Fitowar 21 Oktoba, 2026

Ka ɗauki tarin lambobi (sets). "Sunflower" rukuni ne na tarin da dukkansu ke haɗuwa a tsakiya ɗaya daidai. Duk sauran, wato ganyen fure (petals), ba sa taɓa juna. Masana lissafi suna son su.

A shekarun 1970, Erdős da Szemerédi sun tambaya: tarin nawa za ka iya tattarawa ba tare da wani k daga cikinsu ya zama sunflower ba? Hasashensu: ƙasa da dukkan tarin da za a iya samu ta hanyar exponential. Yanayin ganye uku kawai aka warware, a 2016.

Yanzu masana lissafi uku daga Vienna da KAIST sun tabbatar da shi ga kowane adadin ganyen fure. Iyakar: 3 × (2 − 1/16k³) zuwa ƙarfin n. Kusa da 2ⁿ, amma ƙarami ta hanyar exponential.

ChatGPT 6 Astra Pro ne ya sami babban matakin. Marubutan sun sake rubuta shi, sun duba shi, kuma manhajar Lean ta tabbatar da hujjar.

Tushe: Proof of the Erdős-Szemerédi sunflower conjecture, https://arxiv.org/abs/2610.26686

A ranar 30 ga Mayu 2026, da rana tsaka, wani dutsen sararin samaniya mai faɗin kusan mita 1.6 ya bugi sararin saman Massachusetts. Wata ƙarar sauti mai ƙarfi (sonic boom) ta mamaye gaɓar teku. Wata na'urar gwamnatin Amurka ma ta kama walƙiyarsa. Wani radar na meteor da MIT ke gudanarwa ya kama plasma mai haske da ya samar daga kilomita 90 har zuwa kusan kilomita 34.

Sannan radar na yanayi suka karɓi aikin. Sun hango meteorite masu faɗuwa tsakanin tsayin kilomita 13.6 da 7.6. Guntuwar sun sauka a Cape Cod Bay, a cikin ruwa mai zurfin kusan mita 34.

Na'urorin auna matsi 199 sun saurari raƙumin girgiza, ciki har da na'urori masu araha na talakawa. Hukuncinsu: kusan kilotan 0.5 na TNT.

Mai yiwuwa dutsen yana da nauyi da tauri, wataƙila mai yawan ƙarfe. Hanyar zagayensa (orbit) tana kan iyaka tsakanin taurari masu wutsiya (comets) da taurarin dutse (asteroids). Ba a sami wani sananne da ya fito daga gare shi ba.

Tushe: Radar and Infrasound Observations of the 2026 May 30 Cape Cod Bay Superbolide, https://arxiv.org/abs/2610.24566

Neutron mai 'yanci yana rayuwa kusan minti 15, sannan ya ruɓe zuwa proton, electron da antineutrino. Gell-Mann ya yi hasashen wani tasiri mai laushi a irin waɗannan ruɓewa: "weak magnetism" (maganaɗisu mai rauni). A cikin neutron mai 'yanci, babu wanda ya taɓa ganin sa.

Matsalar: babban awon yana haɗa abubuwa biyu da ba a sani ba. Gwaji ɗaya ba zai iya raba su ba. Don haka masana kimiyyar lissafi kawai suka ɗauki ƙimar da aka hasashe. Kusan shekaru saba'in, gwajin ya kasance ba a iya kai wa gare shi ba.

Masana ka'idoji uku a Spain sun ƙara wasu sinadarai biyu: tsawon rayuwar neutron da bayanai daga wasu tsakiyar atom (nuclei). Hakan yana tantance abin da ba a sani ba na farko kuma yana 'yanta na biyu.

Sakamako: 4.47 ± 0.87, idan aka kwatanta da 4.71 da aka hasashe. An kawar da rashin weak magnetism a sigma 5.1, sama da ma'aunin sigma 5 na tabbatar da gani. Babu buƙatar sabon gwaji.

Tushe: First observation of weak magnetism in neutron decay, https://arxiv.org/abs/2610.26792

Ka yi tunani: ka ari babban faifan ajiya na abokinka, cike da fayilolinsa masu daraja. Za ka iya amfani da shi wajen lissafi. Amma a ƙarshe, kowane bit dole ya koma wurinsa.

Masana kimiyyar kwamfuta suna kiran wannan ƙwaƙwalwa "catalytic". Ƙara ƙaramin littafin rubutu mai tsabta kawai. Shin irin wannan tsari zai iya doke kwamfuta ta yau da kullum? Har zuwa yanzu, babu wanda ya tabbatar da hakan a kan sauri. Sai a kan ƙwaƙwalwa kawai.

Masu bincike uku na MIT yanzu sun yi, da hujjar lissafi. Da faifan da aka aro, jerawa da Fourier transforms suna gudana a kusan lokaci na layi (linear). Ba tare da shi ba, an tabbatar cewa kwamfuta mai ƙaramin ƙwaƙwalwa ba za ta iya yin hakan ba.

