Prime Elements Research Articles

Grain size, carbide distribution and hardness issues pertaining to cutting tools produced from high speed steel scraps

ABSTRACT Single point cutting tool blanks are prepared adopting the centrifugal casting method using only scrapped high-speed steel tools collected from different installations for better mechanical properties and economical production. The cast cylindrical blanks are cut into shapes by wire-cut EDM and subsequently heat-treated. Upon heat treatment, the centrifugal cast tool exhibited a reduction of grain size about 60% accompanied by about 22.7% increase in the hardness. The conventional cast HSS M2 tools procured from the market are compared with centrifugal cast tools. SEM images of both tools showed two different eutectic carbide patterns. Also, the precipitation of M6C and MC carbides are found in XRD analysis for both tools. Upon EDX analysis, W, V, and Cr are found to be the prime elements responsible for carbide formation. Wear characteristics of centrifugal cast tool observed are as par with the HSS M2 tool during turning of mild steel (ASTM A36) under identical environment. This method will be helpful for the development of cutting tools for industrial applications.

Sums of singular series and primes in short intervals in algebraic number fields

Gross and Smith have put forward generalizations of Hardy–Littlewood twin prime conjectures for algebraic number fields. We estimate the behaviour of sums of a singular series that arises in these conjectures, up to lower-order terms. More exactly, where \(\mathfrak {S}(\eta )\) is the singular series, we find asymptotic formulas for smoothed sums of \(\mathfrak {S}(\eta )-1\). Based upon Gross and Smith’s conjectures, we use our result to suggest that for large enough ‘short intervals’ in an algebraic number field K, the variance of counts of prime elements in a random short interval deviates from a Cramér model prediction by a universal factor, independent of K. The conjecture over number fields generalizes a classical conjecture of Goldston and Montgomery over the integers. Numerical data are provided supporting the conjecture.

On the translational invariant intuitionistic fuzzy subset of a Γ-ring

In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γ-ring and generalize some notions of a ring to a Γ-ring. Also, we define ideals of a Γ-ring generated by an intuitionistic fuzzy subset with an element of Γ-ring and study their properties. The notion of units, associate, prime element, irreducible element are also generalized with respect to the intuitionistic fuzzy subset of a Γ-ring. Further, we study the properties of homomorphic image and pre-image of translational invariant intuitionistic fuzzy subset under the Γ-ring homomorphism and we prove that every homomorphic image of a prime ideal of a Γ-ring generated by an Aγ-prime element and translational invariant and f-invariant intuitionistic fuzzy subset is also a prime ideal.

Rapid cooling performance of zirconium rods quenched in natural seawater

The viability of using natural seawater as an effective working coolant to ensure safe and efficient cooling mechanism is a significant study in the Arabian Gulf region. This study investigates transient pool boiling characteristics of natural seawater collected from different locations in the Arabian Gulf coast of Kuwait, compared to the baseline case of distilled water. Seawater samples are collected from prime locations (Shuwaikh, Al Zour, and Doha ports), which are highly capable of accommodating upcoming power plants and nuclear reactors. Extremely heated vertical zirconium rods are quenched in saturated pools at atmospheric pressure. A detailed study of the seawater samples is carried out through semi-quantitative calculation (SQX) results to evaluate the elemental composition, and water quality comparisons are made based on pH, total dissolved solids, and conductivity. The cooling performance is monitored by plotting the quenching and cooling rate curves, and evaluated based on the minimum film boiling temperature (Tmin) and maximum cooling rate. The results demonstrate an excellent improvement in Tmin and maximum cooling rate by employing natural seawater collected from Al Zour, which is located in the southern part of Kuwait. A minimum of 10% increase in Tmin is depicted by Al Zour seawater. The enhancement is attributed to the salt deposition activity caused by sudden evaporation of seawater on the surface. The salt deposits destabilize the vapor film to promote early vapor film breakage and act as an additional nucleation site to initiate early nucleate boiling, leading to an efficient cooling performance. Seawater collected from Shuwaikh port demonstrates a negative influence on the effective change in Tmin. A detailed examination is carried out on the surface of zirconium samples with the help of wavelength dispersive x-ray fluorescence analysis and SQX analysis, to identify and evaluate the prime elements responsible for the enhanced cooling performance. This study proves that even though the seawater is collected along the same coast, its characteristics differ when utilizing it in cooling systems.

