scholarly journals Solutions of the differential inequality with a null Lagrangian: higher integrability and removability of singularities. I

2014 ◽  
Author(s):  
A.A. Egorov
Keyword(s):  
Differential Inequality ◽  
Sobolev Class ◽  
The Self ◽  
Hölder Regularity ◽  
Higher Integrability ◽  
Stability Theorems ◽  
Sobolev Exponent ◽  
Derivatives Of ◽  
Null Lagrangian ◽  
Structural Assumption

The aim of this paper is to derive the self-improving property of integrability for derivatives of solutions of the differential inequality with a null Lagrangian. More precisely, we prove that the solution of the Sobolev class with some Sobolev exponent slightly smaller than the natural one determined by the structural assumption on the involved null Lagrangian actually belongs to the Sobolev class with some Sobolev exponent slightly larger than this natural exponent. We also apply this property to improve Holder regularity and stability theorems of [19].

Intermolecular interactions in dictating the self-assembly of halogen derivatives of bis-(N-substituted oxamato)palladate(ii) complexes

RSC Advances ◽  
2016 ◽  
Vol 6 (8) ◽  
pp. 6164-6170 ◽  
Author(s):  
Francisco Ramón Fortea-Pérez ◽  
Nadia Marino ◽  
Giovanni de Munno ◽  
Donatella Armentano ◽  
Miguel Julve ◽  
...  
Keyword(s):  
Hydrogen Bonds ◽  
Intermolecular Interactions ◽  
Self Assembly ◽  
Supramolecular Assemblies ◽  
The Self ◽  
Derivatives Of

The reaction of aqueous [PdCl4]2−withN-4-Xphenyloxamate ligands (X = F, Cl, Br) afforded three non-isostructural compounds exhibiting intriguing diverse supramolecular assemblies driven by hydrogen bonds and/or halogen⋯halogen interactions.

Partial stability analysis of nonlinear time-varying impulsive systems

2019 ◽  
Vol 12 (06) ◽  
pp. 1950066
Author(s):  
Boulbaba Ghanmi
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Time Varying ◽  
Impulsive Systems ◽  
Partial Stability ◽  
Stability Theorems ◽  
Time Varying Systems ◽  
The Stability ◽  
Derivatives Of ◽  
Theoretical Results

This paper investigates the stability analysis with respect to part of the variables of nonlinear time-varying systems with impulse effect. The approach presented is based on the specially introduced piecewise continuous Lyapunov functions. The Lyapunov stability theorems with respect to part of the variables are generalized in the sense that the time derivatives of the Lyapunov functions are allowed to be indefinite. With the help of the notion of stable functions, asymptotic partial stability, exponential partial stability, input-to-state partial stability (ISPS) and integral input-to-state partial stability (iISPS) are considered. Three numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

Spin radiation effects in the BMT model of spinning charge

2014 ◽  
Vol 29 (31) ◽  
pp. 1450186 ◽  
Author(s):  
S. L. Lebedev
Keyword(s):  
Imaginary Part ◽  
Radiation Effects ◽  
Degrees Of Freedom ◽  
The Self ◽  
Spin Magnetic Moment ◽  
Self Energy ◽  
Radiation Processes ◽  
Nonzero Spin ◽  
Derivatives Of ◽  
Spin Contribution

The radiation processes emerging as a result of interaction between spin and orbit degrees of freedom of spinning charge are investigated with the use of the Bargmann–Michel–Telegdi (BMT) model. The spin contribution to the self-energy of the ultrarelativistic particle is imaginary and proportional to invariant constructed from the derivatives of the worldline and from the spin. This invariant determines up to negative numerical factor of the QED spin contribution to the imaginary part of the mass shift (MS). Particular cases of crossed, electric and magnetic external fields are considered in detail. The influence of an ideal boundary upon the self-energy of the particle is analyzed for the crossed field case. In the presence of the "mirror" the imaginary part of the MS gets an addition and the nonzero spin dependent real part appears, both however giving the small corrections to no-boundary MS. An alternative method to obtain the spin magnetic moment correction to the power of synchrotron radiation entails in generalization of the result known for the planar motion. Special attention is given to disagreement between classical and quantum pictures of spin radiation.

