We prove a bi-sublinear embedding for semigroups generated by non-smooth complex-coefficient elliptic operators in divergence form and for certain mutually dual pairs of Orlicz-space norms. This ...generalizes a result by Carbonaro and Dragičević from power functions to more general Young functions that still behave like powers. To achieve this, we generalize a Bellman function constructed by Nazarov and Treil.
We prove a dimension-free Lp(Ω)×Lq(Ω)×Lr(Ω)→L1(Ω×(0,∞)) embedding for triples of elliptic operators in divergence form with complex coefficients and subject to mixed boundary conditions on Ω, and for ...triples of exponents p,q,r∈(1,∞) mutually related by the identity 1/p+1/q+1/r=1. Here Ω is allowed to be an arbitrary open subset of Rd. Our assumptions involving the exponents and coefficient matrices are expressed in terms of a condition known as p-ellipticity. The proof utilizes the method of Bellman functions and heat flows. As a corollary, we give applications to (i) paraproducts and (ii) square functions associated with the corresponding operator semigroups, moreover, we prove (iii) inequalities of Kato–Ponce type for elliptic operators with complex coefficients. All the above results are the first of their kind for elliptic divergence-form operators with complex coefficients on arbitrary open sets. Furthermore, the approach to (ii),(iii) through trilinear embeddings seems to be new.
Morphodynamic changes in the riverbed may be accelerated by the climate change-induced effects, mostly through the increase of the frequency of extreme climatic events such as floods. This can lead ...to scouring of the riverbed around the bridge substructure and consequently reduces its overall stability. In order to better understand hydromorphological processes at the local scale, the influence of floods on bridge scour requires a detailed analysis of several interacting flood hydrograph characteristics. This paper presents a multivariate analysis of the annual maximum (AM) flood discharge data at four gauging stations on the Drava and Sava Rivers in Croatia (Europe). As part of the hydrograph analysis, multiple baseflow separation methods were tested. Flood volumes and durations were derived after extracting the baseflow from measured discharge data. Suitable marginal distribution functions were fitted to the peak discharge (Q), flood volume (V) and duration (D) data. Bivariate copula analyses were conducted for the next pairs: peak discharge and volume (Q–V), hydrograph volume and duration (V–D) and peak discharge and hydrograph duration (Q–D). The results of the bivariate copula analyses were used to derive joint return periods for different flood variable combinations, which may serve as a preliminary analysis for the pilot bridges of the R3PEAT project where the aim is to investigate the influences on the riverbed erosion around bridges with installed scour countermeasures. Hence, a design hydrograph was derived that could be used as input data in the hydraulic model for the investigation of the bridge scour dynamics within the project and a preliminary methodology is proposed to be applied. The results indicate that bivariate frequency analysis can be very sensitive to the selected baseflow separation methodology. Therefore, future studies should test multiple baseflow separation methods and visually inspect the performance.
We prove failure of the natural formulation of a matrix weighted bilinear Carleson embedding theorem, featuring a matrix–valued Carleson sequence as well as products of norms for the embedding. We ...show that assuming an A2 weight is also not sufficient. Indeed, a uniform bound on the conditioning number of the matrix weight is necessary and sufficient to get the bilinear embedding. We prove the optimal dependence of the embedding on this quantity. We show that any improvement of a recent matrix weighted bilinear embedding, featuring a scalar Carleson sequence and inner products instead of norms must fail. In particular, replacing the scalar sequence by a matrix sequence results in failure even when maintaining the formulation using inner products. Any formulation using norms, even in the presence of a scalar Carleson sequence must fail. As a positive result, we prove the so–called matrix weighted redundancy condition in full generality.
We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real ...harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.
In this paper we introduce a variant of Burkholder's martingale transform associated with two martingales with respect to different filtrations. Even though the classical martingale techniques cannot ...be applied, we show that the discussed transformation still satisfies some expected Lp estimates. Then we apply the obtained inequalities to general-dilation twisted paraproducts, particular instances of which have already appeared in the literature. As another application we construct stochastic integrals ∫0tHsd(XsYs) associated with certain continuous-time martingales (Xt)t≥0 and (Yt)t≥0. The process (XtYt)t≥0 is shown to be a “good integrator”, although it is not necessarily a semimartingale, or even adapted to any convenient filtration.
Chronic lymphocytic leukemia (CLL) is a lymphoproliferative disorder characterized by a specific expansion of mature B-cell clones. We hypothesized that the disease has a heterogeneous clinical ...outcome that depends on the genes and signaling pathways active in the malignant clone of the individual patient. It was found that several signaling pathways are active in CLL, namely, NOTCH1, the Ikaros family genes, BCL2, and NF-κB, all of which contribute to cell survival and the proliferation of the leukemic clone. Therefore, we analyzed primary CLL cells for the gene and protein expression of NOTCH1, DELTEX1, HES1, and AIOLOS in both peripheral blood lymphocytes (PBLs) and the bone marrow (BM) of patients, as well as the expression of BCL2 and miRNAs to see if they correlate with any of these genes. BCL2 and AIOLOS were highly expressed in all CLL samples as previously described, but we show here for the first time that AIOLOS expression was higher in the PBLs than in the BM. On the other hand, NOTCH1 activation was higher in the BM. In addition, miR-15a, miR-181, and miR-146 were decreased and miR-155 had increased expression in most samples. The activation of the NOTCH pathway in vitro increases the susceptibility of primary CLL cells to apoptosis despite high BCL2 expression.
We give an explicit formula for one possible Bellman function associated with the Lp boundedness of dyadic paraproducts regarded as bilinear operators or trilinear forms. Then we apply the same ...Bellman function in various other settings, to give self-contained alternative proofs of the estimates for several classical operators. These include the martingale paraproducts of Bañuelos and Bennett and the paraproducts with respect to the heat flows.
When talking about large infrastructure projects one can often hear – “it is a very complex project”. What does it mean? What makes large infrastructure projects complex? This paper is exploring ...current views on project complexity and its development though history. As part of the research on large infrastructure projects, the perception and elements of complexity was investigated. The research is based on in-depth analysis of large infrastructure projects and project manager's perception of complexity. The result of the paper is proposal of new model of project complexity for large infrastructure projects.
We prove a bi-sublinear embedding for semigroups generated by non-smooth complex-coefficient elliptic operators in divergence form and for certain mutually dual pairs of Orlicz-space norms. This ...generalizes a result by Carbonaro and Dragičevi\'{c} from power functions to more general Young functions that still behave like powers. To achieve this, we generalize a Bellman function constructed by Nazarov and Treil.
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