arXiv subjects
Publications and source records attributed to Pintu Debnath.
There is a long history of studying Ramsey theory using the algebraic structure of Stone-Cech compactification of discrete semigroup. It has been shown that various Ramsey theoretic structures are contained in different algebraic large sets. In this article we will study elementary characterization of essential F sets. And also study the mixing properties arises from essential F sets.
Furstenberg and Glasner proved that for an arbitrary k in N, any piecewise syndetic set contains k length arithmetic progression and such collection is also piecewise syndetic in Z: They used algebraic structure of beta N. The above result was extended for arbitrary semigroups by Bergelson and Hindman, again using the structure of Stone-Cech compactification of general semigroup. However they provided the abundances for various types of large sets. But the abundances in in many large sets is still unknown. In this work we will provide the abundance in Quasi Central sets, J-sets and C-sets.
The ring of polynomial over a finite field $F_q[x]$ has received much attention, both from a combinatorial viewpoint as in regards to its action on measurable dynamical systems. In the case of $(\mathbb{Z},+)$ we know that the ideal generated by any nonzero element is an IP$^*$-set. In the present article we first establish that the analogous result is true for $F_q[x]$. We further use this result to establish some mixing properties of the action of $(F_q[x],+)$. We shall also discuss on Khintchine's recurrence for the action of $(F_q[x]\setminus\{0\},\cdot)$.
In the present paper our main objective is to extend the notion of $D$-sets in countable amenable groups and to discuss its connection with weak mixing for amenable group actions. Further we prove that *-notions are equivalent in the countable amenable group of polynomials generated by finite fields.
Here we report the formation of fluorescent H aggregates of a cyanine dye Oxa18 in ultrathin film and its effect on energy transfer between Oxa18 and sRhb. Ideally H aggregate do not fluoresce. However, due to imperfect stacking of Oxa18 molecules in the aggregates, fluorescence occurred from Oxa18 H aggregates. This H aggregated band has substantial effect on the enhancement of energy transfer from Oxa18 to sRhb both in solution and in ultrathin film.
The applications of Fluorescence resonance energy transfer (FRET) have expanded tremendously in the last 25 years, and the technique has become a staple technique in many biological and biophysical fields. FRET can be used as spectroscopic ruler in various areas such as structural elucidation of biological molecules and their interactions, in vitro assays, in vivo monitoring in cellular research, nucleic acid analysis, signal transduction, light harvesting, and metallic nanomaterials etc. Based on the mechanism of FRET a variety of novel chemical sensors and Biosensors have been developed. This review highlights the recent applications of sensitive and selective ratiometric FRET based sensors.