Prime Factors Research Articles

A COMPARATIVE STUDY OF EFFECT OF DEXMEDETOMIDINE AND DEXAMETHASONE AS AN ADJUVANT TO 0.2% ROPIVACAINE FOR ULTRASOUND GUIDED TRANSVERSUS ABDOMINIS PLANE BLOCK FOR INFRAUMBILICAL SURGERIES

Background: The relief of pain and suffering is, and always has been, one of the primary concerns of mankind and one of the prime factors that has influenced the course of history of medicine. Transversus abdominis plane (TAP) block is a regional anaesthetic technique which blocks the abdominal neural afferents by introducing local anaesthetic into the neuro-fascial plane between the internal oblique and the transversus abdominis muscle. Aim: To compare the efficacy of Dexmedetomidine and dexamethasone as an adjuvant to 0.2%ropivacaine in ultrasound guided transverses abdominis plane block in infra umbilical surgeries in terms of, 1. Time to initial postoperative pain. 2. Time to initial rescue analgesia. 3. Quality of block.. 4. Total postop analgesic consumption. 5. Patient satisfaction with regard to pain relief. 6. Post-operative nausea and vomiting. Materials And Methods: We included 80 patients of age between 18-60 years of American Society of Anesthesiologists status (ASA)I and II scheduled for elective infraumbilical surgeries in our study. We randomly allotted these patients into two groups namely Group A and Group B of each. Patients in Group APatients who received transversus abdominis plane block with - 18ml Ropivacaine 0.2%+ 2 ml Dexamethasone 8mg. Patients in Group B received transversus abdominis plane block with-18ml Ropivacaine 0.2%+ 2 ml Dexmedetomidine .This TAP block was given soon after the surgery is completed. The duration of block and regression of sensory block, time for rescue analgesia, degree of sedation, hemodynamic parameters, post operative analgesia and adverse effects were noted. Result: The two groups were comparable on the basis of duration of surgery, site of surgery, ASA and BMI. Heart rates and mean arterial pressure were compared and it was found to be significantly lower in group B compared to group A until initial 5 hours. In our study we found that the visual analogue score at rest and on coughing between groups A and B was statistically insignificant. However, the time to first rescue analgesia (330 mins vs 240 mins) and total analgsic consumption in the 24 hours period post operatively was significantly lesser for group A compared to group B. Ramsey sedation score was significantly higher in group B compared to group A until 8 hourspost operatively. Nausea and vomiting in 3 cases of group A , and 2 cases in group B. No other significant side effects were noted. Conclusion: USG-guided TAP block is an effective and safe adjunct for postoperative analgesia in infra umblical surgeries. Addition of dexamethasone as an adjuvant prolongs the duration and reduces post-operative analgesic requirement in patients significantly more than dexmedetomidine whereas dexamethasone provides better control of the heart rate and mean arterial pressure.

Parametric Study of Polyethylene Primary Decomposition Using a Micropyrolyzer Coupled with Two-Dimensional Gas Chromatography

Parametric Study of Polyethylene Primary Decomposition Using a Micropyrolyzer Coupled with Two-Dimensional Gas Chromatography

Energy harvest on TSUSUCA DOLPHIN under irregular waves: Experimental studies

Finding sustainable and infinite green energy options in a world that relies primarily on fossil fuels is crucial as traditional sources decline. Wave energy is an excellent example of an environmentally friendly power source. A multi-utility bio-inspired floating device consisting of two TSUSUCA (TSUnami Protection Solar Utilization and other Coastal Applications) Dolphin-shaped bodies integrated with a linear motion electricity generator (LMEG) connected to a rigid deck by a hinged connection is tested experimentally under irregular waves. This novel and innovative multi-utility floating offshore device can function as a tsunami barrier and a wave energy extraction device. Its performance and operating mechanism are investigated under 8 different sets of irregular waves. The examined sea states are represented by JONSWAP and PM wave spectra with a range of significant wave heights (0.05–0.20 m) and peak periods (1.5 and 2.0 s). The experimental results show that the overall electrical power efficiency of LMEG coupled to each Dolphin obtained for set 6 is 32.04 % and 30.81 % for both JONSWAP and PM spectrums, respectively. This bio-inspired device and its performance confirms the proof-of-concept while the presented study shall become a prime factor towards the development of more similar devices to harness wave energy.

