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K-factor

The K-factor is a term used across multiple disciplines, including engineering and technology, mathematics and statistics, telecommunications, and other fields, to denote specific coefficients that quantify key properties or behaviors in systems. Notable applications include viral growth in digital marketing, material deformation in manufacturing, fluid discharge in fire protection, harmonic impacts in electrical engineering, radar propagation, tolerance intervals, multipath fading, and actuarial science. In digital marketing and app development, the K-factor measures an app's or product's virality by calculating the average number of new users that each existing user acquires through referrals or sharing, with a value greater than 1 indicating exponential growth potential.^[1] It is computed using the formula K = i \times c, where i is the number of invitations sent per user and c is the conversion rate of those invitations into new users, helping marketers optimize user acquisition strategies and assess organic uplift from campaigns.^[1] In sheet metal fabrication, the K-factor represents the ratio of the neutral axis position (the theoretical plane within the material that experiences no strain during bending) to the overall material thickness, typically ranging from 0.3 to 0.5 depending on the material and bend radius.^[2]^[3] This factor, expressed as K = t / T (where t is the distance from the inner surface to the neutral axis and T is the material thickness), is essential for accurately calculating bend allowances and flat pattern layouts to compensate for material lengthening and shortening during the bending process.^[2] In fire protection systems, the K-factor is a discharge coefficient that defines the relationship between water flow rate and pressure at a sprinkler's orifice, determining the volume of water released to suppress fires effectively.^[4] It follows the formula K = Q / \sqrt{P}, where Q is the flow in gallons per minute (GPM) and P is the pressure in pounds per square inch (PSI), with standard values like 5.6K used for light-hazard occupancies and higher values (up to 11.2K) for denser discharge needs in high-hazard areas per NFPA 13 standards.^[4] In electrical engineering, particularly for transformers, the K-factor rating quantifies the additional heating losses caused by harmonic currents from non-linear loads, allowing selection of appropriately derated equipment to prevent overheating.^[5] Defined as the ratio of extra eddy current losses due to harmonics to those at fundamental frequency (60 Hz), common ratings include K-4 for moderate loads (up to 50% non-linear) and K-13 for severe applications, influencing transformer size, cost, and efficiency.^[5] Other notable uses include the K-factor in flow measurement devices, where it specifies the number of output pulses per unit volume of fluid (e.g., pulses per gallon), enabling accurate conversion of sensor signals to volumetric flow rates in turbine or paddlewheel meters.^[6]^[7]

Engineering and technology

Sheet metal fabrication

In sheet metal fabrication, the K-factor represents the ratio of the distance from the inner face of the bend to the neutral axis divided by the material thickness t. This neutral axis is the theoretical line within the material that experiences neither compression nor extension during bending, serving as a key parameter for predicting material behavior in deformed regions. The K-factor typically ranges from 0.3 to 0.5 for most metals, with values closer to 0.5 indicating a neutral axis shifted toward the outer surface due to greater outer fiber elongation, and lower values reflecting compression-dominated inner fibers. The K-factor is integral to calculating the bend allowance (BA), the arc length along the neutral axis that must be added to the flat pattern to account for material used in the bend. The formula is:

BA = \left( \frac{\pi}{180} \right) \times \theta \times (r + K \times t)

where \theta is the bend angle in degrees and r is the inside bend radius. This computation enables precise determination of developed flat lengths, minimizing material waste and ensuring dimensional accuracy in fabricated parts. Several factors influence the K-factor, including material type, thickness, grain direction, and bend radius relative to thickness. Thicker materials or tighter radii tend to shift the neutral axis inward, lowering the K-factor, while softer materials exhibit more uniform deformation. Grain direction introduces anisotropy, with bends parallel to the grain often requiring adjusted K-values due to reduced ductility and increased cracking risk. Empirical guidelines suggest a K-factor of approximately 0.33 for mild steel and 0.33 to 0.5 for aluminum alloys, depending on temper and alloy composition. The K-factor is widely applied in CAD/CAM software, such as Autodesk Inventor and SolidWorks, where users input material-specific values to automate flat pattern development and generate accurate CNC programs for press brakes or folding machines. This integration supports efficient prototyping and production in industries like aerospace and automotive manufacturing. The concept originated in mid-20th-century empirical manufacturing standards to standardize bend calculations amid growing sheet metal use in post-war industry. Modern refinements incorporate finite element analysis (FEA) to simulate stress-strain distributions and validate K-factor adjustments under complex loading, improving predictions for advanced alloys and high-precision applications.

