SC-Hamiltonian graphs and digraphs: New necessary conditions and their impacts

A graph G on n vertices is said to be separable cost constant Hamiltonian (SC-Hamiltonian) if and only if G is Hamiltonian and for any cost matrix C=(c_(i,j)) associated with G where all tours have the same cost, there exist vectors a=(a₁,…,a_n) and b=(b₁,…,b_n) such that . In this paper we show that for symmetric digraphs strong Hamiltonicity is a necessary condition for SC-Hamiltonicity. As a surprising consequence, we prove that the symmetric digraph obtained from an undirected SC-Hamiltonian graph by edge duplication need not be SC-Hamiltonian. This settles a conjecture of Kabadi and Punnen. We then show that an undirected graph on an even number of nodes having an edge that appears in every Hamiltonian cycle cannot be SC-Hamiltonian. Using this we establish that multiple subdivision of an edge need not preserve SC-Hamiltonicity, disproving a previous claim. Further, we identify other necessary conditions for SC-Hamiltonicity and obtain new classes of SC-Hamiltonian graphs.     

A novel statistical linearization solution for randomly excited coupled bending-torsional beams resting on non-linear supports

A novel statistical linearization technique is developed for computing stationary response statistics of randomly excited coupled bending-torsional beams resting on non-linear elastic supports. The key point of the proposed technique consists in representing the non-linear coupled response in terms of constrained linear modes. The resulting set of non-linear equations governing the modal amplitudes is then replaced by an equivalent linear one via a classical statistical error minimization procedure, which provides algebraic non-linear equations for the second-order statistics of the beam response, readily solved by a simple iterative scheme. Data from Monte Carlo simulations, generated by a pertinent boundary integral method in conjunction with a Newmark numerical integration scheme, are used as benchmark solutions to check accuracy and reliability of the proposed statistical linearization technique.

     

A Reader’s Comment on: “Hysteresis Model of Unconscious-Conscious Interconnection: Exploring Dynamics on m-Adic Trees”

p-Adic Numbers, Ultrametric Analysis and Applications - This comment is aimed to point out that the recent work due to H. Kim, J-Y. Moon, G. A. Mashour and U. Lee ([22]), in which the clinical and...     

Singularity Formation in Fractional Burgers’ Equations

The formation of singularities in finite time in nonlocal Burgers’ equations, with time-fractional derivative, is studied in detail. The occurrence of finite-time singularity is proved, revealing the underlying mechanism, and precise estimates on the blowup time are provided. The employment of the present equation to model a problem arising in job market is also analyzed.

     

Resonance Assisted Chalcogen Bonding as a New Synthon in the Design of Dyes

Intramolecular chalcogen bonding in arylhydrazones of sulfamethizole is strengthened by conjugation in the π-system of a noncovalent five-membered ring. The S⋅⋅⋅O distance in the sulfamethizole moiety of these compounds ranges from 2.698(3) to 2.806(15) Å, which indicates its strong dependence on the attached arylhydrazone fragments. Information on the nature of the intramolecular chalcogen bond was afforded by DFT calculations.     

Hybrid sol–gel silica adsorbent materials synthesized by molecular imprinting for tannin removal

Journal of Sol-Gel Science and Technology - This study reports the development of a functional adsorbent synthesized by the molecular imprinting method in a sol–gel matrix. The adsorption...     

Axiomatic foundations of quantum physics: Critiques and misunderstandings. Piron's question-proposition system

Some of the most frequent misconceptions about axiomatic quantum physics are discussed with the aim of clarifying their true significance, taking Piron's approach as conceptual framework. In particular, we deal with the following topics: the wrong identification of Piron's questions and Mackey's questions, and some curious alleged empirical consequences; the role of propositions as suitable equivalence classes of questions, their partial order structure, and the paradoxical consequences of the erroneous assignment to questions of some lattice properties involving propositions; the logical and the empirical purport of some negative theorems; the standard Hilbert space model of the theory and the consequent metaphysical disasters related to some identifications, which are peculiar of this model. A controversy between Foulis-Piron-Randall and Hadjisavvas-Thieffine-Mugur-Schächter is analyzed on the basis of the proposed Hilbert space model (in which Piron's questions are realized by Hilbertian effects, i.e., linear bounded operatorsF such that which clarify the different point of views. As an example, we treat the unsharp localization operators inL ₂().     

An asymptotic-preserving well-balanced scheme for the hyperbolic heat equationsUn schema « équilibre » et « asymptotic-preserving » pour les equations de la chaleur hyperboliques

We propose here a well-balanced numerical scheme for the one-dimensional Goldstein–Taylor system which is endowed with all the stability properties inherent to the continuous problem and works in both rarefied and diffusive regimes. To cite this article: L. Gosse, G. Toscani, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 337–342.     

Stochastic Lyapunov method

This paper is devoted to stability properties of solutions to stochastic differential equations obtained by a stochastic Lyapunov method.