A post-quantum secure PUF based cross-domain authentication mechanism for Internet of drones

With the increasing prevalence of drones, guaranteeing their authentication and secure communication has become paramount in drone networks to mitigate unauthorized access and malicious attacks. Cross-domain authentication is crucial in the context of the Internet of Drones (IoD) for safely verifying and establishing trust between diverse drones and their respective control stations, which may belong to different regions or organizations. Effectively accessing resources or services in another domain while maintaining security and efficiency poses a significant challenge. Conventional authentication mechanisms relying on challenging problems like discrete logarithm and integer factorization might not be sufficient to guarantee the security and effectiveness of drone-based systems in the post-quantum era. To address this, we propose a distributed post-quantum cryptography and Physical Unclonable Function (PUF) based cross-domain authentication protocol for IoD. Key contributions of this work include the elimination of secret key storage on drones, mutual authentication, emphasis on hardware security, incorporation of post-quantum security measures, efficient cross-domain authentication and resilience against cyber attacks such as eavesdropping, impersonation, replay attack, untraceability, and PUF-modeling attack. The performance of the proposed protocol is assessed utilizing metrics like processing time, communication cost and storage utilization. In operations associated to the blockchain ledger, variables such as latency, throughput, CPU utilization, and memory utilization are also examined. The protocol shows a reduced computation time and zero sensitive data storage in drone memory, despite a slightly higher communication cost that is manageable with 5G-enabled drones. Comparative analysis against existing solutions in the domain highlights the superior security of the proposed protocol, positioning it as a promising solution for the evolving quantum landscape.

So's conjecture for integral circulant graphs of 4 types

In [Discrete Mathematics 306 (2005) 153-158], So proposed a conjecture saying that integral circulant graphs with different connection sets have different spectra. This conjecture is still open. We prove that this conjecture holds for integral circulant graphs whose orders have prime factorization of 4 types.

Multiplicative arithmetic functions and the generalized Ewens measure

Random integers, sampled uniformly from [1, x], share similarities with random permutations, sampled uniformly from Sn. These similarities include the Erdős–Kac theorem on the distribution of the number of prime factors of a random integer, and Billingsley’s theorem on the largest prime factors of a random integer. In this paper we extend this analogy to non-uniform distributions.Given a multiplicative function α: ℕ → ℝ≥0, one may associate with it a measure on the integers in [1, x], where n is sampled with probability proportional to the value α(n). Analogously, given a sequence {θi}i≥1 of non-negative reals, one may associate with it a measure on Sn that assigns to a permutation a probability proportional to a product of weights over the cycles of the permutation. This measure is known as the generalized Ewens measure.We study the case where the mean value of α over primes tends to some positive θ, as well as the weights α(p) ≈ (log p)γ. In both cases, we obtain results in the integer setting which are in agreement with those in the permutation setting.

A lattice-based efficient certificateless public key encryption for big data security in clouds

With the advancement of technology and the development of digitization, big data has become an integral component of modern society. Due to the huge volume of big data, users generally upload data to the cloud for storage and computation. Because data in the cloud is beyond the control of users, it faces threats such as data security and personal privacy leakage. To address these concerns and achieve big data security and privacy protection in clouds, data encryption is crucial. Traditional public key encryption involves complex certificate management in a public key infrastructure (PKI). Although the identity-based encryption (IBE) scheme avoids the management of public key certificates, it has issues with key escrows and identity revocation. The certificateless public key encryption (CL-PKE) not only solves the key escrows problem in IBE, but also maintains its advantage of not requiring the use of certificate in PKI, making it suitable for the security protection of big data in clouds. However, most CL-PKE schemes are constructed based on large integer factorization and discrete logarithm problems, which cannot resist quantum computing attacks. Therefore, this paper proposes an efficient lattice-based CL-PKE scheme for big data security in clouds. In addition, the proposed scheme is extended to a lattice-based certificateless proxy re-encryption scheme, facilitating secure big data sharing in clouds. The proposed CL-PKE scheme can resist attacks from both internal and external adversaries, and has been proven to be IND-CPA secure under the learning with errors (LWE) assumption. Experiments have shown that the proposed CL-PKE scheme has lower computational and communication costs. The proposed lattice-based schemes can effectively provide post quantum security for the security and privacy protection of big data in clouds.

