scholarly journals On the stability of first order impulsive evolution equations

2014 ◽  
Vol 34 (3) ◽  
pp. 639 ◽  
Author(s):  
JinRong Wang ◽  
Michal Fečkan ◽  
Yong Zhou
Keyword(s):  
Evolution Equations ◽  
First Order ◽  
The Stability ◽  
Impulsive Evolution Equations

scholarly journals Existence Theorem for Noninstantaneous Impulsive Evolution Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-4
Author(s):  
Gul I Hina Aslam ◽  
Amjad Ali ◽  
Maimona Rafiq
Keyword(s):  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Constructive Theory ◽  
First Order ◽  
Linear Evolution ◽  
Semilinear Problems ◽  
Variational Structure ◽  
Linear Evolution Equation ◽  
Variational Form ◽  
Impulsive Evolution Equations

In this note, the variational form of the classical Lax–Milgram theorem is used for the divulgence of variational structure of the first-order noninstantaneous impulsive linear evolution equation. The existence and uniqueness of the weak solution of the problem is obtained. In future, this constructive theory can be used for the corresponding semilinear problems.

scholarly journals Bleaching of chlorophylls by UV irradiation in vitro: The effects on chlorophyll organization in acetone and n-hexane

2008 ◽  
Vol 73 (3) ◽  
pp. 271-282 ◽  
Author(s):  
Jelena Zvezdanovic ◽  
Dejan Markovic
Keyword(s):  
Uv Irradiation ◽  
Photosynthetic Pigments ◽  
Energy Input ◽  
First Order ◽  
First Order Kinetics ◽  
Uv Photons ◽  
The Stability ◽  
Major Factors

The stability of chlorophylls toward UV irradiation was studied by Vis spectrophotometry in extracts containing mixtures of photosynthetic pigments in acetone and n-hexane. The chlorophylls underwent destruction (bleaching) obeying first-order kinetics. The bleaching was governed by three major factors: the energy input of the UV photons, the concentration of the chlorophylls and the polarity of the solvent, implying different molecular organizations of the chlorophylls in the two solvents.

scholarly journals On Minimum-B Stabilization of Electrostatic Drift Instabilities

1966 ◽  
Vol 21 (11) ◽  
pp. 1953-1959 ◽  
Author(s):  
R. Saison ◽  
H. K. Wimmel
Keyword(s):  
Dispersion Relation ◽  
Particle Distribution ◽  
Inhomogeneous Plasma ◽  
Distribution Functions ◽  
Loss Cone ◽  
First Order ◽  
Stabilization Theorem ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Limiting Case

A check is made of a stabilization theorem of ROSENBLUTH and KRALL (Phys. Fluids 8, 1004 [1965]) according to which an inhomogeneous plasma in a minimum-B field (β ≪ 1) should be stable with respect to electrostatic drift instabilities when the particle distribution functions satisfy a condition given by TAYLOR, i. e. when f0 = f(W, μ) and ∂f/∂W < 0 Although the dispersion relation of ROSENBLUTH and KRALL is confirmed to first order in the gyroradii and in ε ≡ d ln B/dx z the stabilization theorem is refuted, as also is the validity of the stability criterion used by ROSEN-BLUTH and KRALL, ⟨j·E⟩ ≧ 0 for all real ω. In the case ωpi ≫ | Ωi | equilibria are given which satisfy the condition of TAYLOR and are nevertheless unstable. For instability it is necessary to have a non-monotonic ν ⊥ distribution; the instabilities involved are thus loss-cone unstable drift waves. In the spatially homogeneous limiting case the instability persists as a pure loss cone instability with Re[ω] =0. A necessary and sufficient condition for stability is D (ω =∞, k,…) ≦ k2 for all k, the dispersion relation being written in the form D (ω, k, K,...) = k2+K2. In the case ωpi ≪ | Ωi | adherence to the condition given by TAYLOR guarantees stability.

scholarly journals Effects of heat treatment and storage temperature on the use of açaí drink by nutraceutical and beverage industries

2012 ◽  
Vol 32 (1) ◽  
pp. 9-14 ◽  
Author(s):  
Tatiane Regina Albarici ◽  
José Dalton Cruz Pessoa
Keyword(s):  
Temperature Effect ◽  
Storage Temperature ◽  
Life Time ◽  
Reaction Rate Constant ◽  
Anthocyanin Content ◽  
Order Kinetic ◽  
First Order ◽  
The Stability ◽  
And Storage ◽  
Anthocyanin Degradation

