Papers by Adrian Sandovici
Results in mathematics, Mar 16, 2024
Acta Universitatis Apulensis. Mathematics - Informatics, 2008
The set of all nonnegative selfadjoint extensions of a nonnegative linear relation (multi-valued ... more The set of all nonnegative selfadjoint extensions of a nonnegative linear relation (multi-valued operator) is described by using a partial order defined on the set of the corresponding quadratic forms. This characterization leads to a generalization of a result due to M.G. Kreȋn.
Indagationes Mathematicae, Oct 1, 2017
Abstract The extremal maximal sectorial extensions of a not necessarily densely defined sectorial... more Abstract The extremal maximal sectorial extensions of a not necessarily densely defined sectorial relation (multivalued linear operator) in a Hilbert space are characterized in terms of a construction which goes back to Sebestyen and Stochel. In particular the two extreme maximal sectorial extensions, namely the Friedrichs extension and the Kreĭn extension, are characterized. For this purpose a survey is given of the connection between closed sectorial forms and maximal sectorial relations.
IOP conference series, Aug 1, 2016
The name of amorphous metals is assigned to metals that have a non-crystalline structure, but the... more The name of amorphous metals is assigned to metals that have a non-crystalline structure, but they are also very similar to glass if we look into their properties. A very distinguished feature is the fact that amorphous metals, also known as metallic glasses, show a good electrical conductivity. The extension of the limit state criteria for different materials makes this type of alloy a choice to validate the new criterions. Using a new criterion developed for biaxial and triaxial state of stress, the results are investigated in order to determine the applicability of the mathematical model for these amorphous metals. Especially for brittle materials, it is extremely important to find suitable fracture criterion. Mohr-Coulomb criterion, which is permitting a linear failure envelope, is often used for very brittle materials. But for metallic glasses this criterion is not consistent with the experimental determinations. For metallic glasses, and other high-strength materials, Rui Tao Qu and Zhe Feng Zhang proposed a failure envelope modeling with an ellipse in σ-τ coordinates. In this paper this model is being developed for principal stresses space. It is also proposed a method for transforming σ-τ coordinates in principal stresses coordinates and the theoretical results are consistent with the experimental ones.
Linear Operators in Almost Krein Spaces.- Generalized Resolvents of a Class of Symmetric Operator... more Linear Operators in Almost Krein Spaces.- Generalized Resolvents of a Class of Symmetric Operators in Krein Spaces.- Block Operator Matrices, Optical Potentials, Trace Class Perturbations and Scattering.- Asymptotic Expansions of Generalized Nevanlinna Functions and their Spectral Properties.- A Necessary Aspect of the Generalized Beals Condition for the Riesz Basis Property of Indefinite Sturm-Liouville Problems.- On Reducible Nonmonic Matrix Polynomials with General and Nonnegative Coefficients.- On Exceptional Extensions Close to the Generalized Friedrichs Extension of Symmetric Operators.- On the Spectrum of the Self-adjoint Extensions of a Nonnegative Linear Relation of Defect One in a Krein Space.- Canonical Differential Equations of Hilbert-Schmidt Type.- Spectral Analysis of Differential Operators with Indefinite Weights and a Local Point Interaction.- Normal Matrices in Degenerate Indefinite Inner Product Spaces.- Symmetric Hermite-Biehler Polynomials with Defect.- A Note on Indefinite Douglas' Lemma.- Some Basic Properties of Polynomials in a Linear Relation in Linear Spaces.
Journal of Operator Theory
An elementary construction of the square root of nonnegative selfadjoint linear relations in Hilb... more An elementary construction of the square root of nonnegative selfadjoint linear relations in Hilbert spaces is presented.
The concept of canonical extension of Hermitian operators has been recently introduced by A. Kuzh... more The concept of canonical extension of Hermitian operators has been recently introduced by A. Kuzhel. This paper deals with a generalization of this notion to the case of symmetric linear relations. Namely, canonical regular extensions of symmetric linear relations in Hilbert spaces are studied. The main result is a characterization of canonical regular extensions in terms of a von-Neumann like formula.
Surveys in Mathematics and its Applications, Feb 3, 2021
A new class of almost paracontact structures on second order tangent bundle built on a Riemannian... more A new class of almost paracontact structures on second order tangent bundle built on a Riemannian space is defined and studied in this paper. In particular, characterizations for the integrability and normality of this class of almost paracontact structures are given. Also, compatible linear connections with this class of almost paracontact structures are introduced and certain characterization of them is obtained.
Certain characterizations of the Friedrichs and the Kre˘r n von-Neumann extensions of the tensor ... more Certain characterizations of the Friedrichs and the Kre˘r n von-Neumann extensions of the tensor product of two nonnegative linear relations A and B in terms of the Friedrichs and the Kre˘r n-von Neumann of A and B are provided. A characterization of the extremal extensions of the tensor product of A and B is also given.
