Prime Factors Research Articles

On sequences of integers with small prime factors

On sequences of integers with small prime factors

A new method of large integer prime decomposition for network public key cryptosystem

A new method of large integer prime decomposition for network public key cryptosystem

Investigating primary decomposition of polypropylene through detailed compositional analysis using two-dimensional gas chromatography and principal component analysis

This work systematically assessed the effects of pyrolysis parameters, such as sample weight, particle size, carrier gas flow rate, and temperature, on product speciation and distribution in the pyrolysis of polypropylene (PP) for intrinsic kinetics. This study employed a Box-Behnken design (BBD), along with the analysis of BBD boundary conditions, as well as conditions beyond the BBD to validate the pyrolysis conditions in the primary decomposition of PP using a micropyrolyzer coupled to two-dimensional chromatography with flame ionization and time-of-flight spectrometer detectors (Py–GC×GC–FID/TOF–MS). Statistical differences and similarities in the product distribution of the experiments were determined using principal component analysis (PCA). Characteristic time analysis indicated that the sample weights employed in the study were within the isothermal kinetically controlled region, with film thickness ranging from 4.85 to 14.46 µm. The analysis of 600 pyrolysis products identified and quantified in the pyrolysis of PP for the condition combinations evaluated in BBD resulted in statistical differences at temperatures of 460, 530, and 600 oC, with C3 to C35 yields ranging from 39.88 ± 2.08 to 66.61 ± 3.26 wt%. However, no statistical differences were found in the pyrolysis product distribution within the ranges of sample weight (50 – 150 µg), particle size (53 – 125, 125 – 300, and >300 µm), and carrier gas flow rate (100 – 300 ml min-1) studied in the BBD experimental space. The analysis of the border conditions showed that a combination of the lowest carrier gas flow rate (100 ml min-1) and the highest sample weight (150 μg) resulted in statistically different product distribution at the studied pyrolysis temperatures compared to the combination suggested by BBD. Conditions beyond the BBD, including a sample weight of 800 µg and a carrier gas flow rate of 30 ml min-1, resulted in statistically different product distributions compared to the BBD. Notably, new products such as polycyclic aromatic hydrocarbons (PAHs) were identified. The findings from this work clearly show the importance of selecting appropriate pyrolysis parameters to obtain kinetically relevant experimental data, which in turn serves as a valuable guide for the development and validation of (micro-) kinetic models.

Associated Prime Ideals in Commutative Algebra

This paper aims to explain how an abstract mathematical object of higher mathematics is learnt and solved the given problem from the pedagogical perspectives resting the explanation based upon the solution of higher mathematical problem in abstract algebra.The purpose is not only to disseminate the solution of the problem but to unfold the learning realities in course of pursuing the pure discovery learning path. The problem of the study was connected to the understandings of associated prime ideals in commutative algebra. Factual materials including books, lecture notes and research articles were used to explore the concepts on associated prime ideals. The concepts learned were summarized, conceptualized, and then analyzed together with established facts of algebraic concepts and developed examples to interpret the abstract concepts: the associated prime ideals. The associated prime ideal was explored and understood within the conceptions of primary decomposition, Noetherian rings, and modules, and then characterized some fundamental notions of it on an A-module M over the Noetherian ring A. The results reveal that repeated reading, writing, rigorous thinking and linking, and engaging on abstraction are the basic characteristics of content researcher in developing and constructing new insights, ideas and knowledge in higher mathematics from pedagogic perspective

Resilience of the United States Economy to External Shocks

A multidimensional analysis of one of main macroeconomic indicators, specifically, unemployment, in the United States was conducted and presented in the article. The research covered several groups of dependent variables, such as: the number of unemployed people in total in the United States monthly, along with unemployment rates, CPI indices, and unemployment in respective US states. The evaluation of the conducted research is that from January 2020 to October 2023 there had been a visible decrease in unemployment rates, and their level is similar to the values recorded from January 2018 to January 2020, which clearly proves that the crisis caused by the COVID-19 pandemic has been averted. The analysis method was used in the study, i.e. distribution of variables into prime factors and comparison dynamically in order to detect the regularities occurring in them.

