Search

The index of a monic irreducible polynomial $f(x)\in\mathbb{Z}[x]$ having a root $\theta$ is the index $[\mathbb{Z}_K:\mathbb{Z}[\theta]]$, where $\mathbb{Z}_K$ is the ring of algebraic integers of the number field $K=\mathbb{Q}(\theta)$. If $[\mathbb{Z}_K:\mathbb{Z}[\theta]]=1$, then $f(x)$ is monogenic. In this paper, we give necessary and sufficient conditions for a monic irreducible power compositional polynomial $f(x^k)$ belonging to $\mathbb{Z}[x]$, to be monogenic. As an application of our results, for a polynomial $f(x)=x^d+A\cdot h(x)\in\mathbb{Z}[x],$ with $d>1, \operatorname{deg} h(x)

Atomic effective pseudopotentials enable atomistic calculations at the level of accuracy of density functional theory for semiconductor nanostructures with up to fifty thousand atoms. Since they are directly derived from ab-initio calculations performed in the local density approximation (LDA), they inherit the typical underestimated band gaps and effective masses. We propose an empirical correction based on the modification of the non-local part of the pseudopotential and demonstrate good performance for bulk binary materials (InP, ZnS, HgTe, GaAs) and quantum dots (InP, CdSe, GaAs) with diameters ranging from 1.0 nm to 4.45 nm. Additionally, we provide a simple analytic expression to obtain accurate quasiparticle and optical band gaps for InP, CdSe, and GaAs QDs, from standard LDA calculation.

Suppose $m$ be a $12$-th power free integer. Let $K=\mathbb{Q}(\theta)$ be an algebraic number field defined by a complex root $\theta$ of an irreducible polynomial $x^{12}-m$ and $O_K$ be its ring of integers. In this paper, we determine the highest power of $p$ dividing the index of the subgroup $\Z[\theta]$ in $O_K$ and $p$-integral basis of $K$ for each prime $p$. These $p$-integral bases lead to the construction of an integral basis of $K$ which is illustrated with examples. In particular, when $m$ is a square free integer, we provide necessary and sufficient conditions for the set $\{1,\theta,\theta^2,\cdots,\theta^{10},\theta^{11}\}$ to be an integral basis of $K.$

Let $f(x)=x^n+ax^2+bx+c \in \Z[x]$ be an irreducible polynomial with $b^2=4ac$ and let $K=\Q(\theta)$ be an algebraic number field defined by a complex root $\theta$ of $f(x)$. Let $\Z_K$ deonote the ring of algebraic integers of $K$. The aim of this paper is to provide the necessary and sufficient conditions involving only $a,c$ and $n$ for a given prime $p$ to divide the index of the subgroup $\Z[\theta]$ in $\Z_K$. As a consequence, we provide families of monogenic algebraic number fields. Further, when $\Z_K \neq \Z[\theta]$, we determine explicitly the index $[\Z_K : \Z[\theta]]$ in some cases.

Let $f(x)=x^7+ax+b$ be an irreducible polynomial having integer coefficients and $K=\mathbb{Q}(\theta)$ be an algebraic number field generated by a root $\theta$ of $f(x)$. In the present paper, for every rational prime $p$, our objective is to determine the necessary and sufficient conditions involving only $a,~b$ so that $p$ is a divisor of the index of the field $K$. In particular, we provide sufficient conditions on $a$ and $b$, for which $K$ is non-monogenic. In a special case, we show that if either $8$ divides both $a\pm1$, $b$ or $32$ divides both $a+4$, $b$, then $K$ is non-monogenic. We illustrate our results through examples., Comment: arXiv admin note: text overlap with arXiv:2011.14348