Monatshefte für Mathematik, 2021
Assume that $${{\mathfrak {H}}}$$ and $${{\mathfrak {K}}}$$ are two real or complex Hilbert space... more Assume that $${{\mathfrak {H}}}$$ and $${{\mathfrak {K}}}$$ are two real or complex Hilbert spaces, A a linear relation from $${{\mathfrak {H}}}$$ to $${{\mathfrak {K}}}$$ and B a linear relation from $${{\mathfrak {K}}}$$ to $${{\mathfrak {H}}}$$ , respectively. Necessary and sufficient conditions for B to be equal to the adjoint of A are provided. New characterizations for closed, skew–adjoint and selfadjoint linear relations are obtained.
A new class of almost paracontact structures on second order tangent bundle built on a Riemannian... more A new class of almost paracontact structures on second order tangent bundle built on a Riemannian space is defined and studied in this paper. In particular, characterizations for the integrability and normality of this class of almost paracontact structures are given. Also, compatible linear connections with this class of almost paracontact structures are introduced and certain characterization of them is obtained.
The tangent manifold T M of a smooth, paracompact manifold M , fibered over M by the natural proj... more The tangent manifold T M of a smooth, paracompact manifold M , fibered over M by the natural projection π , carries an integrable distribution kerπ∗, called vertical distribution. If one takes a supplementary distribution of it, called horizontal, an almost complex structure FS appears. One endowes the vertical distribution with a Riemmanian metric γ . Then γ can be prolonged to a Riemannian metric G S on T M such that the pair (FS ,GS) becomes an almost Hermitian structure. In this paper some deformations of FS and GS are proposed and new almost Hermitian structures are determined. With respect to some gauge objects, some properties of these structures are pointed out. For a smooth gauge geometrical model determined by one of these almost Hermitian structures, the general form of the corresponding Einstein-Yang Mills equations is obtained.
Periodica Mathematica Hungarica, 2021
The main aim of this paper is to provide some range-type criteria for the essentially self-adjoin... more The main aim of this paper is to provide some range-type criteria for the essentially self-adjointness of symmetric linear relations in real or complex Hilbert spaces. The main tool is a matrix whose entries are certain linear relations.
Banach Journal of Mathematical Analysis, 2020
For a Banach space, the notion of a regular linear relation is introduced and studied. Also, the ... more For a Banach space, the notion of a regular linear relation is introduced and studied. Also, the regular resolvent set for a closed linear relation is introduced and investigated. Certain characterizations of regular resolvents are obtained in terms of the gap metric between corresponding null spaces, and in terms of generalized resolvents of the linear relation itself, respectively.
Banach Journal of Mathematical Analysis, 2019
In this paper sectorial operators, or more generally, sectorial relations and their maximal secto... more In this paper sectorial operators, or more generally, sectorial relations and their maximal sectorial extensions in a Hilbert space H are considered. The particular interest is in sectorial relations S, which can be expressed in the factorized form S = T * (I + iB)T or S = T (I + iB)T * , where B is a bounded selfadjoint operator in a Hilbert space K and T : H → K or T : K → H, respectively, is a linear operator or a linear relation which is not assumed to be closed. Using the specific factorized form of S, a description of all the maximal sectorial extensions of S is given with a straightforward construction of the extreme extensions S F , the Friedrichs extension, and S K , the Kreȋn extension of S, which uses the above factorized form of S. As an application of this construction the form sum of maximal sectorial extensions of two sectorial relations is treated.
Materials & Design, 2018
The linear Mohr-Coulomb (M-C) failure criterion is widely used to describe the behaviour of mater... more The linear Mohr-Coulomb (M-C) failure criterion is widely used to describe the behaviour of materials with compression/tension asymmetry, such as geological materials. Difference in compressive and tensile fracture/yielding stress is so-called strength difference or SD effect. A modified M-C criterion was proposed previously to describe the failure of ductile materials and to better fit the experimental data [1]. A circular failure envelope, tangent to the Mohr's circles corresponding to the limit state of stress for uniaxial tension, compression and pure shear, was considered. In this paper, the above circular M-C criterion is extended to brittle materials (with SD effect). The new criterion has been compared with fundamental criteria in plasticity theory and experimental results taken from literature. In the space σ 1-σ 3 it is represented by two segments of hyperbola and allows a smooth transition from linear M-C to Rankine criteria. It proves to be adaptable to a wide range of materials and this is a major advantage. Moreover, the paper demonstrates also that all yield criteria for standard plastic materials, without SD effect, under biaxial state of stress, are insensitive to hydrostatic pressure.
Uploads
Papers by Adrian Sandovici