An object-parameter approach to predicting unknown data in incomplete fuzzy soft sets

Incomplete data in soft sets lead to uncertainty and inaccuracy in representing and handling information. This paper introduces notions of complete distance between two objects and relative dominance degree between two parameters. Based on both the notions, an object-parameter method is proposed to predict unknown data in incomplete fuzzy soft sets. The proposal makes full use of known data, including the information from the relationship between known values of all objects on a certain parameter and the information from the relationship between known values of an object on all parameters. The effectiveness of the proposal is verified by many examples under the compared investigation of classical predicted methods.     

Ideal Free Distribution in Two Patches

In this paper, the formats of Julia sets for a class of nonlinear complex dynamic systems with variable coefficients were studied under certain conditions. For the complex dynamic systems in piecewise cases, we proposed some methods to control the forms of their Julia sets and stable domains analytically. What’s more, we illustrated that our methods worked well by computational simulations. Our work provides a better understanding about how to control the Julia sets of certain complex dynamic systems.     

Operators on Soft Inner Product Spaces

In the present paper, self-adjoint operator and completely continuous operator on soft inner product spaces have been introduced and some basic properties of such operators are studied.     

15-deoxy-isoxeniolide-A,new diterpenoid from a bornean soft coral,Xenia sp.

A new xenicane diterpenoid, 15-deoxy-isoxeniolide-A (1) along with four known compounds 9-deoxy-isoxeniolide-A (2), isoxeniolide-A (3), xeniolide-A (4) and coraxeniolide-B (5) were isolated from the Bornean soft coral Xenia sp. The structures of these metabolites were elucidated on the basis of spectral analysis, NMR and HRESIMS. Compound 5 showed cytotoxic activity against ATL cell line, S1T.     

A variational approach for a generalized emden-fowler equation

Existence of positive solutions of singular boundary value problems related to Emden-Fowler equation is proved. A general minimization theorem in Sobolev spaces is applied.     

Characterizing and Generating Bivariate Empirical Rank Distributions Satisfying Certain Positive Dependence Concepts

Abstract

This article introduces an approach for characterizing the classes of empirical distributions that satisfy certain positive dependence notions. Mathematically, this can be expressed as studying certain subsets of the class S_N of permutations of 1, …, N, where each subset corresponds to some positive dependence notions. Explicit techniques for it-eratively characterizing subsets of S_N that satisfy certain positive dependence concepts are obtained and various counting formulas are given. Based on these techniques, graph-theoretic methods are used to introduce new and more efficient algorithms for constructively generating and enumerating the elements of various of these subsets of S_N. For example, the class of positively quadrant dependent permutations in S_N is characterized in this fashion.     

Approaching compositional limits of perovskite – type oxides and oxynitrides by synthesis of Mg0.25Ca0.65Y0.1Ti(O,N)3, Ca1–xYxZr(O,N)3 (0.1 ≤ x ≤ 0.4), and Sr1–xLaxZr(O,N)3 (0.1 ≤ x ≤ 0.4)

Partial substitution of cations and anions in perovskite-type materials is a powerful way to tune the desired properties. The systematic variation of the cations size, the partial exchange of O²⁻ for N³⁻ and their effect on the size of the optical band gap and the thermal stability was investigated here. The anionic substitution resulted in the formation of the orthorhombic perovskite-type oxynitrides Mg_0.25Ca_0.65Y_0.1Ti(O,N)₃, Ca_1-xY_xZr(O,N)₃, and Sr_1–xLa_xZr(O,N)₃. A two-step synthesis protocol was applied: i) (nano-crystalline) oxide precursors were synthesized by a Pechini method followed by ii) ammonolysis in flowing NH₃ at T = 773 K (Ti) and T = 1273 K (Zr), respectively. High-temperature synthesis of such oxide precursors by solid–state reaction generally resulted in phase separation of the different A-site cations. Changes of the crystal structures were investigated by Rietveld refinements of the powder XRD data, thermal stability by DSC/TG measurements in oxygen atmosphere, oxygen and nitrogen contents by O/N analysis using hot gas extraction technique, and optical band gaps by photoluminescence spectroscopy. By moving from Mg_0.25Ca_0.65Y_0.1Ti(O,N)₃ via Ca_1–xY_xZr(O,N)₃ to Sr_1–xLa_xZr(O,N)₃, the degree of tilting of the octahedral network is reduced, as observed by an increase in the B–X–B angles caused by the simultaneously increasing effective ionic radius of the A-site cation(s). In general, increasing substitution levels on the A-site (Y³⁺ and La³⁺) are accompanied by an enhanced replacement of O²⁻ by N³⁻. In all three systems, this anionic substitution resulted in a reduction of the optical band gap by approximately 1 eV (Ti) and up to 2.1 eV (Zr) compared to the respective oxides. For Mg_0.25Ca_0.65Y_0.1Ti(O,N)₃ an optical band gap of 2.2 eV was observed, appropriate for a solar water splitting photocatalyst. The Zr-based oxynitrides required a by a factor of 2 higher nitrogen contents to significantly reduce the optical band gap and the measured values of 2.9 eV–3.2 eV are larger compared to the Ti-based oxynitride. Bulk thermal stability was revealed up to T = 881 K. In general, the thermal stability decreased with increasing substitution levels due to an increasing deviation from the ideal anionic composition as demonstrated by O/N analysis.     

Extremal A-statistical limit points via ideals

In this paper, following the line of recent work of Savaş et al. [20] we apply the notion of ideals to A-statistical limit superior and inferior for a sequence of real numbers.     

Novel cytotoxic nine-membered macrocyclic polysulfur cembranoid lactones from the soft coral Sinularia sp.

One novel nine-membered macrocyclic polysulfur cembranoid lactone, sinulariaoid A (1); three new multioxygenated cembranoids, sinulariaoid B (2), sinulariaoid C (3), sinulariaoid D (4); and four known cembranoids, capilloloid (5), dihydrosinularin (6), sinularin (7), and dihydrosinuflexolide (8) were isolated from the soft coral Sinularia sp. collected off of Sanya Bay in the South China Sea. Their stereochemical structures were determined on the basis of extensive spectroscopic methods, including single crystal X-ray diffraction analysis. Sinulariaoid A (1) is the first reported nine-membered macrocyclic polysulfur cembranoid from soft coral. The cytotoxic activities of compounds 1–8 were determined in four human cancer cell lines (HepG2, HepG2/ADM, MCF-7, and MCF-7/ADM). Of these, sinulariaoid A (1) exhibited the most potent anticancer activity in vitro, and its cytotoxicity in HepG2/ADM was more potent than in the other three cell lines. Furthermore, it was found that sinulariaoid A (1) induced apoptosis, and its selective toxicity toward HepG2/ADM cells was not related to P-glycoproteins.