Resilience among Caregivers of the Pediatric Cancer Patients

Backgound: Studies portray that one in every nine Indians develops cancer during their lifetime. Admissions to the Pediatric Oncology departments are increasing like any other department. Cancer affects not only the patients but also their caregivers both physically and psychologically. Aims and Objectives: In this scenario, the study aims to understand the caregivers’ level of resilience and the associated risk and protective factors. Materials and Methods: This descriptive study was conducted in Kerala. Sixty caregivers of the children in the age group between 1-17 years, diagnosed with cancer were selected for the study. Mexican Resilience Scale and self-prepared interview schedule were used to collect the quantitative data. Qualitative data were collected using an in-depth interview guide. Results: The study found that the majority of the respondents are moderately resilient, with men exhibiting higher resilience than women. The prime factors contributing to resilience were identified as strength and self-confidence, social competence, family support, social support, and structure. The study further identified individual factors (flexibility, emotional stability, etc.), familial factors (positive family environment), and community factors (support from NGOs and support groups, etc.) as protective factors contributing to resilience. Additionally, the study revealed how individual (lack of emotional stability, introverted nature, etc.), familial (relationship issues), and community (social perceptions about the disease) levels of risk factors impact resilience. Conclusion: The importance of strengthening the support systems around the caregivers and importance of oncology social worker to deal with the psychosocial issues of patients and caregivers are also discussed in this paper.

Performance Analysis of Non-Realistic Routing Protocol using Random Waypoint Model in MANET

A mobile ad hoc network (MANET) is a collection of wireless nodes connected via wireless networks and has no set structure. MANETs feature a self-organized routing topology in which mobile nodes are free to move, making it difficult and crucial to construct a stable and reliable network. Thus, failure of the route is also regarded as a prime factor affecting the efficiency of any MANET routing protocol. The breaking of the connection between two routes or more nodes will cause the failure of the route specifically in the non-realistic routing protocol. In a network of mobile nodes, the link break is mainly based on the mobility of individual nodes. Therefore, the objective of this research is to investigate the performance of proactive DSDV and reactive AODV routing protocol using the Random Waypoint(RWP) mobility model in MANET. NS-2 network simulator is used to simulate the MANET environment and BonnMotion is to create a movement of mobile nodes that integrate with the routing protocol. The network performance metrics used are throughput, packet delivery ratio, and average end-to-end delay. In addition, three simulation scenarios have been conducted to compare AODV and DSDV routing protocols with varying numbers of nodes, a comparison of AODV and DSDV routing protocols with varying pause time, and a comparison of AODV and DSDV routing protocols with varying mobility speed. The result from the three scenarios analysed and concluded that the RWP mobility model with AODV gives a better performance of throughput with 869.69 kbps and Packet Delivery Ratio (PDR) with 83.00% meanwhile, RWP with DSDV is better for the average end-to-end delay(EED) with 212.970 bps.

A quantum-secure certificateless aggregate signature protocol for vehicular ad hoc networks