EXPORT FINANCE: A TOOL FOR PROMOTING EXPORT IN INDIA

Export Finance play a crucial role in growth and development of export sector in any economy, which face a tough competition from rest of world. It is an essential and prime element for successful operation of various internal and external activities to grow the export business sector. In view of many scholars and economists, export is considered as the engine of growth and development of any country. Presently, India’s total export is contributing approx. 2% in the world’s trade. In export trading the 6 Ps concepts of export marketing are depending on the availability of export finance assistance in terms of share, cost and period of time. This study attempts to analyze and review the impact of export finance used by various exporters on their export profitability, performance on varied interest rate, cost of finance and special schemes related to pre and post shipment stage in export trading. To analyze the role and importance of various financial institutions in providing the financial assistance to the exporters in India helps and supports to export sector to grow in the right direction and also to achieve the specific goals. This research paper provides meaningful information to policy maker who want to reform their export structure, promotion schemes and increase the nation’s competitiveness in present era. KEYWORDS: Export Finance, Financial Institutions, Export Credits, Export Insurance

The sub-class sizes of some elements being square free

Let x be an element of a finite group G, and p a prime factor of the order of G. It is clear that there always exists a unique minimal subnormal subgroup containing x, say [Formula: see text]. We call the conjugacy class of x in [Formula: see text] the sub-class of x in G, see [G. Qian and Y. Yang, On sub-class sizes of finite groups, J. Aust. Math. Soc. (2020) 402–411]. In this paper, assume that [Formula: see text] is the product of the subgroups A and B, we investigate the solvability, p-nilpotence and supersolvability of the group G under the condition that the sub-class sizes of prime power order elements in [Formula: see text] are [Formula: see text] free, [Formula: see text] free and square free, respectively, so that some known results relevant to conjugacy class sizes are generalized.

On the Distribution of αp Modulo One in Quadratic Number Fields

Abstract We investigate the distribution of αp modulo one in quadratic number fields 𝕂 with class number one, where p is restricted to prime elements in the ring of integers of 𝕂. Here we improve the relevant exponent 1/4 obtained by the first- and third-named authors for imaginary quadratic number fields [On the distribution of αp modulo one in imaginary quadratic number fields with class number one, J. Théor. Nombres Bordx. 32 (2020), no. 3, 719–760]) and by the first- and second-named authors for real quadratic number fields [Diophantine approximation with prime restriction in real quadratic number fields, Math. Z. (2021)] to 7/22. This generalizes a result of Harman [Diophantine approximation with Gaussian primes, Q. J. Math. 70 (2019), no. 4, 1505–1519] who obtained the same exponent 7/22 for ℚ (i) by extending his method which gave this exponent for ℚ [On the distribution of αp modulo one. II, Proc. London Math. Soc. 72, (1996), no. 3, 241–260]. Our proof is based on an extension of Harman’s sieve method to arbitrary number fields. Moreover, we need an asymptotic evaluation of certain smooth sums over prime ideals appearing in the above-mentioned work by the first- and second-named authors, for which we use analytic properties of Hecke L-functions with Größencharacters.

A Riemann–von Mangoldt-Type Formula for the Distribution of Beurling Primes

In this paper we work out a Riemann–von Mangoldt type formula for the summatory function := , where is an arithmetical semigroup (a Beurling generalized system of integers) and is the corresponding von Mangoldt function attaining with a prime element and zero otherwise. On the way towards this formula, we prove explicit estimates on the Beurling zeta function , belonging to , to the number of zeroes of in various regions, in particular within the critical strip where the analytic continuation exists, and to the magnitude of the logarithmic derivative of , under the sole additional assumption that Knopfmacher’s Axiom A is satisfied. We also construct a technically useful broken line contour to which the technic of integral transformation can be well applied. The whole work serves as a first step towards a further study of the distribution of zeros of the Beurling zeta function, providing appropriate zero density and zero clustering estimates, to be presented in the continuation of this paper.

Reconfigurable content-addressable memory (CAM) on FPGAs: A tutorial and survey

Content-addressable memory (CAM) is a massively parallel searching device that returns the address of a given search input in one clock cycle. Field-programmable gate array (FPGA)-based CAMs are becoming popular due to their applications in the latest networking systems, e.g., software-defined networks (SDNs) leading to upcoming 5G networks. Ternary CAM (TCAM) implements a routing table in a network router to classify and forward data packets where don’t care bits (X-bits) correspond to multiple addresses. FPGAs do not have a hard-core CAM, although it is a prime element in networking applications. This paper serves as a comprehensive survey on FPGA-based CAM/TCAMs implemented using block random-access memory (BRAM), lookup table RAM (LUTRAM), and flip-flops (FFs). BRAM-based TCAM suffers from the pre-processing of mapping data, requires the data to be in a specific order in some cases, and has a large SRAM/TCAM bit ratio. LUTRAM-based CAM/TCAM suffers from wide bit-wise ANDing, high routing complexity, but has a small SRAM/TCAM bit ratio of 14 compared to 16 in the case of BRAM-based TCAM. Shallow and wide RAM blocks are required to implement large-size RAM-based TCAMs (BRAM-based and LUTRAM-based TCAMs). FF-based TCAMs use FFs as their memory elements and have reduced hardware costs per TCAM bit. However, due to the routing complexity, it suffers from scalability and a large amount of power consumption. The update latency of BRAM-based TCAM and LUTRAM-based TCAM is proportional to the depth of BRAM and LUTRAM, respectively. However, FF-based CAM updates in 1 or 2 clock cycles depending on the availability of input/output pins on target FPGA.

