Uniform Convergence of the Newton Method for Aubin Continuous Maps

* This work was supported by National Science Foundation grant DMS 9404431.

A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive condition. This last result slightly improves some earlier work by G. Barles and H. Ishii.

Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds

∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.

Decomposition of Boolean Functions – Recognizing a Good Solution by Traces

The problem of sequent two-block decomposition of a Boolean function is regarded in case when a good solution does exist. The problem consists mainly in finding an appropriate weak partition on the set of arguments of the considered Boolean function, which should be decomposable at that partition. A new fast heuristic combinatorial algorithm is offered for solving this task. At first the randomized search for traces of such a partition is fulfilled. The recognized traces are represented by some "triads" - the simplest weak partitions corresponding to non-trivial decompositions. After that the whole sought-for partition is restored from the discovered trace by building a track initialized by the trace and leading to the solution. The results of computer experiments testify the high practical efficiency of the algorithm.

Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers

Physical systems with co-existence and interplay of processes featuring distinct spatio-temporal scales are found in various research areas ranging from studies of brain activity to astrophysics. The complexity of such systems makes their theoretical and experimental analysis technically and conceptually challenging. Here, we discovered that while radiation of partially mode-locked fibre lasers is stochastic and intermittent on a short time scale, it exhibits non-trivial periodicity and long-scale correlations over slow evolution from one round-trip to another. A new technique for evolution mapping of intensity autocorrelation function has enabled us to reveal a variety of localized spatio-temporal structures and to experimentally study their symbiotic co-existence with stochastic radiation. Real-time characterization of dynamical spatio-temporal regimes of laser operation is set to bring new insights into rich underlying nonlinear physics of practical active- and passive-cavity photonic systems.

Duality in multi-channel Luttinger Liquid with local scatterer

We have devised a general scheme that reveals multiple duality relations valid for all multi-channel Luttinger Liquids. The relations are universal and should be used for establishing phase diagrams and searching for new non-trivial phases in low-dimensional strongly correlated systems. The technique developed provides universal correspondence between scaling dimensions of local perturbations in different phases. These multiple relations between scaling dimensions lead to a connection between different inter-phase boundaries on the phase diagram. The dualities, in particular, constrain phase diagram and allow predictions of emergence and observation of new phases without explicit model-dependent calculations. As an example, we demonstrate the impossibility of non-trivial phase existence for fermions coupled to phonons in one dimension. © 2013 EPLA.

On the Semigroup of all Increasing Full Transformations

Илинка А. Димитрова - Полугрупата Tn от всички пълни преобразувания върху едно n-елементно множество е изучавана в различни аспекти ог редица автори. Обект на разглеждане в настоящата работа е полугрупата Incn състояща се от всички нарастващи пълни преобразувания. Очевидно Incn е подполугрупа на Tn. Доказано е, че всеки елемент на полугрупата Incn от ранг r може да се представи като произведение на идемпотенти от същия ранг и всеки идемпотент от ранг по-малък или равен на r може да се представи като произведение на идемпотенти от ранг r. С помощта на тези твърдения е показано, че полугрупата Incn се поражда от множеството на всички идемпотенти от ранг n − 1 и тъждественото преобразувание. Освен това е доказано, че идемпотентите от ранг n − 1 са неразложими в полугрупата Incn. В резултат на това е получено, че рангът и идемпотичниат ранг на разглежданата полугрупа са равни. Като са използвани тези твърдения е направена пълна класификация на маскималните подполугрупи на полугрупата Incn.

N–Dimensional Orthogonal Tile Sizing Problem

AMS subject classification: 68Q22, 90C90

Strong Consistency of the Conditional Least Squares Estimator for a Nonstationary Process. Example of the Garch Model

2000 Mathematics Subject Classification: Primary: 62M10, 62J02, 62F12, 62M05, 62P05, 62P10; secondary: 60G46, 60F15.

About Strictly Hyperbolic Operators with Non-Regular Coefficients

2002 Mathematics Subject Classification: 35L15, 35L80, 35S05, 35S30

An Iterative Procedure for Solving Nonsmooth Generalized Equation

2000 Mathematics Subject Classification: 47H04, 65K10.

Probabilistic Approach to the Neumann Problem for a Symmetric Operator

2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.

Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials

2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.

Double complexes and vanishing of Novikov cohomology

2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.

A robust preference for cheap-and-easy strategies over reliable strategies when verifying personal memories

People depend on various sources of information when trying to verify their autobiographical memories. Yet recent research shows that people prefer to use cheap-and-easy verification strategies, even when these strategies are not reliable. We examined the robustness of this cheap strategy bias, with scenarios designed to encourage greater emphasis on source reliability. In three experiments, subjects described real (Experiments 1 and 2) or hypothetical (Experiment 3) autobiographical events, and proposed strategies they might use to verify their memories of those events. Subjects also rated the reliability, cost, and the likelihood that they would use each strategy. In line with previous work, we found that the preference for cheap information held when people described how they would verify childhood or recent memories (Experiment 1); personally-important or trivial memories (Experiment 2), and even when the consequences of relying on incorrect information could be significant (Experiment 3). Taken together, our findings fit with an account of source monitoring in which the tendency to trust one’s own autobiographical memories can discourage people from systematically testing or accepting strong disconfirmatory evidence.