A fixed point theorem for multivalued mappings

A generalization of the Leray-Schauder principle for multivalued mappings is given. Using this result, an existence theorem for an integral inclusion is obtained

Some remarks on a fixed point theorem of Krasnoselskii

Using a particular locally convex space and Schaefer's theorem, a generalization of Krasnoselskii's fixed point Theorem is proved. This result is further applied to certain nonlinear integral equation proving the existence of a solution on $\mathbb{R}_{+}=[0,+\infty).

An existence result of asymptotically stable solutions for an integral equation of mixed type

In the present Note an existence result of asymptotically stable solutions for the integral equation $$x\left( t\right) =q\left( t\right) +\int_{0}^{t}K\left( t,s,x\left( s\right) \right) ds +\int_{0}^{\infty }G\left( t,s,x\left( s\right) \right) ds$$ is presented

Limits of solutions of a perturbed linear differential equation

Using interesting techniques, an existence result for the problem $\ddot{x}+2f\left( t\right) \dot{x}+x+g\left( t,x\right) =0,$ $\lim\limits_{t\rightarrow +\infty }x\left( t\right) =\lim\limits_{t\rightarrow +\infty }\dot{x}\left( t\right) =0,$ is given in [2]. This note treates the same problem via Schauder-Tychonoff and Banach theorems

Fixed points for some non-obviously contractive operators defined in a space of continuous functions

Let $X$ be an arbitrary (real or complex) Banach space, endowed with the norm $\left| \cdot \right| .$ Consider the space of the continuous functions $C\left( \left[ 0,T\right] ,X\right)$ $\left( T>0\right)$, endowed with the usual topology, and let $M$ be a closed subset of it. One proves that each operator $A:M\rightarrow M$ fulfilling for all $x,y\in M$ and for all $t\in \left[ 0,T\right]$ the condition \begin{eqnarray*} \left| \left( Ax\right) \left( t\right) -\left( Ay\right) \left( t\right) \right| &\leq &\beta \left| x\left( \nu \left( t\right) \right) -y\left( \nu \left( t\right) \right) \right| + \\ &&+\frac{k}{t^{\alpha }}\int_{0}^{t}\left| x\left( \sigma \left( s\right) \right) -y\left( \sigma \left( s\right) \right) \right| ds, \end{eqnarray*} (where $\alpha ,$ $\beta \in \lbrack 0,1)$, $k\geq 0$, and $\nu ,$ $\sigma :\left[ 0,T\right] \rightarrow \left[ 0,T\right]$ are continuous functions such that $\nu \left( t\right) \leq t,$ $\sigma \left( t\right)\leq t,$ $\forall t\in \left[ 0,T\right]$) has exactly one fixed point in $M$. Then the result is extended in $C\left( \mathbb{R}_{+},X\right) ,$ where $\mathbb{R}_{+}:=[0,\infty ).

THE ORGANIZATION AND TECHNICAL EQUIPMENT OF AN ECO-FRIENDLY LANDFILL FOR URBAN WASTE MATTER

The paper outlines the totality of measures taken in order to determine, provide and coordinate the tools for building, expanding and exploiting an urban waste matter landfill. In order to solve the waste issue we must start with the flow circuit, from the generating factors to the final processing. Urban waste matter is mainly generated by the large public. In Romania, due to the extremely low level of civic education, the public is less receptive to new and not willing to take responsibility for its actions. The research described in this paper is aimed for the construction of an eco-friendly landfill having as model the Iridex landfill. This eco-friendly landfill is made from a number of cells that are closing after becoming full. We based our choice on technical and economic benefits

Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory

We study quartic matrix models with partition function Z[E,J]=\int dM \exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0 is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing \beta-function. As main application we prove that Euclidean \phi^4-quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for N->\infty the same spectrum as the Laplace operator in 4 dimensions. Using the theory of singular integral equations of Carleman type we compute (for N->\infty and after renormalisation of E,\lambda) the free energy density (1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae and vanishing of \beta-function hold for general quartic matrix models. v3: We add the existence proof for a solution of the non-linear integral equation. A rescaling of matrix indices was necessary. v2: We provide Schwinger-Dyson equations for all correlation functions and prove an algebraic recursion formula for their solutio

THEORETICAL RESEARCH REGARDING THE WORKING PROCESS OF THE FERTILIZERS MANAGING SYSTEMS BY CENTRIFUGATION

Achieving a distribution standards per hectare as uniform and as specified by eachculture is the most important objective when it comes to administering fertilizer machine. In this sense the paper aims to highlight the theoretical and experimental research conducted by specialists from home and abroad on the process of working machines administrator chemical fertilizer granulation, according to parameters that can influence this process: as blades, the angle of their and so on

CMOS-compatible SOI micro-hotplate-based oxygen sensor

© 2016 IEEE. The paper reports upon the design and characterization of a resistive O2 sensor, which is fully CMOS-compatible and is based on an ultra-low-power Silicon on Insulator (SOI) micro-hotplate membrane. The microsensor employs SrTi0.4Fe0.6O2.8 (STFO60) as sensing layer. Thermo-Gravimetric Analysis (TGA) Energy-Dispersive X-ray Spectroscopy (EDX), X-ray Diffraction (XRD) and Scanning Electron Microscope (SEM) techniques have been used to assess the quality of both the sensing layer and STFO-SOI interface. At room temperature, the SOI sensor shows good sensitivity and fast response time (≤ 6 seconds) to O2 concentration ranging from 0% to 20% in a nitrogen atmosphere. This is the first experimental result showing the potential of this structure as O2 sensor