Memory in T. S. Eliot’s The Waste Land

The greatest of the issues in modernism emanates from memory in human beings. It is the first condition for people to realize what they have lost in their life, resulting from World War I. Often known as the manifesto of modernism in the West, T. S. Eliot’s 1922 poem The Wasteland deals with the intellectual, social, political, and quotidian issues of the people, basically resulting from memory. The people begin to value the glory of the past as the epitome in contemporary times, meaning that they have been driven out of paradise now. In other words, memory became a tool to rewrite a new Bible in the twentieth century following the trail of John Milton’s The Paradise Lost (1667). The phantoms of negative memories torment the people in the West: for instance, the people set out in search of Christ or metonymically the Holy Grail. Most importantly, the poetic persona is Tiresias who still remembers both his lives. He searches for the images that best represent the experience of living in the Western world shattered at the hand of the destructive forces. The centers of the civilizations have undergone massive destruction and they have remained unable to reconstruct themselves. Both the poet and the poetic persona go through the pages of the books of the Western and Eastern body of knowledge to identify the remedy for the fragmentation or loss of the binding principles of human society. This study aims to explore how memory is treated in modernist literature to examine the presence of history in making sense of the presence. The Eastern myths remind the Western world of the cure to the existing problems of society. In fact, this paper claims that The Wasteland builds its argument in the treatment of memory as the prime factor in the articulation of the central vision about the West in general and modernism in particular.

Smooth Subsum Search A Heuristic for Practical Integer Factorization

The two currently fastest general-purpose integer factorization algorithms are the Quadratic Sieve and the Number Field Sieve. Both techniques are used to find so-called smooth values of certain polynomials, i.e., values that factor completely over a set of small primes (the factor base). As the names of the methods suggest, a sieving procedure is used for the task of quickly identifying smooth values among the candidates in a certain range. While the Number Field Sieve is asymptotically faster, the Quadratic Sieve is still considered the most efficient factorization technique for numbers up to around 100 digits. In this paper, we challenge the Quadratic Sieve by presenting a novel approach based on representing smoothness candidates as sums that are always divisible by several of the primes in the factor base. The resulting values are generally smaller than those considered in the Quadratic Sieve, increasing the likelihood of them being smooth. Using the fastest implementations of the Self-initializing Quadratic Sieve in Python as benchmarks, a Python implementation of our approach runs consistently 5 to 7 times faster for numbers with 45–100 digits, and around 10 times faster for numbers with 30–40 digits. We discuss several avenues for further improvements and applications of the technique.

TRANSFORMATION OF PASSIVE DESIGN ELEMENTS FOR ACHIEVING THERMAL COMFORT IN RESIDENTIAL BUILDINGS OF MANSEHRA CITY, PAKISTAN FROM 1990 TO 2019

Among the most evolving issues in recent years, there is growing concern over global warming throughout the world. The construction industry has been considered among the major contributors to global warming. The use of building envelope along with the heating, cooling, and lighting design, operations, and infrastructures are the prime factors of this contribution. Due to this reason, the thermal comfort of buildings has become a major concern in building design globally. The following research explored the building design elements used for thermal comfort in residential buildings of Mansehra City of Khyber Pakhtunkhwa province in Pakistan and analyzed its transformation during the last three decades. The study proceeded by documenting and comparing various design elements to understand their transformation within documented time periods i.e. thermal mass, fixed shading devices, and the ratio of open and closed spaces. These elements were evaluated for their effectiveness in providing thermal comfort. It was concluded that these design elements have been adapted and modified with time with little concern for sustainability. It was found that the focus has shifted from building orientation, sun path, and wind directions to aesthetically pleasing forms only which makes them saleable and lack human comfort. The use of passive means to achieve thermal comfort was neglected. The research concludes by suggesting incorporation of appropriate thermal comfort components and methods into effective solutions for improved building designs, lower energy demand, and a better indoor atmosphere. Keywords: Thermal Comfort, Passive Design, Residential Building, Mansehra City, Global Warming

Networks in Auxology – proceedings of the 31st Aschauer Soiree, held at Aschau, Germany, June 17th 2023

