We can analyze the properties of the Collatz Conjecture by using Terras’ Theorem, and computational graphical calculations. To do this, we introduce the concept of “tree" which shows the relationship between the input and output positive integers of the Collatz process. This approach offers a novel way for determining the non-existence of loops and diverge trees through computer simulations.

The 3x+1 problem is a problem of continuous iteration for integers. According to the basic theorem of arithmetic and the way of iteration, we derive a general formula for continuous iteration for odd integers. Through this formula, we can construct a loop iteration equation and obtain the result of the equation: the equation has only one positive integer solution. In addition, this general formula can be converted into a linear indeterminate equation. The process of solving this equation shows that the relationship between the iteration result and the odd number being iterated is linear. Extending this result to all positive even numbers, we get the answer to the 3x + 1 question.

This study focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The Collatz conjecture or 3x + 1 Problem is perhaps today's most enigmatic unsolved mathematical problem. It is named after Lothar Collatz, who rst proposed it in 1937. It may be stated as as follow: Take any positive integer n. If n is even then divide it by 2, else do \triple plus one" and get 3n + 1. The conjecture is that this process will eventually reach the number 1, regardless of which positive integer is chosen initially. In this paper, we present a simple proof for the Collatz conjecture.

We propose Reduced Collatz Conjecture that is equivalent to Collatz Conjecture, which states that every positive integer can return to an integer less than it, instead of 1. Reduced Collatz Conjecture should be easier because some properties are presented in reduced dynamics, rather than in original dynamics (e.g., ratio and period). Reduced dynamics is a computation sequence from starting integer to the first integer less than it, and original dynamics is a computation sequence from starting integer to 1. Reduced dynamics is a component of original dynamics. We denote dynamics of x as a sequence of either computations in terms of ``I'' that represents (3*x+1)/2 and ``O'' that represents x/2. Here 3*x+1 and x/2 are combined together, because 3*x+1 is always even and followed by x/2. We formally prove that all positive integers are partitioned into two halves and either presents ``I'' or ``O'' in next ongoing computation. More specifically, (1) if any positive integer x that is i module $2^t$ (i is an odd integer) is given, then the first t computations (each one is either ``I'' or ``O'' corresponding to whether current integer is odd or even) will be identical with that of i. (2) If current integer after t computations (in terms of ``I'' or ``O'') is less than x, then reduced dynamics of x is available. Otherwise, the residue class of x (namely, i module $2^t$) can be partitioned into two halves (namely, i module $2^{t+1}$ and $i+2^t$ module $2^{t+1}$), and either half presents ``I'' or ``O'' in intermediately forthcoming (t+1)-th computation.

Atherosclerosis (AS) is a chronic progressive disease caused by various factors, and causes various cerebrovascular and cardiovascular diseases (CVDs). Reducing the plasma levels of low-density lipoprotein-cholesterol (LDL-C) is the primary goal in preventing and treating AS. Proprotein Convertase Subtilisin/Kexin Type 9 (PCSK9) plays a crucial role in regulating LDL-C metabolism. Panax notoginseng has potent lipid-reducing effects and protects against CVDs, and its saponins induce vascular dilatation, inhibit thrombus formation, and are used in treating CVDs. However, the anti-AS effect of the secondary metabolite, 20(S) -protopanaxatriol (20(S)-PPT), remains unclear. In this study, the anti-AS effect and molecular mechanism of 20(S)-PPT were investigated in vivo and in vitro by western blotting, real time-polymerase chain reaction (RT-PCR), Enzyme-linked Immunosorbent Assay (ELISA), immunofluorescence staining, and other assays. The in vitro experiments revealed that 20(S)-PPT reduced the levels of PCSK9 in the supernatant of HepG2 cells, upregulated low density lipoprotein receptor (LDLR) protein levels, promoted LDL uptake by HepG2 cells, and reduced PCSK9 mRNA transcription by upregulating the levels of FoxO3 protein and mRNA and decreasing the levels of HNF1α protein and mRNA. The in vivo experiments revealed that 20(S)-PPT upregulated aortic αSMA expression, increased the stability of atherosclerotic plaques, and reduced aortic plaque formation induced by a high-cholesterol fed in ApoE-/- mice (HCF group). Additionally, 20(S)-PPT reduced the aortic expression of CD68, reduced inflammation in the aortic root, and alleviated the hepatic lesions in the HCF group. The study revealed that 20(S)-PPT inhibited LDLR degradation via PCSK9 to alleviate AS.

