Format Conversion

Fetch a live web page by URL and convert it to clean Markdown — headings, links, lists, code and optionally images and tables — with reader-mode junk stripping.

Science & Education

Solve ∫|ψ|²dx = 1 for A: infinite well √(2/L), Gaussian (πσ²)^(−1/4), oscillator ground (mω/πℏ)^(1/4), exponential √(2α), with checks and moments.

Math & Numbers

(n−1)! ≡ −1 (mod n) ⟺ n is prime. Exact factorial residue for n ≤ 10⁷, Miller–Rabin cross-check, composite factorial law, optional running-products trace.

Health

Estimate expected adult vital capacity with the Baldwin equations ((27.63 − 0.112×age)×height for males, (21.78 − 0.101×age)×height for females) and optionally grade a measured VC as % predicted. Not medical advice.

Development

Decode raw WebSocket frames (hex or base64) byte by byte per RFC 6455: FIN/RSV/opcode, MASK bit, extended lengths, masking key, unmasked payload, close codes, and protocol-violation warnings.

Cryptography

Decode WebAuthn/FIDO2 assertion fields, inspect authenticatorData flags and signCount, check challenge/origin/rpIdHash binding, and optionally verify ES256, RS256, or Ed25519 signatures with a supplied COSE public key.

Health

Calculate the Wells score to estimate clinical probability of deep vein thrombosis (DVT). Components: active cancer (+1), paralysis/paresis/recent plaster immobilization (+1), recently bedridden ≥3 days or major surgery ≤12 weeks (+1), localized tenderness along deep veins (+1), entire leg swollen (+1), calf swelling ≥3 cm vs other leg (+1), pitting edema confined to symptomatic leg (+1), collateral superficial (nonvaricose) veins (+1), previously documented DVT (+1), alternative diagnosis at least as likely as DVT (−2). Reports BOTH interpretations: three-tier (low ≤0 ~5%, moderate 1–2 ~17%, high ≥3 ~17–53%) and dichotomized two-tier (DVT unlikely ≤1 — a negative D-dimer rules out; DVT likely ≥2 — ultrasound/D-dimer). Derived from Wells 1997 (Lancet) and the Goodacre 2005 (BMJ) meta-analysis. Not medical advice.

Health

Calculate the Wells score to estimate clinical probability of pulmonary embolism (PE). Components: clinical signs/symptoms of DVT (+3), PE is the most likely diagnosis (+3), heart rate >100 (+1.5), immobilization ≥3 days or surgery in last 4 weeks (+1.5), previous objectively diagnosed DVT/PE (+1.5), hemoptysis (+1), active malignancy (+1). Reports BOTH endorsed interpretations: three-tier (low <2 ~1.3%, moderate 2–6 ~16.2%, high >6 ~37.5%) and dichotomized two-tier (PE unlikely ≤4 ~12.1% — a negative D-dimer can rule out; PE likely >4 ~37.5% — imaging required). Derived from Wells 2001 (Ann Intern Med), ACEP 2018 clinical policy, and the ESC 2019 PE guideline. Pair with PERC and D-dimer. Not medical advice.

Health

Adjust warfarin maintenance dose from the current INR using the standard nomogram for a target INR of 2.0–3.0. No-bleed ladder: INR<1.5 → +10–20% weekly dose; 1.5–1.9 → +5–15%; 2.0–3.0 → no change; 3.1–3.5 → −5–15%; 3.6–4.0 → −10–20%; 4.1–4.4 → hold 0–1 dose, ~−20%; 4.5–10 → hold + oral vitamin K₁ 1–2.5 mg; >10 → hold + oral vitamin K₁ 2.5–5 mg. Serious/life-threatening bleed at any INR → hold warfarin, vitamin K₁ 5–10 mg IV (slow, 20–30 min) + 4-factor PCC (FFP if unavailable). Optional current weekly dose computes the concrete new weekly and daily dose. Derived from the 9th-edition ACCP Guidelines (Holbrook et al., Chest 2012) and the UW Anticoagulation Clinic nomogram. Valid for adult maintenance therapy at steady state; not for initial induction, DOAC/heparin overlap, or perioperative bridging. Not medical advice.

Web & Internet

Search the web through the s.stdlang.com SearXNG instance and return its JSON response for automation or downstream tools.

Health

Calculate the apparent volume of distribution Vd in two modes. (A) One-compartment IV bolus: Vd = Dose / C0 (C0 = concentration extrapolated to t=0). (B) From clearance and half-life (linear kinetics): Vd = CL · t½ / 0.693. Vd is an APPARENT (theoretical) volume, not an anatomical one — highly tissue-bound drugs (digoxin ≈ 7 L/kg, amiodarone ≈ 66 L/kg) can exceed total body water, while highly plasma-protein-bound drugs (warfarin ≈ 0.14 L/kg) fall far below it. Optional body-weight input converts the result to L/kg. Note: Vd = Dose/C0 gives Vc (initial); Vss (steady state) and Vz (terminal) differ for multi-compartment models, and oral dosing returns Vd/F. Not medical advice.

Math & Numbers

Compute the discharge over a sharp-crested thin-plate weir. Rectangular (suppressed, no side contraction): Q = (2/3)·C_d·√(2g)·b·H^1.5. V-notch (triangular): Q = (8/15)·C_d·√(2g)·tan(θ/2)·H^2.5. b is the crest width, H the head over the crest (or over the vertex for a V-notch), θ the notch angle. If C_d is left blank it defaults to 0.611 for rectangular weirs (Rehbock/Francis typical value) and 0.58 for V-notch weirs. Crest width in m/cm, head in m/cm/mm; output in m³/s, L/s, L/min and m³/h.