On the structure formation of hydrophobed particles in the boundary layer of water and octane phases

Two-dimensional aggregation of the surface modified glass beads was carried out in the boundary layer of water and octane phases. The effect of particles' hydrophobicity was investigated on the structure of forming aggregates and the growth process. The structure of the aggregates and their growth were characterized by a density function which demonstrates the change of mean particle density as a function of aggregate size. The growth yielded fractal or nonfractal structures in the investigated systems. The fractal structure of the aggregates was observed to be dependent on restructuring processes controlled by the surface properties of the beads.The experimental results are compared with earlier findings for aggregation of hydrophobic beads in the boundary layer of water and air phases.On leave from Loránd Eötvös University, Budapest, Hungary     

Interactions of dicarboxylic porphyrins with membranes in relation to their ionization state

The interactions of dicarboxylic porphyrins with membrane systems are discussed with particular emphasis on the effect of the charge of the porphyrin and the nature of the side-chains. The incorporation of hematoporphyrin or related dicarboxylic porphyrins within small unilamellar vesicles as membrane models is favored by a decrease of the pH in the range of physiological pH values. This effect might play an important role in the retention of porphyrins by tumors, which are more acidic than normal tissues. Kinetics studies also show that the partition of the porphyrin between the lipidic bilayer and the aqueous phase is governed by its release rate rather than by its incorporation rate.     

Some results on the behavior and estimation of the fractal dimensions of distributions on attractors

The strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation. In this paper we first provide a rigorous mathematical framework for the study of dimension, focusing on pointwise dimension(x) and the generalized Renyi dimensionsD(q), and give a rigorous proof of inequalities first derived by Grassberger and Procaccia and Hentschel and Procaccia. We then specialize to the problem of statistical estimation of the correlation dimension and information dimension. It has been recognized for some time that the error estimates accompanying the usual procedures (which generally involve least squares methods and nearest neighbor calculations) grossly underestimate the true statistical error involved. In least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates. We then develop an estimation procedure for which corrects for an important bias term (the local measure density) and provides confidence intervals for. The general applicability of this method is illustrated with various numerical examples.     

Partition function zeros for the one-dimensional ordered plasma in Dirichlet boundary conditions

We consider the grand canonical partition function for the ordered one-dimensional, two-component plasma at fugacity in an applied electric fieldE with Dirichlet boundary conditions. The system has a phase transition from a low-coupling phase with equally spaced particles to a high-coupling phase with particles clustered into dipolar pairs. An exact expression for the partition function is developed. In zero applied field the zeros in the plane occupy the imaginary axis from –i to –i_c and i_c to i for some _c. They also occupy the diamond shape of four straight lines from ±i_c to _c and from ±i_c to –_c. The fugacity acts like a temperature or coupling variable. The symmetry-breaking field is the applied electric fieldE. A finite-size scaling representation for the partition in scaled coupling and scaled electric field is developed. It has standard mean field form. When the scaled coupling is real, the zeros in the scaled field lie on the imaginary axis and pinch the real scaled field axis as the scaled coupling increases. The scaled partition function considered as a function of two complex variables, scaled coupling and scaled field, has zeros on a two-dimensional surface in a domain of four real variables. A numerical discussion of some of the properties of this surface is presented.     

Bounds for the fundamental solutions of elliptic and parabolic equations

It is shown that any elloptic or parabolic operator in nondivergence form with measurable coefficients has a global fundamental solution verifying certain pointwise bounds.     

Dimension polynomials of difference local algebras

We extend the concept of the difference dimension polynomial of a difference field extension to difference local algebras. The main theorem of the paper establishes the existence and form of the dimension polynomial associated with the localization of a finitely generated well-mixed difference algebra at a prime reflexive difference ideal.     

Some Remarks on One-dimensional Functions and Their Riemann–Liouville Fractional Calculus

A one-dimensional continuous function of unbounded variation on [0,1] has been constructed.The length of its graph is infnite,while part of this function displays fractal features.The Box dimension of its Riemann–Liouville fractional integral has been calculated.     

Surface influence on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel

Low-field nuclear magnetic resonance techniques are employed to extract information about the effects introduced by the interaction with the surface on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel. The molecules under study were water, cyclohexane, and hexane. They were chosen due to their different interaction strength with the carbonaceous matrix. Frequency dependent longitudinal relaxation measurements, using the fast field cycling technique, allowed extraction of the fractal dimension of the carbon xerogel surface. It was observed that the measured value is influenced by the molecule affinity to the surface. Diffusion measurements, using the pulse field gradient technique, have revealed that the stronger interaction with the surface of cyclohexane and hexane molecules leads to an increased diffusive tortuosity, as compared with water.     

On cohomological dimension and depth under linkage

Some relations between cohomological dimensions and depths of linked ideals are investigated and discussed by various examples.     

Brownian motion with drift on spaces with varying dimension

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel’s principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift.