arXiv subjects
Publications and source records attributed to Anirban Bandyopadhyay.
In this article we have studied complex linear homogeneous difference equations where the coefficients are meromorphic functions, having finite iterated p-phi order. We have made some estimations on the growth of its nontrivial solutions. Also we have extended some of the previous results of Zhou-Zheng (2017), Belaïdi-Benkarouba (2019) and Belaïdi-Bellaama (2021).
In this paper we have studied the growth of meromorphic solutions of higher order homogeneous and non-homogeneous linear difference equations with entire and meromorphic coefficients. We have extended and improved some results of Zhou and Zheng (2017), Belaidi and Benkarouba (2019) by using (p,q)-order and (p,q)-type.
In this paper our main aim is to develop some basic properties of hyperbolic valued metric spaces. We also establish the hyperbolic version of Banach contraction principle. Further we construct a hyperbolic valued metric on the space of all hyperbolic valued continuous functions and prove some results.
Here, we introduce a new class of computer which does not use any circuit or logic gate. In fact, no program needs to be written: it learns by itself and writes its own program to solve a problem. Godels incompleteness argument is explored here to devise an engine where an astronomically large number of IfThen arguments are allowed to grow by self assembly, based on the basic set of arguments written in the system, thus, we explore the beyond Turing path of computing but following a fundamentally different route adopted in the last half a century old non Turing adventures. Our hardware is a multilayered seed structure. If we open the largest seed, which is the final hardware, we find several computing seed structures inside, if we take any of them and open, there are several computing seeds inside. We design and synthesize the smallest seed, the entire multilayered architecture grows by itself. The electromagnetic resonance band of each seed looks similar, but the seeds of any layer shares a common region in its resonance band with inner and upper layer, hence a chain of resonance bands is formed (frequency fractal) connecting the smallest to the largest seed (hence the name invincible rhythm or Ajeya Chhandam in Sanskrit).
Current computers operate at enormous speeds of ~10^13 bits/s, but their principle of sequential logic operation has remained unchanged since the 1950s. Though our brain is much slower on a per-neuron base (~10^3 firings/s), it is capable of remarkable decision-making based on the collective operations of millions of neurons at a time in ever-evolving neural circuitry. Here we use molecular switches to build an assembly where each molecule communicates-like neurons-with many neighbors simultaneously. The assembly's ability to reconfigure itself spontaneously for a new problem allows us to realize conventional computing constructs like logic gates and Voronoi decompositions, as well as to reproduce two natural phenomena: heat diffusion and the mutation of normal cells to cancer cells. This is a shift from the current static computing paradigm of serial bit-processing to a regime in which a large number of bits are processed in parallel in dynamically changing hardware.
Molecular machines may resolve three distinct bottlenecks of scientific advancement. Nanofactories (Phoenix, 2003) composed of MM may produce atomically perfect products spending negligible amount of energy (Hess, 2004) thus alleviating the energy crisis. Computers made by MM operating thousands of bits at a time may match biological processors mimicking creativity and intelligence (Hall, 2007), thus far considered as the prerogative of nature. State-of-the-art brain surgeries are not yet fatal-less, MMs guided by a nano-brain may execute perfect bloodless surgery (Freitas, 2005). Even though all three bottlenecks converge to a single necessity of nano-brain, futurists and molecular engineers have remained silent on this issue. Our recent invention of 16 bit parallel processor is a first step in this direction (Bandyopadhyay, 2008). However, the device operates inside ultra-high vacuum chamber. For practical application, one needs to design a 3 D standalone architecture. Here, we identify the minimum nano-brain functions for practical applications and try to increase the size from 2 nm to 20 micro-m.
A new mechanism is proposed to explain the origin of negative differential resistance (NDR) in a strongly coupled single molecule-metal junction. A first-principles quantum transport calculation in a Fe-terpyridine linker molecule sandwiched between a pair of gold electrodes is presented. Upon increasing applied bias, it is found that a new phase in the broken symmetry wavefunction of the molecule emerges from the mixing of occupied and unoccupied molecular orbital. As a consequence, a non-linear change in the coupling between molecule and lead is evolved resulting to NDR. This model can be used to explain NDR in other class of metal-molecule junction device.
Negative differential resistance (NDR) is tuned at junctions of electronically different dimer and trimer of Rose Bengal on an atomic flat gold (111) surface. Isolated molecule did not show any NDR. But it was induced to show double NDR with large peak to valley ratio (1.8~3.1) in room temperature via charging its neighbor reproducibly by an electrical pulse. In some sections of junction by applying pulse one could destroy the phenomenon or regenerate it by STM manipulation of molecules. NDR was also independent of polaronic nature. It was possible to write bits 1 and 0 for cationic NDR (in dimer) and 00, 01, 10, 11 for di-anionic NDR (trimer) which generated 2/4 bit memory in a atomic scale junction showing importance of junction electronics in future of moletronics.