The applications of graph coloring are diverse and many so lots of new types of coloring are being proposed and explored. Here we define a safe k-coloring, motivated by the application of coloring to secret sharing. Secret sharing is a way of securing a secret from a number of attackers by dividing it into parts and then distributing those parts to some persons, represented here by graph vertices. Parts of the secret are represented by colors which are then assigned to the vertices under certain conditions, making a coloring safe if a predetermined number of attackers cannot read the whole secret, nor disable the rest of the group from doing so. We observe a fixed number of colors, namely 3, and analyze what kind of graphs have a safe 3-coloring.

In this paper we present some global dynamic scenarios for general competitive maps in the plane. We apply these results to the class of second-order autonomous difference equations whose transition functions are decreasing in the variable xn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$x_{n}$\end{document} and increasing in the variable xn−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$x_{n-1}$\end{document}. We illustrate our results with the application to the difference equation xn+1=Cxn−12+Exn−1axn2+dxn+f,n=0,1,…,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ x_{n+1}=\frac{Cx_{n-1}^{2}+Ex_{n-1}}{a x_{n}^{2}+d x_{n}+f},\quad n=0,1,\ldots, $$\end{document} where the initial conditions x−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$x_{-1}$\end{document} and x0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$x_{0}$\end{document} are arbitrary nonnegative numbers such that the solution is defined and the parameters satisfy C,E,a,d,f≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C,E,a,d,f\geq0$\end{document}, C+E>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C+E>0$\end{document}, a+C>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a+C>0$\end{document}, and a+d>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a+d>0$\end{document}. We characterize the global dynamics of this equation with the basins of attraction of its equilibria and periodic solutions.

Polazeći od I i II zakona termodinamike, primjenjenog upovratnim procesima, a kod kojih je postignuta ravnoteža pritiskai temperature, u radu je izveden izraz za ukupni maksimalnizaprmenski rad zatvorenih sistema. Radi potpunije interpretacijeove problematike za dva karakteristična slučaja, dat je grafičkiprikaz u p-v dijagramu, gdje se na očigledan način zapaža da senajveći rad širenja sastoji iz izenropskog i izotermnog rada kao irada protiv pritiska okoline. Na bazi izvedenog izraza, koristećiodgovarajuće termodinamičke relacije, izveden je izraz zaspecifični maksimalni rad koji je pogodan za analizu. Dobijeni izrazje posmatran kao dvodimenzioni problem odnosno kao funkcijadvije promijenive: početni pritisak i početna temperatura kaoprimarni parametri. Primjenom matematičke analize dokazano jepostojanje minimuma posmatrane funkcije, i dato njeno grafičkopredstavljanje u prostornom koordinatnom sistemu. Detaljnommatematičkom analizom pokazano je da u opštem slučaju funkcijamaksimalnog rada geometrijski predstavlja jednu konkavnupovršinu u prostoru.Radi efikasnijeg rješavanja i analizepostavljenog problema, složena funkcija maksimalnog radaposmatrana je kao dvije funkcije sa jednom promjenljivomodnosno dvodimenzioni problem sveden je na dvajednodimenziona problema. Pokazano je da i kodjednodimenzionih problema takođe postoji tačka u kojoj jemaksimalni rad minimalan a različit od nule. Na kraj rada, date sumogućnosti primjene kompleksne problematike maksimalnograda a koje se odnose na eksergijsku analizu i optimizacijutermodinamičkih procesa, kao i smjernice za naredna istraživanjaproblema za slučaj ostalih gasova, poluidealnih gasova i Van derWaals – ovog gasa. Može se tvrditi, da postupak analizetermodinamičke funkcije maksimalnog rada, prikazanog u radu,nije uobičajen u literaturi.

Loading of microRNAs (miRNAs) into exosomes that are involved in cellular communication is a selective process. The current study investigates whether the enrichment of miRNAs in exosomes reflects the pathogenesis of breast cancer (BC) and ductal carcinoma in situ (DCIS). The levels of miRNAs were quantified in exosomes from plasma of 32 BC patients, 8 DCIS patients and 8 healthy women by TaqMan real-time PCR-based miRNA array cards containing 47 different miRNAs. Then, exosomal miR-16, miR-30b and miR-93 that displayed deregulation in the arrays were selected and analyzed in 111 BC patients, 42 DCIS patients and 39 healthy women by TaqMan real-time PCR. Identification of exosomes was performed by Western blot. The levels of exosomal miR-16 were higher in plasma of BC (p = 0.034) and DCIS (p = 0.047) patients than healthy women, and were associated with estrogen (p = 0.004) and progesterone (p = 0.008) receptor status. Particularly, in estrogen-positive patients miR-16 was significantly enriched in exosomes (p = 0.0001). Lower levels of exosomal miR-30b were associated with recurrence (p = 0.034). Exosomal miR-93 was upregulated in DCIS patients (p = 0.001). Our findings suggest that different signatures of miR-16, miR-30b and miR-93 in exosomes from BC and DCIS patients are associated with a particular biology of breast tumors.

An alternative strategy to increase mass transfer entails geometry optimization of the extraction systems including design of solid-phase microextraction (SPME) probes. In this work, a computational model was employed to elucidate practical aspects such as efficiency and kinetics of extraction by employing several new geometries. Extraction of a model analyte at static conditions with the configurations, such as thin-film, fiber, coated tip, and nanoparticles, was numerically simulated to obtain an in-depth understanding of the advantages and limitations of each geometry in microextraction and exhaustive modes. The attained results associated with the equilibration time dependency on shape were in good agreement with previously reported experimental observations. They demonstrate that the mass-transfer is highly dependent on the size and shape of the coatings and increases with a decrease in size of the devices particularly rapidly below 10 μm caused by radial diffusion effect. Nevertheless, extractions performed using octadecyl-functionalized magnetic nanoparticles demonstrated that higher enrichment factors are achievable with the use of a fewer number of particles in comparison to factors achieved via exhaustive extraction, where a larger number of particles must be employed, confirming theoretical predictions. The conclusions reached are valid for any extraction method. The results obtained herein are very useful toward the design and optimization of future extraction technologies and approaches.

ABSTRACT Quantum-orbit theory of high-order harmonic generation (HHG) by bicircular laser field is presented. HHG is a strong laser-field-induced process in which the energy absorbed from the laser field is emitted in the form of a high-energy photon. This process can be described using the strong-field approximation and its approximation – the quantum-orbit theory. We develop a classification of quantum orbits for HHG by bicircular field which consists of two coplanar counter-rotating circularly polarized field of frequencies and , where r and s are integers and ω is a fundamental frequency. Analysis of the contributions of particular quantum orbits to high-harmonic intensity enables a better understanding of the HHG process. The cases of the ω– and ω– bicircular fields and of the atoms having the s and the p ground state are analysed in detail. Particular attention is devoted to the influence of the ratio of the intensities and of the bicircular field components. For inert gases having the p ground state the asymmetry in the emission of the left- and right-circularly polarized harmonics can be large. This is explained comparing the partial harmonic intensities for HHG from the ground state having the magnetic quantum number m=+1 and m=−1 and analysing the contributions of particular quantum orbits and the corresponding electron trajectories and velocities. The contribution of the shortest quantum orbit is dominant. It was found that the electron velocity at the ionization time, which still allows the return of the electron to the parent ion, determines the height of the high-energy HHG plateau. For this velocity is large which, in the case of the p ground state, leads to a large helicity asymmetry parameter. On the other hand, for this velocity is small and the intensity of the high-energy plateau harmonics is high.