Abstract. Let U be an open bounded subset of $R^d$. We aim to investigate the multiplication operator on Hölder space $C^{1,1}(U)$, specifically focusing on Fredholm operators. Our goal is to provide an interpretation of these operators in these spaces and to discuss and prove their properties. In the case where U is a subset of R, we present and prove results regarding these operators. Furthermore, we establish a necessary condition for the Fredholm property of these operators.

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Holder estimates of solutions of initial-boundary problem degenerate nonlinear parabolic equations are obtained. Estimates for solutions and parabolic Harnack inequality are proved. Also, one variant of weighted Poincare inequality is shown.

This paper introduces a new type of flame holder. Flow field is investigated, using PIV measurements in cold flow regime. The experiments on two types of V-shape flame holder: one with smooth edges and the other with wavy edges. The instantaneous velocity fields, Strouhal number, average velocity, vorticity, and recirculation zone length were among the parameters affected by the flame holder geometry. In this work, we examined the influence of these characteristics. Complex structure and unsteadiness of the flow was obtained with high accuracy. The results indicate an increase in length and width of the recirculation zone when using the wavy edges instead of smooth edges. For both geometries, a symmetrical flow structure was observed behind the flame holder. Also, higher static pressure drop was detected behind the flame holder for geometry with wavy edges.

Based on a two dimensional buckling modeling of an elastic -plastic annular plate and the well - known energy method, the critical conditions for the elastic and plastic wrinkling of the flange during the deep drawing with a blank-holder are studied. The blank-holder is considered to apply a uniform constant force. Using this model, first the critical stress for elastic and plastic wrinkling is obtained. Then the influences of the blank and die geometries and the blank-holder force on the critical stress in relation to wrinkling are discussed. Finally the optimum blank-holder force in relation to the plastic wrinkling in both theoretical and experimental approaches is obtained.

The primary function of the check is that it is used as ainstrument in commercial and non-commercial transactions. In order to fulfill this role, the order for payment of the amount stated in the instrument must be immediate. However, the identification of certain features, and as well as the principles governing this instrument, have led individuals to issue promising check or as a guarantee instrument. An issue that seems to run counter to its function. The use of checks in this regard raises the question of whether such writing may be subject to the rules governing on negotiable instruments. This paper is based on the check that although promising checks are contrary to the primary function of this instrument as an instant payment instrument, , features and principles governing negotiable instruments, as amended by the Issuing Check Law. However, issuing a check to ensure that the objective obligations of this instrument are met by the issue and function of this instrument as an instant payment instrument not only excludes it from the rules and regulations governing check and generally negotiable instruments, but also checks in that regard as a guarantee instrument. Like a bank guarantee, it cannot be recovered unless it is required to fulfill the original obligation and to prove that it has not been fulfilled.

In this paper, we show Hilbert C*-module versions of Holder– McCarthy inequality and its complementary inequality. As an application, we obtain Holder type inequalities and its reverses on a Hilbert C*-module.

Let (X,d) be a compact pointed metric space. In this paper, we investigate the condition on the underlying metric space (X,d) which implies that the little Lipschitz space on (X,d) is predual of L^1(\mu). Then, we conclude that the space of Holder functions on every compact pointed space, and for each 0

Recently, an innovative single-stage approach was developed in [J. Aparicio, J. L. Ruiz, I. Sirvent, Closest targets and minimum distance to the Pareto-efficient frontier in DEA, Journal of Productivity Analysis 28 (2006) 209-218], to determine the closest Pareto-efficient targets for a given inefficient decision making unit (DMU). The purpose of this paper is to perfect this approach via integrating it with the concepts of Holder norms and directional distance function. To this purpose, first, we introduce a furthest-target based directional, named Linear FDHDF, Holder distance function. Then, we characterize the set of Pareto-efficient points of the production possibility set dominating directionally the assessed DMU. Finally, we develop a closest-target based directional, named Linear CDHDF, Holder distance function that, as well as providing an efficiency index, determines the closest targets. Comparing to the earlier approach, our approach is more general and the decision maker’s preference information can be appropriately incorporated into efficiency assessment and target setting. Furthermore, it is more flexible in computer programming.