Dabarar: canza faifan, karanta canjin, sannan a warware kowane mataki a baya-baya. Wannan tunani ɗaya yana hanzarta ninka matrices da ƙirga triangles a cikin hanyar sadarwa.

Tushe: Computing faster with a full memory: Catalytic algorithms break time-space lower bounds, https://arxiv.org/abs/2610.24377

Siffar da ba za ta iya rufe ƙasa kamar tayal ba za ta iya dacewa sosai a cikin kwafinta. Shin za ka iya naɗe ta cikin zobe na kwafinta, ba tare da gibi ba? Sannan zobe na biyu, na uku? Wannan ƙidaya ita ce "lambar Heesch" ɗinta.

A kan shimfiɗaɗɗen fili, babban tarihi (record) shi ne 6. Binciken kwamfuta bai taɓa samun wanda ya fi 4 ba. Shin akwai rufi? Babu wanda ya sani.

A girma uku, amsar yanzu a bayyane take: babu rufi. Bojan Bašić, a Novi Sad, yana gina siffa ga kowane adadin yadudduka da kake so.

Sirrin yana cikin lambobi huɗu: 0, 2n−1, 2n+1 da 4n. Kwafinsu da aka matsar ba sa taɓa cika dukkan layin lambobi, amma suna cika tsawon da ya ninka nasu kusan sau n. Idan aka mayar da su sarƙoƙin ƙananan cubes, wannan gibin yana zama wuri ga yadudduka da yawa yadda kake so.

Tushe: The Heesch number in E³ is unbounded, https://arxiv.org/abs/2610.24281

"Pepper's Ghost" dabarar gidan wasan kwaikwayo ce ta ƙarni na 19. Farantin gilashi mai karkata yana nuna wani hoto da ke kama da yana shawagi a kan dandali. Masu bincike biyu a Notre Dame sun juya shi kan gane fuska.

Hoton da ke bayyana yana ɗora fuskar wani mutum a kan ta gaske. Ga mutum, yana kama da walƙiya mai dishi-dishi. Ga manhaja, yana zama fuska mai haɗaka.

Sun gwada mutane 100 a kan tsarukan buɗaɗɗen tushe (open-source). Na'urorin gano yaudara sun karɓi kashi 80 zuwa 96% na hotunan harin a matsayin fuskoki na gaske. Na'urar daidaita fuska da ta fi rauni ta bar kashi 33% na hotunan masu sojan gona su wuce a ma'aunin da aka gwada.

Harin yana faruwa a cikin iska tsakanin kyamara da fuska, ba tare da samun damar shiga manhajar ba. Marubutan suna kiran sa wurin makanta kuma suna raba bayanansu idan an nema don tallafa wa ƙarin bincike.

Tushe: Ghost Attack: Using 19th-Century Illusions to Fool 21st-Century Biometrics, https://arxiv.org/abs/2610.24238

Rashin nauyi yana rikita kunnenka na ciki. Masu zuwa sararin samaniya da yawa suna jin rashin lafiya a kwanakinsu na farko a falaki. Amma ta yaya masu tashi masu zaman kansu ke jurewa? Babu wanda ya taɓa wallafa bayanai a kansu. Sai yanzu.

Wata ƙungiya a Amurka ta bi ma'aikatan jirgi takwas na Polaris Dawn da Fram2, gajerun tafiye-tafiye biyu na SpaceX. Kafin kowane rahoto, suna ɗaga kai su sunkuyar da shi, su karkatar da shi bisa wani tsari ƙayyadadde, sannan su ba da maki ga rashin lafiyarsu daga 0 zuwa 20 a kan kwamfutar hannu (tablet), a lokacin da abin ke faruwa.

Sakamako: 7 cikin 8 sun ji rashin lafiya a falaki, kuma 5 sun yi amai. Ga kashi ɗaya cikin huɗu na su, ya ɗauki aƙalla kwanaki uku.

Bayan dawowa Duniya, rabinsu sun sake jin rashin lafiya, amma ƙasa da haka. Dukkansu daga Fram2 ne, wanda kumbonsa ya yi lilo kusan ninki biyu a kan raƙuman ruwa.

Tushe: Spaceflight-associated Motion Sickness in Commercial Crew Astronauts, https://arxiv.org/abs/2610.24216

Binciken sararin samaniya na baya-bayan nan yana nuna cewa duhun kuzari (dark energy) zai iya canzawa da lokaci. Wani bayani: yana tura duhun abu da wani "ƙarfi na biyar". Taurari da iskar gas ba za su ji shi ko kaɗan ba.

Masana ilimin sararin samaniya biyu sun lissafa abin da hakan zai yi. Ana jan kwanson duhun abu (halo), faifan taurari yana jinkiri a baya, kuma faifan yana lanƙwasa ya zama kamar kwano.

