Monochromatic tree covers and Ramsey numbers for set-coloured graphs

We consider a generalisation of the classical Ramsey theory setting to a setting where each of the edges of the underlying host graph is coloured with a set of colours (instead of just one colour). We give bounds for monochromatic tree covers in this setting, both for an underlying complete graph, and an underlying complete bipartite graph. We also discuss a generalisation of Ramsey numbers to our setting and propose some other new directions.Our results for tree covers in complete graphs imply that a stronger version of Ryser’s conjecture holds for $k$-intersecting $r$-partite $r$-uniform hypergraphs: they have a transversal of size at most $r?k$. (Similar results have been obtained by Király et al., see below.) However, we also show that the bound $r?k$ is not best possible in general.     

On the existence of 3- and 4-kernels in digraphs

Let $D=(V\left(D\right),A\left(D\right))$ be a digraph. A subset $S?V\left(D\right)$ is $k$-independent if the distance between every pair of vertices of $S$ is at least $k$, and it is $?$-absorbent if for every vertex $u$ in $V\left(D\right)?S$ there exists $v\in S$ such that the distance from $u$ to $v$ is less than or equal to $?$. A $k$-kernel is a $k$-independent and $(k?1)$-absorbent set. A kernel is simply a $2$-kernel.A classical result due to Duchet states that if every directed cycle in a digraph $D$ has at least one symmetric arc, then $D$ has a kernel. We propose a conjecture generalizing this result for $k$-kernels and prove it true for $k=3$ and $k=4$.     

Thermoacoustic tomography for an integro-differential wave equation modeling attenuation

In this article we study the inverse problem of thermoacoustic tomography (TAT) on a medium with attenuation represented by a time-convolution (or memory) term, and whose consideration is motivated by the modeling of ultrasound waves in heterogeneous tissue via fractional derivatives with spatially dependent parameters. Under the assumption of being able to measure data on the whole boundary, we prove uniqueness and stability, and propose a convergent reconstruction method for a class of smooth variable sound speeds. By a suitable modification of the time reversal technique, we obtain a Neumann series reconstruction formula.     

Gradual technical and scale efficiency improvement in DEA

In data envelopment analysis (DEA) an inefficient unit can be projected onto an efficient target that is far away, i.e. reaching the target may demand large reductions in inputs and increases in outputs. When the inputs and outputs modifications planned are large, it may be troublesome to carry them out all at once. In order to help an inefficient unit reach a distant target, a strategy of gradual improvements with successive, intermediate targets has been proposed. This paper extends such approach to the variable returns to scale (VRS) case. In the VRS scenario we distinguish between units that are technical efficient and those that are not. On the one hand, for those units that are not technical efficient the proposed approach determines successive intermediate targets leading to the technical efficiency frontier, i.e. the priority for those units is to attain technical efficiency. On the other hand, for those units that are technical efficient but not scale efficient the proposed approach computes a sequence of targets ending in the global efficiency frontier, i.e. when technical efficiency is guaranteed the goal is then to attain global efficiency. In both cases, the successive targets are obtained by iteratively solving specific DEA models that take into account given bounds on the rates of change in inputs and outputs that the unit can implement in each step.     

Stationary solutions for generalized boussinesq models

We study the existence, regularity and conditioas for uniqueness of solutions of a generalized Boussinesq model for thermally driven convection. The model allows temperature dependent viscosity and thermal conductivity.     

Antibiotic protected silver nanoparticles for microbicidal cotton

Surface coating of metal nanoparticles is one of the major aspects to be optimized in the design of antimicrobial nanoparticles. The novelty of this work is that antimicrobial derivatives have been used as stabilizers to protect silver nanoparticles (Ag NPs). Microbicidal activity studies of fabricated cotton textiles coated with these Ag@Antibio were performed. Protective ligand layers of Ag NPs resulted to be a deterministic factor in their antimicrobial activity. The best bactericidal activity was obtained for Fabric TAM (coated with Ag NPs with triarylmethane derivates in surface, Ag@TAMSH), with a bacterial decrease of 3 log units for the S. aureus strain. Intrinsic antibiotic activity and partial positive charge of the TAMSH probably enhanced their antimicrobial effects. Fabric Eu (coated with Ag NPs with eugenol derivates in surface, Ag@EugenolSH) and Fabric FQPEG (coated with Ag NPs embedded in PEG-fluoroquinolone derivatives in surface, Ag@FQPEG) displayed antibacterial activity for both Staphylococcus aureus and Pseudomonas aeruginosa strains. These coated antimicrobial cotton fabrics can be applied in different medical textiles.     