In hepatocellular carcinoma (HCC), recurrence usually occurs after curative surgical resection. Currently, no approved adjuvant therapy has been shown to reduce recurrence rates. In this report, the in vivo mouse effect of sequential combination treatment with recombinant mouse interferon-alpha (rmIFN-α) and an anti-mouse-PD1 antibody on hepatitis B virus (HBV) clearance was evaluated. A phase I clinical trial was then conducted to assess the safety, tolerability, and inhibitory activity of sequential therapy with ropeginterferon alfa-2b and nivolumab in HCC recurrence in patients who have undergone curative surgery for HBV-related HCC. In animal modeling, HBV suppression was significantly greater with rmIFN-α and anti-PD1 sequential combination treatment than with their treatment alone. In the Phase I study, eleven patients completed the sequential therapy with ropeginterferon alfa-2b every two weeks at the dose of 450 µg for six doses, followed by three doses of nivolumab every two weeks up to 0.75 mg/kg. A notable decrease or clearance of HBV surface antigen was observed in two patients. Dose-limiting toxicity of grade 3 alanine transaminase and aspartate aminotransferase increases was observed in one patient. The maximum tolerated dose was determined. Currently no HCC recurrence has been observed. The treatment modality was well tolerated. The data support further clinical development of sequential combination therapy as a post-surgery prophylactic measure against the recurrence of HBV-related HCC.

Volcanic emissions (ash, gas, aerosols) dispersed in the atmosphere during explosive eruptions generate hazards affecting aviation, human health, air quality and the environment. We document for the first time the contamination of airspace by very fine volcanic ash due to sequences of tran-sient ash plumes from Mount Etna. The atmospheric dispersal of sub-10 μm (PM10) ash is mod-elled using the WRF-Chem model coupled online with meteorology and aerosols and offline with Mass Eruption Rates (MER) derived from near-vent Doppler radar measurements and inferred plume altitudes. We analyse two sequences of paroxysms with widely varied volcanological conditions and contrasted meteorological synoptic patterns in October–December 2013 and on 3-5 December 2015. We analyse the PM10 ash dispersal simulation maps in terms of time-averaged columnar ash density, concentration at specified flight levels averaged over the entire sequence interval, and daily average concentration during selected paroxysm days at these flight levels. The very fine ash from such eruption sequences is shown to easily contaminate the airspace around the volcano within a radius of about 1000 km in a matter of a few days. Synoptic patterns with relatively weak tropospheric currents lead to the accumulation of PM10 ash at a re-gional scale all around Etna. In this context, closely interspersed paroxysms tend to accumulate very fine ash more diffusively in the lower troposphere and in stretched ash clouds higher up in the troposphere. Low-pressure, high-winds weather systems tend to stretch ash clouds into ~100 km-wide clouds forming large-scale vortices 800-1600 km in diameter. Daily average PM10 ash concentrations commonly exceed the aviation hazard threshold up to 1000 km downwind from the volcano and up to the upper troposphere for intense paroxysms. Vertical distributions show ash cloud thicknesses in the range 0.7–3 km, and PM10 sometimes stagnating at ground level, represent a potential health hazard.

