Means of Power Type and Their Inequalities

1999 ◽  
Vol 205 (1) ◽  
pp. 131-147 ◽  
Author(s):  
Dag Lukkassen
Keyword(s):  
Power Type

scholarly journals Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1398
Author(s):  
Natalia Kolkovska ◽  
Milena Dimova ◽  
Nikolai Kutev
Keyword(s):  
Solitary Waves ◽  
Orbital Stability ◽  
Second Derivative ◽  
Cubic Nonlinearity ◽  
Abstract Theory ◽  
Power Type ◽  
Analytical Formulas ◽  
Stability Of Solitary Waves ◽  
The Stability ◽  
Double Dispersion

We consider the orbital stability of solitary waves to the double dispersion equation utt−uxx+h1uxxxx−h2uttxx+f(u)xx=0,h1>0,h2>0 with combined power-type nonlinearity f(u)=a|u|pu+b|u|2pu,p>0,a∈R,b∈R,b≠0. The stability of solitary waves with velocity c, c2<1 is proved by means of the Grillakis, Shatah, and Strauss abstract theory and the convexity of the function d(c), related to some conservation laws. We derive explicit analytical formulas for the function d(c) and its second derivative for quadratic-cubic nonlinearity f(u)=au2+bu3 and parameters b>0, c2∈0,min1,h1h2. As a consequence, the orbital stability of solitary waves is analyzed depending on the parameters of the problem. Well-known results are generalized in the case of a single cubic nonlinearity f(u)=bu3.

scholarly journals Sharp thresholds of blow-up and global existence for the Schrödinger equation with combined power-type and Choquard-type nonlinearities

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongbin Wang ◽  
Binhua Feng
Keyword(s):  
Global Existence ◽  
Finite Time ◽  
Critical Case ◽  
Blow Up ◽  
Critical Mass ◽  
Choquard Equation ◽  
Power Type ◽  
Scale Invariant ◽  
Nonlinear Schrödinger ◽  
Sharp Thresholds

AbstractIn this paper, we consider the sharp thresholds of blow-up and global existence for the nonlinear Schrödinger–Choquard equation $$ i\psi _{t}+\Delta \psi =\lambda _{1} \vert \psi \vert ^{p_{1}}\psi +\lambda _{2}\bigl(I _{\alpha } \ast \vert \psi \vert ^{p_{2}}\bigr) \vert \psi \vert ^{p_{2}-2}\psi . $$iψt+Δψ=λ1|ψ|p1ψ+λ2(Iα∗|ψ|p2)|ψ|p2−2ψ. We derive some finite time blow-up results. Due to the failure of this equation to be scale invariant, we obtain some sharp thresholds of blow-up and global existence by constructing some new estimates. In particular, we prove the global existence for this equation with critical mass in the $L^{2}$L2-critical case. Our obtained results extend and improve some recent results.

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

2021 ◽  
Author(s):  
Kristian Haška ◽  
Stevan Cvetićanin ◽  
Dušan Zorica
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Constitutive Equation ◽  
Magnetic Flux ◽  
Electromotive Force ◽  
Constitutive Models ◽  
Steady State Regime ◽  
Power Type ◽  
State Regime ◽  
Transient And Steady State

Abstract Generalized capacitor (inductor) is constitutively modeled by expressing charge (magnetic flux) in terms of voltage (current) memory as a sum of instantaneous and power type hereditary contributions and it is proved to be a dissipative electric element by thermodynamic analysis. On the contrary, generalized capacitor (inductor) as a generative electric element is modeled using the same form of the constitutive equation, but by expressing voltage (current) in terms of charge (magnetic flux) memory. These constitutive models are used in transient and steady state regime analysis of the series RC and RL circuits subject to electromotive force, as well as in the study of circuits' frequency characteristics including asymptotic behavior.

Surface Roughness at Wire Electrical Discharge Machining

2015 ◽  
Vol 760 ◽  
pp. 551-556 ◽  
Author(s):  
Oana Dodun ◽  
Laurenţiu Slătineanu ◽  
Margareta Coteaţă ◽  
Vasile Merticaru ◽  
Gheorghe Nagîţ
Keyword(s):  
Surface Roughness ◽  
Empirical Model ◽  
Electrical Discharge ◽  
Electrical Discharge Machining ◽  
Roughness Parameter ◽  
Wire Electrical Discharge Machining ◽  
Power Type ◽  
Surface Roughness Parameter ◽  
Pulse On Time ◽  
Pulse Off Time

Wire electrical discharge machining is a machining method by which parts having various contours could be detached from plate workpieces. The method uses the electrical discharges developed between the workpiece and the wire tool electrode found in an axial motion, when in the work zone a dielectric fluid is recirculated. In order to highlight the influence exerted by some input process factors on the surface roughness parameter Ra in case of a workpiece made of an alloyed steel, a factorial experiment with six independent variables at two variation levels was designed and materialized. As input factors, one used the workpiece thickness, pulse on time, pulse off-time, wire axial tensile force, current intensity average amplitude defined by setting button position and travelling wire electrode speed. By mathematical processing of the experimental results, empirical models were established. Om the base of a power type empirical model, graphical representations aiming to highlight the influence of some input factors on the surface roughness parameter Ra were achieved. The power type empirical model facilitated establishing of order of factors able to exert influence on the surface roughness parameter Ra at wire electrical discharge machining.

Analysis of power type singularities using finite elements

1977 ◽  
Vol 11 (8) ◽  
pp. 1225-1233 ◽  
Author(s):  
Dennis M. Tracey ◽  
Thomas S. Cook
Keyword(s):  
Finite Elements ◽  
Power Type

scholarly journals Influence of Some Microchanges Generated by Different Processing Methods on Selected Tribological Characteristics

Micromachines ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 29
Author(s):  
Gheorghe Nagîț ◽  
Laurențiu Slătineanu ◽  
Oana Dodun ◽  
Andrei Marius Mihalache ◽  
Marius Ionuț Rîpanu ◽  
...  
Keyword(s):  
Experimental Research ◽  
Tribological Behavior ◽  
Empirical Models ◽  
Tribological Characteristics ◽  
Ball Burnishing ◽  
Power Type ◽  
Processing Methods ◽  
The Coefficient Of Friction ◽  
Mathematical Processing ◽  
Loss Of Mass

Different processing methods can change the physical–mechanical properties and the microgeometry of the surfaces made by such processes. In turn, such microchanges may affect the tribological characteristics of the surface layer. The purpose of this research was to study the tribological behavior of a test piece surfaces analyzing the changes on the values of the coefficient of friction and loss of mass that appear in time. The surfaces subjected to experimental research were previously obtained by turning, grinding, ball burnishing, and vibroburnishing. The experimental research was performed using a device adaptable to a universal lathe. Mathematical processing of the experimental results led to the establishment of power-type function empirical models that highlight the intensity of the influence exerted by the pressure and duration of the test on the values of the output parameters. It was found that the best results were obtained in the case of applying ball vibroburnishing as the final process.

scholarly journals An inverse problem for a fractional diffusion equation with fractional power type nonlinearities

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Li Li
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Approximation Property ◽  
Fractional Power ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Well Posedness ◽  
Power Type ◽  
First Order ◽  
Dirichlet To Neumann Map

<p style='text-indent:20px;'>We study the well-posedness of a semi-linear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map. Our arguments are based on a first order linearization as well as the parabolic Runge approximation property.</p>

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