Twenty-seven scientists met for the annual Auxological conference held at Aschau, Germany, to particularly discuss the interaction between social factors and human growth, and to highlight several topics of general interest to the regulation of human growth. Humans are social mammals. Humans show and share personal interests and needs, and are able to strategically adjust size according to social position, with love and hope being prime factors in the regulation of growth. In contrast to Western societies, where body size has been shown to be an important predictor of socioeconomic status, egalitarian societies without formalized hierarchy and material wealth-dependent social status do not appear to similarly integrate body size and social network. Social network structures can be modeled by Monte Carlo simulation. Modeling dominance hierarchies suggests that winner-loser effects play a pivotal role in robust self-organization that transcends the specifics of the individual. Further improvements of the St. Nicolas House analysis using re-sampling/bootstrap techniques yielded encouraging results for exploring dense networks of interacting variables. Customized pediatric growth references, and approaches towards a Digital Rare Disease Growth Chart Library were presented. First attempts with a mobile phone application were presented to investigate the associations between maternal pre-pregnancy overweight, gestational weight gain, and the child’s future motor development. Clinical contributions included growth patterns of individuals with Silver-Russell syndrome, and treatment burden in children with growth hormone deficiency. Contributions on sports highlighted the fallacy inherent in disregarding the biological maturation status when interpreting physical performance outcomes. The meeting explored the complex influence of nutrition and lifestyle on menarcheal age of Lithuanian girls and emphasized regional trends in height of Austrian recruits. Examples of the psychosocial stress caused by the forced migration of modern Kyrgyz children and Polish children after World War II were presented, as well as the effects of nutritional stress during and after World War I. The session concluded with a discussion of recent trends in gun violence affecting children and adolescents in the United States, and aspects of life history theory using the example of "Borderline Personality Disorder." The features of this disorder are consistent with the notion that it reflects a "fast" life history strategy, with higher levels of allostatic load, higher levels of aggression, and greater exposure to both childhood adversity and chronic stress. The results were discussed in light of evolutionary guided research. In all contributions presented here, written informed consent was obtained from all participants in accordance with institutional Human investigation committee guidelines in accordance with the Declaration of Helsinki amended October 2013, after information about the procedures used.

Large sums of high‐order characters

AbstractLet be a primitive character modulo a prime , and let . It has previously been observed that if has large order then for some , in analogy with Vinogradov's conjecture on quadratic non‐residues. We give a new and simple proof of this fact. We show, furthermore, that if is squarefree then for any th root of unity the number of such that is whenever . Consequently, when has sufficiently large order the sequence cannot cluster near for any . Our proof relies on a second moment estimate for short sums of the characters , averaged over , that is non‐trivial whenever has no small prime factors. In particular, given any we show that for all but powers , the partial sums of exhibit cancellation in intervals as long as is prime, going beyond Burgess' theorem. Our argument blends together results from pretentious number theory and additive combinatorics. Finally, we show that, uniformly over prime , the Pólya–Vinogradov inequality may be improved for on average over , extending work of Granville and Soundararajan.

Carbon emission price forecasting in China using a novel secondary decomposition hybrid model of CEEMD-SE-VMD-LSTM

Effective forecasting of carbon prices helps investors to judge carbon market conditions and promotes the environment and economic sustainability. The contribution of this paper is constructing a novel secondary decomposition hybrid carbon price forecasting model, namely CEEMD-SE-VMD-LSTM. It is noteworthy that the sample entropy is introduced to identify the highly complex signals rather than empirically determined in previous studies. Specifically, the complementary ensemble empirical mode decomposition (CEEMD) model is used to decompose the original price signals. The sample entropy (SE) and variational mode decomposition (VMD) are conducted to recognize and secondary decompose the highly complex components, while the long short-term memory (LSTM) model is employed to forecast the carbon price by summing up the predicted intrinsic mode function (IMF) components. The conclusion shows the proposed model has the smallest forecasting errors with the values of RMSE, MAE and MAPE are 0.2640, 0.1984 and 0.0044, respectively, the secondary decomposition models are better than other primary decomposition models and the forecasting performances of LSTM-type models are better than those of other GRU-type models. Further evidence convinces us that short-term forecasting accuracy is superior to long-term forecasting. Those conclusions and model innovation can provide a valuable reference for investors to make trading decisions.

