Canonical trace ideal and residue for numerical semigroup rings

Semigroup Forum - For a numerical semigroup ring K[H] we study the trace of its canonical ideal. The colength of this ideal is called the residue of H. This invariant measures how far is H from...     

Families of rational solutions of the <Emphasis Type="Italic">y</Emphasis>-nonlocal Davey–Stewartson II equation

The y-nonlocal Davey–Stewartson II equation is an extension of the usual DS II equation involving a partially parity-time-symmetric potential only with respect to the spatial variable y. By using the Hirota bilinear method, families of n-order rational solutions are obtained, which include lumps in the (x, y)-plane and the (y, t)-plane, growing-and-decaying line waves in the (x, t)-plane, and hybrid solutions of interacting line rogue waves and lumps in the (x, y)-plane.     

$C^1$ error estimation on the boundary for an exterior Neumann problem in $\mathbb R^3$

Summary.   In this paper we establish a error estimation on the boundary for the solution of an exterior Neumann problem in . To solve this problem we consider an integral representation which depends from the solution of a boundary integral equation. We use a full piecewise linear discretisation which on one hand leads to a simple numerical algorithm but on the other hand the error analysis becomes more difficult due to the singularity of the integral kernel. We construct a particular approximation for the solution of the boundary integral equation, for the solution of the Neumann problem and its gradient on the boundary and estimate their error. Received May 11, 1998 / Revised version received July 7, 1999 / Published online August 24, 2000     

On a terminal value problem for a generalization of the fractional diffusion equation with hyper-Bessel operator

In this paper, we consider an inverse problem of recovering the initial value for a generalization of time-fractional diffusion equation, where the time derivative is replaced by a regularized hyper-Bessel operator. First, we investigate the existence and regularity of our terminal value problem. Then we show that the backward problem is ill-posed, and we propose a regularizing scheme using a fractional Tikhonov regularization method. We also present error estimates between the regularized solution and the exact solution using two parameter choice rules.     

Multiple summability properties for Cohen ‐summing operators

We prove that Cohen p‐summing operators satisfy multiple summability properties. Some of these multiple summability properties are new even in the linear case. For example, we prove that the multilinear functional associated to a Cohen p‐summing n‐linear operator is multiple ‐summing.     

Equations of motion for Einstein’s field in non-integer dimensional space

Equations of motion for Einstein’s field in fractional dimension of 4 spatial coordinates are obtained. It is shown that time dependent part of Einstein’s wave function is single valued for only 4-integer dimensional space.     

Statistische Untersuchung des ?quivalenzpunktes von linearen Titrationskurven mit Hilfe numerischer Simulierung

Zusammenfassung Die Statistik der Äquivalenzpunkte linearer Titrationskurven und ihrer Dispersionen wurde durch numerische Simulierung untersucht. Zur Berechnung dienten zwei früher von den Autoren vorgeschlagene Modelle [2,3] (einmal durch Regression und Fehlerfortpflanzung, zum anderen durch normale bidimensionale Verteilung). Die durch Simulierung erhaltenen Äquivalenzpunktgesamtheiten sind im wesentlichen bei beiden Modellen bidimensional normal verteilt Die Dispersion der nach Modell II erhaltenen Äquivalenzpunkte ist beträchtlich kleiner als bei Modell I und stimmt gut mit der Dispersion der simulierten Äquivalenzpunktgesamtheiten überein.

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Statistical investigation of the equivalence point of linear titration curves by means of numerical simulation

Summary The statistics of the equivalence points of linear titrations and their dispersions, determined on the basis of two models, earlier proposed by the authors [2,3] (the first by regression and error propagation, the second by normal bidimensional distributions), are studied by digital simulation. The equivalence point assemblies obtained by simulation are distributed essentially normal bidimensional in both models. The dispersion of the equivalence points estimated by model II is appreciable smaller than that given by model I and in good agreement with the dispersion of the assemblies of simulated equivalence points.

     

Cd(II) extraction in PEG-based two-phase aqueous systems in the presence of iodide ions. Analysis of PEG-rich solid phases

Cd(II) plus iodide species were extracted into PEG-rich phases in the aqueous PEG(1550)-(NH₄)₂SO₄ system at pH 2.05–7.12. IR spectra show that increasing (NH₄)₂SO₄ solution acidity does not protonate PEG ether oxygen atoms, but decreases water content in the PEG-rich phases. Metallic species’ extraction into the PEG predominantly alters how water molecules bind to polymer chains; the changes in their absorption bands depend on pH. Microscopy shows that “fixation” of the extracted metal in the PEG-rich phase occurs by specific interactions which depend on the species. These also determine changes in the polymer chains’ conformation.     

Periodic Solutions for Second-Order Differential Equations involving Nonconvex Superpotentials

The paper establishes the existence of a nonconstant periodic solution of a general second order nonautonomous Hamiltonian system with discontinuous nonlinearities. The multiplicity of solutions is also studied.     

A uniqueness criterion for fractional differential equations with Caputo derivative

We investigate the uniqueness of solutions to an initial value problem associated with a nonlinear fractional differential equation of order α∈(0,1). The differential operator is of Caputo type whereas the nonlinearity cannot be expressed as a Lipschitz function. Instead, the Riemann–Liouville derivative of this nonlinearity verifies a special inequality.