Electrical transformers

In electrical engineering, the K-factor serves as a metric to evaluate the thermal stress imposed on transformers by harmonic currents generated by nonlinear loads. It is defined mathematically as K = \sum_{h=1}^{\infty} \left( \frac{I_h}{I_1} h \right)^2, where I_h represents the root mean square (RMS) value of the current at the h-th harmonic order, and I_1 is the RMS value of the fundamental frequency current.^[8] This formulation weights higher-order harmonics more heavily due to their greater contribution to eddy current and skin effect losses in transformer windings.^[9] The primary purpose of the K-factor is to quantify the additional heating losses in transformers arising from harmonic distortion introduced by nonlinear loads, such as computers, uninterruptible power supplies (UPS), and variable frequency drives (VFDs). These harmonics elevate winding temperatures beyond those expected from sinusoidal currents, potentially leading to insulation degradation and reduced lifespan if not addressed. Standard K-factor ratings, such as K-4 for mixed linear and light nonlinear loads (e.g., office environments with PCs and lighting), K-9 or K-13 for moderate electronic loads (e.g., commercial buildings with VFDs), and K-20 for heavy harmonic environments (e.g., data centers), guide transformer selection to mitigate these effects. The International Electrotechnical Commission (IEC) standard 61378-1 addresses similar considerations for power transformers in converter applications, recommending designs that accommodate harmonic loading up to specified levels.^[10]^[9] To prevent overheating, transformers are derated based on the anticipated K-factor of the load. The derated capacity is calculated as S_{\text{derated}} = \frac{S_{\text{rated}}}{\sqrt{K}}, where S_{\text{rated}} is the transformer's nominal apparent power rating; this adjustment ensures that total losses, including those from harmonics, do not exceed the design limits.^[11] The K-factor is measured by analyzing the load current spectrum with power quality analyzers, which capture harmonic magnitudes over representative operating periods and compute the summation.^[10] In practice, K-factor-rated transformers are essential for dry-type units in industrial settings, where VFDs for motor control introduce significant harmonics (often requiring K-13 or higher ratings). These transformers feature enhanced cooling, larger windings, and electrostatic shields to handle the extra losses, ensuring reliable power distribution in environments like manufacturing plants and hospitals without excessive derating or failure risk.^[12]^[9]

Radar propagation

In radar propagation, the K-factor is defined as the ratio of the effective Earth radius a_e to the actual Earth radius a, where a \approx 6371 km, accounting for atmospheric refraction that bends radar rays toward the Earth's surface.^[13] This adjustment models ray paths as straight lines over a modified spherical Earth, simplifying propagation calculations. Under standard atmospheric conditions, the K-factor is K = 4/3, corresponding to a typical vertical refractive index gradient that causes rays to follow the Earth's curvature more closely than in a vacuum. The K-factor is derived from the vertical gradient of the atmospheric refractive index \frac{dn}{dh}, approximated by the formula K \approx \frac{1}{1 + \frac{a}{n} \frac{dn}{dh}}, where n is the refractive index (approximately 1.0003 at sea level). In a standard troposphere, \frac{dn}{dh} \approx -3.9 \times 10^{-8} m^{-1}, yielding the [K](/page/K) = 4/3 value; more negative gradients increase bending, while less negative or positive gradients reduce it.^[14] Higher K-factors (K > 1) enhance ray bending toward the Earth, extending the radar horizon beyond the geometric line-of-sight and improving low-altitude target detection.^[15] Conversely, low K-factors (K < 1) result in straighter paths and reduced range, while superrefraction (K negative or very low) traps waves in atmospheric ducts, causing anomalous propagation with over-the-horizon effects or coverage gaps.^[16] The K-factor is integral to radar range equations for line-of-sight predictions, influencing coverage in weather radars for precipitation mapping, aviation systems for aircraft tracking, and maritime radars for surface surveillance. It also affects over-the-horizon radar designs by modeling extended propagation under varying conditions.^[16] K-factor values vary seasonally and with weather; for instance, K=1 assumes no refraction (geometric horizon), while evaporation ducts over water can produce K approaching infinity, enabling long-distance trapping of radar signals.^[16]

