﬁeld of (or base for) the Functional Analysis. Several types of inequalities among such operators were established and studied in the last decades, mainly by the early ’50s and then in the ’80s. In this paper there are reviewed some of the most important types of inequalities, introduced and studied by H. Bohr, E. Heinz – T. Kato, H. Weyl, W. Reid and other authors. They were extended and/or sharpened by other authors, mentioned in the Introduction. Some of the deﬁnitions and proofs, found in several references, are completed (by the author) with speciﬁc formulas from Hilbert space theory, some details are also added to certain proofs and deﬁnitions as well. The main ways for establishing inequalities with operators are pointed out: scalar inequalities like the Cauchy-Schwarz and Bohr’s inequalities over C (the complex field) or on an H-space H, certain identities with H-space operators, etc.

• A description of collineations-groups of an affine plane
Orgest Zaka
Based on the literature by following very interesting work in the past [2], [3], [4], [9], [12] In this article becomes a description of collineations in the affine plane [10]. We are focusing at the description of translations and dilatations, and we make a detailed description of them. We describe the translation group and dilatation group in affine plane [11]. A detailed description we have given also for traces of a dilatation. We have proved that translation group is a normal subgroup of the group of dilatations, wherein the translation group is a commutative group and the dilatation group is just a group. We think that in this article have brings about an innovation in the treatment of detailed algebraic structures in affine plane.

• Conjugate covariant derivatives on vector bundles and duality
Mircea Crasmareanu
The notion of {\it conjugate connections}, discussed in \cite{be:c} for a given manifold $M$ and its tangent bundle, is extended here to covariant derivatives on an arbitrary vector bundle $E$ endowed with quadratic endomorphisms. The main property of pairs of such covariant derivatives, namely the duality, is pointed out. As generalization, the case of anchored (particularly Lie algebroid) covariant derivatives on $E$ is considered. As applications we study the Finsler bundle of $M$ as well as the Finsler connections on the slit tangent bundle of a Finsler geometry.

• Equivalent definitions for connections in higher order tangent bundles
Marcela Popescu
We establish a one to one correspondence between the\linebreak connections $C^{(k-1)}$ (in the bundle $% T^{k}M\rightarrow M$, used by R. Miron in his work on higher order spaces) and $C^{(0)}$ (in the affine bundle $% T^{k}M\rightarrow T^{k-1}M$, used for example in \cite{CSC1}).

• Academician Professor RADU MIRON at 90th Birthday: a Life for Mathematics
Mihai Anastasiei
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• Golden warped product Riemannian manifolds
Our aim is to study the problem of tightness of compact subsets of the space $M_r(X)$ of all Radon measures on the space $X$ equipped by the topology of weak convergence. A kernel on a space $Z$ into the space $M_r(S)$ is a continuous mapping $k: Z \longrightarrow M_r(X)$. A space $X$ is called a uniformly Prohorov space if for each $\varepsilon > 0$, any paracompact space $Z$ and any kernel $k: Z \longrightarrow M_r(X)$ there exists an upper semi-continuous compact-valued mapping $S_{(k,\varepsilon )}: Z \longrightarrow X$ such that $\mu _{(k,z)}(X \setminus S_{(k,\varepsilon )}(z)) \leq \varepsilon$ for each $z \in Z$. Any sieve-complete space is a uniformly Prohorov space (Corollary \ref{C5.5}). Any uniformly Prohorov space is a Prohorov space. A space $X$ is sieve-complete if and only if $X$ is an open continuous image of a paracompact \v{C}ech-complete space. The idea of the concept of a uniformly Prohorov goes to A. Bouziad, V. Gutev and V. Valov.