scholarly journals A New Approach on Datko–Zabczyk Method for Nonuniform Exponential Stability

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1095
Author(s):  
Nicolae Lupa
Keyword(s):  
Exponential Stability ◽  
Large Class ◽  
Linear Space ◽  
Difference Equations ◽  
Discrete Dynamics ◽  
New Approach ◽  
Banach Sequence Spaces ◽  
Nonuniform Exponential Stability ◽  
Banach Sequence

We provide a sequence of projections on the linear space of all sequences and connect the existence of nonuniform exponential stability to the restrictions of these projections on a class of Banach sequence spaces defined by a discrete dynamics. As a consequence, we obtain a Datko–Zabczyk type characterization of nonuniform exponential stability. We develop our analysis without any assumption on the invertibility of the dynamics, thus our results are applicable to a large class of difference equations.

scholarly journals Matrix Mappings on the Domains of Invertible Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Muhammed Altun
Keyword(s):  
Sufficient Conditions ◽  
Sequence Spaces ◽  
Banach Sequence Spaces ◽  
The Matrix ◽  
Matrix Domains ◽  
Necessary And Sufficient ◽  
Invertible Matrices ◽  
Matrix Operators ◽  
Banach Sequence

We focus on sequence spaces which are matrix domains of Banach sequence spaces. We show that the characterization of a random matrix operator , where and are matrix domains with invertible matrices and , can be reduced to the characterization of the operator . As an application, the necessary and sufficient conditions for the matrix operators between invertible matrix domains of the classical sequence spaces and norms of these operators are given.

scholarly journals A new periodicity concept for time scales

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Murat Adivar
Keyword(s):  
Periodic Solutions ◽  
Large Class ◽  
Time Scales ◽  
Difference Equations ◽  
New Approach ◽  
Shift Operators

AbstractBy means of the shift operators we introduce a new periodicity concept on time scales. This new approach will enable researchers to investigate periodicity notion on a large class of time scales whose members may not satisfy the condition there exists a P > 0 such that $$t \pm P \in \mathbb{T}$$ for all $$t \in \mathbb{T}$$, which is being currently used. Therefore, the results of this paper open an avenue for the investigation of periodic solutions of q-difference equations and more.

scholarly journals Sustainability Investigation of Vehicles’ CO2 Emission in Hungary

2021 ◽  
Vol 13 (15) ◽  
pp. 8237
Author(s):  
István Árpád ◽  
Judit T. Kiss ◽  
Gábor Bellér ◽  
Dénes Kocsis
Keyword(s):  
Energy Efficiency ◽  
Co2 Emissions ◽  
Energy Supply ◽  
Internal Combustion Engines ◽  
Combustion Engines ◽  
The European Union ◽  
New Approach ◽  
Technology System ◽  
Low Co2

The regulation of vehicular CO2 emissions determines the permissible emissions of vehicles in units of g CO2/km. However, these values only partially provide adequate information because they characterize only the vehicle but not the emission of the associated energy supply technology system. The energy needed for the motion of vehicles is generated in several ways by the energy industry, depending on how the vehicles are driven. These methods of energy generation consist of different series of energy source conversions, where the last technological step is the vehicle itself, and the result is the motion. In addition, sustainability characterization of vehicles cannot be determined by the vehicle’s CO2 emissions alone because it is a more complex notion. The new approach investigates the entire energy technology system associated with the generation of motion, which of course includes the vehicle. The total CO2 emissions and the resulting energy efficiency have been determined. For this, it was necessary to systematize (collect) the energy supply technology lines of the vehicles. The emission results are not given in g CO2/km but in g CO2/J, which is defined in the paper. This new method is complementary to the European Union regulative one, but it allows more complex evaluations of sustainability. The calculations were performed based on Hungarian data. Finally, using the resulting energy efficiency values, the emission results were evaluated by constructing a sustainability matrix similar to the risk matrix. If only the vehicle is investigated, low CO2 emissions can be achieved with vehicles using internal combustion engines. However, taking into consideration present technologies, in terms of sustainability, the spread of electric-only vehicles using renewable energies can result in improvement in the future. This proposal was supported by the combined analysis of the energy-specific CO2 emissions and the energy efficiency of vehicles with different power-driven systems.

scholarly journals An Intrinsic Characterization of Five Points in a CAT(0) Space

2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda
Keyword(s):  
Metric Space ◽  
Isometric Embedding ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
New Approach ◽  
Intrinsic Characterization ◽  
New Family

AbstractGromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.

scholarly journals Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bao-ning Du ◽  
Min-xin Huang
Keyword(s):  
Large Class ◽  
Bethe Ansatz ◽  
Difference Equations ◽  
The Other ◽  
Elementary Functions ◽  
Quantum Dilogarithm ◽  
Thermodynamic Bethe Ansatz ◽  
Dilogarithm Function ◽  
Quantum Operators

Abstract We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev’s quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

scholarly journals Avoided motifs: short amino acid strings missing from protein datasets

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Pablo Mier ◽  
Miguel A. Andrade-Navarro
Keyword(s):  
Amino Acids ◽  
Amino Acid ◽  
Protein Function ◽  
Large Protein ◽  
New Approach ◽  
Cellular Context ◽  
Human Proteins ◽  
Context Specific ◽  
Protein Datasets

Abstract According to the amino acid composition of natural proteins, it could be expected that all possible sequences of three or four amino acids will occur at least once in large protein datasets purely by chance. However, in some species or cellular context, specific short amino acid motifs are missing due to unknown reasons. We describe these as Avoided Motifs, short amino acid combinations missing from biological sequences. Here we identify 209 human and 154 bacterial Avoided Motifs of length four amino acids, and discuss their possible functionality according to their presence in other species. Furthermore, we determine two Avoided Motifs of length three amino acids in human proteins specifically located in the cytoplasm, and two more in secreted proteins. Our results support the hypothesis that the characterization of Avoided Motifs in particular contexts can provide us with information about functional motifs, pointing to a new approach in the use of molecular sequences for the discovery of protein function.

scholarly journals Oscillation of nonlinear third-order difference equations with mixed neutral terms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jehad Alzabut ◽  
Martin Bohner ◽  
Said R. Grace
Keyword(s):  
Difference Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Order Difference ◽  
New Approach ◽  
Comparison Technique

AbstractIn this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered.

A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Talat Körpınar ◽  
Yasin Ünlütürk
Keyword(s):  
Vector Fields ◽  
Elastic Surface ◽  
Geometrical Characterization ◽  
Lorentzian Space ◽  
New Approach ◽  
Darboux Vector ◽  
Moving Particle ◽  
The Relationship ◽  
Surface Curve

AbstractIn this research, we study bienergy and biangles of moving particles lying on the surface of Lorentzian 3-space by using their energy and angle values. We present the geometrical characterization of bienergy of the particle in Darboux vector fields depending on surface. We also give the relationship between bienergy of the surface curve and bienergy of the elastic surface curve. We conclude the paper by providing bienergy-curve graphics for different cases.

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