Tests of the Three-Triplet Models in the Deep-Inelastic Region

We examine the uncertainties involved in the off-mass-shell extrapolation of the K→ππ decay amplitude with emphasis on those aspects that have so far been overlooked or ignored. Among them are initial-state interactions, choice of the extrapolated kaon field, and the relation between the asymptotic behavior and the zeros of the decay amplitude. In the inelastic region the phase of the decay amplitude cannot be determined by strong interaction alone and even its asymptotic value cannot be deduced from experiment. More a fundamental issue is intrinsic nonuniqueness of off-shell values of hadronic matrix elements in general. Though we are hampered with the complexity of intermediate-energy meson interactions, we attempt to obtain a quantitative idea of the uncertainties due to the inelastic region and find that they can be much larger than more optimistic views portray. If large uncertainties exist, they have unfortunate implications in the numerical accuracy of the computation of the direct CP violation parameter ∊′.

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Quasilinear Utility and Two Market Monopoly

International Business Research ◽

10.5539/ibr.v10n3p164 ◽

2017 ◽

Vol 10 (3) ◽

pp. 164

Author(s):

Stephen K. Layson

Keyword(s):

Price Discrimination ◽

Marginal Cost ◽

Utility Functions ◽

Profit Margins ◽

Price Elasticities ◽

Monopoly Pricing ◽

Representative Consumer ◽

Quasilinear Utility ◽

Economic Analyses ◽

Inelastic Region

The use of quasilinear utility functions in economic analyses is widespread. This paper presents an overdue clarification on the implications of quasilinear utility for two market monopoly. The paper begins by deriving the demands facing a two market monopoly from a representative consumer with quasilinear utility. Expressions are derived for the profit margins expressed solely in terms of the own and cross-price elasticities of demand. The paper also analyzes the implications of quasilinear utility for other issues in two market monopoly: pricing below marginal cost in a market, third-degree price discrimination when the monopoly products are substitutes and pricing in the inelastic region of demands.

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Effect of Tensile Prestrain on Fatigue Strength of Aluminum Alloy in High Cycle Fatigue

Journal of Engineering Materials and Technology ◽

10.1115/1.3443135 ◽

1973 ◽

Vol 95 (2) ◽

pp. 76-82 ◽

Cited By ~ 6

Author(s):

P. R. Arora ◽

M. R. Raghavan

Keyword(s):

Aluminum Alloy ◽

Fatigue Strength ◽

Fatigue Loading ◽

Cyclic Stress ◽

Stress Strain ◽

Static Modulus ◽

Material Condition ◽

Rotating Bending Fatigue ◽

Rotating Bending ◽

Inelastic Region

The effect of tensile prestrain on rotating bending fatigue strength of B51-S aluminum alloy in the solution treated and precipitation hardened condition, has been studied at fatigue life in the range of 5 × 104 to 106 cycles. The fatigue strength decreases when the tensile prestrain is 1.5 percent. At a higher prestrain of 3 to 4 percent, fatigue strength is close to that of virgin material. The cyclic stress-strain curves for virgin and prestrained materials are linear. There is no perceptible strain hardening/strain softening of the material under fatigue loading. The cyclic Young’s modulus is about 4 percent lower than the static modulus irrespective of the material condition. The relative disposition of static bending stress-strain curves in the inelastic region for virgin and prestrained materials shows qualitatively the relative disposition of the corresponding S-N curves.

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