Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..

A simple strategy for defining polynomial spline spaces over hierarchical T-meses

[EN]We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision scheme. The proposed technique includes some simple rules for inferring local knot vectors to define C 2 -continuous cubic tensor product spline blending functions. Our conjecture is that these rules allow to obtain, for a given T-mesh, a set of linearly independent spline functions with the property that spaces spanned by nested T-meshes are also nested, and therefore, the functions can reproduce cubic polynomials. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0- balanced mesh...

Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..

Thin Capitalization Rules and Entrepreneurial Capital Structure Decisions

Tax planners often choose debt over equity financing. As this has led to increased corporate debt financing, many countries have introduced thin capitalization rules to secure their tax revenues. In a general capital structure model we analyze if thin capitalization rules affect dividend and financing decisions, and whether they can partially explain why corporations receive both debt and equity capital. We model the Belgian, German and Italian rules as examples. We find that the so-called Miller equilibrium and definite financing effects depend significantly on the underlying tax system. Further, our results are useful for the treasury to decide what thin capitalization type to implement.

Weighted Majoritarian Rules for the Location of Multiple Public Facilities

We consider collective decision problems given by a profile of single-peaked preferences defined over the real line and a set of pure public facilities to be located on the line. In this context, Bochet and Gordon (2012) provide a large class of priority rules based on efficiency, object-population monotonicity and sovereignty. Each such rule is described by a fixed priority ordering among interest groups. We show that any priority rule which treats agents symmetrically — anonymity — respects some form of coherence across collective decision problems — reinforcement — and only depends on peak information — peakonly — is a weighted majoritarian rule. Each such rule defines priorities based on the relative size of the interest groups and specific weights attached to locations. We give an explicit account of the richness of this class of rules.

Changing assessment methods: New rules, new roles

Over the past 20 years,theuse of Computer Algebra Systems(CAS) has helped with the teaching of mathematics inengineer-ingschools. However the traditional use of CAS only in math labs has led to a narrow view by the student: the CAS is an additional work, not included in the learning process. The didactic guidelines of the European Higher Education Area(EHEA) propose a new teaching–learning model based on competencies. We suggest the use of the CAS be adapted to the new rules. In this paper,we present a model for the integrated use of the CAS,and we describe and analyze two experiments carried out in the academic year2011–2012. Our analysis suggests that the use of CAS in all learning and assessment activities has the potential to positively influence the development of competencies.

On a common circle: Natural scenes and Gestalt rules

To understand how the human visual system analyzes images, it is essential to know the structure of the visual environment. In particular, natural images display consistent statistical properties that distinguish them from random luminance distributions. We have studied the geometric regularities of oriented elements (edges or line segments) present in an ensemble of visual scenes, asking how much information the presence of a segment in a particular location of the visual scene carries about the presence of a second segment at different relative positions and orientations. We observed strong long-range correlations in the distribution of oriented segments that extend over the whole visual field. We further show that a very simple geometric rule, cocircularity, predicts the arrangement of segments in natural scenes, and that different geometrical arrangements show relevant differences in their scaling properties. Our results show similarities to geometric features of previous physiological and psychophysical studies. We discuss the implications of these findings for theories of early vision.

Toward rules for 1:1 polyamide:DNA recognition

Polyamides composed of four amino acids, imidazole (Im), pyrrole (Py), hydroxypyrrole (Hp), and β-alanine (β), are synthetic ligands that form highly stable complexes in the minor groove of DNA. Although specific pairing rules within the 2:1 motif can be used to distinguish the four Watson⋅Crick base pairs, a comparable recognition code for 1:1 polyamide:DNA complexes had not been described. To set a quantitative baseline for the field, the sequence specificities of Im, Py, Hp, and β for the four Watson⋅Crick base pairs were determined for two polyamides, Im-β-ImPy-β-Im-β-ImPy-β-Dp (1, for Im, Py, and β) and Im-β-ImHp-β-Im-β-ImPy-β-Dp (2, for Hp), in a 1:1 complex within the DNA sequence context 5′-AAAGAGAAGAG-3′. Im residues do not distinguish G,C from A,T but bind all four base pairs with high affinity. Py and β residues exhibit ≥10-fold preference for A,T over G,C base pairs. The Hp residue displays a unique preference for a single A⋅T base pair with an energetic penalty.

Regulating Water Footprint in Trade: The Role of WTO Rules & Principles

World Water Week is hosted and organised by the Stockholm International Water Institute (SIWI) and takes place each year in Stockholm. The World Water Week has been the annual focal point for the globe's water issues since 1991. Every year, over 200 collaborating organisations convene events at the World Water Week. In addition, individuals from around the globe present their findings at the scientific workshops.

Public hearing on proposed rules for controlling hazardous wastes : Resource Conservation and Recovery Act, Sections 3001-3004, Volume III, March 13, 1979, San Francisco, California 94105, transcript.

Hearing sponsored by EPA Office of Solid Waste.

Chitty's Forms of practical proceedings in the Queen's bench, of the High court of justice, with notes containing the statutes, rules and cases relating thereto.

Mode of access: Internet.

New criminal procedure: or, New commentaries on the law of pleading and evidence and the practice in criminal cases,

"The general rules of practice and procedure are treated in volumes I and II, while volume III is devoted wholly to procedure and evidence in various common law crimes."--Pref, to 2d ed.

Cases and other materials on judicial remedies, from the forms of actions and the classical equity practice to the Federal rules of civil procedure,

"Tables of cases": p. 1295-1301. "Table of statutes, constitutional provisions and rules of court": p. 1303-1309

Globally optimal on-line learning rules for multi-layer neural networks

We present a method for determining the globally optimal on-line learning rule for a soft committee machine under a statistical mechanics framework. This rule maximizes the total reduction in generalization error over the whole learning process. A simple example demonstrates that the locally optimal rule, which maximizes the rate of decrease in generalization error, may perform poorly in comparison.