A simple spectral theory of polynomially bounded solutions and applications to differential equations

Semigroup Forum - In this paper we present a simple spectral theory of polynomially bounded functions on the half line, and then apply it to study the asymptotic behavior of solutions of fractional...     

A strongly regularN-full graph of small order

For every positive integern we show the construction of a strongly regular graph of order at most 2 ⁿ⁺² which contains every graph of ordern as a subgraph. The estimation concerning the construction is best possible.     

Small subgraphs of random regular graphs

The main aim of this short paper is to answer the following question. Given a fixed graph H, for which values of the degree d does a random d-regular graph on n vertices contain a copy of H with probability close to one?     

Experimental investigation of liquid chromatography columns by means of computed tomography

The efficiency of packed chromatographic columns was investigated experimentally by means of computed tomography (CT) techniques. The measurements were carried out by monitoring tracer fronts in situ inside the chromatographic columns. The experimental results were fitted using the equilibrium dispersive model (EDM) and varying the so called apparent axial dispersion coefficient. The additivity of the first and second central moments was exploited to estimate column efficiency in different regions of the column. The results showed that the columns under investigation offered a higher column efficiency in the centre compared to the wall region. Furthermore the void fraction in the vicinity of the walls was lower than that in the column core. For this reason the bands were conveyed faster in the central region of the column where the permeability was higher. This result is in good agreement with earlier findings.     

New observation and analysis of the E(4)Σ state in NaLi

Polarization labeling spectroscopy is applied to study the excited E(4)¹Σ⁺ state of NaLi in the energy range 25 850-27 750 cm⁻¹ above the bottom of the ground state. The potential curve of the E state is constructed using the Inverted Perturbation Approach method.     

Nontrivial periodicity in discrete delay models of population growth

In this paper, we will study the periodicity in discrete model An+1=λAn+F(An−m) of population growth, where the delay m is large enough and the nonlinearity F is unimodal function. Actually, we prove that there is a slowly oscillated periodic solution. Our method is Browder nonextremal fixed point theorem.     

Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers

We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution of squarefree monomial ideals. The theme of this paper is to understand how the combinatorial structure of a hypergraph ℋ appears within the resolution of its edge ideal ℐ(ℋ). We discuss when recursive formulas to compute the graded Betti numbers of ℐ(ℋ) in terms of its sub-hypergraphs can be obtained; these results generalize our previous work (Hà, H.T., Van Tuyl, A. in J. Algebra 309:405–425, 2007) on the edge ideals of simple graphs. We introduce a class of hypergraphs, which we call properly-connected, that naturally generalizes simple graphs from the point of view that distances between intersecting edges are “well behaved.” For such a hypergraph ℋ (and thus, for any simple graph), we give a lower bound for the regularity of ℐ(ℋ) via combinatorial information describing ℋ and an upper bound for the regularity when ℋ=G is a simple graph. We also introduce triangulated hypergraphs that are properly-connected hypergraphs generalizing chordal graphs. When ℋ is a triangulated hypergraph, we explicitly compute the regularity of ℐ(ℋ) and show that the graded Betti numbers of ℐ(ℋ) are independent of the ground field. As a consequence, many known results about the graded Betti numbers of forests can now be extended to chordal graphs. Dedicated to Anthony V. Geramita on the occasion of his 65th birthday.     

Synthesis and Reactivity of Structurally Analogous Phenylimido and Oxo Complexes of Rhenium(V) with N,N‐Dialkyl‐N′‐benzoylthioureas

[ReOCl₃(PPh₃)₂] and [Re(NPh)Br₃(PPh₃)₂] react at room temperature with equivalent amounts of N,N‐dialkyl‐N′‐benzoylthioureas (HR¹R²btu) in CH₂Cl₂ under formation of the rhenium(V) complexes [ReOCl₂(R¹R¹btu)(PPh₃)] and [Re(NPh)Br₂(R¹R²btu)(PPh₃)], respectively. The products are structurally analogous with the oxygen atoms of the benzoylthioureas binding in trans positions to the oxo or phenylimido ligands. Prolonged reaction times result in the reduction of the oxo compound by the released PPh₃ and the formation of rhenium(III) complexes of the composition [ReCl₂(PPh₃)₂(R¹R²btu)], while such a second reaction path is excluded for the phenylimido compound. Phenylimido species with more than one N,N‐dialkyl‐N′‐benzoylthioureato ligand could not be isolated, even when a large excess of HR¹R²btu was used during the reaction.     

Almost-periodic dissipative actions of semigroups

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 1, pp. 110–113, January–February, 1988.