scholarly journals Reconstruction of Differential Operators with Frozen Argument

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 24
Author(s):  
Oles Dobosevych ◽  
Rostyslav Hryniv
Keyword(s):  
Perturbation Theory ◽  
Spectral Properties ◽  
General Framework ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Complete Characterization ◽  
Rank One Perturbation ◽  
Clear Explanation ◽  
Rank One

We study spectral properties of a wide class of differential operators with frozen arguments by putting them into a general framework of rank-one perturbation theory. In particular, we give a complete characterization of possible eigenvalues for these operators and solve the inverse spectral problem of reconstructing the perturbation from the resulting spectrum. This approach provides a unified treatment of several recent studies and gives a clear explanation and interpretation of the obtained results.

scholarly journals Bounds on Mixed State Entanglement

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 62 ◽  
Author(s):  
Bruno Leggio ◽  
Anna Napoli ◽  
Hiromichi Nakazato ◽  
Antonino Messina
Keyword(s):  
Mixed State ◽  
General Framework ◽  
Quantum Correlations ◽  
Thermal Entanglement ◽  
Mixed States ◽  
Clear Explanation ◽  
Finite Dimensionality ◽  
Partial Transpose ◽  
The Subject

In the general framework of d 1 × d 2 mixed states, we derive an explicit bound for bipartite negative partial transpose (NPT) entanglement based on the mixedness characterization of the physical system. The derived result is very general, being based only on the assumption of finite dimensionality. In addition, it turns out to be of experimental interest since some purity-measuring protocols are known. Exploiting the bound in the particular case of thermal entanglement, a way to connect thermodynamic features to the monogamy of quantum correlations is suggested, and some recent results on the subject are given a physically clear explanation.

scholarly journals Application of a Rank-One Perturbation to Pendulum Systems

2020 ◽  
Vol 12 (5) ◽  
pp. 47
Author(s):  
Traor´e. G. Y. Arouna ◽  
M. Dosso ◽  
J.-C. Koua Brou
Keyword(s):  
Perturbation Theory ◽  
Strong Stability ◽  
Double Pendulum ◽  
Simple Pendulum ◽  
Rank One Perturbation ◽  
Stability And Instability ◽  
Rank One

From a perturbation theory proposed by Mehl, et al., a study of the rank-one perturbation of the problems governed by pendulum systems is presented. Thus, a study of motion of the simple pendulum, double and triple pendulums with oscillating support, not coupled as coupled by a spring and double pendulum with fixed support is proposed. Finally (strong) stability and instability zones are calculated for each studied system.

scholarly journals Characterization of Eigenvalues in Spectral Gap for Singular Differential Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Zhaowen Zheng ◽  
Wenju Zhang
Keyword(s):  
Positive Integer ◽  
Spectral Properties ◽  
Differential Operators ◽  
Spectral Gap ◽  
Deficiency Index ◽  
Minimal Operator ◽  
Adjoint Extension

The spectral properties fornorder differential operators are considered. When given a spectral gap(a,b)of the minimal operatorT0with deficiency indexr, arbitrarympointsβi  (i=1,2,…,m)in(a,b), and a positive integer functionpsuch that∑i=1mp(βi)≤r,T0has a self-adjoint extensionT̃such that eachβi  (i=1,2,…,m)is an eigenvalue ofT̃with multiplicity at leastp(βi).

scholarly journals Synthesis and Spectral Properties of Gem-Dimethyl Chlorin Photosensitizers

2020 ◽  
Author(s):  
zoi melissari ◽  
harry sample ◽  
Brendan Twamley ◽  
René M. Williams ◽  
Mathias Senge
Keyword(s):  
Spectral Properties ◽  
Density Functional ◽  
Antimicrobial Agents ◽  
Photophysical Properties ◽  
Complete Characterization ◽  
Free Base ◽  
Resistance To Oxidation ◽  
Td Dft ◽  
Moderate Yield

