Christoffel functions with power type weights

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.

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

Boundary Value Problems ◽

10.1186/s13661-019-01310-6 ◽

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.

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Two-dimensional power-type electronic spectrographs with a symmetry plane

Technical Physics ◽

10.1134/s1063784211060120 ◽

2011 ◽

Vol 56 (6) ◽

pp. 843-849 ◽

Cited By ~ 8

Author(s):

N. K. Krasnova

Keyword(s):

Symmetry Plane ◽

Two Dimensional ◽

Power Type

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Means of Power Type and Their Inequalities

Mathematische Nachrichten ◽

10.1002/mana.3212050107 ◽

1999 ◽

Vol 205 (1) ◽

pp. 131-147 ◽

Cited By ~ 2

Author(s):

Dag Lukkassen

Keyword(s):

Power Type

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

10.21203/rs.3.rs-332858/v1 ◽

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.

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Surface Roughness at Wire Electrical Discharge Machining

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.760.551 ◽

2015 ◽

Vol 760 ◽

pp. 551-556 ◽

Cited By ~ 1

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.

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