Cartesian products of intuitionistic fuzzy sets have been defined using the min-max and the product-probabilistic sum operations. In this paper we introduce and analyse the properties of a generalized cartesian product of intuitionistic fuzzy sets using a general triangular norm and conorm. In particular we investigate the emptiness, the commutativity, the distributivity, the interaction with respect to generalized unions and intersections, the distributivity with respect to the difference, the monotonicity and the cutting in terms of level-sets.
We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption in the existing literature.
The cellular processes underlying individual differences in the Woring Memory Capacity (WMC) of humans are essentially unknown. Psychological experiments suggest that subjects with lower working memory capacity (LWMC), with respect to subjects with higher capacity (HWMC), take more time to recall items from a list because they search through a larger set of items and are much more susceptible to interference during retrieval. However, a more precise link between psychological experiments and cellular properties is lacking and very difficult to investigate experimentally. In this paper, we investigate the possible underlying mechanisms at the single neuron level by using a computational model of hippocampal CA1 pyramidal neurons, which have been suggested to be deeply involved in the recognition of specific items. The model makes a few experimentally testable predictions on the cellular processes underlying the cumulative latency in delayed free recall experimentally observed in humans under different testing conditions. The results suggest, for the first time, a physiologically plausible explanation for individual performances, and establish a proof of principle for the hypothesis that HWMC individuals use a larger portion of the apical tree with a correlated higher level of synaptic background noise.
In this paper, we discuss the conditions for a center for the generalized Liénard system \[ \frac {{\rm d}x}{{\rm d}t}=\varphi (y)-F(x), \qquad \frac {{\rm d}y}{{\rm d}t}=-g(x), \] or \[ \frac {{\rm d}x}{{\rm d}t}=\psi (y), \qquad \frac {{\rm dy}}{{\rm d}t}= -f(x)h(y)-g(x),
\] with $f(x)$, $g(x)$, $\varphi (y)$, $\psi (y)$, $h(y)\: \mathbb R\rightarrow \mathbb R$, $F(x)=\int _0^xf(x)\mathrm{d}x$, and $xg(x)>0$ for $x\ne 0$. By using a different technique, that is, by introducing auxiliary systems and using the differential inquality theorem, we are able to generalize and improve some results in [1], [2].
In this work, we study the properties of central paths, defined with res\-pect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a particular case of convex programming with conic constraints. The studied class of functions consists of spectrally defined functions induced by penalty or barrier maps defined over the real nonnegative numbers. We prove the convergence of the (primal, dual and primal-dual) central path toward a (primal, dual, primal-dual, respectively) solution of our problem. Finally, we prove the global existence of Cauchy trajectories in our context and we recall its relation with primal central path when linear semidefinite programs are considered. Some illustrative examples are shown at the end of this paper.
Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows along a small crack extension.
We characterize Banach lattices E and F on which the adjoint of each operator from E into F which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if E and F are two Banach lattices then each order DunfordPettis and weak Dunford-Pettis operator T from E into F has an adjoint Dunford-Pettis operator T ′ from F ′ into E ′ if, and only if, the norm of E ′ is order continuous or F ′ has the Schur property. As a consequence we show that, if E and F are two Banach lattices such that E or F has the Dunford-Pettis property, then each order Dunford-Pettis operator T from E into F has an adjoint T ′ : F ′ → E ′ which is Dunford-Pettis if, and only if, the norm of E ′ is order continuous or F ′ has the Schur property.