Experimental and modeling study of the N, N-dimethylformamide pyrolysis at atmospheric pressure

As a polar solvent, N, N-Dimethylformamide (DMF) is a potential source of volatile organic compounds during industrial processing. The potential energy surface and pressure-dependent rate coefficients of DMF primary and secondary thermal decomposition were theoretically investigated by automatic ab initio calculations. A singlet aminohydroxycarbene route generating CO is found to be the most energetically favored channel among the unimolecular initiation reactions with a tight transition state. A kinetic model was proposed for DMF pyrolysis prediction and validated against the speciation data newly obtained from synchrotron vacuum ultraviolet photoionization mass spectrometry in a flow reactor within 773 K–1048 K and literature data in a jet stirred reactor within 450 K–900 K at atmospheric pressure. Satisfactory agreements were obtained for the major intermediates and products, but the model failed to capture the formation of some oxygenated compounds, possibly due to the missing reaction pathway for bimolecular addition. During pyrolysis, DMF is mainly consumed by the hydrogen abstraction reaction as the relatively high CN bond energy hinders the barrierless homolytic cleavage. Unlike aldehydes where the carbonyl site is favored, H-abstraction from DMF methyl sites is prevalent, although the acylamino group readily undergoes decarbonylation and β-scission forming oxygenated and nitrogenous parts. Consequently, CO and HCN are the major pyrolysis products. Besides, by incorporating essential high temperature kinetics, extended validation was conducted against the available intermediate temperature autoignition delay times (1000–1350 K, 2 bar) and laminar burning velocity data, and the reason for the discrepancy between the model prediction and experiments was inferred according to the sensitivity analyses.

On some sums involving the integral part function

Denote by [Formula: see text], [Formula: see text] and [Formula: see text] the number of representations of [Formula: see text] as a product of [Formula: see text] natural numbers, the number of distinct prime factors of [Formula: see text] and the characteristic function of the square-free integers, respectively. Let [Formula: see text] be the integral part of real number [Formula: see text]. For [Formula: see text], we prove that [Formula: see text] for [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is an arbitrarily small positive number. These improve the corresponding results of Bordellès.

Evaluation of serum ischemia modified albumin (IMA) level and serum uric acid level as a preliminary biomarker of epilepsy

Oxidative stress, hypoxia, and ischemia are considered prime factors in the pathogenesis of epilepsy. Hyperuricemia (HU) is a common incidental finding in epileptic patients, but the importance of HU as a risk factor in epilepsy is debated. Many hypothetical mechanisms that link HU to increased oxidative stress in epilepsy have been put forward. This research aimed to evaluate the role of serum Ischemia Modified Albumin (IMA) level and serum uric acid (UA) level as a preliminary biomarker in the diagnosis of epilepsy.: The present cross-sectional research was conducted on 25 individuals having epilepsy and 25 healthy individuals. Serum uric acid level had estimated by the uricase method. Serum IMA was evaluated by albumin cobalt binding assay to assess oxidative stress, hypoxia, and ischemia. Mean Serum UA and IMA level were found significantly high (p<0.001) in epileptic group. In the epileptic group, 76 % (19/25) individuals had HU. Mean serum IMA was higher in epileptic individuals with HU compared to epileptic individuals with normal serum UA levels. Correlation between serum UA level and serum IMA level was found positive among the study population. Serum UA showed a significant odd ratio to predict epilepsy on binary logistic analysis.: The present study revealed that serum UA levels and IMA levels escalated in epileptic patients. Thus, serum UA levels and IMA levels can be deemed as preliminary biomarkers for the diagnosis of epilepsy.

On Generalized Sums of Six, Seven and Nine Cube

Let u1, u2, u3,・・・ un be integers such that un − un−1 = un−1 − un−2 = ・ ・ ・ = a2 − a1 = d. In this article, the study of sums of cube in arithmetic progression is discussed. In particular, the study develops and introduces some generalized results on sums of six, seven and nine cube for any arbitrary integers in arithmetic sequences. The method of study involves analogy grounded on integer decomposition and factorization. The result in this study will prove the existing results on sums of cubes.