To date, radiation adaptation response has been reported as a low-dose related phenomenon and has been associated with radiation hormesis. Well-known cancers are caused by non-radiation active reactants, in addition to radiation. A model of suppression for radiation-specific cancers was previously reported, but the model did not target radiation-nonspecific cancers. In this paper, we describe kinetic models of radiation-induced suppressors for general radiation non-specific cancers, estimating the dose that induces the maximum hormesis effect while satisfying the condition that the risk is approximately proportional to dose above 100 mSv. It was found that the radiation hormesis effect is maximal at about 20 mSv when the rate constant for generation is the same as the rate constant for decomposition. When the two rate constants are different, the dose at which the radiation hormesis effect is maximized depends on both rate constants, but the dose increases as the two rate constants approach each other, reaching a maximum of about 20 mSv. This conclusion may lead to the discovery of unknown cancer suppressors at low doses and the development of cancer suppression methods in the future.

For any odd positive integer $x$, define $(x_n)_{n\geqslant 0} $ and $(a_n )_{n\geqslant 1} $ by setting $x_{0}=x, \,\, x_n =\cfrac{3x_{n-1} +1}{2^{a_n }}$ such that all $x_n $ are odd. The 3x+1 problem asserts that there is an $x_n =1$ for all $x$. Usually, $(x_n )_{n\geqslant 0} $ is called the trajectory of $x$. In this paper, we concentrate on $(a_n )_{n\geqslant 1} $ and call it the E-sequence of $x$. The idea is that, we consider any infinite sequence $(a_n )_{n\geqslant 1} $ of positive integers and call it an E-sequence. We then define $(a_n )_{n\geqslant 1} $ to be $\Omega-$convergent to $x$ if it is the E-sequence of $x$ and to be $\Omega-$divergent if it is not the E-sequence of any odd positive integer. We prove a remarkable fact that the $\Omega-$divergence of all non-periodic E-sequences implies the periodicity of $(x_n )_{n\geqslant 0} $ for all $x_0$. The principal results of this paper are to prove the $\Omega-$divergence of several classes of non-periodic E-sequences. Especially, we prove that all non-periodic E-sequences $(a_n )_{n\geqslant 1} $ with $\mathop {\overline {\lim } }\limits_{n\to \infty } \cfrac{b_n }{n}>\log _23$ are $\Omega-$divergent by using the Wendel's inequality and the Matthews and Watts's formula $x_n =\cfrac{3^n x_0 }{2^{b_n }}\prod\limits_{k=0}^{n-1} {(1+\cfrac{1}{3x_k })} $, where $b_n =\sum\limits_{k=1}^n {a_k } $. These results present a possible way to prove the periodicity of trajectories of all positive integers in the 3x + 1 problem and we call it the E-sequence approach.

Enterovirus 71 (EV71) infection hand-foot-mouth disease (HFMD), meningoencephalitis, neonatal sepsis, and even fatal encephalitis in children, thereby representing a serious public health hazard. It is important to determine the mechanisms underlying the regulation of EV71 infection. In this study, we initially reveal that the interleukin enhancer binding factor 2 (ILF2) down-regulates EV71 50% tissue culture infective dose (TCID50), attenuates EV71 plaque formation unit (PFU), thereby repressing EV71 infection. Moreover, we reveal a distinct mechanism by which EV71 antagonizes ILF2-mediated antiviral effects. Chip data analyses show that ILF2 mRNA is reduced upon EV71 infection. Cellular studies indicate that EV71 infection represses ILF2 mRNA expression and protein production in human leukemic monocytes (THP-1) differentiated macrophages and in human rhabdomyosarcoma (RD) cells. Additionally, EV71 non-structural protein 2B interacts with ILF2 in human embryonic kidney (HEK293T) cells. Interestingly, in the presence of EV71 2B, ILF2 is translocated from the nucleus to the cytoplasm and co-localizes with 2B in the cytoplasm. Therefore, we reveal a distinct mechanism by which EV71 antagonizes ILF2-mediated antiviral effects by inhibiting ILF2 expression and promoting ILF2 translocation from the nucleus to cytoplasm through its 2B protein.

