Existence of disjoint weakly mixing operators that fail to satisfy the Disjoint Hypercyclicity Criterion

Recently, Bès, Martin, and Sanders [11] provided examples of disjoint hypercyclic operators which fail to satisfy the Disjoint Hypercyclicity Criterion. However, their operators also fail to be disjoint weakly mixing. We show that every separable, infinite dimensional Banach space admits operators T1,T2,…,TN with N⩾2 which are disjoint weakly mixing, and still fail to satisfy the Disjoint Hypercyclicity Criterion, answering a question posed in [11]. Moreover, we provide examples of disjoint hypercyclic operators T1, T2 whose corresponding set of disjoint hypercyclic vectors is nowhere dense, answering another question posed in [11]. In fact, we explicitly describe their set of disjoint hypercyclic vectors. Those same disjoint hypercyclic operators fail to be disjoint topologically transitive. Lastly, we create examples of two families of d-hypercyclic operators which fail to have any d-hypercyclic vectors in common.

Endonuclease Controlled Aggregation of Gold Nanoparticles for the Ultrasensitive Detection of Pathogenic Bacterial DNA

The development of an ultrasensitive biosensor for the low-cost and on-site detection of pathogenic DNA could transform detection capabilities within food safety, environmental monitoring and clinical diagnosis. Herein, we present an innovative approach exploiting endonuclease-controlled aggregation of plasmonic gold nanoparticles (AuNPs) for label-free and ultrasensitive detection of bacterial DNA. The method utilizes RNA-functionalized AuNPs which form DNA-RNA heteroduplex structures through specific hybridization with target DNA. Once formed, the DNA-RNA heteroduplex is susceptible to RNAse H enzymatic cleavage of the RNA probe, allowing the target DNA to liberate and hybridize with another RNA probe. This continuously happens until all of the RNA probes are cleaved, leaving the nanoparticles unprotected and thus aggregated upon exposure to a high electrolytic medium. The assay is ultrasensitive, allowing the detection of target DNA at femtomolar level by simple spectroscopic analysis (40.7 fM and 2.45 fM as measured by UV-vis and dynamic light scattering (DLS), respectively). The target DNA spiked food matrix (chicken meat) is also successfully detected at a concentration of 1.2 pM (by UV-vis) or 18.0 fM (by DLS). In addition to the ultra-high sensitivity, the total analysis time of the assay is less than 3 hours, thus demonstrating its practicality for food analysis.

Temporal aggregation of migration counts can improve accuracy and precision of trends

Temporal replicate counts are often aggregated to improve model fit by reducing zero-inflation and count variability, and in the case of migration counts collected hourly throughout a migration, allows one to ignore nonindependence. However, aggregation can represent a loss of potentially useful information on the hourly or seasonal distribution of counts, which might impact our ability to estimate reliable trends. We simulated 20-year hourly raptor migration count datasets with known rate of change to test the effect of aggregating hourly counts to daily or annual totals on our ability to recover known trend. We simulated data for three types of species, to test whether results varied with species abundance or migration strategy: a commonly detected species, e.g., Northern Harrier, Circus cyaneus; a rarely detected species, e.g., Peregrine Falcon, Falco peregrinus; and a species typically counted in large aggregations with overdispersed counts, e.g., Broad-winged Hawk, Buteo platypterus. We compared accuracy and precision of estimated trends across species and count types (hourly/daily/annual) using hierarchical models that assumed a Poisson, negative binomial (NB) or zero-inflated negative binomial (ZINB) count distribution. We found little benefit of modeling zero-inflation or of modeling the hourly distribution of migration counts. For the rare species, trends analyzed using daily totals and an NB or ZINB data distribution resulted in a higher probability of detecting an accurate and precise trend. In contrast, trends of the common and overdispersed species benefited from aggregation to annual totals, and for the overdispersed species in particular, trends estimating using annual totals were more precise, and resulted in lower probabilities of estimating a trend (1) in the wrong direction, or (2) with credible intervals that excluded the true trend, as compared with hourly and daily counts.

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

Pico Cell Integration to Operator’s Incident Management Process

Mobile network coverage is traditionally provided by outdoor macro base stations, which have a long range and serve several of customers. Due to modern passive houses and tightening construction legislation, mobile network service is deteriorated in many indoor locations. Typically, solutions for indoor coverage problem are expensive and demand actions from the mobile operator. Due to these, superior solutions are constantly researched. The solution presented in this thesis is based on Small Cell technology. Small Cells are low power access nodes designed to provide voice and data services.. This thesis concentrates on a specific Small Cell solution, which is called a Pico Cell. The problem regarding Pico Cells and Small Cells in general is that they are a new technological solution for the mobile operator, and the possible problem sources and incidents are not properly mapped. The purpose of this thesis is to figure out the possible problems in the Pico Cell deployment and how they could be solved within the operator’s incident management process. The research in the thesis is carried out with a literature research and a case study. The possible problems are investigated through lab testing. Pico Cell automated deployment process was tested in the lab environment and its proper functionality is confirmed. The related network elements were also tested and examined, and the emerged problems are resolvable. Operators existing incident management process can be used for Pico Cell troubleshooting with minor updates. Certain pre-requirements have to be met before Pico Cell deployment can be considered. The main contribution of this thesis is the Pico Cell integrated incident management process. The presented solution works in theory and solves the problems found during the lab testing. The limitations in the customer service level were solved by adding the necessary tools and by designing a working question pattern. Process structures for automated network discovery and pico specific radio parameter planning were also added for the mobile network management layer..

