In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtai...

We report the magnetocaloric effect of a bilayered perovskite ruthenate Ca3Ru2O7 that has recently been recognized as an antiferromagnetic polar metal. The magnetic entropy change obtained from temperature dependence DC magnetization measurements shows peaks and valleys under field near metamagnetic transitions, enable us to map out thermodynamic field–temperature phase-diagram. area surrounded...

The diagram showing off-center nested spheres which is traditionally used to illustrate the Doppler effect, misleading and its trigonometric analysis leads errors concerning light, because electromagnetic aberration effects conform a wavefront surface that not sphere but an ellipsoid stretched along trajectory of source. Cartesian polar equations spherical ellipsoidal wavefronts are compared he...

Let (f, g) be a pair of complex analytic functions on a singular analytic space X. We give “the correct” definition of the relative polar curve of (f, g), and we give a very formal generalization of Lê’s attaching result, which relates the relative polar curve to the relative cohomology of the Milnor fiber modulo a hyperplane slice. We also give the technical arguments which allow one to work w...

In many real world problems, data sometimes comes from n agents (n≥2), multipolar information exists. For issues that are associated with uncertainty, this information can not be showed with the values of crisp, fuzzy, intuitionistic or bipolar. Graph is one of the mathematical models widely used in different sciences. Ambiguity in a graph where data depends on the n parameter can not be showed...

We describe a relation between Arnold’s strange duality and a polar duality between the Newton polytopes which is mostly due to M. Kobayashi. We show that this relation continues to hold for the extension of Arnold’s strange duality found by C. T. C. Wall and the author. By a method of Ehlers-Varchenko, the characteristic polynomial of the monodromy of a hypersurface singularity can be computed...

sponges are the simplest multicellular animals that lack defense mechanisms and rely on chemical defense  that have been used by mankind to develop antimicrobial drugs against diseases.  the present study was designed to demonstrate the antibacterial and antifungal activities of marine sponge dysidea pallescens semipolar and nonpolar extracts. in this study, d. pallescens were collected from he...

beside ziegler-natta and phillips catalysts the development of methylaluminoxane (mao) as cocatalyst incombination with metallocenes or other transition metal complexes for the polymerization of olefins haswidely increased the possibilities in controlling the polymer composition, polymer structure, tacticity and special properties with high precision. these catalysts allow the synthesis of isot...