Effect of methyl substituent on adamantane pyrolysis at atmospheric and high pressure: A combined experimental and theoretical study

Adamantane derivatives, as promising high-density fuels, have been widely concerned in fields of volume-limited aerospace vehicles due to high density, heat of combustion and thermal oxidation stability. To reveal insights into their high-temperature decomposition behaviors, an experimental and theoretical investigation of adamantane (A) and 1-methyl adamantane (1-MA) pyrolysis was performed in a flow tube reactor at atmospheric to high pressure. Over twenty species were detected and identified, including C1-C5 light hydrocarbons, C5-C7 cyclic olefins as well as C6-C12 aromatics. The favorable decomposition channels of A and 1-MA are proposed and the effects of fuel structure characteristics and pressures on product formation behaviors are revealed. For the primary decomposition of A and 1-MA, the contributions of reaction types exhibit the obvious dependence on the pressures and temperatures, involving the unimolecular C-C dissociations by ring-opening, CH3-elimination as well as H-abstractions by H and CH3 attacking. Considering methyl-substitution weakens dissociation energies of C-C and C-H bonds and leads more H-abstraction sites, 1-MA shows a higher pyrolysis reactivity than A. The effects of structure characteristics are also embodied in the formation of newly chain-branched unsaturated species and the concentrations of common small hydrocarbons and aromatics. Compared to A decomposition, the methyl substituent in 1-MA promotes the emergence of 1-butene, 2-methyl-1-butene, mesitylene, methylindane and methylnaphthalene, and increases the concentrations of methane, 2-methylpropene and xylene isomers, formed via β-scission, hydrogen transfer, isomerization and dehydrogenation routes of fuel radicals. Meanwhile, more methyl-substitutions accelerate the decomposition of alkyl-adamantanes and pyrolysis activity follows by a sequence of dimethyl-adamantane > methyl-adamantane > adamantane, boosting the production of methyl-specific species.

Effects of bipolar plate flow channel configuration on thermal-electric performance of direct ammonia solid oxide fuel cell: Part Ⅱ- Promoting in-cell ammonia endothermic decomposition via a novel parallel S-type channel arrangement

This study explores impact of novel parallel S-type flow channels on ammonia decomposition and thermal-electric performance of direct ammonia solid oxide fuel cells (DA-SOFC). Four channel arrangements were numerically studied using single cell models: conventional unbent channels (UC–SOFC) and proposed single S-type channels (SSC–SOFC), double S-type channels (DSC-SOFC), triple S-type channels (TSC-SOFC). Cells with parallel S-type channel configurations outperformed unbent channel. Particularly, TSC-SOFC demonstrated the highest electrical performance, followed by DSC-SOFC, SSC-SOFC, and UC-SOFC, with power density improvements of 33.6%, 28.9%, and 28.9%, respectively, compared to UC-SOFC. Further results show that S-type channels exhibit self-heating effects, namely heat released from electrochemical reactions in the rear supplies ammonia decomposition in the front part of channel, enhancing H2 concentration and electrochemical reactions. Quantitatively, back-heat supplied to primary ammonia decomposition region increases by 33.3% in TSC-SOFC compared to UC-SOFC. Moreover, higher velocities in S-type channels enhance species diffusion towards rib underside, finally reducing concentration polarization and, improving power density. Besides of electrical performance, recycling waste heat from exhaust gases also improve the temperature uniformity cell, potentially benefiting the stability and lifetime of cell.

Quantum Circuit Design for Integer Multiplication Based on Schönhage–Strassen Algorithm

Quantum arithmetic circuits has attracted extensive attention recently since it plays fundamental roles in many applications of quantum computing. Specifically, quantum circuits for integer multiplication are of great significance to various quantum algorithms including Shor’s integer factorization and discrete logarithm algorithm. In this paper, we design a family of quantum circuits for integer multiplication based on the famous classical integer multiplication algorithm, Schönhage-Strassen algorithm. We have made slight modifications to the algorithm to simplify its quantum circuit implementation. As a result, the quantum circuit we designed has gate depth O(log2n). To the best of our knowledge, this is the first poly-logarithmic depth quantum circuit for integer multiplication which keeps the circuit size and the number of ancillary qubits sub-quadratic. Our design has size O(nlognloglogn) counted by elementary quantum gates which is the same as the time complexity of Schönhage-Strassen algorithm, and it consumes O(nlognloglogn) clean ancillary qubits. In addition, we also utilize a weaker version of Schönhage-Strassen algorithm to give a family of circuits which has depth at the same order O(log2n) but with significantly smaller constants, while still keeping the size and number of ancillary qubits sub-quadratic.