Miniribozymes, small derivatives of the sunY intron, are catalytically active

1989 ◽  
Vol 9 (12) ◽  
pp. 5480-5483
Author(s):  
J A Doudna ◽  
J W Szostak
Keyword(s):  
Bacteriophage T4 ◽  
Complete Loss ◽  
The Self ◽  
Group I Introns ◽  
Structural Requirements ◽  
Group I ◽  
Catalytically Active ◽  
Conserved Core ◽  
Self Splicing ◽  
Derivatives Of

The self-splicing sunY intron from bacteriophage T4 has the smallest conserved core secondary structure of any of the active group I introns. Here we show that several nonconserved regions can be deleted from this intron without complete loss of catalytic activity. The 3' stems P9, P9.1, and P9.2 can be deleted while retaining 5' cleaving activity. Two base-paired stems (P7.1 and P7.2) that are peculiar to the group IA introns can also be deleted; however, the activities of the resulting derivatives depend greatly on the choice of replacement sequences and their lengths. The smallest active derivative is less than 180 nucleotides long. These experiments help to define the minimum structural requirements for catalysis.

scholarly journals II. On the interchange of the variables in certain linear differential operators

1890 ◽  
Vol 181 ◽  
pp. 19-51
Keyword(s):  
Differential Operators ◽  
The Self ◽  
Differential Invariants ◽  
Linear Differential Operators ◽  
Independent Variable ◽  
The Subject ◽  
Functional Differential ◽  
Linear Differential ◽  
Derivatives Of ◽  
Single Relation

The operators to be considered, include or involve all those which have presented themselves as annihilators and generators in recent theories of functional differential invariants, reciprocants, cyclicants, &c. The general form of the binary operators, operators whose arguments are the derivatives of one dependent with regard to one independent variable, which I propose first to consider, is adopted in accordance with that used in two remarkable papers by Major MacMahon. They are his operators in four elements. The analogous ternary operators to which I subsequently devote attention, are distinct from his operators of six elements. Their arguments are the partial derivatives of one of three variables, supposed connected by a single relation, with regard to the two others. The only'previous contribution, of which I am aware, to the subject of the reversion of MacMahon operators, is a paper by Professor L. J. Rogers, in which he obtains the operator reciprocal to { μ, v ; 1, 1}, and alludes to the self reciprocal property of V which is expressed with more precision in (38) below.

SINGULAR FERMI SURFACES II: THE TWO-DIMENSIONAL CASE

2008 ◽  
Vol 20 (03) ◽  
pp. 275-334 ◽  
Author(s):  
JOEL FELDMAN ◽  
MANFRED SALMHOFER
Keyword(s):  
Perturbation Theory ◽  
Spatial Dimension ◽  
Physical Significance ◽  
The Self ◽  
Two Dimensional ◽  
Singular Case ◽  
Fermi Surfaces ◽  
Self Energy ◽  
Fermion Systems ◽  
Derivatives Of

We consider many-fermion systems with singular Fermi surfaces, which contain Van Hove points where the gradient of the band function k ↦ e(k) vanishes. In a previous paper, we have treated the case of spatial dimension d ≥ 3. In this paper, we focus on the more singular case d = 2 and establish properties of the fermionic self-energy to all orders in perturbation theory. We show that there is an asymmetry between the spatial and frequency derivatives of the self-energy. The derivative with respect to the Matsubara frequency diverges at the Van Hove points, but, surprisingly, the self-energy is C1 in the spatial momentum to all orders in perturbation theory, provided the Fermi surface is curved away from the Van Hove points. In a prototypical example, the second spatial derivative behaves similarly to the first frequency derivative. We discuss the physical significance of these findings.

scholarly journals Miniribozymes, small derivatives of the sunY intron, are catalytically active.

1989 ◽  
Vol 9 (12) ◽  
pp. 5480-5483 ◽  
Author(s):  
J A Doudna ◽  
J W Szostak
Keyword(s):  
Bacteriophage T4 ◽  
Complete Loss ◽  
The Self ◽  
Group I Introns ◽  
Structural Requirements ◽  
Group I ◽  
Catalytically Active ◽  
Conserved Core ◽  
Self Splicing ◽  
Derivatives Of

The self-splicing sunY intron from bacteriophage T4 has the smallest conserved core secondary structure of any of the active group I introns. Here we show that several nonconserved regions can be deleted from this intron without complete loss of catalytic activity. The 3' stems P9, P9.1, and P9.2 can be deleted while retaining 5' cleaving activity. Two base-paired stems (P7.1 and P7.2) that are peculiar to the group IA introns can also be deleted; however, the activities of the resulting derivatives depend greatly on the choice of replacement sequences and their lengths. The smallest active derivative is less than 180 nucleotides long. These experiments help to define the minimum structural requirements for catalysis.

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