Vehicular ad hoc networks (VANETs) have revolutionized communication between vehicles and infrastructure, notably enhancing traffic management and passenger safety. However, VANETs are vulnerable to security threats, especially regarding data authenticity. Aggregate signature is a powerful technique that reduces computational and communication burdens by aggregating multiple signatures from different signers into a single signature. Traditional aggregate signature schemes, based on large prime number decomposition and the discrete logarithm problem, cannot effectively resist quantum attacks. This paper introduces a novel quantum secure certificateless aggregate signature (QSCLAS) scheme designed to enhance data security and privacy in VANETs. Our proposed scheme employs the number theory research unit (NTRU) algorithm. As a lattice-based cryptographic algorithm, NTRU is renowned for its security against quantum computer attacks, making it an essential component of our quantum-secure solution. By eliminating the need for expensive bilinear pairing operations, our proposed scheme achieves high efficiency and practicality in resource-limited VANETs environments. The security analysis demonstrates our scheme's resilience against both Type-I and Type-II adversaries in the random oracle model under the small integer solution (SIS) problem on the NTRU lattice. Furthermore, compared with existing approaches, the results illustrate that our proposed scheme offers significant advantages in signature generation and verification cost, as well as lower transmission overhead than other lattice-based schemes, thereby making it highly suitable for VANETs environments.

Post‐quantum attack resilience blockchain‐assisted data authentication protocol for smart healthcare system

AbstractThe smart healthcare system (SHS), a significant medical domain underpinning the Internet of Things (IoT), which collects and analyzes health data from many sources to provide better medical treatment. The smart healthcare system is a combination of hardware and software used in the medical care field, providing remote diagnosis and treatment via a patient‐based health data‐sharing system. To increase security, a large variety of authenticated techniques have been developed over the past several decades, most of which are based on conventional number‐theoretic assumptions such as discrete logarithms and integer factorization problems. However, Shor's method is capable of solving number‐theory‐based problems. As a result, Shor's technique might be used to resolve challenging number theory problems on a quantum computer effectively. Therefore, this article presents blockchain‐based healthcare record solutions with lattice RLWE‐based key exchange protocol using a smart card. Blockchain applications may correctly detect errors, including those that are risky, in the medical industry. It can also improve the efficiency, security, and transparency of transferring medical data throughout the healthcare protocol. The formal security of this protocol is shown under the ROM (random oracle model), and the informal security is also given in this article against well‐known attacks. The presented protocol outperforms related earlier mechanisms in terms of communication and computational cost overheads, according to the performance study.

Systematic review on efficacy of various Pratisarneeya Kshar application in Ayurveda for the management of hemorrhoids w.s.r. size reduction of pile mass

Background: "Mandagni, the prime etiopathogeni factor of Arshas, leads to constipation, initiating the development of Arshas through prolonged contact of accumulated Mala or excretory material with Gudavali. Among the available treatment modalities, Kshara karma stands out for its convenience, easy adaptability, cost-effectiveness, and curative results. Within this para-surgical approach, various forms of external Kshara application, such as Ksharasutra Ligation (KSL) and Pratisarneeya kshar, are employed to treat Arsha. While Ksharasutra ligation is a surgical procedure, Pratisarneeya kshar involves local application and exhibits effectiveness with a straightforward procedure. Numerous studies on Pratisarneeya kshar have been conducted."Objectives: This study aims to investigate the impact of various types of Pratisarniya kshara on Haemorrhoids. Methods and Materials: The materials were gathered from classical Ayurvedic literature, various magazines, and research journals. Results: Pratisaraneeya Kshara application demonstrates high efficacy in reducing the size of pile mass. Conclusion: Despite recent advancements, these invented techniques exhibit certain limitations and have not been proven entirely free from post-operative complications. This underscores the need for a new and improved treatment that is devoid of complications, ensures a faster cure, and proves economically superior.

Granular computing in zero-divisor graphs of [formula omitted]