This study assesses the storage temperature effect on the anthocyanins of pasteurized and unpasteurized açaí pulp. The data was obtained using a pasteurized and lyophilized pulp (PLP) to evaluate the temperature effect (0, 25, and 40 °C). Part of non-pasteurized frozen pulp (NPP) was pasteurized (NPP-P) at 90 °C for 30 seconds; both pulps were stored at 40 °C. The anthocyanin content reduction in the drink was evaluated from the half-life time (t1/2), activation energy (Ea), temperature quotient (Q10), and the reaction rate constant (k). The t1/2 of the PLP anthocyanins stored at 40 °C was 1.8 times less than that stored at 25 °C and 15 times less than that stored at 0 °C; therefore, the higher temperatures decreased the stability of anthocyanins. The pasteurization increased the t1/2 by 6.6 times (10.14 hours for NPP and 67.28 hours for NPP-P). The anthocyanin degradation on NPP-P followed a first order kinetic, while NPP followed a second order kinetic; thus it can be said that the pasteurization process can improve the preservation of anthocyanins in the pulp.

STUDIES ON HOMOGENEOUS FIRST ORDER GAS REACTIONS: II. THE DECOMPOSITION OF THE ISOMERIC ESTERS BUTYLIDENE DIACETATE AND ETHYLIDENE DIPROPIONATE

1932 ◽  
Vol 6 (4) ◽  
pp. 417-427 ◽  
Author(s):  
C. C. Coffin
Keyword(s):  
Activation Energy ◽  
Degrees Of Freedom ◽  
Maximum Energy ◽  
Velocity Measurements ◽  
First Order ◽  
Gas Reactions ◽  
Points Of View ◽  
The Stability ◽  
Future Work ◽  
Internal Degrees Of Freedom

The gaseous decompositions of the esters butylidene diacetate and ethylidene dipropionate have been studied from points of view previously outlined in papers on the decomposition of ethylidene diacetate (2, 3). The decomposition velocities have been measured at initial pressures of from 5 to 56 cm. of mercury and at temperatures between 211 and 265 °C. The reactions are homogeneous and of the first order. They agree with the Arrhenius equation and give 100% yields (within experimental error) of an aldehyde and an anhydride. The preparation of the compounds and improvements in the technique of the velocity measurements are described.While the specific velocities of the three reactions at any temperature are somewhat different, their activation energies are the same. It is suggested that in the case of such simple reactions, which are strictly localized within the molecular structure, the activation energy can be identified as the maximum energy that the reactive bonds may possess and still exist; i.e., it may be taken as a measure of the stability of the bonds which are broken in the reaction. The suggestion is also made that for a series of reactions which have the same activation energy, the specific velocities can be taken as a relative measure of the number of internal degrees of freedom that contribute to the energy of activation. On the basis of these assumptions it becomes possible to use reaction-velocity measurements for the investigation of intramolecular energy exchange. The theoretical significance of the data is further discussed and the scope of future work in this connection is indicated.The monomolecular velocity constants (sec−1) of the decomposition of ethylidene diacetate, ethylidene dipropionate and butylidene diacetate are given respectively by the equations [Formula: see text], [Formula: see text], and [Formula: see text].

scholarly journals Dynamical system analysis of three-form field dark energy model with baryonic matter

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Soumya Chakraborty ◽  
Sudip Mishra ◽  
Subenoy Chakraborty
Keyword(s):  
Dynamical System ◽  
Dark Energy ◽  
Cold Dark Matter ◽  
System Analysis ◽  
Evolution Equations ◽  
Matter Field ◽  
Baryonic Matter ◽  
Form Field ◽  
The Stability ◽  
Manifold Theory

AbstractA cosmological model having matter field as (non) interacting dark energy (DE) and baryonic matter and minimally coupled to gravity is considered in the present work with flat FLRW space time. The DE is chosen in the form of a three-form field while radiation and dust (i.e; cold dark matter) are the baryonic part. The cosmic evolution is studied through dynamical system analysis of the autonomous system so formed from the evolution equations by suitable choice of the dimensionless variables. The stability of the non-hyperbolic critical points are examined by Center manifold theory and possible bifurcation scenarios have been examined.

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