Riemann bm$\zeta$-functions on semigroups

By introducing prime elements in semigroups, divisor functions and Möbius functions are defined and studied on a class of semigroups. The Riemann $\\zeta$-function can be naturally generalized through different means on these semigroups. The semigroup associated with Thompsons group is a typical example of our interest. We show that zeta functions on Thompsons semigroup obtained through different definitions agree with each other. Moreover, this zeta function has at least another real pole less than 1 besides a simple pole at 1. Many other arithmetic results are obtained on some noncommutative semigroups such as analogs of the prime number theorem on natural numbers.

Conch maximal subrings

It is shown that if R is a ring, p a prime element of an integral domain with and then R has a conch maximal subring (see [14]). We prove that either a ring R has a conch maximal subring or for each subring S of R (i.e., each subring of R is closed with respect to taking inverse, see [25]). In particular, either R has a conch maximal subring or U(R) is integral over the prime subring of R. We observe that if R is an integral domain with then either R has a maximal subring or and in particular if in addition dim(R) = 1, then R has a maximal subring. If is an integral ring extension, then we prove that whenever R has a conch maximal subring S with then T has a conch maximal subring V such that and It is shown that if K is an algebraically closed field which is not algebraic over its prime subring and R is affine ring over K, then for each prime ideal P of R with there exists a maximal subring S of R with If R is a normal affine integral domain over a field K, then we prove that R is an integrally closed maximal subring of a ring T if and only if dim(R) = 1 and in particular in this case

Wave Transport and Localization in Prime Number Landscapes

In this paper, we study the wave transport and localization properties of novel aperiodic structures that manifest the intrinsic complexity of prime number distributions in imaginary quadratic fields. In particular, we address structure-property relationships and wave scattering through the prime elements of the nine imaginary quadratic fields (i.e., of their associated rings of integers) with class number one, which are unique factorization domains (UFDs). Our theoretical analysis combines the rigorous Green’s matrix solution of the multiple scattering problem with the interdisciplinary methods of spatial statistics and graph theory analysis of point patterns to unveil the relevant structural properties that produce wave localization effects. The onset of a Delocalization-Localization Transition (DLT) is demonstrated by a comprehensive study of the spectral properties of the Green’s matrix and the Thouless number as a function of their optical density. Furthermore, we employ Multifractal Detrended Fluctuation Analysis (MDFA) to establish the multifractal scaling of the local density of states in these complex structures and we discover a direct connection between localization, multifractality, and graph connectivity properties. Finally, we use a semi-classical approach to demonstrate and characterize the strong coupling regime of quantum emitters embedded in these novel aperiodic environments. Our study provides access to engineering design rules for the fabrication of novel and more efficient classical and quantum sources as well as photonic devices with enhanced light-matter interaction based on the intrinsic structural complexity of prime numbers in algebraic fields.

Kinematic Modelling and Motion Mapping of Robotic Arms

Robotic systems are known for their precision and accuracy. To achieve a desired set of operating parameters the system must have a good control system. Robotic arms can vary in size shape and purpose of use. With increasing DOF (Degree of Freedom) the complexity of the system increases and hence a DAQ system is required to check various parameters of the process. This paper discusses the implementation of kinematic and inverse kinematic modelling of a 6 Degree of Freedom (DOF) hydraulic arm in MATLAB environment. The forward kinematic model is based on Denavit-Hartenberg parameters. To obtain a given set of position and orientation of end effector, inverse kinematics gives the required set of joint angles. Potentiometers mounted on arm joint are used as the prime feedback elements for extracting the joint angles. All six joints of the arm are revolute joints. The values of potentiometer obtained are compared to the desired input values. Proportional direction control valve is the main controlling element of the hydraulic circuit. The forward and inverse kinematics is validated and implemented in MATLAB robotics toolbox (developed by Peter Croke). A GUI is also used to ease the process of retrieving and feeding the information in the system. The results of forward and inverse kinematics from MATLAB are verified by the physical model discussed in this paper.

