The interest in using fractal theory and its applications has grown the field of image processing. Image enhancement is one feature processing tools, which aims to improve details an image. digital pictures a challenging task due unforeseeable variation quality captured images. In this study, we present mathematical model local conformable differential operator (LCDO). proposed formulated by ca...

To lower the concentration of organic pollutants in effluent stream, wastewater must be treated before being discharged into environment. The question whether treatment facilities can successfully reduce micropollutants found their influent streams is becoming increasingly pressing. removal plants investigated using a model that incorporates biodegradation and sorption as key processes micropol...

Richard V. Kadison As attested to by his recent (2002) National Medal of Science, and a host of other honors, James Glimm is one of this country’s leading mathematical scientists. The citation for Jim’s Medal of Science states: “To James G. Glimm, Distinguished Leading Professor of Applied Mathematics and Statistics, State University of New York at Stony Brook and Brookhaven National Laboratory...

One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

In this paper, we study how to automatically classify mathematical expressions written in MathML (Mathematical Markup Language). It is an essential preprocess to resolve analysis problems originated from multi-meaning mathematical symbols. We first define twelve equation classes based on chapter information of mathematics textbooks and then conduct various experiments. Experimental results show...

Let us revisit briefly the foundation of n-dimensional elasticity theory as it can be found today in any textbook, restricting our study to n = 2 for simplicity. If x = (x, x) is a point in the plane and ξ = (ξ(x), ξ(x)) is the displacement vector, lowering the indices by means of the Euclidean metric, we may introduce the ”small” deformation tensor ǫ = (ǫij = ǫij = (1/2)(∂iξj + ∂jξi)) with n(n...

We derive a mathematical mechanism of infrared catastrophe from the idea for the proof in [22, 23] and generalize it so that we can apply it to several models in quantum field theory. We define the Carleman operator from the operator-theoretical pull-through formula on ground states. Characterizing infrared catastrophe by the Carleman operator, we study the mechanism of infrared catastrophe. An...

We present a survey of past research activities and current results in constructing a mathematical framework describing the principle of local reflexivity for operator ideals and reveal further applications involving operator ideal products consisting of operators which factor through a Hilbert space.

After some earlier work on single operators, von Neumann turned to families of operators in [1]. He initiated the study of rings of operators which are commonly called von Neumann algebras today. The papers which constitute the series “Rings of operators” opened a new field in mathematics and influenced research for half a century (or even longer). In the standard theory of modern operator alge...