Whitney equisingularity of families of surfaces in ℂ3

2018 ◽  
Vol 166 (2) ◽  
pp. 353-369 ◽  
Author(s):  
M.A.S. RUAS ◽  
O.N. SILVA
Keyword(s):  
Singular Surfaces ◽  
Complete Answer ◽  
Whitney Equisingularity

AbstractIn this paper, we study families of singular surfaces in ℂ3 parametrised by $\mathcal {A}$-finitely determined map germs. We consider the topological triviality and Whitney equisingularity of an unfolding F of a finitely determined map germ f : (ℂ2, 0) → (ℂ3, 0). We investigate the following question: topological triviality implies Whitney equisingularity of the unfolding F? We provide a complete answer to this question, by giving counterexamples showing how the conjecture can be false.

The influence of singular surfaces and morphological changes on coarsening

2005 ◽  
Vol 96 (2) ◽  
pp. 191-196 ◽  
Author(s):  
Gregory S. Rohrer ◽  
Chang-Soo Kim
Keyword(s):  
Morphological Changes ◽  
Singular Surfaces

scholarly journals Toughness, Forbidden Subgraphs and Pancyclicity

2021 ◽  
Vol 37 (3) ◽  
pp. 839-866
Author(s):  
Wei Zheng ◽  
Hajo Broersma ◽  
Ligong Wang
Keyword(s):  
Recent Article ◽  
Forbidden Subgraph ◽  
Forbidden Subgraphs ◽  
Free Graph ◽  
Induced Subgraph ◽  
Complete Answer ◽  
Open Case

AbstractMotivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of $$K_1\cup P_4$$ K 1 ∪ P 4 can act as a forbidden subgraph to ensure that every 1-tough H-free graph is hamiltonian, and that there is no other forbidden subgraph with this property, except possibly for the graph $$K_1\cup P_4$$ K 1 ∪ P 4 itself. The hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs, as conjectured by Nikoghosyan, was left there as an open case. In this paper, we consider the stronger property of pancyclicity under the same condition. We find that the results are completely analogous to the hamiltonian case: every graph H such that any 1-tough H-free graph is hamiltonian also ensures that every 1-tough H-free graph is pancyclic, except for a few specific classes of graphs. Moreover, there is no other forbidden subgraph having this property. With respect to the open case for hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs we give infinite families of graphs that are not pancyclic.

Growth Kinetics of Molecular Beam Epitaxy on Non-Singular Surfaces

1992 ◽  
Vol 280 ◽  
Author(s):  
J. F. Egler ◽  
N. Otsuka ◽  
K. Mahalingam
Keyword(s):  
Surface Roughness ◽  
Monte Carlo ◽  
Growth Kinetics ◽  
Molecular Beam ◽  
Singular Surface ◽  
Sticking Coefficient ◽  
Singular Surfaces ◽  
Vicinal Surfaces ◽  
Kinetics Of ◽  
Multiple Configurations

ABSTRACTGrowth kinetics on non-singular surfaces were studied by Monte Carlo simulations. In contrast to the growth on singular and vicinal surfaces, the sticking coefficient on the non-singular surfaces was found to decrease with increase of the surface roughness. Simulations of annealing processes showed that surface diffusion of atoms leads to a stationary surface roughness, which is explained by multiple configurations having the lowest energy in the non-singular surface.

Two open problems in the fixed point theory of contractive type mappings on quasimetric spaces

2017 ◽  
Vol 33 (2) ◽  
pp. 169-180
Author(s):  
MITROFAN M. CHOBAN ◽  
◽  
VASILE BERINDE ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Answer ◽  
Open Problems ◽  
Complete Answer ◽  
Contractive Type ◽  
Generalized Distances

Two open problems in the fixed point theory of quasi metric spaces posed in [Berinde, V. and Choban, M. M., Generalized distances and their associate metrics. Impact on fixed point theory, Creat. Math. Inform., 22 (2013), No. 1, 23–32] are considered. We give a complete answer to the first problem, a partial answer to the second one, and also illustrate the complexity and relevance of these problems by means of four very interesting and comprehensive examples.

On the logic of incomplete answers

1965 ◽  
Vol 30 (1) ◽  
pp. 65-68 ◽  
Author(s):  
M. J. Cresswell
Keyword(s):  
Formal Analysis ◽  
Complete List ◽  
Strict Implication ◽  
Complete Answer ◽  
Questions And Answers ◽  
Image Position

I have argued in [1] that a concept bearing some resemblance to ‘p is the answer to d’ (p a proposition and d a question) can be defined wherever d has the form,‘For which a's is it the case that A (a)?’ (Qa)A(a)where a is a variable and A a wff containing a. To say that p is the true and complete answer to (Qa)A(a) is expressed as saying that p is logically equivalent to the true conjunction of A(a) or ~A(a) for each a. It is defined as;Such a concept of answer is like Belnap's [2] direct true answer to a complete list question, or like Harrah's use [3] (p. 43) of the notion of a state description. The main difference between my approach and that of Belnap and Harrah is that while they are concerned to develop a formal metalanguage for discussion of questions and answers I am concerned to express, as far as possible in existing systems, certain interrogative statements; in particular statements of the form ‘— is the (an) answer to —’.While the account in [1] does give a formal analysis of one ‘answer’ concept there are respects in which it is inadequate.1. Since it uses entailment (or strict implication) to define the relation between p the answer and d the question we can shew that if p is the answer to d and q is logically equivalent to p then q is the answer to d.

Counting Partial Orders with a Fixed Number of Comparable Pairs

2001 ◽  
Vol 10 (2) ◽  
pp. 159-177 ◽  
Author(s):  
HANS JÜRGEN PRÖMEL ◽  
ANGELIKA STEGER ◽  
ANUSCH TARAZ
Keyword(s):  
Lattice Gas ◽  
Fixed Number ◽  
Partial Orders ◽  
Complete Answer

In 1978, Dhar suggested a model of a lattice gas whose states are partial orders. In this context he raised the question of determining the number of partial orders with a fixed number of comparable pairs. Dhar conjectured that in order to find a good approximation to this number, it should suffice to enumerate families of layer posets. In this paper we prove this conjecture and thereby prepare the ground for a complete answer to the question.

scholarly journals 4–manifolds as covers of the 4–sphere branched over non-singular surfaces

2002 ◽  
Vol 6 (1) ◽  
pp. 393-401 ◽  
Author(s):  
Massimiliano Iori ◽  
Riccardo Piergallini
Keyword(s):  
Singular Surfaces
Sign in / Sign up

Export Citation Format

Share Document