Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth a, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered. (C) 2011 Elsevier Ltd. All rights reserved.

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered.

Oscillation for a second-order neutral differential equation with impulses

We consider a certain type of second-order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations (called impulses). As a matter of fact, some particular non-impulsive cases of the system are oscillatory already. Thus, we are interested in finding adequate impulse controls under which our system remains oscillatory. (C) 2009 Elsevier Inc. All rights reserved.

EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.

Stability switches in a first-order complex neutral delay equation

Stability of the first-order neutral delay equation x’ (t) + ax’ (t – τ) = bx(t) + cx(t – τ) with complex coefficients is studied, by analyzing the existence of stability switches.

Necessary and Sufficient Condition for Oscillations of Neutral Differential Equation

2000 Mathematics Subject Classification: 34K15, 34C10.

An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions

Pitzer`s equation for the excess Gibbs energy of aqueous solutions of low-molecular electrolytes is extended to aqueous solutions of polyelectrolytes. The model retains the original form of Pitzer`s model (combining a long-range term, based on the Debye-Huckel equation, with a short-range term similar to the virial equation where the second osmotic virial coefficient depends on the ionic strength). The extension consists of two parts: at first, it is assumed that a constant fraction of the monomer units of the polyelectrolyte is dissociated, i.e., that fraction does not depend on the concentration of the polyelectrolyte, and at second, a modified expression for the ionic strength (wherein each charged monomer group is taken into account individually) is introduced. This modification is to account for the presence of charged polyelectrolyte chains, which cannot be regarded as punctual charges. The resulting equation was used to correlate osmotic coefficient data of aqueous solutions of a single polyelectrolyte as well as of binary mixtures of a single polyelectrolyte and a salt with low-molecular weight. It was additionally applied to correlate liquid-liquid equilibrium data of some aqueous two-phase systems that might form when a polyelectrolyte and another hydrophilic but neutral polymer are simultaneously dissolved in water. A good agreement between the experimental data and the correlation result is observed for all investigated systems. (c) 2008 Elsevier B.V. All rights reserved.

Asymptotically almost periodic solutions for abstract neutral integro-differential equations

We study the existence of asymptotically almost periodic classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations which arise in the study of heat conduction in fading memory material is considered. (C) 2011 Elsevier Inc. All rights reserved.

Global solutions for abstract neutral differential equations

We study the existence of global solutions for a class of abstract neutral differential equation defined on the whole real axis. Some concrete applications related to ordinary and partial differential equations are considered. (C) 2009 Elsevier Ltd. All rights reserved.

Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations

The paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro-differential equation with unbounded delay. An example is given to illustrate our results. (C) 2008 Elsevier Ltd. All rights reserved.

Global solutions for abstract impulsive neutral differential equations

We study the existence of mild solutions for a class of impulsive neutral functional differential equation defined on the whole real axis. Some concrete applications to ordinary and partial neutral differential equations with impulses are considered. (C) 2010 Elsevier Ltd. All rights reserved.

The Wage-Productivity gap revisited: is the labour share neutral to employment?

This paper challenges the prevailing view of the neutrality of the labour income share to labour demand, and investigates its impact on the evolution of employment. Whilst maintaining the assumption of a unitary long-run elasticity of wages with respect to productivity, we demonstrate that productivity growth affects the labour share in the long run due to frictional growth (that is, the interplay of wage dynamics and productivity growth). In the light of this result, we consider a stylised labour demand equation and show that the labour share is a driving force of employment. We substantiate our analytical exposition by providing empirical models of wage setting and employment equations for France, Germany, Italy, Japan, Spain, the UK, and the US over the 1960-2008 period. Our findings show that the timevarying labour share of these countries has significantly influenced their employment trajectories across decades. This indicates that the evolution of the labour income share (or, equivalently, the wage-productivity gap) deserves the attention of policy makers.

In situ degradability of dry matter and neutral-detergent fibre of thorn scrubland forage consumed by goats in the semi-arid region of north Mexico

Three goats provided with oesophageal and ruminal cannulae were used to determine variations in dry matter (DM) and neutral-detergent fibre (NDF) degradability of the forage consumed when grazing thorn scrubland in the semi-arid region of north Mexico, during two consecutive dry and wet periods. Ingesta samples were incubated intraruminally, the data were fitted to the exponential equation P = a + b (1-e(-ct)) and statistically analysed using a randomized-block design. Organic matter and crude protein (CP) contents were higher (P < 0.05) in the wet seasons. Values of NDF were similar in dry and wet season of both years whereas higher numerical values of acid-detergent fibre (ADF), lignin and cellulose were registered in the dry seasons. DM and NDF degradabilities after 24 and 48 h of ruminal incubation were higher (P < 0.05) in the wet seasons. Higher values (P < 0.05) in DM and NDF bag losses at zero time (A fraction) were registered in the two wet seasons. The insoluble but fermentable DM and NDF (B fractions) were higher (P < 0.05) in the 1999 wet season and variable in the rest of the studied period. Numerically higher values of DM and NDF c fraction were found in wet periods, whereas DM and NDF potential degradabilities were higher (P < 0.05) in the wet season in 1999 and similar across seasons in 2000. Lowest (P < 0.05) contents of CP in grazed forage, DM and NDF degradabilities after 48 h of ruminal incubation, and A, and B, and c fractions were observed in the dry seasons. Thus, these results may be related to both the lower feeding value of forage consumed by the animals and lower performance of livestock during this period. Then, the DM and NDF degradability after 48 h, together with the insoluble but fermentable matter and the c fraction permit the nutritive value of the forage consumed by grazing goats to be accurately described.

Available potential energy density for a multicomponent Boussinesq fluid with arbitrary nonlinear equation of state

In this paper, the concept of available potential energy (APE) density is extended to a multicomponent Boussinesq fluid with a nonlinear equation of state. As shown by previous studies, the APE density is naturally interpreted as the work against buoyancy forces that a parcel needs to perform to move from a notional reference position at which its buoyancy vanishes to its actual position; because buoyancy can be defined relative to an arbitrary reference state, so can APE density. The concept of APE density is therefore best viewed as defining a class of locally defined energy quantities, each tied to a different reference state, rather than as a single energy variable. An important result, for which a new proof is given, is that the volume integrated APE density always exceeds Lorenz’s globally defined APE, except when the reference state coincides with Lorenz’s adiabatically re-arranged reference state of minimum potential energy. A parcel reference position is systematically defined as a level of neutral buoyancy (LNB): depending on the nature of the fluid and on how the reference state is defined, a parcel may have one, none, or multiple LNB within the fluid. Multiple LNB are only possible for a multicomponent fluid whose density depends on pressure. When no LNB exists within the fluid, a parcel reference position is assigned at the minimum or maximum geopotential height. The class of APE densities thus defined admits local and global balance equations, which all exhibit a conversion with kinetic energy, a production term by boundary buoyancy fluxes, and a dissipation term by internal diffusive effects. Different reference states alter the partition between APE production and dissipation, but neither affect the net conversion between kinetic energy and APE, nor the difference between APE production and dissipation. We argue that the possibility of constructing APE-like budgets based on reference states other than Lorenz’s reference state is more important than has been previously assumed, and we illustrate the feasibility of doing so in the context of an idealised and realistic oceanic example, using as reference states one with constant density and another one defined as the horizontal mean density field; in the latter case, the resulting APE density is found to be a reasonable approximation of the APE density constructed from Lorenz’s reference state, while being computationally cheaper.