The strategy of any organization is based on the growth of its customer base, and one of 5 its principles is that selling a product to an existing customer is much more profitable than acquiring 6 a new customer. However, this approach has several opportunities for improvement, since it usu- 7 ally has a totally reactive approach, which does not give opportunity to the areas specialized in 8 customer experience and recovery, to give an effective response for that moment, since the customer 9 is gone at the time of the intervention. This happens because usually a diagnostic analysis of cus- 10 tomers who have stopped buying products or services in a defined period, commonly three (3) pe- 11 riods or months, is performed. This thesis work challenges the way to face this problem, and pro- 12 poses the development of a complete solution, which does not focus exclusively on the prediction 13 of churn, as is usually done in the state of the art research, but to intervene in different interactions 14 that can be carried out with customers. The above focused not only to prevent customer churn, but 15 to generate an added value of continuous improvement in sales processes, increase customer pene- 16 tration, leading to an improvement in customer experience and consequently, an increase in cus- 17 tomer loyalty.

The strategy of any organization is based on the growth of its customer base, and one of 5 its principles is that selling a product to an existing customer is much more profitable than acquiring 6 a new customer. However, this approach has several opportunities for improvement, since it usu- 7 ally has a totally reactive approach, which does not give opportunity to the areas specialized in 8 customer experience and recovery, to give an effective response for that moment, since the customer 9 is gone at the time of the intervention. This happens because usually a diagnostic analysis of cus- 10 tomers who have stopped buying products or services in a defined period, commonly three (3) pe- 11 riods or months, is performed. This paper challenges the way to face this problem, and proposes 12 the development of a complete solution, which does not focus exclusively on the prediction of 13 churn, as is usually done in the state of the art research, but to intervene in different interactions 14 that can be carried out with customers. The above focused not only to prevent customer churn, but 15 to generate an added value of continuous improvement in sales processes, increase customer pene- 16 tration, leading to an improvement in customer experience and consequently, an increase in cus- 17 tomer loyalty.

In this paper, I introduce a new concept of representing numbers in base ; in other words, I have found new series for any number similar to series that could be written according to the collatz sequence which is called zi(n) in this article. These series need to end with 1. Then, we use two sets of rules to make a diagram which then proves the existence of such series for any number.In this diagram, by branching numbers into different branches in accordance to the modularity of 4 and continuing branching to the point that their numbers have enough common terms in their collatz series, we could reduce zi(n) to zi(k) so that k<n in any branch by Rule Number One. This diagram shows that zi(n) exists for every number, in other words, this proves the theorem (A) or zi-existence theorem. The proof of zi-existence theorem leads to a proof of the collatz conjecture because the collatz series could be written as a linear combination of such series that all of them end with 1, so the collatz series for any number ends with 1.

The pathogenesis of coronavirus disease 2019 (COVID-19) is associated with a hyperinflammatory response. The mechanisms of SARS-CoV-2-induced inflammation are scantly known. Methylglyoxal (MG) is a glycolysis-derived by-product, endowed with a potent glycating action, leading to the formation of advanced glycation end products (AGEs), the major of which is MG-H1. MG-H1 exerts strong pro-inflammatory effects, frequently mediated by the receptor for AGEs (RAGE). Here, we investigated the involvement of MG-H1/RAGE axis as a potential novel mechanism in SARS-CoV-2-induced inflammation by resorting to human bronchial (BEAS-2B) and alveolar (A549) epithelial cells, expressing different levels of ACE2 receptor (R), exposed to SARS-CoV-2 spike protein 1 (S1). Interestingly, we found in BEAS-2B cells that do not express ACE2-R, that S1 exerted a pro-inflammatory action through a novel MG-H1/RAGE-based pathway. RAGE expression levels in nasopharyngeal swabs from SARS-Cov-2 positive and negative individuals, as well as glyoxalase 1 expression, the major scavenging enzyme of MG, seem to support the results obtained in vitro. Altogether, our findings reveal a novel mechanism involved in the inflammation triggered by S1, paving the way to the study of MG-H1/RAGE inflammatory axis in SARS-CoV-2 infection as a potential therapeutic target to mitigate COVID-19 associated pathogenic inflammation.

