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The Cykloid-Adelic Recursive Expansive Field Equation (CARE)
出版 2025“...<p dir="ltr">The full expression lives alongside the original paper RED34Section </p><p dir="ltr">1: Mathematical Framework Definitions Core Functions – r₁(t)=exp(t·α), r₂(t)=tᵅ, d(t)=2 sin(t·α)+3 Time Derivatives – ṙ₁=α exp(t α), ṙ₂=tᵅ·(α/t), ḋ=2 α cos(t α) </p><p dir="ltr">Section 2: Partial Derivatives of the Area Function Auxiliary terms θ₁…θ₄ defined from r₁, r₂, d and Δ=√(θ₁θ₂θ₃θ₄) Exact formulas for ∂A/∂r₁, ∂A/∂r₂, ∂A/∂d, each featuring: – a Heron-type square‐root term – a cyclic product of three θ’s divided by 2 θ₁θ₂θ₃θ₄ – an arccos term – additional correction factors </p><p dir="ltr">Section 3: Total Time Derivative of Area dA/dt = (∂A/∂r₁)ṙ₁ + (∂A/∂r₂)ṙ₂ + (∂A/∂d)ḋ Substitution of ṙ₁, ṙ₂, ḋ yields a sprawling multi-line expression combining all three partial contributions </p><p dir="ltr">Section 4: Key Mathematical Constructs Golden ratio φ = (1+√5)/2 ≈ 1.618 Fractal Hausdorff dimension D_H ≈ 3.48 Tribonacci constant ≈ 1.839 Adelic prime-based product structures Recursive operator ℛ(x)=limₙ→∞φ⁻ⁿ P_stratumₙ∘Tⁿx Eigenvergence at rate O(φ⁻ⁿ) </p><p dir="ltr">Section 5: Validation Metrics χ²/ν = 1.03 (ν=112) Gelman–Rubin R̂ = 1.002 ± 0.0003 Energy conservation: d(E_epic+E_epitro)/dt = 0 CMB multipoles C_ℓ ∼ ℓ^{–α} cos(2π ℓ φ) Gravitational-wave echo frequencies fₙ = f₀ φ⁻ⁿ </p><p dir="ltr">We develop a unified field framework, the Cykloid-Adelic Recursive Expansive Field Equation (CARE), which scaffolds stratified geometric manifolds with adelic number-theoretic dynamics via recursive cycloidal parameter spaces. ...”
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Rotational grazing supports coexistence of the endangered pygmy bluetongue and livestock on a productive agricultural property
出版 2025“...Agricultural grasslands have the potential to complement conservation initiatives whilst maintaining productivity. ...”
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Impact of SH3 domain-containing proteins on the vegetative growth of <i>F. graminearum.</i>
出版 2025“...In addition to SH3 domains, the proteins may have some other domains. SH3, Src homology 3 domain; BAR, Bin/Amphiphysin/Rvs (BAR) domain; DOCK_N, the N-terminal domain of the DOCK protein family, which plays a critical role in membrane localization and phosphoinositide binding; DOCK-C2, A highly conserved subregion within the DHR2 domain (C-terminal subdomain 2) that directly engages GTPase binding and catalysis; DHR-2, which is the enzymatic heart of DOCK proteins, driving Rho GTPase activation to orchestrate cell motility, immune responses, and development; PALP, Pyridoxal-phosphate; FCH, FER-CIP4 homology domain, which collaborates with the BAR (Bin-Amphiphysin-Rvs) domain to regulate membrane curvature sensing, remodeling, and cytoskeletal dynamics; PAT1, Partitioning defective 1 homolog domain; DUF, Domain of Unknown Function; SAM, Sterile alpha motif domain; PH, Phospholipase D pleckstrin homology (PH) domain; SHD1, Sla1 homology domain; Trans_glut, Transglutaminase domain; Ysc84, YAB domain of <i>S. cerevisiae,</i> which is associated with actin cytoskeleton remodeling and membrane trafficking; CLF, Cohesin loading factor; C1, Phorbol esters/diacylglycerol binding domain; C3HC4, Zinc finger. ...”
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liverRegression code.
出版 2025“...Previous machine learning models have focused on the binary task of predicting the presence or absence of open chromatin, but yet to demonstrate an ability to predict continuous differences in signal. ...”
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DNADRV: Gathering insect biodiversity data by swabbing vehicle number plates
出版 2025“...</p><p dir="ltr">Our results indicate the value of this approach in documenting data deficient and neglected insect taxa as well as identifying insects that are of interest for biosecurity and conservation. We also chronical how running these preliminary studies, and the consequent feedback that we have had, has led to many adjustments and refinements to the sampling kits that we are now distributing to the general public as a broad scale citizen science initiative to determine insect biodiversity. ...”
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Data Sheet 1_Importance of near-bottom oceanographic data in modeling the distribution of eulachon bycatch in the U.S. West Coast shrimp trawl fishery.docx
出版 2025“...These findings can inform Best Management Practices (BMPs), which have historically led to regulatory changes such as the adoption of excluder grates and LED lights. ...”
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Video 1_Importance of near-bottom oceanographic data in modeling the distribution of eulachon bycatch in the U.S. West Coast shrimp trawl fishery.mp4
出版 2025“...These findings can inform Best Management Practices (BMPs), which have historically led to regulatory changes such as the adoption of excluder grates and LED lights. ...”
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A Four-Wavelength Photoplethysmography dataset for non-invasive hemoglobin assessment
出版 2025“...Non-invasive blood glucose detection system based on conservation of energy method. <b><i>Physiological measurement</i></b>, <b>2017</b>, 38: 325-342....”
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Data Sheet 1_Genome-wide analysis of the CrRLK1L gene family in Puccinellia tenuiflora and functional study of PutFER1 in Arabidopsis underpinning salt tolerance.pdf
出版 2025“...<p>CrRLK1L receptor-like kinases have attracted significant interest in plant biology owing to their pivotal roles in development, stress response, and signal transduction. ...”
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Data Sheet 5_Genome-wide analysis of the CrRLK1L gene family in Puccinellia tenuiflora and functional study of PutFER1 in Arabidopsis underpinning salt tolerance.pdf
出版 2025“...<p>CrRLK1L receptor-like kinases have attracted significant interest in plant biology owing to their pivotal roles in development, stress response, and signal transduction. ...”
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Table 2_Genome-wide analysis of the CrRLK1L gene family in Puccinellia tenuiflora and functional study of PutFER1 in Arabidopsis underpinning salt tolerance.xlsx
出版 2025“...<p>CrRLK1L receptor-like kinases have attracted significant interest in plant biology owing to their pivotal roles in development, stress response, and signal transduction. ...”
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Table 4_Genome-wide analysis of the CrRLK1L gene family in Puccinellia tenuiflora and functional study of PutFER1 in Arabidopsis underpinning salt tolerance.xlsx
出版 2025“...<p>CrRLK1L receptor-like kinases have attracted significant interest in plant biology owing to their pivotal roles in development, stress response, and signal transduction. ...”
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Data Sheet 2_Genome-wide analysis of the CrRLK1L gene family in Puccinellia tenuiflora and functional study of PutFER1 in Arabidopsis underpinning salt tolerance.pdf
出版 2025“...<p>CrRLK1L receptor-like kinases have attracted significant interest in plant biology owing to their pivotal roles in development, stress response, and signal transduction. ...”