Apoptosis in tongue squamous cell carcinoma and its correlation with clinically occult cervical metastasis

Squamous cell carcinoma of the tongue is one of the most common head and neck cancer. Treatment in the early stages is still controversial. This study aims to correlate the apoptosis rate of primary tongue cancer with cervical node metastasis, found in the histopathological studies of specimens obtained from neck dissections or during clinical follow-up. Twenty patients, 65% males, mean age 64.5 years, without clinical evidence of cervical metastasis was included. Eighty-five percent were smokers and 40% were alcohol abusers. Mann-Whitney test was used for statistical analysis (p相似文献   

Controllability results for the Moore–Gibson–Thompson equation arising in nonlinear acoustics

We show that the Moore–Gibson–Thomson equation

$\tau {?}_{ttt}y+\alpha {?}_{tt}y?c^2\mathrm{\Delta }y?b\mathrm{\Delta }{?}_{t}y=k{?}_{tt}(y^2)+{\chi }_{\omega (t)}u,$

is controlled by a force that is supported on an moving subset $\omega (t)$ of the domain, satisfying a geometrical condition. Using the concept of approximately outer invertible map, a generalized implicit function theorem and assuming that $\gamma :=\alpha ?\frac{\tau c^2}{b}>0$, the local null controllability in the nonlinear case is established. Moreover, the analysis of the critical value $\gamma =0$ for the linear equation is included.     

Polar Order,Mirror Symmetry Breaking,and Photoswitching of Chirality and Polarity in Functional Bent-Core Mesogens

In recent years, liquid crystals (LCs) responding to light or electrical fields have gained significant importance as multifunctional materials. Herein, two new series of photoswitchable bent-core liquid crystals (BCLCs) derived from 4-cyanoresorcinol as the central core connected to an azobenzene based wing and a phenyl benzoate wing are reported. The self-assembly of these molecules was characterized by differential scanning calorimetry (DSC), polarizing light microscopy (POM), electro-optical, dielectric, second harmonic generation (SHG) studies, and XRD. Depending on the direction of the COO group in the phenyl benzoate wing, core-fluorination, temperature, and the terminal alkyl chain length, cybotactic nematic and lamellar (smectic) LC phases were observed. The coherence length of the ferroelectric fluctuations increases continuously with decreasing temperature and adopts antipolar correlation upon the condensation into superparaelectric states of the paraelectric smectic phases. Finally, long-range polar order develops at distinct phase transitions; first leading to polarization modulated and then to nonmodulated antiferroelectric smectic phases. Conglomerates of chiral domains were observed in the high permittivity ranges of the synclinic tilted paraelectric smectic phases of these achiral molecules, indicating mirror symmetry breaking. Fine-tuning of the molecular structure leads to photoresponsive bent-core (BC)LCs exhibiting a fast and reversible photoinduced change of the mode of the switching between ferroelectric- and antiferroelectric-like as well as a light-induced switching between an achiral and a spontaneous mirror-symmetry-broken LC phase.     

A Zn(II) luminescent complex with a Schiff base ligand: solution,computational and solid state studies

Abstract

A new mononuclear complex of zinc(II), [Zn(HL)₂]?2DMF (H₂L = (E)-N′-((E)-(hydroxyimino)butan-2-ylidene)salicyloylhydrazide, DMF = N,N-dimethylformamide), was prepared and characterized. Single-crystal X-ray crystallography revealed a six-coordinate zinc(II) surrounded by nitrogen of the oxime function and oxygen and distal nitrogens of the acylhydrazone group. This entity also exists in solution as demonstrated by ¹H-NMR and potentiometric titrations. The computational analysis showed that the molecular orbitals involved in the main electronic transitions of the complex species in solution are centered on the ligand with negligible contribution of the metal ion. The photophysical properties of the complex were evaluated in solution and in the solid state. Luminescence studies showed that the solid has a strong emission at 550 nm with a large Stokes shift with respect to absorption. The solid state fluorescence emission is ascribed to ligand-centered and/or ligand-to-ligand charge transfer transitions, following the DFT results in solution. A comparison with a previously reported mononuclear [Zn(HL)₂] allowed the investigation of the influence of DMF molecules in the structural packing and the luminescence properties.