Regularity Index of S + 2 Fat Points not on a Linear (S − 1)-Space

We will give a formula to compute the regularity index of s + 2 fat points not lying on a linear (s ? 1)-space in ? ⁿ , s ≤ n (Theorem 3.4). Our result generalizes a formula to compute the regularity index of fat points in general position in ? ⁿ ([3 Catalisano , M. V. , Trung , N. V. , Valla , G. ( 1993 ). A sharp bound for the regularity index of fat points in general position . Proc. Amer. Math. Soc. 118 : 717 – 724 .[Crossref], [Web of Science ®] , [Google Scholar]], Corollary 8). Our result also shows that the Segre bound is attained by s + 2 points not lying on a linear (s ? 1)-space.     

Convex underestimators of polynomials

Convex underestimators of a polynomial on a box. Given a non convex polynomial ${f\in \mathbb{R}[{\rm x}]}$ and a box ${{\rm B}\subset \mathbb{R}^n}$ , we construct a sequence of convex polynomials ${(f_{dk})\subset \mathbb{R}[{\rm x}]}$ , which converges in a strong sense to the “best” (convex and degree-d) polynomial underestimator ${f^{*}_{d}}$ of f. Indeed, ${f^{*}_{d}}$ minimizes the L ₁-norm ${\Vert f-g\Vert_1}$ on B, over all convex degree-d polynomial underestimators g of f. On a sample of problems with non convex f, we then compare the lower bounds obtained by minimizing the convex underestimator of f computed as above and computed via the popular α BB method and some of its other refinements. In most of all examples we obtain significantly better results even with the smallest value of k.     

Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives

We propose higher-order radial sets and corresponding derivatives of a set-valued map and prove calculus rules for sums and compositions, which are followed by direct applications in discussing optimality conditions for several particular optimization problems. Our main results are both necessary and sufficient higher-order conditions for weak efficiency in a general set-valued vector optimization problem without any convexity assumptions. Many examples are provided to explain advantages of our results over a number of existing ones in the literature.     

Effects of electrolyte on ZnO nanostructures synthesized by galvanostatic electrochemical deposition and their UV sensing properties

In this study, ZnO nanorods (NRs) and nanocombs (NCs) are synthesized by simple galvanostatic electrochemical deposition technique, without prepared any ZnO seed-layer or catalyst. The effect of the different morphologies on the UV sensing characteristics has been studied under ambient conditions. The photoluminescence (PL) spectra and time-dependent photoresponse of the ZnO nanostructures exhibited good optical properties. At room temperature, NCs showed superior response with 9% change of its resistance, few seconds response time and fully recovery. Inversely, in high temperature ZnO NRs indicated better response than NCs with the variation of 25% of its resistance. The dependence photoresponse on temperature demonstrated clearly how surface-defects affect on UV response of ZnO nanostructures. Our approach is to provide a simple and cost-effective way to fabricate UV detectors.     

Boron‐Containing Probes for Non‐optical High‐Resolution Imaging of Biological Samples

Boron has been employed in materials science as a marker for imaging specific structures by electron energy loss spectroscopy (EELS) or secondary ion mass spectrometry (SIMS). It has a strong potential in biological analyses as well; however, the specific coupling of a sufficient number of boron atoms to a biological structure has proven challenging. Herein, we synthesize tags containing closo‐1,2‐dicarbadodecaborane, coupled to soluble peptides, which were integrated in specific proteins by click chemistry in mammalian cells and were also coupled to nanobodies for use in immunocytochemistry experiments. The tags were fully functional in biological samples, as demonstrated by nanoSIMS imaging of cell cultures. The boron signal revealed the protein of interest, while other SIMS channels were used for imaging different positive ions, such as the cellular metal ions. This allows, for the first time, the simultaneous imaging of such ions with a protein of interest and will enable new biological applications in the SIMS field.     

General one-loop formulas for $$H\rightarrow f\bar{f}\gamma $$ H → f f ¯ γ and its applications

The European Physical Journal C - Considering supergravity theory is a natural step in the development of gravity models. This paper follows the “algebraic“ path and constructs possible...     

Tribology of thin wetting films between bubble and moving solid surface

This work shows a successful example of coupling of theory and experiment to study the tribology of bubble rubbing on solid surface. Such kind of investigation is reported for the first time in the literature. A theory about wetting film intercalated between bubble and moving solid surface was developed, thus deriving the non-linear evolution differential equation which accounted for the friction slip coefficient at the solid surface. The stationary 3D film thickness profile, which appears to be a solution of the differential equation, for each particular speed of motion of the solid surface was derived by means of special procedure and unique interferometric experimental setup. This allowed us to determine the 3D map of the lift pressure within the wetting film, the friction force per unit area and the friction coefficient of rubbing at different speeds of motion of the solid surface. Thus, we observed interesting tribological details about the rubbing of the bubble on the solid surface like for example:     

Derivation of Hartreeʼs theory for generic mean-field Bose systems

In this paper we provide a novel strategy to prove the validity of Hartree?s theory for the ground state energy of bosonic quantum systems in the mean-field regime. For the known case of trapped Bose gases, this can be shown using the strong quantum de Finetti theorem, which gives the structure of infinite hierarchies of k-particles density matrices. Here we deal with the case where some particles are allowed to escape to infinity, leading to a lack of compactness. Our approach is based on two ingredients: (1) a weak version of the quantum de Finetti theorem, and (2) geometric techniques for many-body systems. Our strategy does not rely on any special property of the interaction between the particles. In particular, our results cover those of Benguria–Lieb and Lieb–Yau for, respectively, bosonic atoms and boson stars.