Dissociable influences of maternal vs paternal Alzheimer’s risk on neurocognitive and cardiovascular health in men and women

AbstractBackgroundParental history of sporadic Alzheimer’s disease (AD) is considered a prime risk factor since at least the late 1980s. Routinely used clinical samples of at‐risk individuals (8‐16 subjects) may conceal weaker population‐based effects, especially those of paternal inheritance. We performed a phenome‐wide examination of the dissociable influences of maternal vs. paternal AD risk on male vs. female probands in the largest single‐site family‐based at‐risk AD cohort: PREVENT‐AD.MethodWe built sex‐specific PLS‐regression models in which the APOE genotypes (e.g., ɛ3/3, ɛ3/4, ɛ3/2) were estimated based on ∼1,000 patient visits, each covering ∼260 risk indicators, to derive three APOE‐driven intermediate phenotypes (IPs). We examined how much the three IPs vary with regard to sex and maternal vs. paternal AD lineage across the phenome. We assessed the sex‐specific and lineage‐specific variation of the IPs over a 4‐year follow‐up period. Lastly, we examined how matri‐ vs. patrilinear AD risk captured by the IPs were expressed in AD‐vulnerable brain structures.ResultAcross IPs, we linked patrilinear AD risk to verbal‐numerical cognition and cardiovascular health in males. In contrast, we linked matrilinear AD risk to memory performance in both sexes. Over time, the mean difference in cognitive performance decreases with regard to sex but increases with regard to AD lineage. Cis‐ and trans‐generational sex effects in neocortex subregions (e.g., mPFC, PCu) were captured by the first and second IPs, respectively. The third IP mainly captured trans‐generational sex effects in hippocampus subregions (e.g., CA1, CA4).ConclusionWe uncovered IPs of AD susceptibility differently expressed in male and female probands and affected by the diagnosed parent’s sex. Maternal inheritance highlighted memory performance in both sexes, whereas paternal inheritance was particularly linked to cardiovascular health in males. The inheritance of the IPs was reflected in the brain structure at both superficial and deeper layers of the cortex. As the first study of its kind, our cross‐generational analysis of matri‐ vs. patrilinear AD risk bridges the epidemiological and clinical literature by leveraging the power of ∼1,000 patient visits. Our completely data‐driven framework ultimately dissociated phenotypes of maternal and paternal AD risk single‐handedly expressed in male and female probands.

Role of SIRT-1 as a Target for Treatment and Prevention of Diabetic Nephropathy: A Review.

Type-2 diabetes mellitus is a prime factor for the development of Diabetic Nephropathy (DN) that affects the vital organ namely the kidneys, and further alters the functions of the nephron system. DN is nowadays becoming a challenge for scientists towards the world because of its high pervasiveness and complexity of medication. Various risk factors are involved in the initiation of pathogenic DN, which are associated with different pathways against drug activity. Due to this DN becomes an unpredictable query to the researchers. SIRT1 is a silent information regulator factor 2 related enzyme 1 (SIRT1) is nicotinamide adenine dinucleotide (NAD+) dependent deacetylase that functions as an intracellular regulator of transcriptional activity. An activated version of SIRT-1 improves the metabolic diseased conditions associated with other molecular pathways. SIRT1 attenuates diabetic nephropathy in in vitro and in vivo experimental models of diabetes containing Podocytes, Mesangial cells, and Renal proximal tubular cells. SIRT1 shows nephroprotective effects in DN in part through deacetylation of transcription factors i.e., imply in the disease like p53, PTP1B, FOXO, RelA, NF- kβ, STAT-3, and PGC-1α/ PPARγ. It has been shown that some natural products like resveratrol and synthetic compounds are activating the SIRT1, this further involved the cascade pathways to prevent the DN. This review will help regarding the effectiveness of SIRT1as target in the prevention and treatment of DN.