Fluid flow measurement

In fluid flow measurement, the K-factor is defined as the calibration constant representing the number of electrical pulses generated by a flow meter per unit volume of fluid, typically expressed in pulses per liter (PPL) or pulses per gallon (PPG), and is established during factory calibration for turbine and positive displacement meters.^[7] This constant directly relates the meter's pulse output to the actual volume of liquid or gas passing through, enabling precise quantification in volumetric flow applications.^[17] The K-factor is used to compute flow rates and total volumes through standard equations: the volumetric flow rate Q is given by Q = \frac{f}{K} \times C, where f is the pulse frequency in hertz, K is the K-factor, and C is a unit conversion factor (e.g., to convert to liters per minute); total accumulated volume is V = \frac{N}{K}, with N as the total pulse count.^[18] These calculations assume a linear response, which holds for turbine meters in clean, low-viscosity liquids but requires multi-point calibration curves for broader ranges.^[19] Accuracy of K-factor-based measurements can be affected by fluid properties such as viscosity, density, and temperature, which alter rotor speed or displacement mechanics in turbine and positive displacement meters, respectively; turbine meters exhibit linearity for clean liquids but nonlinearity for gases, slurries, or high-viscosity fluids due to increased drag or uneven flow.^[17] Electronic signal processing often applies corrections for these variations to maintain precision within ±0.5% to ±1% of reading.^[20] K-factors find widespread application in custody transfer for oil and gas pipelines, municipal water metering, and chemical processing industries, where reliable volume tracking is essential for billing, inventory, and process control.^[19] In these contexts, meters with pulse outputs integrate with totalizers or SCADA systems for automated data logging and correction of environmental influences.^[17] Calibrations for K-factors are performed using NIST-traceable standards, ensuring traceability to national measurement references with uncertainties as low as 0.033% for mass flow in water calibrations.^[21] Typical K-factor values vary by meter size and design, such as approximately 200 pulses per U.S. gallon for mid-range turbine meters or higher (e.g., 7500 PPG) for smaller units to achieve finer resolution.^[19] Since the 2010s, advancements in IoT-enabled flow meters have facilitated real-time monitoring and dynamic adjustments to K-factor outputs via integrated sensors for viscosity and temperature, enhancing adaptability in variable process conditions.^[22]

Mathematics and statistics

Tolerance intervals

In statistical tolerance intervals, the K-factor serves as a critical multiplier that constructs bounds to encompass at least a specified proportion p of a population with a given confidence level \gamma = 1 - \alpha. For data assumed to follow a normal distribution, the two-sided tolerance interval is typically formed as \bar{x} \pm k s, where \bar{x} is the sample mean, s is the sample standard deviation, and k is the K-factor ensuring the interval covers proportion p (e.g., 95%) of the population with confidence \gamma (e.g., 95%). This approach originated in the 1940s, with foundational work by Samuel S. Wilks introducing tolerance limits for setting statistical bounds in quality assurance, particularly for determining sample sizes to achieve reliable coverage, and Gerald J. Lieberman extending these ideas through tables and methods for practical computation in process control.^[23] The K-factor is derived from statistical distributions to account for sampling variability. For the normal distribution, an approximate formula for the two-sided K-factor is given by

k \approx \sqrt{\frac{(n-1) \left(1 + \frac{1}{n}\right) z^2_{(1+p)/2}}{\chi^2_{\alpha, n-1}}},

