Optimal Interpolating Spaces Preserving Shape

In this paper we study the existence and characterization of spaces which are images of minimal-norm projections that are required to interpolate at given functionals and satisfy additional shape-preserving requirements. We will call such spaces optimal interpolating spaces preserving shape. This investigation leads to concrete solutions in classical settings and, as examples, Π_n will be determined to be such spaces with regard to certain interpolation and shape-preserving requirements on the projections. Restated, the theory of this paper gives rist to an n-dimensional Hahn–Banach extension theorem, where the minimal-norm extension is required to keep invariant a fixed cone.     

Differential Substrate Sensing in Terpene Synthases from Plants and Microorganisms: Insight from Structural,Bioinformatic, and EnzyDock Analyses

Terpene synthases (TPSs) catalyze the first step in the formation of terpenoids, which comprise the largest class of natural products in nature. TPSs employ a family of universal natural substrates, composed of isoprenoid units bound to a diphosphate moiety. The intricate structures generated by TPSs are the result of substrate binding and folding in the active site, enzyme-controlled carbocation reaction cascades, and final reaction quenching. A key unaddressed question in class I TPSs is the asymmetric nature of the diphosphate-(Mg²⁺)₃ cluster, which forms a critical part of the active site. In this asymmetric ion cluster, two diphosphate oxygen atoms protrude into the active site pocket. The substrate hydrocarbon tail, which is eventually molded into terpenes, can bind to either of these oxygen atoms, yet to which is unknown. Herein, we employ structural, bioinformatics, and EnzyDock docking tools to address this enigma. We bring initial data suggesting that this difference is rooted in evolutionary differences between TPSs. We hypothesize that this alteration in binding, and subsequent chemistry, is due to TPSs originating from plants or microorganisms. We further suggest that this difference can cast light on the frequent observation that the chiral products or intermediates of plant and bacterial terpene synthases represent opposite enantiomers.     

Discovery of rare sulfated N-unsubstituted glucosamine based heparan sulfate analogs selectively activating chemokines

Achieving selective inhibition of chemokines with structurally well-defined heparan sulfate (HS) oligosaccharides can provide important insights into cancer cell migration and metastasis. However, HS is highly heterogeneous in chemical composition, which limits its therapeutic use. Here, we report the rational design and synthesis of N-unsubstituted (NU) and N-acetylated (NA) heparan sulfate tetrasaccharides that selectively inhibit structurally homologous chemokines. HS analogs were produced by divergent synthesis, where fully protected HS tetrasaccharide precursor was subjected to selective deprotection and regioselectively O-sulfated, and O-phosphorylated to obtain 13 novel HS tetrasaccharides. HS microarray and SPR analysis with a wide range of chemokines revealed the structural significance of sulfation patterns and NU domain in chemokine activities for the first time. Particularly, HT-3,6S-NH revealed selective recognition by CCL2 chemokine. Further systematic interrogation of the role of HT-3,6S-NH in cancer demonstrated an effective blockade of CCL2 and its receptor CCR2 interactions, thereby impairing cancer cell proliferation, migration and invasion, a step towards designing novel drug molecules.     

On Measuring the Efficiency of Kernel Operators in L p (R d )

It is well known that it is possible to enhance the approximation properties of a kernel operator by increasing its support size. There is an obvious tradeoff between higher approximation order of a kernel and the complexity of algorithms that employ it. A question is then asked: how do we compare the efficiency of kernels with comparable support size? We follow Blu and Unser and choose as a measure of the efficiency of the kernels the first leading constant in a certain error expansion. We use time domain methods to treat the case of globally supported kernels in L _p (R ^d), 1≤p≤∞.

     

Shape-Preserving Widths of Weighted Sobolev-Type Classes of Positive, Monotone, and Convex Functions on a Finite Interval

   Abstract. Let I be a finite interval, r∈ N and ρ(t)= dist {t, I} , t∈ I . Denote by Δ ^s ₊ L _q the subset of all functions y∈ L _q such that the s -difference Δ ^s _τ y(t) is nonnegative on I ,

Systemic chemical characterization of Lemna minor by UHPLC-Q-Exactive Orbitrap MS coupled with parallel reaction monitoring

Lemna minor L. (LM) has been used for measles opacity, rubella itching, edema, and oliguria, and the main active ingredients were flavonoids, namely, apigenin, apigenin-7-O-glucoside, and luteolin-7-O-glucoside. However, few systematic analyses of their constituents have been performed; thus, it was necessary to establish a fast and efficient method to identify the chemical composition of LM. In this study, the UHPLC-Q-Exactive Orbitrap mass spectrometry coupled with parallel reaction monitoring was established. Finally, a total of 112 constituents, including 30 dipeptides, 28 nucleosides, 11 amino acids, 10 organic acids, 10 flavonoids, and 23 other compounds, were identified by MS, diagnostic fragment ions, and retention time. One hundred one of those chemicals were first found in LM, which was very beneficial for the further development and utilization of nutriments and the medicinal use of LM.     

Direct Observation of the Ethyl Radical in the Pyrolysis of Ethane

We report the first direct detection of ethyl radical in the pyrolysis of ethane. Observation of this vital intermediate was made possible in this extremely reactive environment by the use of a microreactor coupled with synchrotron radiation and photoelectron photoion coincidence (PEPICO) spectroscopy, despite its short lifetime and low concentration. Together with ab-initio master equation-calculated rates and fully coupled computational fluid dynamics simulations, our measurements show that even under the low pressures and short residence times in our experiment, ethyl formation can only be explained by bimolecular reactions; the most important is the catalytic attack of ethane by H atoms, which are then regenerated by decomposition of the nascent ethyl radicals. Our results complete the observation of all hypothesized intermediates in this industrially important process and highlight the need for further studies under additional conditions using similar methods to improve existing models and optimize process chemistries.     

Are the degrees of best (co)convex and unconstrained polynomial approximation the same?

Let ℂ[−1,1] be the space of continuous functions on [−,1], and denote by Δ² the set of convex functions f ∈ ℂ[−,1]. Also, let E _n (f) and E _n ⁽²⁾ (f) denote the degrees of best unconstrained and convex approximation of f ∈ Δ² by algebraic polynomials of degree < n, respectively. Clearly, En (f) ≦ E _n ⁽²⁾ (f), and Lorentz and Zeller proved that the inverse inequality E _n ⁽²⁾ (f) ≦ cE _n (f) is invalid even with the constant c = c(f) which depends on the function f ∈ Δ². In this paper we prove, for every α > 0 and function f ∈ Δ², that