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

Invertibility characterization of Wiener-Hopf plus Hankel operators on variable exponent Lebesgue spaces via even asymmetric factorization

We obtain invertibility and Fredholm criteria for the Wiener-Hopf plus Hankel operators acting between variable exponent Lebesgue spaces on the real line. Such characterizations are obtained via the so-called even asymmetric factorization which is applied to the Fourier symbols of the operators under study.

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

One Person, Many Votes: Divided Majority and Information Aggregation

In elections, majority divisions pave the way to focal manipulations and coordination failures, which can lead to the victory of the wrong candidate. This paper shows how this flaw can be addressed if voter preferences over candidates are sensitive to information. We consider two potential sources of divisions: majority voters may have similar preferences but opposite information about the candidates, or opposite preferences. We show that when information is the source of majority divisions, Approval Voting features a unique equilibrium with full information and coordination equivalence. That is, it produces the same outcome as if both information and coordination problems could be resolved. Other electoral systems, such as Plurality and Two-Round elections, do not satisfy this equivalence. The second source of division is opposite preferences. Whenever the fraction of voters with such preferences is not too large, Approval Voting still satisfies full information and coordination equivalence.

Strictly singular operators in pairs of L (p) space

Let E and F be Banach spaces. A linear operator from E to F is said to be strictly singular if, for any subspace Q aS, E, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from L (p) to L (q) is found. There exists a strictly singular but not superstrictly singular operator on L (p) , provided that p not equal 2.

Effect of the synthetic coumarin, ethyl 2-oxo-2H-chromene-3-carboxylate, on activity of Crotalus durissus ruruima sPLA2 as well as on edema and platelet aggregation induced by this factor

We show that ethyl 2-oxo-2H-chromene-3-carboxylate (EOCC), a synthetic coumarin, irreversibly inhibits phospholipase A(2) (sPLA2) from Crotalus durissus ruruima venom (sPLA2r) with an IC(50) of 3.1 +/- 0.06 nmol. EOCC strongly decreased the V(max) and K(m), and it virtually abolished the enzyme activity of sPLA2r as well as sPLA2s from other sources. The edema induced by 5PLA2r + EOCC was less than that induced by 5PLA2r treated with p-bromophenacyl bromide, which was more efficient at neutralizing the platelet aggregation activity of native 5PLA2r. Native 5PLA2r induced platelet aggregation of 91.54 +/- 9.3%, and sPLA2r +/- EOCC induced a platelet aggregation of 18.56 +/- 6.5%. EOCC treatment also decreased the myotoxic effect of sPLA2r. Mass spectrometry showed that EOCC formed a stable complex with sPLA2r, which increased the mass of native 5PLA2r from 14,299.34 da to 14,736.22 Da. Moreover, the formation of this complex appeared to be involved in the loss of 5PLA2r activity. Our results strongly suggest that EOCC can be used as a pharmacological agent against the 5PLA2 in Crotalus durissus sp. venom as well as other sPLA2s. (C) 2010 Elsevier Ltd. All rights reserved.

Harpalycin 2 inhibits the enzymatic and platelet aggregation activities of PrTX-III, a D49 phospholipase A(2) from Bothrops pirajai venom

Background: Harpalycin 2 (HP-2) is an isoflavone isolated from the leaves of Harpalyce brasiliana Benth., a snakeroot found in northeast region of Brazil and used in folk medicine to treat snakebite. Its leaves are said to be anti-inflammatory. Secretory phospholipases A(2) are important toxins found in snake venom and are structurally related to those found in inflammatory conditions in mammals, as in arthritis and atherosclerosis, and for this reason can be valuable tools for searching new anti-phospholipase A(2) drugs.Methods: HP-2 and piratoxin-III (PrTX-III) were purified through chromatographic techniques. The effect of HP-2 in the enzymatic activity of PrTX-III was carried out using 4-nitro-3-octanoyloxy-benzoic acid as the substrate. PrTX-III induced platelet aggregation was inhibited by HP-2 when compared to aristolochic acid and p-bromophenacyl bromide (p-BPB). In an attempt to elucidate how HP-2 interacts with PrTX-III, mass spectrometry, circular dichroism and intrinsic fluorescence analysis were performed. Docking scores of the ligands (HP-2, aristolochic acid and p-BPB) using PrTX-III as target were also calculated.Results: HP-2 inhibited the enzymatic activity of PrTX-III (IC50 11.34 +/- 0.28 mu g/mL) although it did not form a stable chemical complex in the active site, since mass spectrometry measurements showed no difference between native (13,837.34 Da) and HP-2 treated PrTX-III (13,856.12 Da). A structural analysis of PrTX-III after treatment with HP-2 showed a decrease in dimerization and a slight protein unfolding. In the platelet aggregation assay, HP-2 previously incubated with PrTX-III inhibited the aggregation when compared with untreated protein. PrTX-III chemical treated with aristolochic acid and p-BPB, two standard PLA(2) inhibitors, showed low inhibitory effects when compared with the HP-2 treatment. Docking scores corroborated these results, showing higher affinity of HP-2 for the PrTX-III target (PDB code: 1GMZ) than aristolochic acid and p-BPB. HP-2 previous incubated with the platelets inhibits the aggregation induced by untreated PrTX-III as well as arachidonic acid.Conclusion: HP-2 changes the structure of PrTX-III, inhibiting the enzymatic activity of this enzyme. In addition, PrTX-III platelet aggregant activity was inhibited by treatment with HP-2, p-BPB and aristolochic acid, and these results were corroborated by docking scores.