where n is the sample size, z_{(1+p)/2} is the (1+p)/2 quantile of the standard normal distribution, and \chi^2_{\alpha, n-1} is the upper \alpha quantile of the chi-squared distribution with n-1 degrees of freedom; this approximation, proposed by Howe, provides good accuracy for moderate to large n and is widely used for its computational simplicity. Exact values of k are obtained by solving equations involving the non-central chi-squared or non-central t-distribution to ensure the probabilistic coverage statement holds precisely.^[24]^[25] Formulas for the K-factor differ between two-sided and one-sided intervals due to the asymmetry in coverage requirements. Two-sided intervals aim to capture p of the population symmetrically around the mean, using the above approximation or exact non-central methods, whereas one-sided intervals (e.g., lower bound \bar{x} - k s) ensure at least p of the population exceeds the bound with confidence \gamma, often yielding smaller k values; for instance, Natrella's approximations for one-sided cases involve direct normal quantile adjustments scaled by sample variability. The exact one-sided k also relies on the non-central t-distribution for precision, particularly in small samples where approximations may underestimate coverage.^[25] Tolerance intervals based on the K-factor assume the underlying data follow a normal distribution, which underpins the use of z- and chi-squared quantiles in the formulas; violations of normality can lead to inaccurate coverage, prompting the development of nonparametric alternatives that rely on order statistics rather than a parametric K-factor. These assumptions make the method suitable for symmetric, bell-shaped data but require validation, such as through goodness-of-fit tests, in applied settings.^[25] Applications of K-factor tolerance intervals are prominent in quality control within manufacturing, where they establish specification limits for product characteristics, such as dimensional tolerances in automotive parts to ensure consistency across production batches. In environmental monitoring, they define acceptable ranges for pollutant levels or ecological metrics, providing probabilistic bounds for regulatory compliance with specified confidence. Software implementations, such as the tolerance package in R, facilitate computation of these intervals and K-factors for practical use in these domains.^[26]^[27]

Particle physics cross-sections

In particle physics, the K-factor quantifies the ratio of the next-to-leading order (NLO) cross-section to the leading order (LO) cross-section for processes involving quantum chromodynamics (QCD) interactions, defined as K = \frac{\sigma_\mathrm{NLO}}{\sigma_\mathrm{LO}}, where \sigma_\mathrm{NLO} incorporates one-loop corrections and additional real emissions beyond the tree-level LO prediction.^[28] This scaling factor encapsulates the dominant effects of higher-order perturbative QCD corrections, which enhance the accuracy of theoretical predictions for particle collision cross-sections without requiring full NLO event simulations.^[28] Typical K-factors range from 1.2 to 2.0, varying by process; for instance, in Higgs boson production via gluon fusion at the LHC, the inclusive K-factor is approximately 2.0.^[29]^[28] The primary purpose of the K-factor is to account for perturbative QCD corrections and resummation of large logarithmic terms arising from soft and collinear gluon emissions, thereby bridging the gap between simplistic LO calculations and more precise higher-order results.^[30] These factors are computed using dedicated Monte Carlo event generators such as MCFM, which supports NLO and NNLO fixed-order predictions for processes like vector boson production through methods including q_T-slicing and zero-jettiness subtraction, and MadGraph, which applies NLO/LO K-factor reweighting to loop-induced processes for improved background modeling.^[31] By applying K-factors, researchers can efficiently scale LO matrix elements to match NLO accuracy, reducing computational demands while maintaining reliability for differential distributions.^[28] At the Large Hadron Collider (LHC) at CERN, K-factors play a crucial role in interpreting collision data for searches of new physics beyond the Standard Model, where precise Standard Model background estimates are vital to identify subtle deviations in event rates.^[32] They vary with the center-of-mass energy scale and experimental kinematic cuts, such as jet transverse momentum thresholds; for example, the NLO K-factor for top-antitop (t\bar{t}) pair production at 13 TeV is approximately 1.5, reflecting enhanced gluon-initiated contributions at higher energies.^[33]^[32] Similarly, for W and Z boson production, the K-factor is typically 1.2–1.3, aiding in the normalization of electroweak processes amid QCD backgrounds.^[28]^[32] The application of K-factors has evolved significantly within perturbative QCD, transitioning from fixed-order LO analyses predominant before the 1990s—which suffered uncertainties up to a factor of two—to NLO implementations in the 1990s, and further to NNLO plus next-to-next-to-leading logarithmic (NNLL) resummation since the 2010s, which combines fixed-order expansions with logarithmic improvements to shrink scale uncertainties below 5% for key LHC processes like Higgs and t\bar{t} production.^[30] This progression has rendered early LO-only approaches obsolete, enabling high-precision comparisons between theory and data that are essential for constraining extensions of the Standard Model.^[30]