While buying a product from the e-commerce websites, customers generally have a plethora of questions. From the perspective of both the e-commerce service provider as well as the customers, there must be an effective question answering system to provide immediate answers to the user queries. While certain questions can only be answered after using the product, there are many questions which can be answered from the product specification itself. Our work takes a first step in this direction by finding out the relevant product specifications, that can help answering the user questions. We propose an approach to automatically create a training dataset for this problem. We utilize recently proposed XLNet and BERT architectures for this problem and find that they provide much better performance than the Siamese model, previously applied for this problem. Our model gives a good performance even when trained on one vertical and tested across different verticals., Comment: 5 pages

Clustering is an important concept to reduce the energy consumption and prolonging the life of a wireless sensor network. In heterogeneous wireless sensor network some of the nodes are equipped with more energy than the other nodes. Many routing algorithms are proposed for heterogeneous wireless sensor network. Stable Election Protocol (SEP) is one of the important protocol in this category. In this research paper a novel energy efficient distance based cluster protocol (DBCP) is proposed for single hop heterogeneous wireless sensor network to increase the life and energy efficiency of a sensor network. DBCP use the average distance of the sensor from the base station as the major issue for the selection of a cluster head in the sensor network., Comment: 6 Pages, 4 Figures, http://www.ijcaonline.org/archives/volume76/number9/2013

Energy conservation of sensor nodes for increasing the network life is the most crucial design goal while developing efficient routing protocol for wireless sensor networks. Recent technological advances help in the development of wide variety of sensor nodes. Heterogeneity takes the advantage of different types of sensor nodes and improves the energy efficiency and network life. Generally sensors are deployed randomly and densely in a sensing region so short distance multihop communication reduces the long distance transmission in the sensor network. In this research paper MEEP (multihop energy efficient protocol for heterogeneous sensor network) is proposed. The proposed protocol combines the idea of clustering and multihop communication. Heterogeneity is created in the network by using some nodes of high energy. Low energy nodes use a residual energy based scheme to become a cluster head. High energy nodes act as the relay nodes for low energy cluster head when they are not performing the duty of a cluster head to save their energy further. Protocol also suggests a sleep state for nodes in the cluster formation process for saving energy and increasing the life of sensor network. Simulation result shows that the proposed scheme is better than other two level heterogeneous sensor network protocol like SEP in energy efficiency and network life., Comment: 9 Pages, 10 Figures, http://www.ijcst.org/Volume5/Issue3/2014. arXiv admin note: substantial text overlap with arXiv:1408.3110

Energy Conservation and prolonging the life of Wireless Sensor Network is one of the major issues in the wireless sensor network as sensor nodes are highly energy constrained devices. Many routing protocols have been proposed for sensor network, especially cluster based routing protocols. Cluster based routing protocols are best known for its energy efficiency, network stability and for increasing the life time of the sensor network. Low Energy Adaptive Clustering Hierarchy (LEACH) is one of the fundamental protocols in this class. In this research paper we propose a new energy efficient cluster based protocol (EECP) for single hop heterogeneous wireless sensor network to increase the life of a sensor network. Our sensor protocol use the distance of the sensor from the sink as the major issue for the selection of a cluster in the sensor network., Comment: 6 pages, 6 figures, http://www.ijarcsse.com/7_July2013.php. arXiv admin note: text overlap with arXiv:1408.2914

Energy saving to prolong the network life is an important design issue while developing a new routing protocol for wireless sensor network. Clustering is a key technique for this and helps in maximizing the network lifetime and scalability. Most of the routing and data dissemination protocols of WSN assume a homogeneous network architecture, in which all sensors have the same capabilities in terms of battery power, communication, sensing, storage, and processing. Recently, there has been an interest in heterogeneous sensor networks, especially for real deployments. This research paper has proposed a new energy aware clustering protocol (EACP) for heterogeneous wireless sensor networks. Heterogeneity is introduced in EACP by using two types of nodes: normal and advanced. In EACP cluster heads for normal nodes are elected with the help of a probability scheme based on residual and average energy of the normal nodes. This will ensure that only the high residual normal nodes can become the cluster head in a round. Advanced nodes use a separate probability based scheme for cluster head election and they will further act as a gateway for normal cluster heads and transmit their data load to base station when they are not doing the duty of a cluster head. Finally a sleep state is suggested for some sensor nodes during cluster formation phase to save network energy. The performance of EACP is compared with SEP and simulation result shows the better result for stability period, network life and energy saving than SEP., Comment: 15 Pages, 10 figures. in print at http://airccse.org/journal/ijc2014.html