105.24 Conditional 2 × 2 matrices with three prime elements and given determinant

105.24 Conditional 2 × 2 matrices with three prime elements and given determinant

An Overview on Validation Process in Pharmaceutical Industries

Medicinal products are the prime element in the healthcare and must manufacture with the highest quality, safety & efficacy level. There are multiple principles to obtain such quality are now biggest interest in pharmaceutical industry. One of the important principles that industries follow is Validation. It is the art of designing and practicing the designed steps alongside with the documentation for all processes, methods, computer systems, equipment qualification & revalidation. According to GMP validation studies it is the necessary part of GMP and required to be done as per predefined protocols. Validation master plan (VMP) defines the principles involved in the qualification of a facility, describes the systems to be validated, and provides a updated plan for accomplishing and keeping a qualified facility. The VMP is quite different than validation procedure (SOP), which explains the specific process for performing validation activities.

φ-Prime and φ-Primary Elements in Lattice Modules

In this paper, we introduce φ-prime and φ-primary elements in an L-module M. Many of its characterizations and properties are obtained. By counter examples, it is shown that a φ-prime element of M need not be prime, a φ-primary element of M need not be φ-prime, a φ-primary element of M need not be prime and a φ-primary element of M need not be primary. Finally, some results for almost prime and almost primary elements of an L-module M with their characterizations are obtained. Also, we introduce the notions of n-potent prime (respectively n-potent primary) elements in L and M to obtain interrelations among them where n≥2.Â

Optical rogue waves in multifractal photonic arrays

Optical rogue waves are demonstrated in the far-field scattered radiation from photonic arrays designed according to the aperiodic distributions of prime elements in complex quadratic fields. Specifically, by studying light diffraction from Eisenstein and Gaussian prime arrays we establish a connection between the formation of optical rogue waves and multifractality in the visible single-scattering regime. We link strong multifractality with the heavy-tail probability distributions that describe the fluctuations of scattered radiation from the fabricated arrays. Our findings pave the way to control high-intensity rogue waves using deterministic arrays of dielectric nanostructures for enhanced sensing and lithographic applications.

Integrative analysis of liver-specific non-coding regulatory SNPs associated with the risk of coronary artery disease

Genetic factors underlying coronary artery disease (CAD) have been widely studied using genome-wide association studies (GWASs). However, the functional understanding of the CAD loci has been limited by the fact that a majority of GWAS variants are located within non-coding regions with no functional role. High cholesterol and dysregulation of the liver metabolism such as non-alcoholic fatty liver disease confer an increased risk of CAD. Here, we studied the function of non-coding single-nucleotide polymorphisms in CAD GWAS loci located within liver-specific enhancer elements by identifying their potential target genes using liver cis-eQTL analysis and promoter Capture Hi-C in HepG2 cells. Altogether, 734 target genes were identified of which 121 exhibited correlations to liver-related traits. To identify potentially causal regulatory SNPs, the allele-specific enhancer activity was analyzed by (1) sequence-based computational predictions, (2) quantification of allele-specific transcription factor binding, and (3) STARR-seq massively parallel reporter assay. Altogether, our analysis identified 1,277 unique SNPs that display allele-specific regulatory activity. Among these, susceptibility enhancers near important cholesterol homeostasis genes (APOB, APOC1, APOE, and LIPA) were identified, suggesting that altered gene regulatory activity could represent another way by which genetic variation regulates serum lipoprotein levels. Using CRISPR-based perturbation, we demonstrate how the deletion/activation of a single enhancer leads to changes in the expression of many target genes located in a shared chromatin interaction domain. Our integrative genomics approach represents a comprehensive effort in identifying putative causal regulatory regions and target genes that could predispose to clinical manifestation of CAD by affecting liver function.

Inquisitive Heyting Algebras

In this paper we introduce a class of inquisitive Heyting algebras as algebraic structures that are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. It is argued that these structures are suitable for algebraic semantics of inquisitive superintuitionistic logics, i.e. logics of questions based on intuitionistic logic and its extensions. We explain how questions are represented in these structures (prime elements represent declarative propositions, non-prime elements represent questions, join is a question-forming operation) and provide several alternative characterizations of these algebras. For instance, it is shown that a Heyting algebra is inquisitive if and only if its prime filters and filters generated by sets of prime elements coincide and prime elements are closed under relative pseudocomplement. We prove that the weakest inquisitive superintuitionistic logic is sound with respect to a Heyting algebra iff the algebra is what we call a homomorphic p-image of some inquisitive Heyting algebra. It is also shown that a logic is inquisitive iff its Lindenbaum–Tarski algebra is an inquisitive Heyting algebra.

COMPLETELY PRIME ONE-SIDED IDEALS IN SKEW POLYNOMIAL RINGS

AbstractLet R = K[x, σ] be the skew polynomial ring over a field K, where σ is an automorphism of K of finite order. We show that prime elements in R correspond to completely prime one-sided ideals – a notion introduced by Reyes in 2010. This extends the natural correspondence between prime elements and prime ideals in commutative polynomial rings.