Search results for " Integra"
showing 10 items of 2527 documents
Modelling Spatial Memory
2018
Among the different capabilities of animals, the formation of spatial memories is crucial for their life. Living beings able to move, constantly need to orient themselves in the environment to reach a target that might be not always visible. This chapter investigates the process of spatial memory formation as an essential ingredient for orientation in open and unstructured environments. Neural centres devoted to spatial memory and path integration were deeply investigated both in rats and different insect species like ants, bees and fruit flies. In this chapter a neural-inspired model for the formation of a spatial working memory is discussed considering some key elements of the insect neur…
Private Pre-University Education in Romania
2014
This paper approaches private provision of pre-university education in Romania, exploring available data on the sector's size and main characteristics and evaluating the extent to which the current regulatory framework enables positive effects in terms of freedom of choice, quality, equity, and social cohesion. The paper argues that the lack of a clear strategy mixed with strict control in key areas and lax implementation of support instruments has led to private providers not being a legitimate alternative to public education.
From the poster boy of Europeanization to the sick man of Europe: thirty years (1990–2019) of Poland’s European policy
2020
The Eurosceptic turnabout which has taken place in the CEE constitutes one of the most significant factors weakening the cohesion of the EU. In this group, Poland is the key element in view of its ...
Integrable systems, Frobenius manifolds and cohomological field theories
2022
In this dissertation, we study the underlying geometry of integrable systems, in particular tausymmetric bi-Hamiltonian hierarchies of evolutionary PDEs and differential-difference equations.First, we explore the close connection between the realms of integrable systems and algebraic geometry by giving a new proof of the Witten conjecture, which constructs the string taufunction of the Korteweg-de Vries hierarchy via intersection theory of the moduli spaces of stable curves with marked points. This novel proof is based on the geometry of double ramification cycles, tautological classes whose behavior under pullbacks of the forgetful and gluing maps facilitate the computation of intersection…
Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations
2011
In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.
Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems
1999
The tangential Hilbert 16th problem is to place an upper bound for the number of isolated ovals of algebraic level curves { H ( x , y ) = const } \{H(x,y)=\operatorname {const}\} over which the integral of a polynomial 1-form P ( x , y ) d x + Q ( x , y ) d y P(x,y)\,dx+Q(x,y)\,dy (the Abelian integral) may vanish, the answer to be given in terms of the degrees n = deg H n=\deg H and d = max ( deg P , deg Q ) d=\max (\deg P,\deg Q) . We describe an algorithm producing this upper bound in the form of a primitive recursive (in fact, elementary) function of n n and d d for the particular case of hyperelliptic polynomials H ( x , y ) = y 2 + U ( x ) H(x,y)=y^2+U(x) under the additional as…
The Cauchy problem for linear growth functionals
2003
In this paper we are interested in the Cauchy problem $$ \left\{ \begin{gathered} \frac{{\partial u}}{{\partial t}} = div a (x, Du) in Q = (0,\infty ) x {\mathbb{R}^{{N }}} \hfill \\ u (0,x) = {u_{0}}(x) in x \in {\mathbb{R}^{N}}, \hfill \\ \end{gathered} \right. $$ (1.1) where \( {u_{0}} \in L_{{loc}}^{1}({\mathbb{R}^{N}}) \) and \( a(x,\xi ) = {\nabla _{\xi }}f(x,\xi ),f:{\mathbb{R}^{N}}x {\mathbb{R}^{N}} \to \mathbb{R} \)being a function with linear growth as ‖ξ‖ satisfying some additional assumptions we shall precise below. An example of function f(x, ξ) covered by our results is the nonparametric area integrand \( f(x,\xi ) = \sqrt {{1 + {{\left\| \xi \right\|}^{2}}}} \); in this case …
Direct Evaluation of Path Integrals
2001
Every time τ n is assigned a point y n . We now connect the individual points with a classical path y(τ). y(τ) is not necessarily the (on-shell trajectory) extremum of the classical action. It can be any path between τ n and τn−1 specified by the classical Lagrangian \(L(y,\dot{y},t).\)
Some Aspects of Vector-Valued Singular Integrals
2009
Let A, B be Banach spaces and \(1 < p < \infty. \; T\) is said to be a (p, A, B)- CalderoLon–Zygmund type operator if it is of weak type (p, p), and there exist a Banach space E, a bounded bilinear map \(u: E \times A \rightarrow B,\) and a locally integrable function k from \(\mathbb{R}^n \times \mathbb{R}^n \backslash \{(x, x): x \in \mathbb{R}^n\}\) into E such that $$T\;f(x) = \int u(k(x, y), f(y))dy$$ for every A-valued simple function f and \(x \notin \; supp \; f.\)
Product Integration for Weakly Singular Integral Equations In ℝm
1985
In this note we discuss the numerical solution of the second kind Fredholm integral equation: $$ y(t) = f(t) + \lambda \int\limits_{\Omega } {{{\psi }_{\alpha }}(|t - s|)g(t,s)y(s)ds,\;t \in \bar{\Omega },} $$ (1) Where \( \lambda \in ;\not{ \subset }\backslash \{ 0\} \) , the functions f,g are given and continuous, |.| denotes the Euclidean norm, and φα, 0 \alpha > 0} \\ {\left\{ {\begin{array}{*{20}{c}} {\ln (r),} & {j = 0} \\ {{{r}^{{ - j}}}} & {j > 0} \\ \end{array} } \right\},\alpha = m} \\ \end{array} ,} \right. $$ with Cj not depending on r. Here Ω _ is the closure of a bounded domain Ω⊂ℝm.