Запропонована методика спрямована на визначення та прогнозування технічного стану елементів мосту, що може слугувати прогресивним інженерним інструментом для оцінки надійності та довговічності. Розроблено на основі фундаментальних досліджень, які узагальнюють досвід вивчення фізико-механічних і фізико-хімічних властивостей матеріалів мостових конструкцій, що експлуатуються в реальних умовах. Теоретичною основою методики є модель надійності та прогнозування залишкового ресурсу елементів мосту на основі теорії Маркова. Розроблена методика призначена для оцінки технічного стану окремих елементів мосту з подальшою комплексною оцінкою всієї конструкції. За показник технічного стану прийнята надійність при експлуатації. Цей кількісний показник надійності в моделі є критерієм для: оцінки рівня безпеки елементів мосту; ранжування елементів мосту за необхідністю для конкретних видів ремонту, реконструкції або заміни; стратегічне планування витрат на ремонт або реконструкцію в умовах обмеженого фінансування; прогнозування залишкового ресурсу елементів. Для застосування розробленої методики запропоновано алгоритм оцінки та прогнозування технічного стану мостів. Було проведено математичний експеримент розробленої методики, який підтвердив адекватність висунутої гіпотези, тобто використання моделі надійності та прогнозування залишкового ресурсу елементів мосту. По-перше, запропоновано триступеневий механізм уточнення технічного стану мосту, суттєво підвищення точності розрахунків. Тому розроблена методика має практичне значення і може слугувати основою для інформаційно-аналітичних систем управління станом мостів.

The timely diagnosis of defects at their incipient stage of formation is crucial to extend the life-cycle of technical appliances. This is the case of mechanical-related stress, either due to long aging degradation processes (e.g., corrosion) or in-operation forces (e.g., impact events), which might provoke detrimental damages, such as cracks, disbonding or delaminations, most commonly followed by the release of acoustic energy. The localization of these sources can be successfully fulfilled via adoption of Acoustic Emission (AE)-based inspection techniques through the computation of the Time of Arrival (ToA), namely the time at which the induced mechanical wave released at the occurrence of the acoustic event arrives to the acquisition unit. However, the accurate estimation of the ToA may be hampered by poor Signal-to-Noise ratios (SNRs). In these conditions, standard statistical methods typically fail. In this work, two alternative Deep Learning methods are proposed for ToA retrieval, namely a Dilated Convolutional Neural Network (DilCNN) and a Capsule Neural Network for ToA (CapsToA). These methods have the additional benefit of being portable on resource-constrained microprocessors. Their performance has been extensively studied on both synthetic and experimental data, focusing on the problem of ToA identification for the case of a metallic plate. Results show that the two novel methods can achieve localization errors which are up to 70% more precise than those yielded by conventional strategies, even when the SNR is severely compromised (i.e., down to 2 dB). Moreover, DilCNN and CapsNet have been implemented in a tiny machine learning environment and then deployed on microcontroller units, showing a negligible loss of performance with respect to offline realizations.

During the last trimester of gestation and for the first 18 months after birth, both docosahexaenoic acid,22:6n-3 (DHA) and arachidonic acid,20:4n-6 (ARA) are preferentially deposited within the cerebral cortex at a rapid rate. Although, the structural and functional roles of DHA in brain development are well investigated, similar roles of ARA are not well documented. The mode of action of these two fatty acids and their derivatives at different structural-functional roles and their levels in the gene expression and signaling pathways of the brain have been continuously emanating. In addition to DHA, importance of ARA has been much discussed in recent years for fetal and postnatal brain development and the maternal supply of ARA and DHA. These fatty acids are also involved in various brain developmental processes; however, their mechanistic cross talks are not clearly known yet. This review describes the importance of ARA, in addition to DHA to support the optimal brain development and growth and functional roles in the brain.