In this article, we study the zero-divisor graphs Γ(Zn) of rings of integers modulo n as information systems I(Γ(Zn)) using equivalence classes and rough sets. Equivalence classes are referred as granules and partitions are referred as indiscernible partitions. We define an indiscernibility relation on the vertex set and identify different sets of attributes that induce the same indiscernibility partition. A reduct is a minimal subset of attributes which yields the same partition as the original attribute set. We compute all reducts of the defined information system and classify them in to two types including: (i) the set P of all prime divisors of n and (ii) the set consisting of P∖pi, prime powers of pi in the prime factorization of n and the elements of the form pipj, where pj∈P∖pi. Moreover, we give the structures and the cardinalities of the attribute subsets whose removal yields a different indiscernibility partition than that of the set of all attributes, referred as essential sets. We prove that the essential sets of I(Γ(Zn)) either consist of two prime divisors of n or one prime divisor pi combined with prime powers of pi. Further, we determine the lower and upper approximations of various vertex subsets to study the properties of the zero-divisor graphs. We also study properties of the rough membership function for Γ(Zn). Furthermore, we introduce the class-based discernibility matrix induced by indiscernibility classes of zero divisors and determine general form of its entries. We also prove that the minimal entries of the class-based discernibility matrix coincide with the essential sets of Γ(Zn). Based on these results, we determine information-granularity measures corresponding to the notable partitions of Γ(Zn) and provide an example to establish consistency of the proved results with these well-known measures. Thus, starting from introducing an information system, we investigate the components of granular computing and utilize our findings to compute information granularity measures, contributing to a deeper understanding of the zero divisor graphs via rough set theory.

On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices

On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices

The least primary factor of the multiplicative group

Let [Formula: see text] denote the least primary factor in the primary decomposition of the multiplicative group [Formula: see text]. We give an asymptotic formula, with order of magnitude [Formula: see text], for the counting function of those integers [Formula: see text] for which [Formula: see text]. We also give an asymptotic formula, for any prime power [Formula: see text], for the counting function of those integers [Formula: see text] for which [Formula: see text]. This group-theoretic problem can be reduced to problems of counting integers with restrictions on their prime factors, allowing it to be addressed by classical techniques of analytic number theory.

On the largest prime factor of the k–generalized Lucas numbers

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Partial prime factor exposure attacks on some RSA variants

In this paper, we consider five variants of the RSA cryptosystem, where the modulus is N=pq, and the public key e and the secret key d satisfy ed−k(p2+p+1)(q2+q+1)=1 or ed−k(p2−1)(q2−1)=1. Our results show that if a certain amount of the most significant bits of p are known so that |p−p0|=Nβ with a known p0, then one can factor the RSA modulus with a better bound than low private exponent attacks. We also present the experimental results to verify our analysis.

Cloud service ranking with an integration of k-means algorithm and decision-making trail and evaluation laboratory approach

The present research focuses on ranking cloud services by using the k-means algorithm with multi-criteria decision-making (MCDM) approaches that are the prime factor in the decision-making process and have been used to choose cloud services. The tools offered by MCDM can solve almost any decision-making problem. When faced with a selection challenge in the cloud environment, the trusted party would need to weigh the client’s choice against a predetermined list of criteria. There is a wide range of approaches to evaluating the quality of cloud services. The deep learning model has been considered a branch of artificial intelligence that assesses datasets to perform training and testing and makes decisions accordingly. This paper presents a concise overview of MCDM approaches and discusses some of the most commonly used MCDM methods. Also, a model based on deep learning with the k-means algorithm based decision-making trial and evaluation laboratory (kDE-MATEL) and analytic network process (ANP) is proposed as k-means algorithm based decision-making trial and evaluation laboratory with analytic network process (kD-ANP) for selecting cloud services. The proposed model uses the k-means algorithm and gives different levels of priority and weight to a set of criteria. A traditional model is also compared with a proposed model to reflect the efficiency of the proposed approach.

Prime number factorization with light beams carrying orbital angular momentum

We point out a link between orbital angular momentum (OAM) carrying light beams and number theory. The established link makes it possible to formulate and implement a simple and ultrafast protocol for prime number factorization by employing OAM endowed beams that are modulated by a prime number sieve. We are able to differentiate factors from non-factors of a number by simply measuring the on-axis intensity of light in the rear focal plane of a thin lens focusing on a source beam. The proposed protocol solely relies on the periodicity of the OAM phase distribution, and hence, it is applicable to fully as well as partially coherent fields of any frequency and physical nature—from optical or x-ray to matter waves—endowed with OAM. Our experimental results are in excellent agreement with our theory. We anticipate that our protocol will trigger new developments in optical cryptography and information processing with OAM beams.

The number of prime factors in $h$-free and $h$-full polynomials over function fields

The number of prime factors in $h$-free and $h$-full polynomials over function fields