Three solutions for pertubed Dirichilet problem

\begin{abstract} In this paper we prove the existence of at least three distinct solutions to the following perturbed Dirichlet problem \begin{displaymath} \left\{ \begin{array}{ll} -\Delta u= f(x,u)+\lambda g(x,u) & \mbox{in\ } \Omega\\ u=0 & \mbox{on\ } \partial \Omega, \end{array}\right. \end{displaymath} where $\Omega\subset\mathbb{R}^N$ is an open bounded set with smooth boundary $\partial \Omega$ and $\lambda\in \mathbb{R}$. Under very mild conditions on $g$ and some assumptions on the behaviour of the potential of $f$ at $0$ and $+\infty$, our result assures the existence of at least three distinct solutions to the above problem for $\lambda$ small enough. Moreover such solutions belong to a ball of the space $W_0^{1,2}(\Omega)$ centered in the origin and with radius not dependent on $\lambda$. \end{abstract

Three periodic solutions for pertubed second order Hamiltonian system

Three periodic solutions for perturbed second order Hamiltonian systems \begin{abstract} In this paper we study the existence of three distinct solutions for the following problem \begin{displaymath} \begin{array}{ll} -\ddot{u}+A(t)u=\nabla F(t,u)+\lambda \nabla G(t,u) & \mbox{a.e\ in\ } [0,T] \\ u(T)-u(0)=\dot{u}(T)-\dot{u}(0)=0, \end{array} \end{displaymath} where $\lambda\in \mathbb{R}$, $T$ is a real positive number, $A:[0,T]\rightarrow \mathbb{R}^{N}\times \mathbb{R}^{N}$ is a continuous map from the interval $[0,T]$ to the set of $N$-order symmetric matrices. We propose sufficient conditions only on the potential $F$. More precisely, we assume that $G$ satisfies only a usual growth condition which allows us to use a variational approach. \end{abstract

Anaerobic Digestion of Olive Mill Wastewater in the Presence of Biochar

Biological treatments focused on stabilizing and detoxifying olive mill wastewater facilitate agronomic reuse for irrigation and fertilization. Anaerobic digestion is particularly attractive in view of energy recovery, but is severely hampered by the microbial toxicity of olive mill wastewater. In this work, the addition of biochar to the digestion mixture was studied to improve the stability and efficiency of the anaerobic process. Kinetics and yields of biogas production were evaluated in batch digestion tests with biochar concentrations ranging from 0 to 45 g L−1. The addition of biochar reduced sensibly the lag phase for methanogenesis and increased the maximum rate of biogas generation. Final yields of hydrogen and methane were not affected. Upon addition of biochar, soluble COD removal increased from 66% up to 84%, and phenolics removal increased from 50% up to 95%. Digestate phytotoxicity, as measured by seed germination tests, was reduced compared to raw wastewater. Addition of biochar further reduced phytotoxicity and, furthermore, a stimulatory effect was observed for a twenty-fold dilution. In conclusion, biochar addition enhances the anaerobic digestion of olive mill wastewaters by effectively reducing methanogenesis inhibition and digestate phytotoxicity, thus improving energy and biomass recovery

Electro-optical modulation at 1550 nm in an as-deposited hydrogenated amorphous silicon p-i-n waveguiding device.

Hydrogenated amorphous silicon (a-Si:H) has been already considered for the objective of passive optical elements, like waveguides and ring resonators, within photonic integrated circuits at λ = 1.55 μm. However the study of its electro-optical properties is still at an early stage, therefore this semiconductor in practice is not considered for light modulation as yet. We demonstrated, for the first time, effective electrooptical modulation in a reverse biased a-Si:H p-i-n waveguiding structure. In particular, phase modulation was studied in a waveguide integrated Fabry-Perot resonator in which the Vπ·Lπ product was determined to be 63 V·cm. Characteristic switch-on and switch-off times of 14 ns were measured. The device employed a wider gap amorphous silicon carbide (a-SiC:H) film for the lower cladding layer instead of silicon oxide. In this way the highest temperature involved in the fabrication process was 170°C, which ensured the desired technological compatibility with CMOS processes. © 2011 Optical Society of America

