The Vector Valued Quartile Operator

Certain vector-valued inequalities are shown to hold for a Walsh analog of the bilinear Hilbert transform. These extensions are phrased in terms of a recent notion of quartile type of a UMD (Unconditional Martingale Differences) Banach space X. Every known UMD Banach space has finite quartile type, and it was recently shown that the Walsh analog of Carleson's Theorem holds under a closely related assumption of finite tile type. For a Walsh model of the bilinear Hilbert transform however, the quartile type should be sufficiently close to that of a Hilbert space for our results to hold. A full set of inequalities is quantified in terms of quartile type.Comment: 32 pages, 5 figures, incorporates referee's report, to appear in Collect. Mat

INNOVATIVE EQUIPMENT FOR CULTIVATING MEDICINAL AND AROMATIC PLANTS ON SMALL SURFACES

Medicinal and aromatic plant cultures are part of the niche culture category. Although the local pedoclimatic conditions are favourable, the application of culture technologies is carried out on small farms. To this fact also contributes, in addition to other factors, the lack of adequate technical means, farmers usually using physical workforce (family or local labour). In order to support the small growers, it was necessary to design and develop equipment for the cultivation of medicinal and aromatic plants on small surfaces.This paper presents the tests performed on the experimental plots at INMA Bucharest, regarding the sowing and harvesting works, on a culture of Basil - Ocimum basilicum L., Lamiaceae family

Strichartz Estimates for the Vibrating Plate Equation

We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr\"odinger-type equations we show its close relation with the Schr\"odinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate equation.Comment: 18 pages, 4 figures, some misprints correcte

Some singular value inequalities via convexity

If $c_1(Z) \geq ... \geq c_n(Z)$ denote the Euclidean lengths of the column vectors of any $n \times n$ matrix $Z,$ then a fundamental inequality related to Hadamard products states that $$\sum_{i=1}^k \sigma_i(X^*Y \circ B) \leq \sum_{i=1}^k c_i(X) c_i(Y) \sigma_i(B) \qquad 1 \leq k \leq n,$$ where $\sigma_i(\cdot)$ is the $i$th singular value. In this paper, we shall offer a simple proof of this result via convexity arguments. In addition, this technique is applied to obtain some further singular value inequalities as well

TECHNOLOGY FOR ORGANIC WEED CONTROL

In recent years, crop maintenance works have become a major challenge for organic farming systems, where the application of chemical treatments is totally forbidden. The effect of weeds on crops varies according to pedoclimatic, biological or technological parameters, the resulting damages being both quantitative and qualitative. By weed control, we aim to prevent their competition in order to obtain maximum crop yields.Among the methods of thermal weed control, used as an alternative to chemical weeding, steam or hot water-based ones have been increasingly used as they provide an efficient, environmentally friendly and economical way of removing harmful plants.This paper presents a technology for the maintenance of medicinal and aromatic plant organic crops, based on the use of innovative equipment for weed thermal control by using hot water

SEPARATION OF CHOPPED NETTLE MATERIAL ON PLANE SIEVE LENGTH

The paper presents the results of several experimental researches regarding to a separation mixture of dried and chopped nettle fragments on a dimensional separator of medicinal plants, equipped with oscillating flat sieves. Three parameters were varied (material flow rate, sieves angle of inclination and oscillations sieves frequency). For separation process description along chopped vegetal material sieves, the experimental results have been tested by Rosin-Rammler distribution law

AGRICULTURE 4.0 - A CHALLENGE FOR ROMANIAN AGRICULTURE

Given that the labor market in Romania has an acute shortage of labor (about 1 million people), in agriculture this lack is felt even more acutely because the population in the villages is declining and aging, thus it is increasingly difficult for Romanian farmers to find labor, let alone skilled labor. One solution can be the digitization of agriculture, ie the introduction of the latest management concepts, sensors, automation, robots, etc. in the modernization of work processes in agriculture, thus reducing the need for labor, while increasing productivity and efficiency in agriculture

Modulation Invariant Bilinear T(1) Theorem

We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a one-dimensional modulation symmetry

Distribution of resonances for open quantum maps

We analyze simple models of classical chaotic open systems and of their quantizations (open quantum maps on the torus). Our models are similar to models recently studied in atomic and mesoscopic physics. They provide a numerical confirmation of the fractal Weyl law for the density of quantum resonances of such systems. The exponent in that law is related to the dimension of the classical repeller (or trapped set) of the system. In a simplified model, a rigorous argument gives the full resonance spectrum, which satisfies the fractal Weyl law. For this model, we can also compute a quantity characterizing the fluctuations of conductance through the system, namely the shot noise power: the value we obtain is close to the prediction of random matrix theory.Comment: 60 pages, no figures (numerical results are shown in other references