Five series of strontium hexaferrite nanomaterials with nominal compositions, SrZrxNixFe12-2xO19, SrZrxCuxFe12-2xO19, SrZrxMnxFe12-2xO19, SrZrxZnxFe12-2xO19 and SrZrxAlxGaxFe12-2xO19 (where x = 0.0-0.8) have been synthesized by the chemical co- precipitation method. The structural analysis is carried out by thermogravimetry (TG/DTG), powder X-ray diffraction (XRD) and energy dispersive X-ray fluorescence (ED-XRF) techniques. The DC electrical resistivity (ρ), dielectric constant (έ) and dielectric loss (tanδ) are measured by a two-point probe method and inductance capacitance resistance (LCR) meter, respectively. The magnetic susceptibility (χ) is measured by a magnetic susceptometer and the hysteresis loops, the saturation magnetization (Ms), remanence (Mr) and coercivity (Hc) has been determined by the induction method. Thermal analysis reveals that the magnetoplumbite phase begins to form at a temperature of 873 K and is completed at 1193 K which is also complimented by the XRD studies. The average crystallites sizes of the samples of the five series are in the range of 26-62 nm. All the samples consist of pure single phase as confirmed by the magnetic susceptibility and XRD analysis. The nominal theoretical compositions of the samples are experimentally confirmed by the ED-XRF analysis. Except Zr-Mn substituted series all the samples show metal to semiconductor transition (TM-S). The drift mobility (μd) and activation energy (Ea) are calculated from the electrical resistivity data. The observed variation of electrical resistivity is explained on the basis of the electrons hopping between ferric and ferrous ions. The room temperature electrical resistivity and activation energy are increased by doping with Zr-Ni, Zr-Cu, Zr-Mn and Al-Ga series up to specific concentration but decreases continuously by substitution of Zr-Zn. The dielectric constant (έ) and dielectric loss (tanδ) are calculated in the frequency range of 100 Hz -1MHz and both the parameters decrease with increase in frequency. This behavior is explained on the basis of the Maxwell- Wagner and Koop’s models. The dielectric constant, dielectric loss and drift mobility increase with the increase in the dopant (Zr-Ni, Zr-Cu, Zr-Mn and Al-Ga) contents but increase by the substitution of Zr-Zn. The Curie temperature (Tc) is determined from the temperature dependence of magnetic susceptibility (χ) at temperature from 300 to 800 K. the value of Tc decreases for all the five series investigated here. The saturation magnetization (Ms) increases for Zr-M series (where M = Ni, Cu, Mn and Zn) but decreases for the Al-Ga series. The coercivity (Hc) decreases for all the present series. The variation of saturation magnetization,remanence (Mr) and coercivity with substituent concentration is explained on the basis of occupation of the substituted cations at different hexagonal sites. The increase in saturation magnetization, electrical resistivity and decrease in coercivity, dielectric constant, dielectric loss and drift mobility suggest that the Sr-hexaferrites doped with Zr-Ni, Zr-Cu and Zr-Mn are suitable for applications in high density recording media as well as in microwave devices but the Zr-Zn and Al-Ga substituted samples are more suitable for high density recording media and microwave devices, respectively.
In this article, some basic elements of Islamic society have been clarified in the light of Surah Al Hujurāt. Just as a solid foundation of a building is essential for a strong building, so a strong foundation is essential for a successful society and a strong foundation of an Islamic society has its principles, which are derived from the Qur'an and Hadith. Since these principles are important for the well-being and development of the Muslim society, their observance is necessary for the Muslim society. This article presents a picture of an ideal society in the light of Surah Al Hujurāt. Have presented the following topics in this article: Role of leadership and its elements, unity of Islamic society, ethics and beliefs are some of the principles discussed in this article. The research concludes that the principles stated in Surah Al Hujurāt play a vital role in establishing a stable Islamic society.
The idea of fuzzy sets has opened new door of research in the world of contemporary Mathematics. The concept of fuzzy sets provided a new approach to model imprecision and uncertainty present in phenomena without sharp boundaries. The fuzzi cation of algebraic structures, play a dynamic role in Mathematics with diverse applications in many other branches such as computer arithmetic''s, control engineering, error correcting codes and formal languages and many more. Moreover, during the course of the last decade, non-associative algebraic structures have gained popularity among the researchers. In this background, many researchers initiated the notion of AG-groupoids, its newly introduced subclasses and its fuzzi cation. The present research is among the very few where non-associative algebraic structures are investigated and fuzzi ed. In this thesis various constructions of AG-groups over theeld Zn are introduced, some related results and example of AG-groups are provided. Further, the structural properties of fuzzy AG-subgroup are introduced and various notions of fuzzy AG-subgroups are investigated, e.g. conjugate of a fuzzy AG-subgroup, fuzzy normal AG-subgroups, relations between fuzzy normal AG-subgroup and commutators in AG-groups and equal-height elements in fuzzy AG-subgroups. Moreover, the notion of fuzzy AG-subgroups is further extended and a fuzzy coset in AG-subgroups is introduced. It is worth mentioning that if A is any fuzzy AGsubgroup of G, thenA(xy) =A(yx) for all x; y 2 G, i.e. each fuzzy left coset is fuzzy right coset and vice versa. Also, fuzzy coset in AG-subgroup could be empty contrary to coset in group theory. However, order of the nonempty fuzzy coset is the same as the index number [G : A] where H is an AG-subgroup of an AG-group G. The notion of fuzzy quotient AG-subgroup, fuzzy AG-subgroup of the quotient (factor) AG-subgroup, fuzzy homomorphism of AG-group and fuzzy Lagrange''s Theorem ofnite AG-group is introduced. Finally, cubic AG-subgroups and its properties are explored.