Unifying Foundation Models with Quadrotor Control for Visual Tracking Beyond Object Categories

Visual control enables quadrotors to adaptively navigate using real-time sensory data, bridging perception with action. Yet, challenges persist, including generalization across scenarios, maintaining reliability, and ensuring real-time responsiveness. This paper introduces a perception framework grounded in foundation models for universal object detection and tracking, moving beyond specific training categories. Integral to our approach is a multi-layered tracker integrated with the foundation detector, ensuring continuous target visibility, even when faced with motion blur, abrupt light shifts, and occlusions. Complementing this, we introduce a model-free controller tailored for resilient quadrotor visual tracking. Our system operates efficiently on limited hardware, relying solely on an onboard camera and an inertial measurement unit. Through extensive validation in diverse challenging indoor and outdoor environments, we demonstrate our system's effectiveness and adaptability. In conclusion, our research represents a step forward in quadrotor visual tracking, moving from task-specific methods to more versatile and adaptable operations

The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables

This study aims at comparing non-linear modal interactions in shallow horizontal cables with kinematically non-condensed vs. condensed modeling, under simultaneous primary external and internal resonances. Planar 1:1 or 2:1 internal resonance is considered. The governing partial-differential equations of motion of non-condensed model account for spatio-temporal modification of dynamic tension, and explicitly capture non-linear coupling of longitudinal/ vertical displacements. On the contrary, in the condensed model, a single integro-differential equation is obtained by eliminating the longitudinal inertia according to a quasi-static cable stretching assumption, which entails spatially uniform dynamic tension. This model is largely considered in the literature. Based on a multi-modal discretization and a second-order multiple scales solution accounting for higher-order quadratic effects of a infinite number of modes, coupled/uncoupled dynamic responses and the associated stability are evaluated by means of frequency- and force-response diagrams. Direct numerical integrations confirm the occurrence of amplitude-steady or -modulated responses. Non-linear dynamic configurations and tensions are also examined. Depending on internal resonance condition, system elasto-geometric and control parameters, the condensed model may lead to significant quantitative and/or qualitative discrepancies, against the non-condensed model, in the evaluation of resonant dynamic responses, bifurcations and maximal/minimal stresses. Results of even shallow cables reveal meaningful drawbacks of the kinematic condensation and allow us to detect cases where the more accurate non-condensed model has to be used

Hydrogenated amorphous silicon multi-SOI waveguide modulator with low voltage-length product

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ANALOGUE OF DINI-RIEMANN THEOREM FOR NON-ABSOLUTELY CONVERGENT INTEGRALS

An analogue of classical Dini-Riemann theorem related to non-absolutelyconvergent series of real number is proved for the Lebesgue improper integral.An analogue of classical Dini-Riemann theorem related to non-absolutely convergent series of real number is proved for the Lebesgue improper integral

Henstock integral and Dini-Riemann theorem

In [5] an analogue of the classical Dini-Riemann theorem related to non-absolutely convergent series of real number is obtained for the Lebesgue improper integral. Here we are extending it to the case of the Henstock integral

synthesis characterization and applications of nano micro carbonaceous inerts a review

Abstract In recent years, a scientific shift has been observed towards the use of carbon based nano materials in different composites to enhance their mechanical and electrical properties. However, carbonaceous nano/micro inert particles synthesized through pyrolysis of agricultural and industrial wastes offer a very cost effective alternate to the commercially available carbon based materials such as carbon fibres, carbon nanotubes, graphene and graphene oxide. A comprehensive survey of reported data on the synthesis of carbon particles is presented in this article. The utilization of synthesized carbon particles as reinforcing material has also been explored together with an attempt of proposing future novel applications of synthesized carbon particles in cement based systems. In this paper, meticulous efforts have been made to overview the potential beneficial effects of synthesized carbon particles intrusions to cementitious systems for modifying/improving their mechanical characteristics