On Boas-Type Problem

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α(0 & α & 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of modulus of continuity. The aim of this paper is to obtain Boas-type theorems for generalized Lipschitz classes. To define generalized Lipschitz classes we use the concept of modulus of smoothness of fractional order.

The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

Botulinum neurotoxin type A blocks the morphological changes induced by chemical stimulation on the presynaptic membrane of Torpedo synaptosomes.

The action of botulinum neurotoxin on acetylcholine release, and on the structural changes at the presynaptic membrane associated with the transmitter release,was studied by using a subcellular fraction of cholinergic nerve terminals (synaptosomes) isolated from the Torpedo electric organ. Acetylcholine and ATP release were continuously monitored by chemiluminescent methods.To catch the membrane morphological changes, the quick-freezing method was applied. Our results show that botulinum neurotoxin inhibits the release of acetylcholine from these isolated nerve terminals in a dose-dependent manner, whereas ATP release is not affected. The maximal inhibition (70%) is achieved at neurotoxin concentrations as low as 125 pM with an incubation time of 6 min. This effect is not linked to an alteration of the integrity of the synaptosomes since, after poisoning by botulinum neurotoxin type A, they show a nonmodified occluded lactate dehydrogenase activity. Moreover, membrane potential is not altered by the toxin with respect to the control, either in resting condition or after potassium depolarization. In addition to acetylcholine release inhibition, botulinum neurotoxin blocks the rearrangement of the presynaptic intramembrane particles induced by potassium stimulation. The action of botulinum neurotoxin suggests that the intramembrane particle rearrangement is related to the acetylcholine secretion induced by potassium stimulation in synaptosomes isolated from the electric organ of Torpedo marmorata.

Botulinum neurotoxin type A blocks the morphological changes induced by chemical stimulation on the presynaptic membrane of Torpedo synaptosomes.

The action of botulinum neurotoxin on acetylcholine release, and on the structural changes at the presynaptic membrane associated with the transmitter release,was studied by using a subcellular fraction of cholinergic nerve terminals (synaptosomes) isolated from the Torpedo electric organ. Acetylcholine and ATP release were continuously monitored by chemiluminescent methods.To catch the membrane morphological changes, the quick-freezing method was applied. Our results show that botulinum neurotoxin inhibits the release of acetylcholine from these isolated nerve terminals in a dose-dependent manner, whereas ATP release is not affected. The maximal inhibition (70%) is achieved at neurotoxin concentrations as low as 125 pM with an incubation time of 6 min. This effect is not linked to an alteration of the integrity of the synaptosomes since, after poisoning by botulinum neurotoxin type A, they show a nonmodified occluded lactate dehydrogenase activity. Moreover, membrane potential is not altered by the toxin with respect to the control, either in resting condition or after potassium depolarization. In addition to acetylcholine release inhibition, botulinum neurotoxin blocks the rearrangement of the presynaptic intramembrane particles induced by potassium stimulation. The action of botulinum neurotoxin suggests that the intramembrane particle rearrangement is related to the acetylcholine secretion induced by potassium stimulation in synaptosomes isolated from the electric organ of Torpedo marmorata.

Mediation incomplete information bargaining with filtered communication

We analyze a continuous-time bilateral double auction in the presence of two-sided incomplete information and a smallest money unit. A distinguishing feature of our model is that intermediate concessions are not observable by the adversary: they are only communicated to a passive auctioneer. An alternative interpretation is that of mediated bargaining. We show that an equilibrium using only the extreme agreements always exists and display the necessary and sufficient condition for the existence of (perfect Bayesian) equilibra which yield intermediate agreements. For the symmetric case with uniform type distribution we numerically calculate the equilibria. We find that the equilibrium which does not use compromise agreements is the least efficient, however, the rest of the equilibria yield the lower social welfare the higher number of compromise agreements are used.

Absolute type shaft encoding using LFSR

Maximal-length binary sequences have been known for a long time. They have many interesting properties, one of them is that when taken in blocks of n consecutive positions they form 2ⁿ-1 different codes in a closed circular sequence. This property can be used for measuring absolute angular positions as the circle can be divided in as many parts as different codes can be retrieved. This paper describes how can a closed binary sequence with arbitrary length be effectively designed with the minimal possible block-length, using linear feedback shift registers (LFSR). Such sequences can be used for measuring a specified exact number of angular positions, using the minimal possible number of sensors that linear methods allow.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

The identity type weak factorisation system

We show that the classifying category C(T)of a dependent type theory T with axioms for identity types admits a nontrivial weak factorisation system. After characterising this weak factorisation system explicitly, we relate it to the homotopy theory of groupoids.

Moduli of flat conformal structures of hyperbolic type

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Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

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Weak-type estimates for Haar shift operators: Sharp power on the A(p) characteristic

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Gehring-Hayman theorem for conformal deformations

We study conformal deformations of a uniform space that satisfies the Ahlfors Q-regularity condition on balls of Whitney type. We verify the Gehring–Hayman Theorem by using a Whitney Covering of the space.

Wiener type theorems for Jacobi series with nonnegative coefficients

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Repeated Interaction and the Revelation of the Monitor's Type: A Principal-Monitor-Agent Problem

This paper studies a dynamic principal-monitor-agent relation where a strategic principal delegates the task of monitoring the effort of a strategic agent to a third party. The latter we call the monitor, whose type is initially unknown. Through repeated interaction the agent might learn his type. We show that this process damages the principal's payoffs. Compensation is assumed exogenous, limiting to a great extent the provision of incentives. We go around this difficulty by introducing costly replacement strategies, i.e. the principal replaces the monitor, thus disrupting the agent's learning. We found that even when replacement costs are null, if the revealed monitor is strictly preferred by both parties, there is a loss in efficiency due to the impossibility of bene…tting from it. Nonetheless, these strategies can partially recover the principal's losses. Additionally, we establish upper and lower bounds on the payoffs that the principal and the agent can achieve. Finally we characterize the equilibrium strategies under public and private monitoring (with communication) for different cost and impatience levels.

A type of perturbation of the harmonic oscillator

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