Sun auna siffar galaxies 3,968 da ake gani ta gefe a cikin hotunan Sloan Digital Sky Survey. Sun kwatanta ta da jan da kowane galaxy ya kamata ya ji daga maƙwabtansa. Babu wata dacewa ko kaɗan.

Ƙarfi na biyar dole ya kasance ƙasa da kashi 0.17% na ƙarfin jan hankali (gravity), ko da an ƙirga kowane shakku. Wannan ya fi mafi kyawun iyakar ilimin sararin samaniya tsauri sau uku. Wasu daidaitawa na sabbin bayanan sun rasa goyon baya a kusan sigma 2 zuwa 3.

Tushe: Galactic warps constrain equivalence-principle violation in the dark sector, https://arxiv.org/abs/2610.24618

Masana tattalin arziki suna auna rashin daidaito da Gini coefficient: 0 idan kowa yana da abu ɗaya, 1 idan mutum ɗaya ya mallaki komai. Arzikin duniya yana da maki 0.843. Yanzu a yi amfani da shi a kimiyya.

Masana kimiyyar lissafi biyu na Toulouse sun yi amfani da shi kan ambato (citations) a Google Scholar, takarda bayan takarda. Einstein: takardu 498, Gini 0.883. Rabin takardunsa suna tara kashi 1.5% kawai na ambatonsa.

A tsakanin waɗanda suka ci kyautar Nobel 15, matsakaicin Gini shi ne 0.81. Kashi 10% na sama na takardu suna ɗaukar kashi 71% na ambato. Jami'o'i suna kama da juna, kamar ƙananan ƙasashe marasa daidaito: a Princeton, rabin masu bincike suna samar da kashi 2.6% na ambato.

Marubutan sun yi samfurin waɗannan layuka da wani tunani na kimiyyar lissafi da aka aro daga zafi da haske: "Rayleigh-Jeans condensation". Lissafi iri ɗaya, in ji su, yana bayyana yadda arziki ke taruwa a cikin al'umma.

Tushe: Gini coefficient of scientists and universities, https://arxiv.org/abs/2610.26053

Kusan shekaru goma sha biyar, masana kimiyya suna saka ƙananan ma'aunin zafi (nano-thermometers) a cikin ƙwayoyin halitta masu rai. Da yawa suna ruwaito wurare masu zafi da suka fi muhallinsu da digiri 1 zuwa 10. Duk da haka aikin jikin ƙwayar halitta (metabolism) bai kamata ya ɗumama komai ba sosai.

Wani masanin kimiyyar lissafi a Queensland ya juya tambayar. Ka manta da tushen zafin, wanda ke da wuyar tantancewa a cikin ƙwayar halitta. Ka tambayi yaya ma'aunin zafin da kansa zai iya yin zafi a mafi yawa.

Theorem ɗinsa yana buƙatar lambobi uku kawai: jimillar zafin da aka samar, ƙarfin gudanar da zafi (thermal conductivity) da girman na'urar ji. Ga ƙwayar halitta da ke samar da picowatts 50 da na'urar ji mai girman nanomita 60: kusan digiri 0.002 a mafi yawa, ko daga ina zafin ya fito.

Don haka idan karatun da ke kan sikelin kelvin zafi ne na gaske, wani abu daban na faruwa. Na'urar ji za ta iya kasancewa ba a daidaito ba, ta sami ƙarin kuzari, ko ta amsa wani abu da ba zafi ba.

Tushe: Maximum-Temperature Theorem for a Nanothermometer, https://arxiv.org/abs/2610.24340

A wasu kayayyaki, ƙwayar haske ɗaya za ta iya samar da masu ɗaukar kuzari biyu maimakon ɗaya. Ana kiran wannan rabuwar singlet (singlet fission), kuma za ta iya tura ƙwayoyin hasken rana (solar cells) fiye da iyakarsu ta yau da kullum.

Masana kimiyyar lissafi sun yi fatan za su iya sarrafa ta da madubai. Ka kulle ƙwayoyin sinadarai a cikin wani ƙaramin rami (cavity), sai haske da abu su gauraye su zama yanayi masu haɗaka. Wani bincike na 2019 ya ruwaito cewa hakan ya rage saurin rabuwar a cikin rubrene, wani ƙwayar sinadarin halitta (organic).

Wata ƙungiya a Birtaniya ta sake gina gwajin kuma ta auna a cikin hasken infrared, inda madubai kusan suke bayyane. Ingancin rami iri biyu, daidaitawa biyar. Rabuwar ta gudana daidai kamar babu rami.

Ƙananan bambance-bambancen da suka gani sun fito ne daga amon haske tsakanin madubai, ba daga sabon sinadaranci ba. Hanyarsu tana ba da hanya mafi tsabta ta duba iƙirarai na gaba.

Tushe: NIR-probe transient absorption on rubrene microcavities demonstrates no changes to singlet fission by strong-coupling, https://arxiv.org/abs/2610.26675