Delay in data transmission is one of key performance indicators (KPIs) of a network. The planning and project value of delay in network management is of crucial importance for the optimal allocation of network resources and their performance focuses. To create optimal solutions, predictive models, which are currently most often based on machine learning (ML), are used. This paper aims to investigate the training, testing and selection of the best predictive delay model for a VoIP service in an Long Term Evolution (LTE) network using three ML techniques - Neural Networks (NN), Support Vector Machines (SVM) and k-Nearest Neighbors (k-NN). The space of model input variables is optimized by dimensionality reduction techniques: RReliefF algorithm, Backward selection via the recursive feature elimination algorithm and the Pareto 80/20 rule. A three-segment road in the geo-space between the cities of Banja Luka (BL) and Doboj (Db) in the Republic of Srpska (RS), Bosnia and Herzegovina (BiH), covered by the cellular network (LTE) of the M:tel BL operator was chosen for the case study. The results show that, in all three optimization approaches, the k-NN model is selected as the best solution. For the RReliefF optimization algorithm, the best model has 6 inputs and minimum relative error (RE), RE=0.109; for the Backward selection via the recursive feature elimination algorithm, the best model has 4 inputs and RE=0.041; and for the Pareto 80/20 rule, the best model has 11 inputs and RE= 0.049. The comparative analysis of the results concludes that according to observed criteria for the selection of the final model, the best solution is an approach to optimizing the number of predictors based on the Backward selection via the recursive feature elimination algorithm.

This contribution is an attempt to reconstruct the favorable atmosphere that prevailed in Lau-sanne in 1986-87 and provided the backdrop of our invention of two-dimensional ion cyclotron resonance mass spectroscopy (2D ICR-MS). To avoid a self-centered histoire d’ancien combattant, we shall try to emphasize the context, the contributions of key players within our nascent research group at UNIL and the established group of Tino Gäumann at EPFL, the role of external speakers, and the open atmosphere that was not yet polluted by bibliometrics, obsessive concern with im-pact factors, and top-down management of research. We shall also explain why the idea of 2D ICR-MS has been ignored for many years and still has a limited impact: different scientific cul-tures in the ICR and NMR communities, different concerns with fundamental vs. applied research, different status of theory and numerical simulations, different levels of commitment of instrument manufacturers, not to mention many theoretical problems that appear to be at least as challenging in ICR as in NMR.

This paper presents work done as part of a transformation effort towards a greener and more sustainable Aluminium manufacturing plant. The effort includes reducing the carbon footprint by minimising waste and increasing operational efficiency. The contribution of this work includes the reduction of waste through the implementation of autonomous, real-time quality measurement and classification at an Aluminium casthouse. Data is collected from the MV20/20 which uses ultrasound pulses to detect molten Aluminium inclusions, which degrade the quality of the metal and cause subsequent metal waste. The sensor measures cleanliness, inclusion counts and distributions from 20 - 160 microns. The contribution of this work is in the development of business analytics to implement condition-based monitoring through anomaly detection, and to classify inclusion types for samples that failed. For anomaly detection, multivariate K-Means and DBSCAN algorithms are compared as they have been proven to work in a wide range of datasets. For classification, a two-stage classifier is implemented. The first stage classifies the success or failure of the sample, while the second stage classifies the inclusion responsible for the failed sample. The algorithms considered include logistic regression, support vector machine, multi-layer perceptron and radial basis function network. The multi-layer perceptron offers the best performance using k-fold cross-validation, and is further tuned using grid search to explore the possibility of an even better performance. The results reveal that the model has achieved a global maximum in performance. Recommendations include the integration of additional sensor systems and the improvements in quality assurance practices.