Telecommunications

Multipath fading

In the context of multipath fading in telecommunications, the K-factor quantifies the relative strength of the direct line-of-sight (LOS) signal path compared to the scattered non-line-of-sight (NLOS) multipath components, defined as the ratio of LOS power \Omega to NLOS power $2\sigma^2, where \sigma^2 is the variance of the Gaussian-distributed scatter components, expressed either in linear scale or decibels.^[34] A high K-factor, exceeding 10 dB, characterizes Ricean fading where the LOS dominates, resulting in milder signal fluctuations, whereas a K-factor approaching 0 dB signifies Rayleigh fading with equal contribution from all multipath paths and no dominant LOS, leading to deeper fades.^[35] The received signal envelope in a Ricean fading channel follows a Rice distribution, modeling the amplitude as the magnitude of a constant LOS vector plus a zero-mean complex Gaussian random vector representing multipath scatter. The probability density function (PDF) of the envelope r is

f(r) = \frac{r}{\sigma^2} \exp\left( -\frac{r^2 + A^2}{2\sigma^2} \right) I_0 \left( \frac{r A}{\sigma^2} \right), \quad r \geq 0,

where A = \sqrt{\Omega} is the LOS amplitude, \sigma^2 is the scatter power per dimension, and I_0(\cdot) is the modified Bessel function of the first kind and zeroth order; this formulation enables accurate simulation of fading effects on system performance, such as bit error rate (BER) prediction under various modulation schemes.^[34]^[36] This K-factor model finds essential applications in mobile communications, including 5G and emerging 6G systems, where it describes urban and rural propagation environments to optimize handover procedures and antenna diversity techniques that mitigate fading-induced errors. For emerging 6G systems under 3GPP Release 19 studies (as of 2025), the K-factor model is being extended to terahertz frequencies, incorporating higher values to account for near-field effects and AI-based predictions in diverse environments.^[35]^[37] In satellite links, particularly for land mobile satellite systems, the Ricean model with varying K-factors accounts for direct satellite-to-user paths combined with ground reflections, influencing link reliability and adaptive modulation strategies.^[38] Estimation of the K-factor from received signal measurements typically employs moment-based methods that leverage statistical properties of the envelope samples, such as the second and fourth moments to derive parameters \Omega and \sigma^2; one such approach yields K = \left( \sqrt{2\sigma^2 + \Omega} - \sigma \right)^2 / \sigma^2, providing a practical means to characterize channel conditions in real-time without pilot symbols in low-mobility scenarios.^[34] In modern standards, the K-factor is integrated into 3GPP channel models for millimeter-wave (mmWave) bands in 5G NR, as specified in TR 38.901 (Release 18, 2024), where for CDL-E LOS in urban micro scenarios, it follows a lognormal distribution with mean 9 dB and standard deviation 5 dB to reflect strong direct paths in street canyon environments, enhancing simulation accuracy for beamforming and massive MIMO deployments. Examples in the standard use values up to 22 dB.^[39]

Amplifier stability

In RF and microwave engineering, the K-factor, also known as the Rollett stability factor, serves as a key metric for assessing the stability of two-port networks such as amplifiers to prevent oscillations under varying source and load impedances.^[40] Introduced by J. M. Rollett in his seminal 1962 paper, it provides a necessary condition for unconditional stability, ensuring the amplifier remains stable across all passive terminations within the frequency band of interest.^[41] This factor has become indispensable in the design of modern high-frequency circuits, particularly monolithic microwave integrated circuits (MMICs), where parasitic effects can lead to unintended feedback and instability.^[40] The K-factor is defined in terms of scattering (S) parameters as follows:

