Search results for "Calculus"
showing 10 items of 617 documents
Second-Order Calculus on RCD Spaces
2020
In this conclusive chapter we introduce the class of those metric measure spaces that satisfy the Riemannian curvature-dimension condition, briefly called RCD spaces, and we develop a thorough second-order differential calculus over these structures.
On the Calmness of a Class of Multifunctions
2002
The paper deals with the calmness of a class of multifunctions in finite dimensions. Its first part is devoted to various conditions for calmness, which are derived in terms of coderivatives and subdifferentials. The second part demonstrates the importance of calmness in several areas of nonsmooth analysis. In particular, we focus on nonsmooth calculus and solution stability in mathematical programming and in equilibrium problems. The derived conditions find a number of applications there.
A tour of the theory of absolutely minimizing functions
2004
A detailed analysis of the class of absolutely minimizing functions in Euclidean spaces and the relationship to the infinity Laplace equation
Knot Theory, Jones Polynomial and Quantum Computing
2005
Knot theory emerged in the nineteenth century for needs of physics and chemistry as these needs were understood those days. After that the interest of physicists and chemists was lost for about a century. Nowadays knot theory has made a comeback. Knot theory and other areas of topology are no more considered as abstract areas of classical mathematics remote from anything of practical interest. They have made deep impact on quantum field theory, quantum computation and complexity of computation.
A cognitive architecture for inner speech
2020
Abstract A cognitive architecture for inner speech is presented. It is based on the Standard Model of Mind, integrated with modules for self-talking. Briefly, the working memory of the proposed architecture includes the phonological loop as a component which manages the exchanging information between the phonological store and the articulatory control system. The inner dialogue is modeled as a loop where the phonological store hears the inner voice produced by the hidden articulator process. A central executive module drives the whole system, and contributes to the generation of conscious thoughts by retrieving information from long-term memory. The surface form of thoughts thus emerges by …
Classification générique de synthèses temps minimales avec cible de codimension un et applications
1997
In this article we consider the problem of constructing the optimal closed loop control in the time minimal control problem, with terminal constraints belonging to a manifold of codimension one, for systems of the form v = X + uY, v ϵ R2, R3, |u| ≤ 1 under generic assumptions. The analysis is localized near the terminal manifold and is motivated by the problem of controlling a class of chemical systems.
The best choice problem with an unknown number of objects
1993
The secretary problem with a known prior distribution of the number of candidates is considered. Ifp(i)=p(N=i),i ∈ [α, β] ∩ ℕ, whereα=inf{i ∈ℕ:p(i) > 0} andβ=sup{i ∈ℕ:p(i)≳0}, is the prior distribution of the numberN of candidates it will be shown that, if the optimal stopping rule is of the simple form, then the optimal stopping indexj=minΓ satisfies asymptotically (asβ → ∞) the equationj=exp $${{\left[ {\left( {\sum\limits_{i = max(\alpha ,j)}^\beta {p(i) \log (i)/i} } \right)} \right]} \mathord{\left/ {\vphantom {{\left[ {\left( {\sum\limits_{i = max(\alpha ,j)}^\beta {p(i) \log (i)/i} } \right)} \right]} {\left. {\left( {\sum\limits_{i = max(\alpha ,j)}^\beta {p(i)/i} } \right) - 1} \ri…
Extension of The Stochastic Differential Calculus To Complex Processes
1996
In structural engineering complex processes arise to predict the first excursion failure, fatigue failure, etc. Indeed to solve these problems the envelope function, which is the modulus of a complex process, is usually introduced. In this paper the statistics of the complex response process related to the envelope statistics of linear systems subjected to parametric stationary normal white noise input are evaluated by using extensively the properties of stochastic differential calculus.
State-specific multireference coupled-cluster theory
2012
The multireference problem is considered one of the great challenges in coupled-cluster (CC) theory. Most recent developments are based on state-specific approaches, which focus on a single state and avoid some of the numerical problems of more general approaches. We review various state-of-the-art methods, including Mukherjee's state-specific multireference coupled-cluster (Mk-MRCC) theory, multireference Brillouin–Wigner coupled-cluster (MR-BWCC) theory, the MRexpT method, and internally contracted multireference coupled-cluster (ic-MRCC) theory. Related methods such as extended single-reference schemes [e.g., the complete active space coupled-cluster (CASCC) theory] and canonical transfo…
Descriptive Complexity, Lower Bounds and Linear Time
1999
This paper surveys two related lines of research: Logical characterizations of (non-deterministic) linear time complexity classes, and non-expressibility results concerning sublogics of existential second-order logic. Starting from Fagin’s fundamental work there has been steady progress in both fields with the effect that the weakest logics that are used in characterizations of linear time complexity classes are closely related to the strongest logics for which inexpressibility proofs for concrete problems have been obtained. The paper sketches these developments and highlights their connections as well as the obstacles that prevent us from closing the remaining gap between both kinds of lo…