Deciding the existence of uniform interpolants over transitive models

We consider the problem of the existence of uniform interpolants in the modal logic K4. We first prove that all ${\square}$ -free formulas have uniform interpolants in this logic. In the general case, we shall prove that given a modal formula ${\phi}$ and a sublanguage L of the language of the formula, we can decide whether ${\phi}$ has a uniform interpolant with respect to L in K4. The ${\square}$ -free case is proved using a reduction to the G?del L?b Logic GL, while in the general case we prove that the question of whether a modal formula has uniform interpolants over transitive frames can be reduced to a decidable expressivity problem on the???-calculus.     

Optimal contracting with effort and misvaluation

We propose a new continuous-time contracting model, in which the firm value process can only be observed with noise, and there are two sources of moral hazard: the agent’s effort and misvaluation. The principal can induce the agent to alter the perceived fundamental value of the firm through misvaluation, thus changing the market estimate of that value. We consider two cases in detail: the one in which the market correctly anticipates only the effort, and the other in which it correctly anticipates both the effort and the amount of misvaluation. In the first case, we find that it is optimal for the principal to induce the agent to apply a non-zero amount of misvaluation. Using calculus of variation techniques, we find the optimal pay-per-performance sensitivity (PPS) of the contract and optimal effort and misvaluation amount, by means of solving of a second order ordinary differential equation. In the second case, which can be viewed as an extension of the seminal Holmstrom-Milgrom model to the case of noisy observations, we find that the optimal misvaluation value is zero, and we compare the resulting optimal contract to the Holmstrom-Milgrom contract.     

The Hilbert functions which force the Weak Lefschetz Property

The purpose of this note is to characterize the finite Hilbert functions which force all of their artinian algebras to enjoy the Weak Lefschetz Property (WLP). Curiously, they turn out to be exactly those (characterized by Wiebe in [A. Wiebe, The Lefschetz property for componentwise linear ideals and Gotzmann ideals, Comm. Algebra 32 (12) (2004) 4601-4611]) whose Gotzmann ideals have the WLP.This implies that, if a Gotzmann ideal has the WLP, then all algebras with the same Hilbert function (and hence lower Betti numbers) have the WLP as well. However, we will answer in the negative, even in the case of level algebras, the most natural question that one might ask after reading the previous sentence: If A is an artinian algebra enjoying the WLP, do all artinian algebras with the same Hilbert function as A and Betti numbers lower than those of A have the WLP as well?Also, as a consequence of our result, we have another (simpler) proof of the fact that all codimension 2 algebras enjoy the WLP (this fact was first proven in [T. Harima, J. Migliore, U. Nagel, J. Watanabe, The weak and strong Lefschetz properties for Artinian K-algebras, J. Algebra 262 (2003) 99-126], where it was shown that even the Strong Lefschetz Property holds).     

Ruthenium‐Catalyzed Cross‐Dehydrogenative ortho‐N‐Carbazolation of Diarylamines: Versatile Access to Unsymmetrical Diamines

The dehydrogenative C–N cross‐coupling of unprotected, secondary anilines through ortho‐N‐carbazolation has been achieved using a Ru catalytic system with O₂ as the terminal oxidant. The reactions proceed in an intermolecular fashion, selectively in the ortho position. Implications for the field of organic synthesis are discussed.     

Surface-enhanced Raman spectroscopy of blood plasma and serum using Ag and Au nanoparticles: a systematic study

Surface-enhanced Raman spectroscopy (SERS) is a good candidate for the development of fast and easy-to-use diagnostic tools, possibly used on biofluids in point-of-care or screening tests. In particular, label-free SERS spectra of blood serum and plasma, two biofluids widely used in diagnostics, could be used as a metabolic fingerprinting approach for biomarker discovery. This study aims at a systematic evaluation of SERS spectra of blood serum and plasma, using various Ag and Au aqueous colloids, as SERS substrates, in combination with three excitation lasers of different wavelengths, ranging from the visible to the near-infrared. The analysis of the SERS spectra collected from 20 healthy subjects under a variety of experimental conditions revealed that intense and repeatable spectra are quickly obtained only if proteins are filtered out from samples, and an excitation in the near-infrared is used in combination with Ag colloids. Moreover, common plasma anticoagulants such as EDTA and citrate are found to interfere with SERS spectra; accordingly, filtered serum or heparin plasma are the samples of choice, having identical SERS spectra. Most bands observed in SERS spectra of these biofluids are assigned to uric acid, a metabolite whose blood concentration depends on factors such as sex, age, therapeutic treatments, and various pathological conditions, suggesting that, even when the right experimental conditions are chosen, great care must be taken in designing studies with the purpose of developing diagnostic tests.     

Catalytic Decarboxylative Cross‐Coupling of Aryl Chlorides and Benzoates without Activating ortho Substituents

The restriction of decarboxylative cross‐coupling reactions to ortho‐substituted or heterocyclic carboxylate substrates was overcome by holistic optimization of a bimetallic Cu/Pd catalyst system. The combination of a CuI/Me₄phen decarboxylation catalyst and a [(MeCN)₄Pd](OTf)₂/XPhos cross‐coupling catalyst enables the synthesis of biaryls from inexpensive aryl chlorides and potassium benzoates regardless of their substitution pattern.     

Microwave, high-resolution infrared, and quantum chemical investigations of CHBrF2: ground and v4 = 1 states

A combined microwave, infrared, and computational investigation of CHBrF(2) is reported. For the vibrational ground state, measurements in the millimeter- and sub-millimeter-wave regions for CH(79)BrF(2) and CH(81)BrF(2) provided rotational and centrifugal-distortion constants up to the sextic terms as well as the hyperfine parameters (quadrupole-coupling and spin-rotation interaction constants) of the bromine nucleus. The determination of the latter was made possible by recording of spectra at sub-Doppler resolution, achieved by means of the Lamb-dip technique, and supporting the spectra analysis by high-level quantum chemical calculations at the coupled-cluster level. In this context, the importance of relativistic effects, which are of the order of 6.5% and included in the present work using second-order direct perturbation theory, needs to be emphasized for accurate predictions of the bromine quadrupole-coupling constants. The infrared measurements focused on the ν(4) fundamental band of CH(79)BrF(2). Fourier transform investigations using a synchrotron radiation source provided the necessary resolution for the observation and analysis of the rotational structure. The spectroscopic parameters of the v(4) = 1 state were found to be close to those of the vibrational ground state, indicating that the ν(4) band is essentially unaffected by perturbations.