K = \frac{1 - |S_{11}|^2 - |S_{22}|^2 + |\Delta|^2}{2 |S_{12} S_{21}|}

where \Delta = S_{11} S_{22} - S_{12} S_{21} is the determinant of the S-parameter matrix.^[42] A value of K > 1 indicates that the input and output reflection coefficients do not simultaneously exceed unity in magnitude, contributing to stability, though it must be paired with the condition |\Delta| < 1 for full unconditional stability across the Smith chart.^[40] If K < 1, stability circles on the Smith chart reveal regions of potential instability, guiding matching network adjustments to avoid oscillatory behavior.^[42] As an alternative or complementary check, the \mu-factor (also called the Bode stability factor) evaluates robustness against specific port interactions, with \mu > 1 confirming stability when the classic K-factor alone may overlook asymmetric risks.^[42] In practice, the K-factor is computed from S-parameters measured using a vector network analyzer (VNA), allowing engineers to identify frequency points where K < 1 signals potential instability, such as low-K regions near transistor cut-off frequencies.^[43] Applications of the K-factor are prominent in transistor-based amplifier design, including gallium nitride (GaN) power amplifiers for 5G base stations, where maintaining K > 1 across multi-GHz bands ensures reliable high-power operation without oscillations.^[44] For instance, in GaN MMIC designs operating at 3.5 GHz, stability analysis via K-factor informs input/output matching to achieve efficiencies exceeding 60% while avoiding unstable load regions on the Smith chart.^[44] This criterion remains essential for broadband RF systems, from low-noise amplifiers to high-efficiency PAs, underpinning the performance of telecommunications infrastructure.^[45]

Other uses

Viral marketing

In viral marketing, the K-factor, also known as the viral coefficient, quantifies the average number of new users each existing user recruits through invitations that result in active participation, serving as a key indicator of organic growth potential for digital products like apps and websites. This metric enables teams to assess whether user-driven sharing can sustain expansion without heavy reliance on paid acquisition.^[46] The K-factor is defined by the formula K = i \times c, where i is the average number of invitations sent per user and c is the conversion rate of those invitations into active users.^[46] When K > 1, the product experiences exponential growth, as the user base compounds over time; values below 1 imply stagnation or contraction unless supplemented by other channels.^[46] Calculation involves aggregating data from user analytics platforms, often focusing on referral mechanisms within apps. For instance, in Dropbox's referral program, which rewarded users with additional storage space for successful invites, the K-factor was derived from tracked invitation volumes and signup completions.^[46] A hypothetical scenario illustrates this: if users send an average of 5 invitations each and 30% convert to active users, then K = 5 \times 0.3 = 1.5, signaling strong virality.^[46] Startups leverage the K-factor for user acquisition in sectors like social networks and mobile games, where tactics such as gamified rewards or seamless sharing prompts elevate invitation rates and conversions.^[46] These strategies, including double-sided incentives that benefit both referrer and invitee, have been instrumental in scaling platforms by embedding virality into core product experiences.^[46] A notable case is early Facebook's expansion in the 2000s, where exclusive campus invitation systems drove rapid adoption among students through high-conversion peer referrals that propelled membership from thousands to millions within months.^[46] Despite its utility, the K-factor assumes static rates of invitations and conversions, overlooking real-world factors like user fatigue or market saturation that cause decay over time.^[47] To address this, practitioners employ cohort analysis—grouping users by acquisition period to monitor evolving metrics—a refinement that gained traction in the 2010s amid the explosion of social media analytics tools.^[47] High K-factors alone do not ensure long-term success if undermined by poor retention, as sustained engagement is required to perpetuate the loop.^[46]

Actuarial science

In actuarial science, the K-factor primarily refers to a key metric used in the accounting and amortization of deferred acquisition costs (DAC) for certain insurance products, particularly universal life-type contracts under U.S. GAAP (ASC 944). It represents the ratio of the present value of deferrable acquisition expenses to the present value of estimated gross profits (EGP) over the life of the product, serving as the amortization rate to align expense recognition with expected earnings. This approach ensures that upfront costs, such as commissions and policy issuance fees, are deferred and expensed in proportion to the revenues they generate, promoting matching principles in financial reporting.^[48] The K-factor is calculated at inception and updated retrospectively for changes in assumptions or experience, using the policy's interest crediting rate as the discount rate. Formally,

k = \frac{\sum_{t=0}^{T} \frac{\text{Deferrable Expenses}_t}{(1 + i)^t}}{\sum_{t=0}^{T} \frac{\text{EGP}_t}{(1 + i)^t}}

where i is the crediting rate, t indexes periods from 0 to maturity T, deferrable expenses include direct incremental costs of successful contract acquisition, and EGP comprises elements like investment income, mortality and surrender charges, minus policy benefits and maintenance expenses. During each period, DAC amortization equals k \times current-period EGP, with interest accrued on the unamortized DAC balance at rate i; recoverability is tested periodically to ensure the DAC asset does not exceed future EGP.^[49]^[48] This mechanism, originating from FAS 97 and retained in post-LDTI frameworks like ASU 2018-12, supports actuarial valuation by dynamically adjusting for variances in mortality, lapses, or investment yields, thereby influencing balance sheet assets and income statement volatility. For example, adverse experience unlocking reduces the K-factor, accelerating amortization and potentially impairing profitability. Actuaries rely on stochastic modeling and sensitivity analyses to project these impacts, ensuring compliance with recoverability tests under ASC 944-30-35-7 through -10.^[49]