Chlorins that bear a gem-dimethyl group, which attributes their resistance to oxidation, are of interest for applications in photomedicine. Herein, we present the synthesis and the photophysical properties of two geminal-dimethyl chlorins (dihydroporphyrins) and their free base counterparts that act as efficient singlet oxygen generators and thus exhibit potential for use in photodynamic therapy (PDT) as anticancer or antimicrobial agents upon further derivatization. A complete characterization of their spectral and photophysical properties is accompanied by density functional calculations (DFT) as well as time dependent (TD) DFT to investigate the features of the frontier molecular orbitals. To demonstrate the potential of these compounds, standard palladium mediated reaction yielded a porphyrin-chlorin dyad in moderate yield.

scholarly journals INVERSE SPECTRAL PROBLEMS FOR SINGULAR RANK-ONE PERTURBATIONS OF A HILL OPERATOR

2009 ◽  
Vol 87 (3) ◽  
pp. 421-428
Author(s):  
KAZUSHI YOSHITOMI
Keyword(s):  
Inverse Spectral Problem ◽  
Real Sequence ◽  
Inverse Spectral Problems ◽  
Necessary And Sufficient Condition ◽  
Hill Operator ◽  
Rank One Perturbation ◽  
Rank One ◽  
Inverse Spectral ◽  
Necessary And Sufficient ◽  
The Hill

AbstractWe investigate an inverse spectral problem for the singular rank-one perturbations of a Hill operator. We give a necessary and sufficient condition for a real sequence to be the spectrum of a singular rank-one perturbation of the Hill operator.

scholarly journals Synthesis and Spectral Properties of Gem-Dimethyl Chlorin Photosensitizers

2020 ◽  
Author(s):  
zoi melissari ◽  
harry sample ◽  
Brendan Twamley ◽  
René M. Williams ◽  
Mathias Senge
Keyword(s):  
Spectral Properties ◽  
Density Functional ◽  
Antimicrobial Agents ◽  
Photophysical Properties ◽  
Complete Characterization ◽  
Free Base ◽  
Resistance To Oxidation ◽  
Td Dft ◽  
Moderate Yield

Chlorins that bear a gem-dimethyl group, which attributes their resistance to oxidation, are of interest for applications in photomedicine. Herein, we present the synthesis and the photophysical properties of two geminal-dimethyl chlorins (dihydroporphyrins) and their free base counterparts that act as efficient singlet oxygen generators and thus exhibit potential for use in photodynamic therapy (PDT) as anticancer or antimicrobial agents upon further derivatization. A complete characterization of their spectral and photophysical properties is accompanied by density functional calculations (DFT) as well as time dependent (TD) DFT to investigate the features of the frontier molecular orbitals. To demonstrate the potential of these compounds, standard palladium mediated reaction yielded a porphyrin-chlorin dyad in moderate yield.

Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

1982 ◽  
Vol 10 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Kumar ◽  
C. W. Bert
Keyword(s):  
Response Characteristic ◽  
Cord Compression ◽  
Complete Characterization ◽  
Strain Response ◽  
Strain Gages ◽  
Experimental Characterization ◽  
Rubber Composites ◽  
Stress Strain ◽  
Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

Characterization of CMOS Structures (0.6 µm process) Submitted to HBM and COM ESD Stress Tests

1997 ◽  
Author(s):  
G. Meneghesso ◽  
E. Zanoni ◽  
P. Colombo ◽  
M. Brambilla ◽  
R. Annunziata ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Electrostatic Discharge ◽  
Stress Test ◽  
Complete Characterization ◽  
Stress Tests ◽  
Test Procedures ◽  
Emission Microscopy ◽  
Fast Rise ◽  
Scanning Electron

Abstract In this work, we present new results concerning electrostatic discharge (ESD) robustness of 0.6 μm CMOS structures. Devices have been tested according to both HBM and socketed CDM (sCDM) ESD test procedures. Test structures have been submitted to a complete characterization consisting in: 1) measurement of the tum-on time of the protection structures submitted to pulses with very fast rise times; 2) ESD stress test with the HBM and sCDM models; 3) failure analysis based on emission microscopy (EMMI) and Scanning Electron Microscopy (SEM).

scholarly journals Complete characterization of spin chains with two Ising symmetries

2019 ◽  
Vol 125 (1) ◽  
pp. 10008 ◽  
Author(s):  
Bat-el Friedman ◽  
Atanu Rajak ◽  
Emanuele G. Dalla Torre
Keyword(s):  
Complete Characterization ◽  
Spin Chains
Sign in / Sign up

Export Citation Format

Share Document