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1

Oscillation conditions for difference equations with several variable delays

El-Matary Bassant M., El-Morshedy Hassan A., Benekas Vasileios, Stavroulakis Ioannis P.

Opuscula Mathematica

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2023

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Vol. 43, no. 6

789--801

EN

A technique is developed to establish a new oscillation criterion for a first-order linear difference equation with several delays and non-negative coefficients. Our result improves recent oscillation criteria and covers the cases of monotone and non-monotone delays. Moreover, the paper is concluded with an illustrative example to show the applicability and strength of our result.

2

Second order inferencje in natural language semantics

Pulman S.

Journal of Language Modelling

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2018

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Vol. 6, No. 1

1--40

EN

In this paper I look at a number of apparently trivial valid inferences (as well as some invalid and missing inferences) associated with the possessive construction and with different types of adjectival modification of nouns. In the case of possessives, all analyses I know of, whether implemented or not, systematically sanction invalid inferences. In the case of adjectives, there are some model-theoretic linguistic analyses that are adequate at a theoretical level, but no satisfactory practical computational implementations that I am aware of which capture the correct inference patterns. A common thread between the possessive and the adjectival construction is that to derive the correct inferences we need secondo order quantification. This is an uncontroversial move within modeltheoretic formal semantics but a problem for computational semantics, since we have no fully automated theorem provers for anything Rother than first order logic (and only for subsets of first order logic do we have provers that are both fully decidable and efficient). I explore what is needed to provide a proof-theoretic account of the relevant inference patterns, and suggest some analyses requiring second order axioms. In order to make this a practical computational possibility I go on to propose two techniques for approximating such inferences in a first order setting. The suggested analyses have been fully implemented, and in an appendix I provide a small FraCaS-like corpus of relevant examples, all of which are handled correctly by the implementation.

3

Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales

Anderson D. R., Onitsuka M.

Demonstratio Mathematica

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2018

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Vol. 51, nr 1

198--210

EN

We establish the Hyers-Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, which include the continuous (step size zero) and the discrete (step size constant and nonzero) dynamic equations as important special cases. In particular, for certain parameter values in relation to the graininess of the time scale, we find the minimum HUS constants. A few nontrivial examples are provided. Moreover, an application to a perturbed linear dynamic equation is also included.

4

On the stability of first order impulsive evolution equations

Wang J., Feckan M., Zhou Y.

Opuscula Mathematica

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2014

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Vol. 34, no. 3

639--657

EN

In this paper, concepts of Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for impulsive evolution equations are raised. Ulam-Hyers-Rassias stability results on a compact interval and an unbounded interval are presented by using an impulsive integral inequality of the Gronwall type. Two examples are also provided to illustrate our results. Finally, some extensions of the Ulam-Hyers-Rassias stability for the case with infinite impulses are given.

5

Theoretical study of heat transfer effects on flow past a parabolic started vertical plate in the presence of chemical reaction of first order

Muthucumaraswamy R., Velmurugan S.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 2

275--284

EN

An exact solution of an unsteady flow past a parabolic starting motion of an infinite vertical plate with variable temperature and mass diffusion, in the presence of a homogeneous chemical reaction of first order has been studied. The plate temperature as well as concentration level near the plate are raised linearly with time t. The dimensionless governing equations are solved using the Laplace-transform technique. The effects of velocity profiles are studied for different physical parameters such as the chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time. It is observed that the velocity increases with increasing values of the thermal Grashof number or mass Grashof number. The trend is just reversed with respect to the chemical reaction parameter.