Wireless sensor network consists of large number of inexpensive tiny sensors which are connected with low power wireless communications. Most of the routing and data dissemination protocols of WSN assume a homogeneous network architecture, in which all sensors have the same capabilities in terms of battery power, communication, sensing, storage, and processing. However the continued advances in miniaturization of processors and low-power communications have enabled the development of a wide variety of nodes. When more than one type of node is integrated into a WSN, it is called heterogeneous. Multihop short distance communication is an important scheme to reduce the energy consumption in a sensor network because nodes are densely deployed in a WSN. In this paper M-EECDA (Multihop Energy Efficient Clustering & Data Aggregation Protocol for Heterogeneous WSN) is proposed and analyzed. The protocol combines the idea of multihop communications and clustering for achieving the best performance in terms of network life and energy consumption. M-EECDA introduces a sleep state and three tier architecture for some cluster heads to save energy of the network. M-EECDA consists of three types of sensor nodes: normal, advance and super. To become cluster head in a round normal nodes use residual energy based scheme. Advance and super nodes further act as relay node to reduce the transmission load of a normal node cluster head when they are not cluster heads in a round., Comment: 8 pages, 11 figures. available at http://ijcaonline.org/2014. arXiv admin note: substantial text overlap with arXiv:1408.2914

Wireless sensor network consists of large number of tiny sensor nodes which are usually deployed in a harsh environment. Self configuration and infrastructure less are the two fundamental properties of sensor networks. Sensor nodes are highly energy constrained devices because they are battery operated devices and due to harsh environment deployment it is impossible to change or recharge their battery. Energy conservation and prolonging the network life are two major challenges in a sensor network. Communication consumes the large portion of WSN energy. Several protocols have been proposed to realize power- efficient communication in a wireless sensor network. Cluster based routing protocols are best known for increasing energy efficiency, stability and network lifetime of WSNs. Low Energy Adaptive Clustering Hierarchy (LEACH) is an important protocol in this class. One of the disadvantages of LEACH is that it does not consider the nodes energy and distance for the election of cluster head. This paper proposes a new energy efficient clustering protocol DE-LEACH for homogeneous wireless sensor network which is an extension of LEACH. DE-LEACH elects cluster head on the basis of distance and residual energy of the nodes. Proposed protocol increases the network life, stability and throughput of sensor network and simulations result shows that DE-LEACH is better than LEACH., Comment: 7 pages, 5 figures. available online at http://ijcaonline.org/2014

Coordinated checkpointing is an effective fault tolerant technique in distributed system as it avoids the domino effect and require minimum storage requirement. Most of the earlier coordinated checkpoint algorithms block their computation during checkpointing and forces minimum-process or non-blocking but forces all nodes to takes checkpoint even though many of them may not be necessary or non-blocking minimum-process but takes useless checkpoints or reduced useless checkpoint but has higher synchronization message overhead or has high checkpoint request propagation time. Hence in mobile distributed systems there is a great need of minimizing the number of communication message and checkpointing overhead as it raise new issues such as mobility, low bandwidth of wireless channels, frequently disconnections, limited battery power and lack of reliable stable storage on mobile nodes. In this paper, we propose a minimum-process coordinated checkpointing algorithm for mobile distributed system where no useless checkpoints are taken, no blocking of processes takes place and enforces a minimum-number of processes to take checkpoints. Our algorithm imposes low memory and computation overheads on MH's and low communication overheads on wireless channels. It avoids awakening of an MH if it is not required to take its checkpoint and has reduced latency time as each process involved in a global checkpoint can forward its own decision directly to the checkpoint initiator., Comment: 19 Pages, IJMA