This study investigates the spatio-temporal variability of the onset, offset, and Length of the rainy season in Senegal over the 1981-2018 period. The onset, offset dates, and length of the rainy season are crucial parameters for agricultural planning in West Africa, which exhibits high interannual and spatial variability in rainfall. The objective is to detect and spatially classify these phenological parameters across Senegal using different approaches. Daily precipitation data from the Climate Hazards group InfraRed Precipitation with Stations (CHIRPS) dataset over the study period and ERA5 reanalysis were used. The method of was applied to detect the onset, offset dates, and length of the rainy season. The Kohonen algorithm was then used to spatially classify these parameters on topological maps. A hierarchical ascendant classification was also performed to reduce the number of classes obtained. Finally, a composite analysis of moisture transport before the onset and end of the 1984 and 2007 seasons was conducted with ERA5 data. The results show a meridional gradient of the start of the season, progressively later from southeast to northwest, while the end follows a north-south gradient. The duration of the rainy season ranges from 45 days in northern Senegal to 150 days in the south. The maximum number of dry days also decreases from north to south. The Kohonen self-organizing maps allow spatial prediction of the onset, end date, and duration of the rainy season across Senegal. The dynamics analysis reveals that early onset years are associated with stronger and earlier northward moisture transport over West Africa, underscoring the role of this parameter in triggering the rainy season. These promising results can provide an early warning to policymakers and farmers on the start and end dates of the season in each area of Senegal.

This study investigates the long-term stability of the Suomi National Polar-orbiting Partnership (S-NPP) Visible Infrared Imaging Radiometer Suite (VIIRS) moderate-resolution Thermal Emissive Bands (M TEBs; M12 – M16) covering a period from February 2012 to August 2020. It also assesses inter-sensor consistency of the VIIRS M TEBs among three satellites-S-NPP, NOAA-20, and NOAA-21 over eight months spanning from March 18 to November 30, 2023. The field of interesting is limited to the ocean surface between 60°S and 60°N, specifically under clear-sky conditions. Taking radiative transfer modeling (RTM) as the transfer reference, we employed the Community Radiative Transfer Model (CRTM) to simulate VIIRS TEB brightness temperature (BTs), incorporating European Centre for Medium-range Weather Forecasts (ECMWF) reanalysis data as inputs. Our results reveal two key findings. Firstly, the reprocessed S-NPP VIIRS TEBs exhibit a robust long-term stability, as demonstrated through analyses of the observation minus background BT differences (O-B ∆BTs) between VIIRS measurements (O) and CRTM simulations (B). The drifts of the O-B BT differences are consistently less than 0.105 K/Decade across all S-NPP VIIRS M TEB bands. Notably, observations from VIIRS M14 and M16 stand out with drifts well within 0.04 K/Decade, reinforcing their exceptional reliability for climate change studies. Secondly, excellent inter-sensor consistency among these three VIIRS instruments is confirmed through the double-difference analysis method (O-O). This method relies on the O-B BT differences obtained from daily data. The mean inter-VIIRS O-O BT differences remain within 0.08 K for all M TEBs, except for M13. Even in the case of M13, the O-O BT differences between NOAA-21 and NOAA-20/S-NPP have values of 0.312 K and 0.234 K, respectively, which are comparable to the 0.2 K difference between some TEBs among VIIRS and MODIS. These disparities are primarily attributed to the significant differences in the Spectral Response Function (SRF) of NOAA-21 compared to NOAA-20 and S-NPP. Our study confirms the RTM-based TEB quality evaluation method’s versatility and effectiveness in assessing long-term sensor stability and inter-sensor consistency. The double-difference approach effectively mitigates uncertainties and biases inherent to CRTM simulations, establishing itself a robust mechanism for assessing inter-sensor consistency. In addition, we’ve observed that, except for M13, M12 always exhibits larger spatial variations of O-O BT differences with greater uncertainties compared to the other M TEBs. The influence of solar contribution through sea surface reflection on the Top of Atmosphere (TOA) radiance measurements during daytime in M12 should not be underestimated.