Irrational Numbers of Constant Type --- A New Characterization

We obtain a new characterization for irrational numbers of constant type -- defined as irrationals with bounded partial quotients in their continued fraction expansion. The result is essential in the formulation of stability criteria for orbits of quantum twist maps in a class of dynamical systems.Comment: 7 pages, AMS-LaTeX, with changes in reference

Logarithmic corrections to finite size spectrum of SU(N) symmetric quantum chains

We consider SU(N) symmetric one dimensional quantum chains at finite temperature. For such systems the correlation lengths, ground state energy, and excited state energies are investigated in the framework of conformal field theory. The possibility of different types of excited states are discussed. Logarithmic corrections to the ground state energy and different types of excited states in the presence of a marginal opeartor, are calculated. Known results for SU(2) and SU(4) symmetric systems follow from our general formula.Comment: 5 pages, 1 figure; Typos corrected and minor changes made for clarit

A scalar invariant and the local geometry of a class of static spacetimes

The scalar invariant, I, constructed from the "square" of the first covariant derivative of the curvature tensor is used to probe the local geometry of static spacetimes which are also Einstein spaces. We obtain an explicit form of this invariant, exploiting the local warp-product structure of a 4-dimensional static spacetime, $~^{(3)}\Sigma \times_{f} \reals$, where $^{(3)}\Sigma$ is the Riemannian hypersurface orthogonal to a timelike Killing vector field with norm given by a positive function, $f$ on $^{(3)}\Sigma$. For a static spacetime which is an Einstein space, it is shown that the locally measurable scalar, I, contains a term which vanishes if and only if $^{(3)}\Sigma$ is conformally flat; also, the vanishing of this term implies (a) $~^{(3)}\Sigma$ is locally foliated by level surfaces of $f$, $^{(2)}S$, which are totally umbilic spaces of constant curvature, and (b) $^{(3)}\Sigma$ is locally a warp-product space. Futhermore, if $^{(3)}\Sigma$ is conformally flat it follows that every non-trivial static solution of the vacuum Einstein equation with a cosmological constant, is either Nariai-type or Kottler-type - the classes of spacetimes relevant to quantum aspects of gravity.Comment: LaTeX, 13 pages, JHEP3.cls; The paper is completely rewritten with a new title and introduction as well as additional results and reference

Nanotechnology Application and Intellectual Property Right Prospects of Mammalian Cell Culture

The significant challenges faced by modern-day medicine include designing a target-specific drug delivery system with a controlled release mechanism, having the potential to avoid opsonization and reduce bio-toxicity. Nanoparticles are materials with nanoscale dimensions and maybe natural and synthetic in origin. Engineered nano-sized materials are playing an indispensable role in the field of nanomedicine and nanobiotechnology. Besides, engineered nano-sized particles impart therapeutic applications with enhanced specificity because of their unique bespoke properties. Moreover, such application-customized nanoparticles offer an enormous possibility for their compatibility with different biological molecules like proteins, genetic materials, cell membranes, and organelles at the nano-bio frame. Besides, surface functionalization with targeting moieties such as small molecule ligands, monoclonal antibodies, aptamers, cell-penetrating peptides, and proteins facilitate nanoparticle-based specific tissue targeting. This review summarizes some of the advances in nanoparticle-based therapeutics and theranostics. A better understanding of idealistic preparation methods, physicochemical attributes, surface functionalization, biocompatibility can empower the potential translation of nanomaterials from the ‘bench-to-bedside’. In modern-day medicine, engineered nanoparticles have a wide range of demands ranging from bio-imaging, theranostics, tissue engineering, sensors, drug and nucleic acid delivery, and other pharmaceuticals applications. 2D and 3D mammalian cell-based assays are widely used to model diseases, screening of drugs, drug discovery, and toxicity analyses. Recent advances in cell culture technology and associated progress in nanotechnology have enabled researchers to study a wide variety of physiologically relevant questions. This chapter explores the properties of nanoparticles, different targeted delivery methods, biological analysis, and theranostics. Moreover, this chapter also emphasizes biosafety and bioethics associated with mammalian cell culture and discusses the significance of intellectual property rights from an industrial and academic perspective