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Sep 25, 2019 · MCFM is a parton-level Monte Carlo program that gives predictions for a wide range of processes at hadron colliders. Almost all processes are ...Missing: MadGraph | Show results with:MadGraph
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https://arxiv.org/pdf/2402.16276.pdf
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[PDF] The Ricean Factor: Estimation and Performance Analysis - NJIT
order modified Bessel function of the first kind. Notice that when } | , there is no LoS component, in which case (3) reduces to the Rayleigh distribution.
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[PDF] Ricean K-Factor Measurements and Analysis for Wideband High ...
Ricean K-factor is a popular parameter to quantify the channel fading severity, which is defined as the power ratio of LOS components to multipath components.
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[PDF] Effect of AWGN & Fading (Raleigh & Rician) channels on BER ...
The simulation model built for this research work, demonstrates that AWGN channel has better performance than Rayleigh and Rician fading channels. Synthetic ...
[36]
[PDF] Effect of Rician Factor in Satellite Communication Signal with MAP ...
May 3, 2015 · This paper presents the effect of rician factors in satellite communications with Maximum A Posteriori (MAP) demodulation.
[37]
[PDF] ETSI TR 138 900 V14.2.0 (2017-06)
- Proposed 3 areas for 5G mmWave channel modeling which are small modifications or extensions from 3GPP's ... For LOS channel models, the K-factor of CDL-D and ...<|control11|><|separator|>
[38]
Microwaves101 | Stability factor - Microwave Encyclopedia
A download spreadsheet for calculating stability factor and available gain (and many other parameters) from vector S-parameters that you can get from ...
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[PDF] Stability and Power-Gain Invariants of Linear Twoports
Stability and Power-Gain Invariants of Linear Twoports · J. Rollett · Published 1 March 1962 · Engineering, Physics · IEEE Transactions on Circuits and Systems I- ...Missing: original | Show results with:original<|control11|><|separator|>
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2.6: Amplifier Stability - Engineering LibreTexts
May 22, 2022 · The $k$-factor, part of Rollet's unconditional stability criterion, is a test of whether a device is unconditionally stable or not. It does ...Missing: history John 1957
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RF Amplifier Stability Factors and Stabilization Techniques
Dec 6, 2023 · Note that K accounts for both input and output ports. Rollet's conditions are necessary and sufficient for unconditional stability. If these ...Missing: history John 1957<|control11|><|separator|>
[42]
Efficient GaN-on-Si Power Amplifier Design Using Analytical and ...
This paper presents the design procedure of an efficient compact monolithic microwave integrated circuit power amplifier (MMIC PA) in a 0.1 μm GaN-on-Si ...
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Efficiently Detect Instabilities in Wideband GaN MMIC Power ...
Aug 30, 2022 · Different tools for the stability analysis of RF and microwave circuits are available in commercial simulators, with the Rollett factor, K, and ...
[44]
K-factor: The Metric Behind Virality - First Round Review
K-Factor (also called the virality coefficient) measures how many new users each existing user or customer brings in over a defined time period.
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Facebook viral marketing: When and why do apps “jump the shark?”
Apps "jump the shark" when growth slows due to network saturation and poor user retention, as new invites can't sustain growth.
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[PDF] The Calculus of DAC - SOA
Jun 3, 2016 · As you are all aware, the k factor is calculated as the ratio of the present value of deferrable expenses to EGPs over the life of the product:.Missing: science | Show results with:science
[47]
[PDF] Accounting for certain life insurance and annuity products - EY
• Compute the amortization rate (k-factor) by calculating the present value of the estimated ... DAC amortization k-factor will need to be updated and a ...