Solving Generalized Equations with Bounded Variables and Multiple Residuated Operators

This paper studies the resolution of sup-inequalities and sup-equations with bounded variables such that the sup-composition is defined by using different residuated operators of a given distributive biresiduated multi-adjoint lattice. Specifically, this study has analytically determined the whole set of solutions of such sup-inequalities and sup-equations. Since the solvability of these equations depends on the character of the independent term, the resolution problem has been split into three parts distinguishing among the bottom element, join-irreducible elements and join-decomposable elements.

Rewet in wet pressing of paper

Wet pressing in papermaking removes water by pressure applied over time, but some of the expelled water may return to the web in an action called “rewet.” This water, and the other remaining water, must be removed by drying. To understand the underlying factors of rewet, we have developed a mathematical model of it comprised of a time-dependent term that accounts for water flow from the felt to paper and a time-independent term that accounts for splitting of interfacial water between the felt and paper. Our model is consistent with measurements from the literature and can be used to understand how paper properties, press operation, and felt design can minimize rewet.

NONHOMOGENEOUS PATTERNS ON NUMERICAL SEMIGROUPS

Patterns on numerical semigroups are multivariate linear polynomials, and they are said to admit a numerical semigroup if evaluating the pattern at any nonincreasing sequence of elements of the semigroup gives integers belonging to the semigroup. In a first approach, only homogeneous patterns were analyzed. In this contribution we study conditions for a nonhomogeneous pattern to admit a nontrivial numerical semigroup, and particularize this study to the case the independent term of the pattern is a multiple of the multiplicity of the semigroup. Moreover, for the so-called strongly admissible patterns, the set of numerical semigroups admitting these patterns with fixed multiplicity m forms an m-variety, which allows us to represent this set in a tree and to describe minimal sets of generators of the semigroups in the variety with respect to the pattern. Furthermore, we characterize strongly admissible patterns having a finite associated tree.

Exact quantization formula for affine linearly energy-dependent potentials

We construct an exact quantization formula for Schrödinger equations with potentials thatdepend affine linearly on the energy, that is, they contain a term linear in the energy plus an energy-independent term. If such an energy-dependent potential admits a discrete spectrum and its ground state solution is known, our formula predicts the complete energy spectrum in exact form.

REVISITING THE CHARGE TRANSPORT IN QUANTUM HALL SYSTEMS

We re-examine the charge transport induced by a weak electric field in two-dimensional quantum Hall systems in a finite, periodic box at very low temperatures. Our model covers random vector and electrostatic potentials and electron–electron interactions. The resulting linear response coefficients consist of the time-independent term σxy corresponding to the Hall conductance and the linearly time-dependent term γsy · t in the transverse and longitudinal directions s=x,y in a slow switching limit for adiabatically applying the initial electric field. The latter terms γsy · t are due to the acceleration of the electrons by the uniform electric field in the finite and isolated system, and so the time-independent term σyy corresponding to the diagonal conductance which generates dissipation of heat always vanishes. The well-known topological argument yields the integral and fractional quantization of the averaged Hall conductance [Formula: see text] over gauge parameters under the assumption that there exists a spectral gap above the ground state. In addition to this fact, we show that the averaged acceleration coefficients [Formula: see text] vanish under the same assumption. In the non-interacting case, the spectral gap between the neighboring Landau levels persists if the vector and the electrostatic potentials together satisfy a certain condition, and then the Hall conductance σxy without averaging exhibits the exact integral quantization with the vanishing acceleration coefficients in the infinite volume limit. We also estimate their finite size corrections. In the interacting case, the averaged Hall conductance [Formula: see text] for a non-integer filling of the electrons is quantized to a fraction not equal to an integer under the assumption that the potentials satisfy certain conditions in addition to the gap assumption. We also discuss the relation between the fractional quantum Hall effect and the Atiyah–Singer index theorem for non-Abelian gauge fields.

An application and e aluation of the C/NC-value approach for the automatic term recognition of multi-word units in Japanese

Technical terms are important for knowledge mining, especially as vast amounts of multi-lingual documents are available over the Internet. Thus, a domain and language-independent method for term recognition is necessary to automatically recognize terms from Internet documents. The C-/NC-value method is an efficient domain-independent multi-word term recognition method which combines linguistic and statistical knowledge. Although the C-value/NC-value method is originally based on the recognition of nested terms in English, our aim is to evaluate the application of the method to other languages and to show its feasibility for multi-language environments. In this article, we describe the application of the C/NC-value method to Japanese texts. Several experiments analysing the performance of the method using the NACSIS Japanese AI-domain corpus demonstrate that the method can be utilized to realize a practical domain-and language-independent term rec- ognition system.