ON SMARANDACHE RINGS

It is proved that a ring R in which for every x ∈ R there exists a (and hence the smallest) natural number n(x) > 1 such that xn(x) = x is always a Smarandache Ring. Two examples are provided for justification

Thermal conductance of two dimensional constrictions Interim report

Thermal resistance of heat flow through two dimensional symmetrical, and eccentric constriction

Signatures of two-step impurity mediated vortex lattice melting in Bose-Einstein Condensates

We simulate a rotating 2D BEC to study the melting of a vortex lattice in presence of random impurities. Impurities are introduced either through a protocol in which vortex lattice is produced in an impurity potential or first creating the vortex lattice in the absence of random pinning and then cranking up the (co-rotating) impurity potential. We find that for a fixed strength, pinning of vortices at randomly distributed impurities leads to the new states of vortex lattice. It is unearthed that the vortex lattice follow a two-step melting via loss of positional and orientational order. Also, the comparisons between the states obtained in two protocols show that the vortex lattice states are metastable states when impurities are introduced after the formation of an ordered vortex lattice. We also show the existence of metastable states which depend on the history of how the vortex lattice is created.Comment: Accepted in Euro. Phys. Let

Cultural Inscriptions in the Hymns of Anonymous Sangam Poets

Among the languages of the world, Tamil is hailed as the supreme classical language. Tamil is an ancient, classical, and prosperous language. Literature is one factor that enriches the language. In the Sangam society, which was centred on human life, honour for men and chastity for women became ornaments. People lived a cultured life where they lived and let others live. They accepted married life in the community wholeheartedly. Hospitality was prized as the chief virtue. The author names of many hymns are unknown in the Sangam literature, ‘Ettuthogai’, which is such a cultural treasury and primary literature. This research explores the richness of cultural richness, lifestyles, and beliefs found in the songs of anonymous poets

Family Confromation in Periyapuranam

Homelessness is the life of a husband and wife who stay in the eye of the house. The husband and wife should work together for homelessness. It is learnt that women were instrumental in the ups and downs of their husbands in the family structure shown by periyapuranam. It is seen that the husband himself respected the husband's word as a visible deity. He describes how he lived as a good family, husband, wife and children in a life of conception. It is clear from the lives of the Nayanmars that in family life, Shiva charity and hospitality have lived with two eyes

Saiva Siddhanta in Thiruvasagam

Manivasagar says, there is just one and only God. He specifies many epithets to the Supreme Deity. He sings, God is the Primary Deity for all living beings. SaivaSidhantha also describes, God (Pathi) is the primary thing among all. Manivasagar narrated that the Grace of God (Pathi) is required to detach the soul (Pasu) from the bondage (Pasam) and to reach the God. According to SaivaSidhantha, the cause of every birth is the effect of past karma which includes both-right and wrong deeds. Manivasagar has also mentioned the same as SaivaSidhantha. This paper talks about the relationships and characteristics of three primary saivasidhantha truths, that is pathi, pasu, pasam. It also talks about vinai principle, which is the primal cause for pasu tp undergo rebirth and also it suggests that by worshipping almighty a soul can cut this cycle of rebirth and merge with god. All the above concepts are illustrated with the quotes from thiruvasagam. Manivasagar narrated in his Thiruvasagam that The Soul (Pasu) should experience the impact of past karma, but at the same time, by worshipping the God (Pathi), the Soul (Pasu) will be freed from the Karma. This is also told in SaivaSidhantha

The Ising phase in the J1-J2 Heisenberg Model

The two dimensional Heisenberg antiferromagnet on the square lattice with nearest (J1) and next-nearest (J2) neighbor couplings is investigated in the strong frustration regime (J2/J1>1/2). A new effective field theory describing the long wavelength physics of the model is derived from the quantum hamiltonian. The structure of the resulting non linear sigma model allows to recover the known spin wave results in the collinear regime, supports the presence of an Ising phase transition at finite temperature and suggests the possible occurrence of a non-magnetic ground state breaking rotational symmetry. By means of Lanczos diagonalizations we investigate the spin system at T=0, focusing our attention on the region where the collinear order parameter is strongly suppressed by quantum fluctuations and a transition to a non-magnetic state occurs. Correlation functions display a remarkable size independence and allow to identify the transition between the magnetic and non-magnetic region of the phase diagram. The numerical results support the presence of a non-magnetic phase with orientational ordering.Comment: 6 pages, 4 figures, to be published in PR